Struct ODSolution

pub struct ODSolution<StateType, EstType, MsrSize, Trk>
where
    StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>,
    EstType: Estimate<StateType>,
    MsrSize: DimName,
    Trk: TrackerSensitivity<StateType, StateType>,
    <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send,
    DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,
{
    pub estimates: Vec<EstType>,
    pub residuals: Vec<Option<Residual<MsrSize>>>,
    pub gains: Vec<Option<OMatrix<f64, <StateType as State>::Size, MsrSize>>>,
    pub filter_smoother_ratios: Vec<Option<OVector<f64, <StateType as State>::Size>>>,
    pub devices: BTreeMap<String, Trk>,
    pub measurement_types: IndexSet<MeasurementType>,
}

The ODSolution structure is designed to manage and analyze the results of an OD process, including smoothing. It provides various functionalities such as splitting solutions by tracker or measurement type, joining solutions, and performing statistical analyses.

Note: Many methods in this structure assume that the solution has been split into subsets using the split() method. Calling these methods without first splitting will make analysis of operations results less obvious.

Fields

• estimates: A vector of state estimates generated during the OD process.
• residuals: A vector of residuals corresponding to the state estimates.
• gains: Filter gains used for measurement updates. These are set to None after running the smoother.
• filter_smoother_ratios: Filter-smoother consistency ratios. These are set to None before running the smoother.
• devices: A map of tracking devices used in the OD process.
• measurement_types: A set of unique measurement types used in the OD process.

Implementation detail: these are not stored in vectors to allow for multiple estimates at the same time, e.g. when there are simultaneous measurements of angles and the filter processes each as a scalar.

Fields

estimates: Vec<EstType>

Vector of estimates available after a pass

residuals: Vec<Option<Residual<MsrSize>>>

Vector of residuals available after a pass

gains: Vec<Option<OMatrix<f64, <StateType as State>::Size, MsrSize>>>

Vector of filter gains used for each measurement update, all None after running the smoother.

filter_smoother_ratios: Vec<Option<OVector<f64, <StateType as State>::Size>>>

Filter-smoother consistency ratios, all None before running the smoother.

devices: BTreeMap<String, Trk>

Tracking devices

measurement_types: IndexSet<MeasurementType>

Implementations

impl<MsrSize: DimName, Trk: TrackerSensitivity<Spacecraft, Spacecraft>> ODSolution<Spacecraft, KfEstimate<Spacecraft>, MsrSize, Trk>

where DefaultAllocator: Allocator<MsrSize> + Allocator<MsrSize, <Spacecraft as State>::Size> + Allocator<Const<1>, MsrSize> + Allocator<<Spacecraft as State>::Size> + Allocator<<Spacecraft as State>::Size, <Spacecraft as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<Spacecraft as State>::Size, MsrSize> + Allocator<<Spacecraft as State>::VecLength>,

pub fn to_parquet<P: AsRef<Path>>( &self, path: P, cfg: ExportCfg, ) -> Result<PathBuf, ODError>

Store the estimates and residuals in a parquet file

Examples found in repository

examples/02_jwst_covar_monte_carlo/main.rs (line 128)

fn main() -> Result<(), Box<dyn Error>> {
    pel::init();
    // Dynamics models require planetary constants and ephemerides to be defined.
    // Let's start by grabbing those by using ANISE's latest MetaAlmanac.
    // For details, refer to https://github.com/nyx-space/anise/blob/master/data/latest.dhall.

    // Download the regularly update of the James Webb Space Telescope reconstucted (or definitive) ephemeris.
    // Refer to https://naif.jpl.nasa.gov/pub/naif/JWST/kernels/spk/aareadme.txt for details.
    let mut latest_jwst_ephem = MetaFile {
        uri: "https://naif.jpl.nasa.gov/pub/naif/JWST/kernels/spk/jwst_rec.bsp".to_string(),
        crc32: None,
    };
    latest_jwst_ephem.process(true)?;

    // Load this ephem in the general Almanac we're using for this analysis.
    let almanac = Arc::new(
        MetaAlmanac::latest()
            .map_err(Box::new)?
            .load_from_metafile(latest_jwst_ephem, true)?,
    );

    // By loading this ephemeris file in the ANISE GUI or ANISE CLI, we can find the NAIF ID of the JWST
    // in the BSP. We need this ID in order to query the ephemeris.
    const JWST_NAIF_ID: i32 = -170;
    // Let's build a frame in the J2000 orientation centered on the JWST.
    const JWST_J2000: Frame = Frame::from_ephem_j2000(JWST_NAIF_ID);

    // Since the ephemeris file is updated regularly, we'll just grab the latest state in the ephem.
    let (earliest_epoch, latest_epoch) = almanac.spk_domain(JWST_NAIF_ID)?;
    println!("JWST defined from {earliest_epoch} to {latest_epoch}");
    // Fetch the state, printing it in the Earth J2000 frame.
    let jwst_orbit = almanac.transform(JWST_J2000, EARTH_J2000, latest_epoch, None)?;
    println!("{jwst_orbit:x}");

    // Build the spacecraft
    // SRP area assumed to be the full sunshield and mass if 6200.0 kg, c.f. https://webb.nasa.gov/content/about/faqs/facts.html
    // SRP Coefficient of reflectivity assumed to be that of Kapton, i.e. 2 - 0.44 = 1.56, table 1 from https://amostech.com/TechnicalPapers/2018/Poster/Bengtson.pdf
    let jwst = Spacecraft::builder()
        .orbit(jwst_orbit)
        .srp(SRPData {
            area_m2: 21.197 * 14.162,
            coeff_reflectivity: 1.56,
        })
        .mass(Mass::from_dry_mass(6200.0))
        .build();

    // Build up the spacecraft uncertainty builder.
    // We can use the spacecraft uncertainty structure to build this up.
    // We start by specifying the nominal state (as defined above), then the uncertainty in position and velocity
    // in the RIC frame. We could also specify the Cr, Cd, and mass uncertainties, but these aren't accounted for until
    // Nyx can also estimate the deviation of the spacecraft parameters.
    let jwst_uncertainty = SpacecraftUncertainty::builder()
        .nominal(jwst)
        .frame(LocalFrame::RIC)
        .x_km(0.5)
        .y_km(0.3)
        .z_km(1.5)
        .vx_km_s(1e-4)
        .vy_km_s(0.6e-3)
        .vz_km_s(3e-3)
        .build();

    println!("{jwst_uncertainty}");

    // Build the Kalman filter estimate.
    // Note that we could have used the KfEstimate structure directly (as seen throughout the OD integration tests)
    // but this approach requires quite a bit more boilerplate code.
    let jwst_estimate = jwst_uncertainty.to_estimate()?;

    // Set up the spacecraft dynamics.
    // We'll use the point masses of the Earth, Sun, Jupiter (barycenter, because it's in the DE440), and the Moon.
    // We'll also enable solar radiation pressure since the James Webb has a huge and highly reflective sun shield.

    let orbital_dyn = OrbitalDynamics::point_masses(vec![MOON, SUN, JUPITER_BARYCENTER]);
    let srp_dyn = SolarPressure::new(vec![EARTH_J2000, MOON_J2000], almanac.clone())?;

    // Finalize setting up the dynamics.
    let dynamics = SpacecraftDynamics::from_model(orbital_dyn, srp_dyn);

    // Build the propagator set up to use for the whole analysis.
    let setup = Propagator::default(dynamics);

    // All of the analysis will use this duration.
    let prediction_duration = 6.5 * Unit::Day;

    // === Covariance mapping ===
    // For the covariance mapping / prediction, we'll use the common orbit determination approach.
    // This is done by setting up a spacecraft Kalman filter OD process, and predicting for the analysis duration.

    // Build the propagation instance for the OD process.
    let odp = SpacecraftKalmanOD::new(
        setup.clone(),
        KalmanVariant::DeviationTracking,
        None,
        BTreeMap::new(),
        almanac.clone(),
    );

    // The prediction step is 1 minute by default, configured in the OD process, i.e. how often we want to know the covariance.
    assert_eq!(odp.max_step, 1_i64.minutes());
    // Finally, predict, and export the trajectory with covariance to a parquet file.
    let od_sol = odp.predict_for(jwst_estimate, prediction_duration)?;
    od_sol.to_parquet("./02_jwst_covar_map.parquet", ExportCfg::default())?;

    // === Monte Carlo framework ===
    // Nyx comes with a complete multi-threaded Monte Carlo frame. It's blazing fast.

    let my_mc = MonteCarlo::new(
        jwst, // Nominal state
        jwst_estimate.to_random_variable()?,
        "02_jwst".to_string(), // Scenario name
        None, // No specific seed specified, so one will be drawn from the computer's entropy.
    );

    let num_runs = 5_000;
    let rslts = my_mc.run_until_epoch(
        setup,
        almanac.clone(),
        jwst.epoch() + prediction_duration,
        num_runs,
    );

    assert_eq!(rslts.runs.len(), num_runs);
    // Finally, export these results, computing the eclipse percentage for all of these results.

    // For all of the resulting trajectories, we'll want to compute the percentage of penumbra and umbra.
    let eclipse_loc = EclipseLocator::cislunar(almanac.clone());
    let umbra_event = eclipse_loc.to_umbra_event();
    let penumbra_event = eclipse_loc.to_penumbra_event();

    rslts.to_parquet(
        "02_jwst_monte_carlo.parquet",
        Some(vec![&umbra_event, &penumbra_event]),
        ExportCfg::default(),
        almanac,
    )?;

    Ok(())
}

examples/04_lro_od/main.rs (line 290)

fn main() -> Result<(), Box<dyn Error>> {
    pel::init();

    // ====================== //
    // === ALMANAC SET UP === //
    // ====================== //

    // Dynamics models require planetary constants and ephemerides to be defined.
    // Let's start by grabbing those by using ANISE's MetaAlmanac.

    let data_folder: PathBuf = [env!("CARGO_MANIFEST_DIR"), "examples", "04_lro_od"]
        .iter()
        .collect();

    let meta = data_folder.join("lro-dynamics.dhall");

    // Load this ephem in the general Almanac we're using for this analysis.
    let mut almanac = MetaAlmanac::new(meta.to_string_lossy().to_string())
        .map_err(Box::new)?
        .process(true)
        .map_err(Box::new)?;

    let mut moon_pc = almanac.planetary_data.get_by_id(MOON)?;
    moon_pc.mu_km3_s2 = 4902.74987;
    almanac.planetary_data.set_by_id(MOON, moon_pc)?;

    let mut earth_pc = almanac.planetary_data.get_by_id(EARTH)?;
    earth_pc.mu_km3_s2 = 398600.436;
    almanac.planetary_data.set_by_id(EARTH, earth_pc)?;

    // Save this new kernel for reuse.
    // In an operational context, this would be part of the "Lock" process, and should not change throughout the mission.
    almanac
        .planetary_data
        .save_as(&data_folder.join("lro-specific.pca"), true)?;

    // Lock the almanac (an Arc is a read only structure).
    let almanac = Arc::new(almanac);

    // Orbit determination requires a Trajectory structure, which can be saved as parquet file.
    // In our case, the trajectory comes from the BSP file, so we need to build a Trajectory from the almanac directly.
    // To query the Almanac, we need to build the LRO frame in the J2000 orientation in our case.
    // Inspecting the LRO BSP in the ANISE GUI shows us that NASA has assigned ID -85 to LRO.
    let lro_frame = Frame::from_ephem_j2000(-85);

    // To build the trajectory we need to provide a spacecraft template.
    let sc_template = Spacecraft::builder()
        .mass(Mass::from_dry_and_prop_masses(1018.0, 900.0)) // Launch masses
        .srp(SRPData {
            // SRP configuration is arbitrary, but we will be estimating it anyway.
            area_m2: 3.9 * 2.7,
            coeff_reflectivity: 0.96,
        })
        .orbit(Orbit::zero(MOON_J2000)) // Setting a zero orbit here because it's just a template
        .build();
    // Now we can build the trajectory from the BSP file.
    // We'll arbitrarily set the tracking arc to 24 hours with a five second time step.
    let traj_as_flown = Traj::from_bsp(
        lro_frame,
        MOON_J2000,
        almanac.clone(),
        sc_template,
        5.seconds(),
        Some(Epoch::from_str("2024-01-01 00:00:00 UTC")?),
        Some(Epoch::from_str("2024-01-02 00:00:00 UTC")?),
        Aberration::LT,
        Some("LRO".to_string()),
    )?;

    println!("{traj_as_flown}");

    // ====================== //
    // === MODEL MATCHING === //
    // ====================== //

    // Set up the spacecraft dynamics.

    // Specify that the orbital dynamics must account for the graviational pull of the Earth and the Sun.
    // The gravity of the Moon will also be accounted for since the spaceraft in a lunar orbit.
    let mut orbital_dyn = OrbitalDynamics::point_masses(vec![EARTH, SUN, JUPITER_BARYCENTER]);

    // We want to include the spherical harmonics, so let's download the gravitational data from the Nyx Cloud.
    // We're using the GRAIL JGGRX model.
    let mut jggrx_meta = MetaFile {
        uri: "http://public-data.nyxspace.com/nyx/models/Luna_jggrx_1500e_sha.tab.gz".to_string(),
        crc32: Some(0x6bcacda8), // Specifying the CRC32 avoids redownloading it if it's cached.
    };
    // And let's download it if we don't have it yet.
    jggrx_meta.process(true)?;

    // Build the spherical harmonics.
    // The harmonics must be computed in the body fixed frame.
    // We're using the long term prediction of the Moon principal axes frame.
    let moon_pa_frame = MOON_PA_FRAME.with_orient(31008);
    let sph_harmonics = Harmonics::from_stor(
        almanac.frame_from_uid(moon_pa_frame)?,
        HarmonicsMem::from_shadr(&jggrx_meta.uri, 80, 80, true)?,
    );

    // Include the spherical harmonics into the orbital dynamics.
    orbital_dyn.accel_models.push(sph_harmonics);

    // We define the solar radiation pressure, using the default solar flux and accounting only
    // for the eclipsing caused by the Earth and Moon.
    // Note that by default, enabling the SolarPressure model will also enable the estimation of the coefficient of reflectivity.
    let srp_dyn = SolarPressure::new(vec![EARTH_J2000, MOON_J2000], almanac.clone())?;

    // Finalize setting up the dynamics, specifying the force models (orbital_dyn) separately from the
    // acceleration models (SRP in this case). Use `from_models` to specify multiple accel models.
    let dynamics = SpacecraftDynamics::from_model(orbital_dyn, srp_dyn);

    println!("{dynamics}");

    // Now we can build the propagator.
    let setup = Propagator::default_dp78(dynamics.clone());

    // For reference, let's build the trajectory with Nyx's models from that LRO state.
    let (sim_final, traj_as_sim) = setup
        .with(*traj_as_flown.first(), almanac.clone())
        .until_epoch_with_traj(traj_as_flown.last().epoch())?;

    println!("SIM INIT:  {:x}", traj_as_flown.first());
    println!("SIM FINAL: {sim_final:x}");
    // Compute RIC difference between SIM and LRO ephem
    let sim_lro_delta = sim_final
        .orbit
        .ric_difference(&traj_as_flown.last().orbit)?;
    println!("{traj_as_sim}");
    println!(
        "SIM v LRO - RIC Position (m): {:.3}",
        sim_lro_delta.radius_km * 1e3
    );
    println!(
        "SIM v LRO - RIC Velocity (m/s): {:.3}",
        sim_lro_delta.velocity_km_s * 1e3
    );

    traj_as_sim.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_sim_truth_error.parquet",
        ExportCfg::default(),
    )?;

    // ==================== //
    // === OD SIMULATOR === //
    // ==================== //

    // After quite some time trying to exactly match the model, we still end up with an oscillatory difference on the order of 150 meters between the propagated state
    // and the truth LRO state.

    // Therefore, we will actually run an estimation from a dispersed LRO state.
    // The sc_seed is the true LRO state from the BSP.
    let sc_seed = *traj_as_flown.first();

    // Load the Deep Space Network ground stations.
    // Nyx allows you to build these at runtime but it's pretty static so we can just load them from YAML.
    let ground_station_file: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "dsn-network.yaml",
    ]
    .iter()
    .collect();

    let devices = GroundStation::load_named(ground_station_file)?;

    // Typical OD software requires that you specify your own tracking schedule or you'll have overlapping measurements.
    // Nyx can build a tracking schedule for you based on the first station with access.
    let trkconfg_yaml: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "tracking-cfg.yaml",
    ]
    .iter()
    .collect();

    let configs: BTreeMap<String, TrkConfig> = TrkConfig::load_named(trkconfg_yaml)?;

    // Build the tracking arc simulation to generate a "standard measurement".
    let mut trk = TrackingArcSim::<Spacecraft, GroundStation>::new(
        devices.clone(),
        traj_as_flown.clone(),
        configs,
    )?;

    trk.build_schedule(almanac.clone())?;
    let arc = trk.generate_measurements(almanac.clone())?;
    // Save the simulated tracking data
    arc.to_parquet_simple("./04_lro_simulated_tracking.parquet")?;

    // We'll note that in our case, we have continuous coverage of LRO when the vehicle is not behind the Moon.
    println!("{arc}");

    // Now that we have simulated measurements, we'll run the orbit determination.

    // ===================== //
    // === OD ESTIMATION === //
    // ===================== //

    let sc = SpacecraftUncertainty::builder()
        .nominal(sc_seed)
        .frame(LocalFrame::RIC)
        .x_km(0.5)
        .y_km(0.5)
        .z_km(0.5)
        .vx_km_s(5e-3)
        .vy_km_s(5e-3)
        .vz_km_s(5e-3)
        .build();

    // Build the filter initial estimate, which we will reuse in the filter.
    let initial_estimate = sc.to_estimate()?;

    println!("== FILTER STATE ==\n{sc_seed:x}\n{initial_estimate}");

    // Build the SNC in the Moon J2000 frame, specified as a velocity noise over time.
    let process_noise = ProcessNoise3D::from_velocity_km_s(
        &[1.8e-9, 1.8e-9, 1.8e-9],
        1 * Unit::Hour,
        10 * Unit::Minute,
        None,
    );

    println!("{process_noise}");

    // We'll set up the OD process to reject measurements whose residuals are move than 3 sigmas away from what we expect.
    let odp = SpacecraftKalmanOD::new(
        setup,
        KalmanVariant::ReferenceUpdate,
        Some(ResidRejectCrit::default()),
        devices,
        almanac.clone(),
    )
    .with_process_noise(process_noise);

    let od_sol = odp.process_arc(initial_estimate, &arc)?;

    let ric_err = traj_as_flown
        .at(od_sol.estimates.last().unwrap().epoch())?
        .orbit
        .ric_difference(&od_sol.estimates.last().unwrap().orbital_state())?;
    println!("== RIC at end ==");
    println!("RIC Position (m): {}", ric_err.radius_km * 1e3);
    println!("RIC Velocity (m/s): {}", ric_err.velocity_km_s * 1e3);

    println!(
        "Num residuals rejected: #{}",
        od_sol.rejected_residuals().len()
    );
    println!(
        "Percentage within +/-3: {}",
        od_sol.residual_ratio_within_threshold(3.0).unwrap()
    );
    println!("Ratios normal? {}", od_sol.is_normal(None).unwrap());

    od_sol.to_parquet("./04_lro_od_results.parquet", ExportCfg::default())?;

    // In our case, we have the truth trajectory from NASA.
    // So we can compute the RIC state difference between the real LRO ephem and what we've just estimated.
    // Export the OD trajectory first.
    let od_trajectory = od_sol.to_traj()?;
    // Build the RIC difference.
    od_trajectory.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_od_truth_error.parquet",
        ExportCfg::default(),
    )?;

    Ok(())
}

impl<StateType, EstType, MsrSize, Trk> ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>, EstType: Estimate<StateType>, MsrSize: DimName, Trk: TrackerSensitivity<StateType, StateType>, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

pub fn unique(&self) -> IndexSet<(String, MeasurementType)>

Returns a set of tuples of tracker and measurement types in this OD solution, e.g. {(Canberra, Range), (Canberra, Doppler)}.

pub fn drop_time_updates(self) -> Self

Returns this OD solution without any time update

pub fn filter_by_msr_type(self, msr_type: MeasurementType) -> Self

Returns this OD solution with only data from the desired measurement type, dropping all time updates.

pub fn filter_by_tracker(self, tracker: String) -> Self

Returns this OD solution with only data from the desired tracker, dropping all time updates.

pub fn exclude_tracker(self, excluded_tracker: String) -> Self

Returns this OD solution with all data except from the desired tracker, including all time updates

pub fn split(self) -> Vec<Self>

Split this OD solution per tracker and per measurement type, dropping all time updates.

pub fn merge(self, other: Self) -> Self

Merge this OD solution with another one, returning a new OD solution.

pub fn at(&self, epoch: Epoch) -> Option<ODRecord<StateType, EstType, MsrSize>>

impl<MsrSize, Trk> ODSolution<Spacecraft, KfEstimate<Spacecraft>, MsrSize, Trk>

where MsrSize: DimName + Debug + Clone, Trk: TrackerSensitivity<Spacecraft, Spacecraft> + Clone, DefaultAllocator: Allocator<MsrSize> + Allocator<MsrSize, <Spacecraft as State>::Size> + Allocator<Const<1>, MsrSize> + Allocator<<Spacecraft as State>::Size> + Allocator<<Spacecraft as State>::Size, <Spacecraft as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<Spacecraft as State>::Size, MsrSize> + Allocator<<Spacecraft as State>::VecLength>, <DefaultAllocator as Allocator<<Spacecraft as State>::VecLength>>::Buffer<f64>: Send, <DefaultAllocator as Allocator<<Spacecraft as State>::Size>>::Buffer<f64>: Copy, <DefaultAllocator as Allocator<<Spacecraft as State>::Size, <Spacecraft as State>::Size>>::Buffer<f64>: Copy,

pub fn from_parquet<P: AsRef<Path>>( path: P, devices: BTreeMap<String, Trk>, ) -> Result<Self, InputOutputError>

Loads an OD solution from a Parquet file created by ODSolution::to_parquet.

The devices map must be provided by the caller as it contains potentially complex state (like Almanac references) that isn’t serialized in the Parquet file.

Note: This function currently assumes the StateType is Spacecraft and the estimate type is KfEstimate<Spacecraft>.

impl<StateType, EstType, MsrSize, Trk> ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>, EstType: Estimate<StateType>, MsrSize: DimName, Trk: TrackerSensitivity<StateType, StateType>, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

pub fn smooth(self, almanac: Arc<Almanac>) -> Result<Self, ODError>

Smoothes this OD solution, returning a new OD solution and the filter-smoother consistency ratios, with updated postfit residuals, and where the ratio now represents the filter-smoother consistency ratio.

Notes:

1. Gains will be scrubbed because the smoother process does not recompute the gain.
2. Prefit residuals, ratios, and measurement covariances are not updated, as these depend on the filtering process.
3. Note: this function consumes the current OD solution to prevent reusing the wrong one.

To assess whether the smoothing process improved the solution, compare the RMS of the postfit residuals from the filter and the smoother process.

Filter-Smoother consistency ratio

The filter-smoother consistency ratio is used to evaluate the consistency between the state estimates produced by a filter (e.g., Kalman filter) and a smoother. This ratio is called “filter smoother consistency test” in the ODTK MathSpec.

It is computed as follows:

1. Define the State Estimates

Filter state estimate: $ \hat{X}_{f,k} $ This is the state estimate at time step $ k $ from the filter.

Smoother state estimate: $ \hat{X}_{s,k} $ This is the state estimate at time step $ k $ from the smoother.

2. Define the Covariances

Filter covariance: $ P_{f,k} $ This is the covariance of the state estimate at time step $ k $ from the filter.

Smoother covariance: $ P_{s,k} $ This is the covariance of the state estimate at time step $ k $ from the smoother.

3. Compute the Differences

State difference: $ \Delta X_k = \hat{X}{s,k} - \hat{X}{f,k} $

Covariance difference: $ \Delta P_k = P_{s,k} - P_{f,k} $

4. Calculate the Consistency Ratio

For each element $ i $ of the state vector, compute the ratio:

$$ R_{i,k} = \frac{\Delta X_{i,k}}{\sqrt{\Delta P_{i,k}}} $$

5. Evaluate Consistency

• If $ |R_{i,k}| \leq 3 $ for all $ i $ and $ k $, the filter-smoother consistency test is satisfied, indicating good consistency.
• If $ |R_{i,k}| > 3 $ for any $ i $ or $ k $, the test fails, suggesting potential modeling inconsistencies or issues with the estimation process.

impl<StateType, EstType, MsrSize, Trk> ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>, EstType: Estimate<StateType>, MsrSize: DimName, Trk: TrackerSensitivity<StateType, StateType>, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

pub fn rms_prefit_residuals(&self) -> f64

Returns the root mean square of the prefit residuals

pub fn rms_postfit_residuals(&self) -> f64

Returns the root mean square of the postfit residuals

pub fn rms_residual_ratios(&self) -> f64

Returns the root mean square of the prefit residual ratios

pub fn residual_ratio_within_threshold( &self, threshold: f64, ) -> Result<f64, ODError>

Computes the fraction of residual ratios that lie within ±threshold.

Examples found in repository

examples/04_lro_od/main.rs (line 286)

fn main() -> Result<(), Box<dyn Error>> {
    pel::init();

    // ====================== //
    // === ALMANAC SET UP === //
    // ====================== //

    // Dynamics models require planetary constants and ephemerides to be defined.
    // Let's start by grabbing those by using ANISE's MetaAlmanac.

    let data_folder: PathBuf = [env!("CARGO_MANIFEST_DIR"), "examples", "04_lro_od"]
        .iter()
        .collect();

    let meta = data_folder.join("lro-dynamics.dhall");

    // Load this ephem in the general Almanac we're using for this analysis.
    let mut almanac = MetaAlmanac::new(meta.to_string_lossy().to_string())
        .map_err(Box::new)?
        .process(true)
        .map_err(Box::new)?;

    let mut moon_pc = almanac.planetary_data.get_by_id(MOON)?;
    moon_pc.mu_km3_s2 = 4902.74987;
    almanac.planetary_data.set_by_id(MOON, moon_pc)?;

    let mut earth_pc = almanac.planetary_data.get_by_id(EARTH)?;
    earth_pc.mu_km3_s2 = 398600.436;
    almanac.planetary_data.set_by_id(EARTH, earth_pc)?;

    // Save this new kernel for reuse.
    // In an operational context, this would be part of the "Lock" process, and should not change throughout the mission.
    almanac
        .planetary_data
        .save_as(&data_folder.join("lro-specific.pca"), true)?;

    // Lock the almanac (an Arc is a read only structure).
    let almanac = Arc::new(almanac);

    // Orbit determination requires a Trajectory structure, which can be saved as parquet file.
    // In our case, the trajectory comes from the BSP file, so we need to build a Trajectory from the almanac directly.
    // To query the Almanac, we need to build the LRO frame in the J2000 orientation in our case.
    // Inspecting the LRO BSP in the ANISE GUI shows us that NASA has assigned ID -85 to LRO.
    let lro_frame = Frame::from_ephem_j2000(-85);

    // To build the trajectory we need to provide a spacecraft template.
    let sc_template = Spacecraft::builder()
        .mass(Mass::from_dry_and_prop_masses(1018.0, 900.0)) // Launch masses
        .srp(SRPData {
            // SRP configuration is arbitrary, but we will be estimating it anyway.
            area_m2: 3.9 * 2.7,
            coeff_reflectivity: 0.96,
        })
        .orbit(Orbit::zero(MOON_J2000)) // Setting a zero orbit here because it's just a template
        .build();
    // Now we can build the trajectory from the BSP file.
    // We'll arbitrarily set the tracking arc to 24 hours with a five second time step.
    let traj_as_flown = Traj::from_bsp(
        lro_frame,
        MOON_J2000,
        almanac.clone(),
        sc_template,
        5.seconds(),
        Some(Epoch::from_str("2024-01-01 00:00:00 UTC")?),
        Some(Epoch::from_str("2024-01-02 00:00:00 UTC")?),
        Aberration::LT,
        Some("LRO".to_string()),
    )?;

    println!("{traj_as_flown}");

    // ====================== //
    // === MODEL MATCHING === //
    // ====================== //

    // Set up the spacecraft dynamics.

    // Specify that the orbital dynamics must account for the graviational pull of the Earth and the Sun.
    // The gravity of the Moon will also be accounted for since the spaceraft in a lunar orbit.
    let mut orbital_dyn = OrbitalDynamics::point_masses(vec![EARTH, SUN, JUPITER_BARYCENTER]);

    // We want to include the spherical harmonics, so let's download the gravitational data from the Nyx Cloud.
    // We're using the GRAIL JGGRX model.
    let mut jggrx_meta = MetaFile {
        uri: "http://public-data.nyxspace.com/nyx/models/Luna_jggrx_1500e_sha.tab.gz".to_string(),
        crc32: Some(0x6bcacda8), // Specifying the CRC32 avoids redownloading it if it's cached.
    };
    // And let's download it if we don't have it yet.
    jggrx_meta.process(true)?;

    // Build the spherical harmonics.
    // The harmonics must be computed in the body fixed frame.
    // We're using the long term prediction of the Moon principal axes frame.
    let moon_pa_frame = MOON_PA_FRAME.with_orient(31008);
    let sph_harmonics = Harmonics::from_stor(
        almanac.frame_from_uid(moon_pa_frame)?,
        HarmonicsMem::from_shadr(&jggrx_meta.uri, 80, 80, true)?,
    );

    // Include the spherical harmonics into the orbital dynamics.
    orbital_dyn.accel_models.push(sph_harmonics);

    // We define the solar radiation pressure, using the default solar flux and accounting only
    // for the eclipsing caused by the Earth and Moon.
    // Note that by default, enabling the SolarPressure model will also enable the estimation of the coefficient of reflectivity.
    let srp_dyn = SolarPressure::new(vec![EARTH_J2000, MOON_J2000], almanac.clone())?;

    // Finalize setting up the dynamics, specifying the force models (orbital_dyn) separately from the
    // acceleration models (SRP in this case). Use `from_models` to specify multiple accel models.
    let dynamics = SpacecraftDynamics::from_model(orbital_dyn, srp_dyn);

    println!("{dynamics}");

    // Now we can build the propagator.
    let setup = Propagator::default_dp78(dynamics.clone());

    // For reference, let's build the trajectory with Nyx's models from that LRO state.
    let (sim_final, traj_as_sim) = setup
        .with(*traj_as_flown.first(), almanac.clone())
        .until_epoch_with_traj(traj_as_flown.last().epoch())?;

    println!("SIM INIT:  {:x}", traj_as_flown.first());
    println!("SIM FINAL: {sim_final:x}");
    // Compute RIC difference between SIM and LRO ephem
    let sim_lro_delta = sim_final
        .orbit
        .ric_difference(&traj_as_flown.last().orbit)?;
    println!("{traj_as_sim}");
    println!(
        "SIM v LRO - RIC Position (m): {:.3}",
        sim_lro_delta.radius_km * 1e3
    );
    println!(
        "SIM v LRO - RIC Velocity (m/s): {:.3}",
        sim_lro_delta.velocity_km_s * 1e3
    );

    traj_as_sim.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_sim_truth_error.parquet",
        ExportCfg::default(),
    )?;

    // ==================== //
    // === OD SIMULATOR === //
    // ==================== //

    // After quite some time trying to exactly match the model, we still end up with an oscillatory difference on the order of 150 meters between the propagated state
    // and the truth LRO state.

    // Therefore, we will actually run an estimation from a dispersed LRO state.
    // The sc_seed is the true LRO state from the BSP.
    let sc_seed = *traj_as_flown.first();

    // Load the Deep Space Network ground stations.
    // Nyx allows you to build these at runtime but it's pretty static so we can just load them from YAML.
    let ground_station_file: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "dsn-network.yaml",
    ]
    .iter()
    .collect();

    let devices = GroundStation::load_named(ground_station_file)?;

    // Typical OD software requires that you specify your own tracking schedule or you'll have overlapping measurements.
    // Nyx can build a tracking schedule for you based on the first station with access.
    let trkconfg_yaml: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "tracking-cfg.yaml",
    ]
    .iter()
    .collect();

    let configs: BTreeMap<String, TrkConfig> = TrkConfig::load_named(trkconfg_yaml)?;

    // Build the tracking arc simulation to generate a "standard measurement".
    let mut trk = TrackingArcSim::<Spacecraft, GroundStation>::new(
        devices.clone(),
        traj_as_flown.clone(),
        configs,
    )?;

    trk.build_schedule(almanac.clone())?;
    let arc = trk.generate_measurements(almanac.clone())?;
    // Save the simulated tracking data
    arc.to_parquet_simple("./04_lro_simulated_tracking.parquet")?;

    // We'll note that in our case, we have continuous coverage of LRO when the vehicle is not behind the Moon.
    println!("{arc}");

    // Now that we have simulated measurements, we'll run the orbit determination.

    // ===================== //
    // === OD ESTIMATION === //
    // ===================== //

    let sc = SpacecraftUncertainty::builder()
        .nominal(sc_seed)
        .frame(LocalFrame::RIC)
        .x_km(0.5)
        .y_km(0.5)
        .z_km(0.5)
        .vx_km_s(5e-3)
        .vy_km_s(5e-3)
        .vz_km_s(5e-3)
        .build();

    // Build the filter initial estimate, which we will reuse in the filter.
    let initial_estimate = sc.to_estimate()?;

    println!("== FILTER STATE ==\n{sc_seed:x}\n{initial_estimate}");

    // Build the SNC in the Moon J2000 frame, specified as a velocity noise over time.
    let process_noise = ProcessNoise3D::from_velocity_km_s(
        &[1.8e-9, 1.8e-9, 1.8e-9],
        1 * Unit::Hour,
        10 * Unit::Minute,
        None,
    );

    println!("{process_noise}");

    // We'll set up the OD process to reject measurements whose residuals are move than 3 sigmas away from what we expect.
    let odp = SpacecraftKalmanOD::new(
        setup,
        KalmanVariant::ReferenceUpdate,
        Some(ResidRejectCrit::default()),
        devices,
        almanac.clone(),
    )
    .with_process_noise(process_noise);

    let od_sol = odp.process_arc(initial_estimate, &arc)?;

    let ric_err = traj_as_flown
        .at(od_sol.estimates.last().unwrap().epoch())?
        .orbit
        .ric_difference(&od_sol.estimates.last().unwrap().orbital_state())?;
    println!("== RIC at end ==");
    println!("RIC Position (m): {}", ric_err.radius_km * 1e3);
    println!("RIC Velocity (m/s): {}", ric_err.velocity_km_s * 1e3);

    println!(
        "Num residuals rejected: #{}",
        od_sol.rejected_residuals().len()
    );
    println!(
        "Percentage within +/-3: {}",
        od_sol.residual_ratio_within_threshold(3.0).unwrap()
    );
    println!("Ratios normal? {}", od_sol.is_normal(None).unwrap());

    od_sol.to_parquet("./04_lro_od_results.parquet", ExportCfg::default())?;

    // In our case, we have the truth trajectory from NASA.
    // So we can compute the RIC state difference between the real LRO ephem and what we've just estimated.
    // Export the OD trajectory first.
    let od_trajectory = od_sol.to_traj()?;
    // Build the RIC difference.
    od_trajectory.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_od_truth_error.parquet",
        ExportCfg::default(),
    )?;

    Ok(())
}

pub fn ks_test_normality(&self) -> Result<f64, ODError>

Computes the Kolmogorov–Smirnov statistic for the aggregated residual ratios, by tracker and measurement type.

Returns Ok(ks_statistic) if residuals are available.

pub fn is_normal(&self, alpha: Option<f64>) -> Result<bool, ODError>

Checks whether the residual ratios pass a normality test at a given significance level alpha, default to 0.05.

This uses a simplified KS-test threshold: D_alpha = c(α) / √n. For example, for α = 0.05, c(α) is approximately 1.36. α=0.05 means a 5% probability of Type I error (incorrectly rejecting the null hypothesis when it is true). This threshold is standard in many statistical tests to balance sensitivity and false positives

The computation of the c(alpha) is from https://en.wikipedia.org/w/index.php?title=Kolmogorov%E2%80%93Smirnov_test&oldid=1280260701#Two-sample_Kolmogorov%E2%80%93Smirnov_test

Returns Ok(true) if the residuals are consistent with a normal distribution, Ok(false) if not, or None if no residuals are available.

Examples found in repository

examples/04_lro_od/main.rs (line 288)

fn main() -> Result<(), Box<dyn Error>> {
    pel::init();

    // ====================== //
    // === ALMANAC SET UP === //
    // ====================== //

    // Dynamics models require planetary constants and ephemerides to be defined.
    // Let's start by grabbing those by using ANISE's MetaAlmanac.

    let data_folder: PathBuf = [env!("CARGO_MANIFEST_DIR"), "examples", "04_lro_od"]
        .iter()
        .collect();

    let meta = data_folder.join("lro-dynamics.dhall");

    // Load this ephem in the general Almanac we're using for this analysis.
    let mut almanac = MetaAlmanac::new(meta.to_string_lossy().to_string())
        .map_err(Box::new)?
        .process(true)
        .map_err(Box::new)?;

    let mut moon_pc = almanac.planetary_data.get_by_id(MOON)?;
    moon_pc.mu_km3_s2 = 4902.74987;
    almanac.planetary_data.set_by_id(MOON, moon_pc)?;

    let mut earth_pc = almanac.planetary_data.get_by_id(EARTH)?;
    earth_pc.mu_km3_s2 = 398600.436;
    almanac.planetary_data.set_by_id(EARTH, earth_pc)?;

    // Save this new kernel for reuse.
    // In an operational context, this would be part of the "Lock" process, and should not change throughout the mission.
    almanac
        .planetary_data
        .save_as(&data_folder.join("lro-specific.pca"), true)?;

    // Lock the almanac (an Arc is a read only structure).
    let almanac = Arc::new(almanac);

    // Orbit determination requires a Trajectory structure, which can be saved as parquet file.
    // In our case, the trajectory comes from the BSP file, so we need to build a Trajectory from the almanac directly.
    // To query the Almanac, we need to build the LRO frame in the J2000 orientation in our case.
    // Inspecting the LRO BSP in the ANISE GUI shows us that NASA has assigned ID -85 to LRO.
    let lro_frame = Frame::from_ephem_j2000(-85);

    // To build the trajectory we need to provide a spacecraft template.
    let sc_template = Spacecraft::builder()
        .mass(Mass::from_dry_and_prop_masses(1018.0, 900.0)) // Launch masses
        .srp(SRPData {
            // SRP configuration is arbitrary, but we will be estimating it anyway.
            area_m2: 3.9 * 2.7,
            coeff_reflectivity: 0.96,
        })
        .orbit(Orbit::zero(MOON_J2000)) // Setting a zero orbit here because it's just a template
        .build();
    // Now we can build the trajectory from the BSP file.
    // We'll arbitrarily set the tracking arc to 24 hours with a five second time step.
    let traj_as_flown = Traj::from_bsp(
        lro_frame,
        MOON_J2000,
        almanac.clone(),
        sc_template,
        5.seconds(),
        Some(Epoch::from_str("2024-01-01 00:00:00 UTC")?),
        Some(Epoch::from_str("2024-01-02 00:00:00 UTC")?),
        Aberration::LT,
        Some("LRO".to_string()),
    )?;

    println!("{traj_as_flown}");

    // ====================== //
    // === MODEL MATCHING === //
    // ====================== //

    // Set up the spacecraft dynamics.

    // Specify that the orbital dynamics must account for the graviational pull of the Earth and the Sun.
    // The gravity of the Moon will also be accounted for since the spaceraft in a lunar orbit.
    let mut orbital_dyn = OrbitalDynamics::point_masses(vec![EARTH, SUN, JUPITER_BARYCENTER]);

    // We want to include the spherical harmonics, so let's download the gravitational data from the Nyx Cloud.
    // We're using the GRAIL JGGRX model.
    let mut jggrx_meta = MetaFile {
        uri: "http://public-data.nyxspace.com/nyx/models/Luna_jggrx_1500e_sha.tab.gz".to_string(),
        crc32: Some(0x6bcacda8), // Specifying the CRC32 avoids redownloading it if it's cached.
    };
    // And let's download it if we don't have it yet.
    jggrx_meta.process(true)?;

    // Build the spherical harmonics.
    // The harmonics must be computed in the body fixed frame.
    // We're using the long term prediction of the Moon principal axes frame.
    let moon_pa_frame = MOON_PA_FRAME.with_orient(31008);
    let sph_harmonics = Harmonics::from_stor(
        almanac.frame_from_uid(moon_pa_frame)?,
        HarmonicsMem::from_shadr(&jggrx_meta.uri, 80, 80, true)?,
    );

    // Include the spherical harmonics into the orbital dynamics.
    orbital_dyn.accel_models.push(sph_harmonics);

    // We define the solar radiation pressure, using the default solar flux and accounting only
    // for the eclipsing caused by the Earth and Moon.
    // Note that by default, enabling the SolarPressure model will also enable the estimation of the coefficient of reflectivity.
    let srp_dyn = SolarPressure::new(vec![EARTH_J2000, MOON_J2000], almanac.clone())?;

    // Finalize setting up the dynamics, specifying the force models (orbital_dyn) separately from the
    // acceleration models (SRP in this case). Use `from_models` to specify multiple accel models.
    let dynamics = SpacecraftDynamics::from_model(orbital_dyn, srp_dyn);

    println!("{dynamics}");

    // Now we can build the propagator.
    let setup = Propagator::default_dp78(dynamics.clone());

    // For reference, let's build the trajectory with Nyx's models from that LRO state.
    let (sim_final, traj_as_sim) = setup
        .with(*traj_as_flown.first(), almanac.clone())
        .until_epoch_with_traj(traj_as_flown.last().epoch())?;

    println!("SIM INIT:  {:x}", traj_as_flown.first());
    println!("SIM FINAL: {sim_final:x}");
    // Compute RIC difference between SIM and LRO ephem
    let sim_lro_delta = sim_final
        .orbit
        .ric_difference(&traj_as_flown.last().orbit)?;
    println!("{traj_as_sim}");
    println!(
        "SIM v LRO - RIC Position (m): {:.3}",
        sim_lro_delta.radius_km * 1e3
    );
    println!(
        "SIM v LRO - RIC Velocity (m/s): {:.3}",
        sim_lro_delta.velocity_km_s * 1e3
    );

    traj_as_sim.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_sim_truth_error.parquet",
        ExportCfg::default(),
    )?;

    // ==================== //
    // === OD SIMULATOR === //
    // ==================== //

    // After quite some time trying to exactly match the model, we still end up with an oscillatory difference on the order of 150 meters between the propagated state
    // and the truth LRO state.

    // Therefore, we will actually run an estimation from a dispersed LRO state.
    // The sc_seed is the true LRO state from the BSP.
    let sc_seed = *traj_as_flown.first();

    // Load the Deep Space Network ground stations.
    // Nyx allows you to build these at runtime but it's pretty static so we can just load them from YAML.
    let ground_station_file: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "dsn-network.yaml",
    ]
    .iter()
    .collect();

    let devices = GroundStation::load_named(ground_station_file)?;

    // Typical OD software requires that you specify your own tracking schedule or you'll have overlapping measurements.
    // Nyx can build a tracking schedule for you based on the first station with access.
    let trkconfg_yaml: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "tracking-cfg.yaml",
    ]
    .iter()
    .collect();

    let configs: BTreeMap<String, TrkConfig> = TrkConfig::load_named(trkconfg_yaml)?;

    // Build the tracking arc simulation to generate a "standard measurement".
    let mut trk = TrackingArcSim::<Spacecraft, GroundStation>::new(
        devices.clone(),
        traj_as_flown.clone(),
        configs,
    )?;

    trk.build_schedule(almanac.clone())?;
    let arc = trk.generate_measurements(almanac.clone())?;
    // Save the simulated tracking data
    arc.to_parquet_simple("./04_lro_simulated_tracking.parquet")?;

    // We'll note that in our case, we have continuous coverage of LRO when the vehicle is not behind the Moon.
    println!("{arc}");

    // Now that we have simulated measurements, we'll run the orbit determination.

    // ===================== //
    // === OD ESTIMATION === //
    // ===================== //

    let sc = SpacecraftUncertainty::builder()
        .nominal(sc_seed)
        .frame(LocalFrame::RIC)
        .x_km(0.5)
        .y_km(0.5)
        .z_km(0.5)
        .vx_km_s(5e-3)
        .vy_km_s(5e-3)
        .vz_km_s(5e-3)
        .build();

    // Build the filter initial estimate, which we will reuse in the filter.
    let initial_estimate = sc.to_estimate()?;

    println!("== FILTER STATE ==\n{sc_seed:x}\n{initial_estimate}");

    // Build the SNC in the Moon J2000 frame, specified as a velocity noise over time.
    let process_noise = ProcessNoise3D::from_velocity_km_s(
        &[1.8e-9, 1.8e-9, 1.8e-9],
        1 * Unit::Hour,
        10 * Unit::Minute,
        None,
    );

    println!("{process_noise}");

    // We'll set up the OD process to reject measurements whose residuals are move than 3 sigmas away from what we expect.
    let odp = SpacecraftKalmanOD::new(
        setup,
        KalmanVariant::ReferenceUpdate,
        Some(ResidRejectCrit::default()),
        devices,
        almanac.clone(),
    )
    .with_process_noise(process_noise);

    let od_sol = odp.process_arc(initial_estimate, &arc)?;

    let ric_err = traj_as_flown
        .at(od_sol.estimates.last().unwrap().epoch())?
        .orbit
        .ric_difference(&od_sol.estimates.last().unwrap().orbital_state())?;
    println!("== RIC at end ==");
    println!("RIC Position (m): {}", ric_err.radius_km * 1e3);
    println!("RIC Velocity (m/s): {}", ric_err.velocity_km_s * 1e3);

    println!(
        "Num residuals rejected: #{}",
        od_sol.rejected_residuals().len()
    );
    println!(
        "Percentage within +/-3: {}",
        od_sol.residual_ratio_within_threshold(3.0).unwrap()
    );
    println!("Ratios normal? {}", od_sol.is_normal(None).unwrap());

    od_sol.to_parquet("./04_lro_od_results.parquet", ExportCfg::default())?;

    // In our case, we have the truth trajectory from NASA.
    // So we can compute the RIC state difference between the real LRO ephem and what we've just estimated.
    // Export the OD trajectory first.
    let od_trajectory = od_sol.to_traj()?;
    // Build the RIC difference.
    od_trajectory.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_od_truth_error.parquet",
        ExportCfg::default(),
    )?;

    Ok(())
}

impl<StateType, EstType, MsrSize, Trk> ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>, EstType: Estimate<StateType>, MsrSize: DimName, Trk: TrackerSensitivity<StateType, StateType>, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

pub fn new( devices: BTreeMap<String, Trk>, measurement_types: IndexSet<MeasurementType>, ) -> Self

pub fn results( &self, ) -> Zip<Iter<'_, EstType>, Iter<'_, Option<Residual<MsrSize>>>>

Returns a zipper iterator on the estimates and the associated residuals.

pub fn is_filter_run(&self) -> bool

Returns True if this is the result of a filter run

pub fn is_smoother_run(&self) -> bool

Returns True if this is the result of a smoother run

pub fn to_traj(&self) -> Result<Traj<StateType>, NyxError>

where DefaultAllocator: Allocator<StateType::VecLength>,

Builds the navigation trajectory for the estimated state only

Examples found in repository

examples/04_lro_od/main.rs (line 295)

fn main() -> Result<(), Box<dyn Error>> {
    pel::init();

    // ====================== //
    // === ALMANAC SET UP === //
    // ====================== //

    // Dynamics models require planetary constants and ephemerides to be defined.
    // Let's start by grabbing those by using ANISE's MetaAlmanac.

    let data_folder: PathBuf = [env!("CARGO_MANIFEST_DIR"), "examples", "04_lro_od"]
        .iter()
        .collect();

    let meta = data_folder.join("lro-dynamics.dhall");

    // Load this ephem in the general Almanac we're using for this analysis.
    let mut almanac = MetaAlmanac::new(meta.to_string_lossy().to_string())
        .map_err(Box::new)?
        .process(true)
        .map_err(Box::new)?;

    let mut moon_pc = almanac.planetary_data.get_by_id(MOON)?;
    moon_pc.mu_km3_s2 = 4902.74987;
    almanac.planetary_data.set_by_id(MOON, moon_pc)?;

    let mut earth_pc = almanac.planetary_data.get_by_id(EARTH)?;
    earth_pc.mu_km3_s2 = 398600.436;
    almanac.planetary_data.set_by_id(EARTH, earth_pc)?;

    // Save this new kernel for reuse.
    // In an operational context, this would be part of the "Lock" process, and should not change throughout the mission.
    almanac
        .planetary_data
        .save_as(&data_folder.join("lro-specific.pca"), true)?;

    // Lock the almanac (an Arc is a read only structure).
    let almanac = Arc::new(almanac);

    // Orbit determination requires a Trajectory structure, which can be saved as parquet file.
    // In our case, the trajectory comes from the BSP file, so we need to build a Trajectory from the almanac directly.
    // To query the Almanac, we need to build the LRO frame in the J2000 orientation in our case.
    // Inspecting the LRO BSP in the ANISE GUI shows us that NASA has assigned ID -85 to LRO.
    let lro_frame = Frame::from_ephem_j2000(-85);

    // To build the trajectory we need to provide a spacecraft template.
    let sc_template = Spacecraft::builder()
        .mass(Mass::from_dry_and_prop_masses(1018.0, 900.0)) // Launch masses
        .srp(SRPData {
            // SRP configuration is arbitrary, but we will be estimating it anyway.
            area_m2: 3.9 * 2.7,
            coeff_reflectivity: 0.96,
        })
        .orbit(Orbit::zero(MOON_J2000)) // Setting a zero orbit here because it's just a template
        .build();
    // Now we can build the trajectory from the BSP file.
    // We'll arbitrarily set the tracking arc to 24 hours with a five second time step.
    let traj_as_flown = Traj::from_bsp(
        lro_frame,
        MOON_J2000,
        almanac.clone(),
        sc_template,
        5.seconds(),
        Some(Epoch::from_str("2024-01-01 00:00:00 UTC")?),
        Some(Epoch::from_str("2024-01-02 00:00:00 UTC")?),
        Aberration::LT,
        Some("LRO".to_string()),
    )?;

    println!("{traj_as_flown}");

    // ====================== //
    // === MODEL MATCHING === //
    // ====================== //

    // Set up the spacecraft dynamics.

    // Specify that the orbital dynamics must account for the graviational pull of the Earth and the Sun.
    // The gravity of the Moon will also be accounted for since the spaceraft in a lunar orbit.
    let mut orbital_dyn = OrbitalDynamics::point_masses(vec![EARTH, SUN, JUPITER_BARYCENTER]);

    // We want to include the spherical harmonics, so let's download the gravitational data from the Nyx Cloud.
    // We're using the GRAIL JGGRX model.
    let mut jggrx_meta = MetaFile {
        uri: "http://public-data.nyxspace.com/nyx/models/Luna_jggrx_1500e_sha.tab.gz".to_string(),
        crc32: Some(0x6bcacda8), // Specifying the CRC32 avoids redownloading it if it's cached.
    };
    // And let's download it if we don't have it yet.
    jggrx_meta.process(true)?;

    // Build the spherical harmonics.
    // The harmonics must be computed in the body fixed frame.
    // We're using the long term prediction of the Moon principal axes frame.
    let moon_pa_frame = MOON_PA_FRAME.with_orient(31008);
    let sph_harmonics = Harmonics::from_stor(
        almanac.frame_from_uid(moon_pa_frame)?,
        HarmonicsMem::from_shadr(&jggrx_meta.uri, 80, 80, true)?,
    );

    // Include the spherical harmonics into the orbital dynamics.
    orbital_dyn.accel_models.push(sph_harmonics);

    // We define the solar radiation pressure, using the default solar flux and accounting only
    // for the eclipsing caused by the Earth and Moon.
    // Note that by default, enabling the SolarPressure model will also enable the estimation of the coefficient of reflectivity.
    let srp_dyn = SolarPressure::new(vec![EARTH_J2000, MOON_J2000], almanac.clone())?;

    // Finalize setting up the dynamics, specifying the force models (orbital_dyn) separately from the
    // acceleration models (SRP in this case). Use `from_models` to specify multiple accel models.
    let dynamics = SpacecraftDynamics::from_model(orbital_dyn, srp_dyn);

    println!("{dynamics}");

    // Now we can build the propagator.
    let setup = Propagator::default_dp78(dynamics.clone());

    // For reference, let's build the trajectory with Nyx's models from that LRO state.
    let (sim_final, traj_as_sim) = setup
        .with(*traj_as_flown.first(), almanac.clone())
        .until_epoch_with_traj(traj_as_flown.last().epoch())?;

    println!("SIM INIT:  {:x}", traj_as_flown.first());
    println!("SIM FINAL: {sim_final:x}");
    // Compute RIC difference between SIM and LRO ephem
    let sim_lro_delta = sim_final
        .orbit
        .ric_difference(&traj_as_flown.last().orbit)?;
    println!("{traj_as_sim}");
    println!(
        "SIM v LRO - RIC Position (m): {:.3}",
        sim_lro_delta.radius_km * 1e3
    );
    println!(
        "SIM v LRO - RIC Velocity (m/s): {:.3}",
        sim_lro_delta.velocity_km_s * 1e3
    );

    traj_as_sim.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_sim_truth_error.parquet",
        ExportCfg::default(),
    )?;

    // ==================== //
    // === OD SIMULATOR === //
    // ==================== //

    // After quite some time trying to exactly match the model, we still end up with an oscillatory difference on the order of 150 meters between the propagated state
    // and the truth LRO state.

    // Therefore, we will actually run an estimation from a dispersed LRO state.
    // The sc_seed is the true LRO state from the BSP.
    let sc_seed = *traj_as_flown.first();

    // Load the Deep Space Network ground stations.
    // Nyx allows you to build these at runtime but it's pretty static so we can just load them from YAML.
    let ground_station_file: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "dsn-network.yaml",
    ]
    .iter()
    .collect();

    let devices = GroundStation::load_named(ground_station_file)?;

    // Typical OD software requires that you specify your own tracking schedule or you'll have overlapping measurements.
    // Nyx can build a tracking schedule for you based on the first station with access.
    let trkconfg_yaml: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "tracking-cfg.yaml",
    ]
    .iter()
    .collect();

    let configs: BTreeMap<String, TrkConfig> = TrkConfig::load_named(trkconfg_yaml)?;

    // Build the tracking arc simulation to generate a "standard measurement".
    let mut trk = TrackingArcSim::<Spacecraft, GroundStation>::new(
        devices.clone(),
        traj_as_flown.clone(),
        configs,
    )?;

    trk.build_schedule(almanac.clone())?;
    let arc = trk.generate_measurements(almanac.clone())?;
    // Save the simulated tracking data
    arc.to_parquet_simple("./04_lro_simulated_tracking.parquet")?;

    // We'll note that in our case, we have continuous coverage of LRO when the vehicle is not behind the Moon.
    println!("{arc}");

    // Now that we have simulated measurements, we'll run the orbit determination.

    // ===================== //
    // === OD ESTIMATION === //
    // ===================== //

    let sc = SpacecraftUncertainty::builder()
        .nominal(sc_seed)
        .frame(LocalFrame::RIC)
        .x_km(0.5)
        .y_km(0.5)
        .z_km(0.5)
        .vx_km_s(5e-3)
        .vy_km_s(5e-3)
        .vz_km_s(5e-3)
        .build();

    // Build the filter initial estimate, which we will reuse in the filter.
    let initial_estimate = sc.to_estimate()?;

    println!("== FILTER STATE ==\n{sc_seed:x}\n{initial_estimate}");

    // Build the SNC in the Moon J2000 frame, specified as a velocity noise over time.
    let process_noise = ProcessNoise3D::from_velocity_km_s(
        &[1.8e-9, 1.8e-9, 1.8e-9],
        1 * Unit::Hour,
        10 * Unit::Minute,
        None,
    );

    println!("{process_noise}");

    // We'll set up the OD process to reject measurements whose residuals are move than 3 sigmas away from what we expect.
    let odp = SpacecraftKalmanOD::new(
        setup,
        KalmanVariant::ReferenceUpdate,
        Some(ResidRejectCrit::default()),
        devices,
        almanac.clone(),
    )
    .with_process_noise(process_noise);

    let od_sol = odp.process_arc(initial_estimate, &arc)?;

    let ric_err = traj_as_flown
        .at(od_sol.estimates.last().unwrap().epoch())?
        .orbit
        .ric_difference(&od_sol.estimates.last().unwrap().orbital_state())?;
    println!("== RIC at end ==");
    println!("RIC Position (m): {}", ric_err.radius_km * 1e3);
    println!("RIC Velocity (m/s): {}", ric_err.velocity_km_s * 1e3);

    println!(
        "Num residuals rejected: #{}",
        od_sol.rejected_residuals().len()
    );
    println!(
        "Percentage within +/-3: {}",
        od_sol.residual_ratio_within_threshold(3.0).unwrap()
    );
    println!("Ratios normal? {}", od_sol.is_normal(None).unwrap());

    od_sol.to_parquet("./04_lro_od_results.parquet", ExportCfg::default())?;

    // In our case, we have the truth trajectory from NASA.
    // So we can compute the RIC state difference between the real LRO ephem and what we've just estimated.
    // Export the OD trajectory first.
    let od_trajectory = od_sol.to_traj()?;
    // Build the RIC difference.
    od_trajectory.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_od_truth_error.parquet",
        ExportCfg::default(),
    )?;

    Ok(())
}

pub fn accepted_residuals(&self) -> Vec<Residual<MsrSize>>

Returns the accepted residuals.

pub fn rejected_residuals(&self) -> Vec<Residual<MsrSize>>

Returns the rejected residuals.

Examples found in repository

examples/04_lro_od/main.rs (line 282)

fn main() -> Result<(), Box<dyn Error>> {
    pel::init();

    // ====================== //
    // === ALMANAC SET UP === //
    // ====================== //

    // Dynamics models require planetary constants and ephemerides to be defined.
    // Let's start by grabbing those by using ANISE's MetaAlmanac.

    let data_folder: PathBuf = [env!("CARGO_MANIFEST_DIR"), "examples", "04_lro_od"]
        .iter()
        .collect();

    let meta = data_folder.join("lro-dynamics.dhall");

    // Load this ephem in the general Almanac we're using for this analysis.
    let mut almanac = MetaAlmanac::new(meta.to_string_lossy().to_string())
        .map_err(Box::new)?
        .process(true)
        .map_err(Box::new)?;

    let mut moon_pc = almanac.planetary_data.get_by_id(MOON)?;
    moon_pc.mu_km3_s2 = 4902.74987;
    almanac.planetary_data.set_by_id(MOON, moon_pc)?;

    let mut earth_pc = almanac.planetary_data.get_by_id(EARTH)?;
    earth_pc.mu_km3_s2 = 398600.436;
    almanac.planetary_data.set_by_id(EARTH, earth_pc)?;

    // Save this new kernel for reuse.
    // In an operational context, this would be part of the "Lock" process, and should not change throughout the mission.
    almanac
        .planetary_data
        .save_as(&data_folder.join("lro-specific.pca"), true)?;

    // Lock the almanac (an Arc is a read only structure).
    let almanac = Arc::new(almanac);

    // Orbit determination requires a Trajectory structure, which can be saved as parquet file.
    // In our case, the trajectory comes from the BSP file, so we need to build a Trajectory from the almanac directly.
    // To query the Almanac, we need to build the LRO frame in the J2000 orientation in our case.
    // Inspecting the LRO BSP in the ANISE GUI shows us that NASA has assigned ID -85 to LRO.
    let lro_frame = Frame::from_ephem_j2000(-85);

    // To build the trajectory we need to provide a spacecraft template.
    let sc_template = Spacecraft::builder()
        .mass(Mass::from_dry_and_prop_masses(1018.0, 900.0)) // Launch masses
        .srp(SRPData {
            // SRP configuration is arbitrary, but we will be estimating it anyway.
            area_m2: 3.9 * 2.7,
            coeff_reflectivity: 0.96,
        })
        .orbit(Orbit::zero(MOON_J2000)) // Setting a zero orbit here because it's just a template
        .build();
    // Now we can build the trajectory from the BSP file.
    // We'll arbitrarily set the tracking arc to 24 hours with a five second time step.
    let traj_as_flown = Traj::from_bsp(
        lro_frame,
        MOON_J2000,
        almanac.clone(),
        sc_template,
        5.seconds(),
        Some(Epoch::from_str("2024-01-01 00:00:00 UTC")?),
        Some(Epoch::from_str("2024-01-02 00:00:00 UTC")?),
        Aberration::LT,
        Some("LRO".to_string()),
    )?;

    println!("{traj_as_flown}");

    // ====================== //
    // === MODEL MATCHING === //
    // ====================== //

    // Set up the spacecraft dynamics.

    // Specify that the orbital dynamics must account for the graviational pull of the Earth and the Sun.
    // The gravity of the Moon will also be accounted for since the spaceraft in a lunar orbit.
    let mut orbital_dyn = OrbitalDynamics::point_masses(vec![EARTH, SUN, JUPITER_BARYCENTER]);

    // We want to include the spherical harmonics, so let's download the gravitational data from the Nyx Cloud.
    // We're using the GRAIL JGGRX model.
    let mut jggrx_meta = MetaFile {
        uri: "http://public-data.nyxspace.com/nyx/models/Luna_jggrx_1500e_sha.tab.gz".to_string(),
        crc32: Some(0x6bcacda8), // Specifying the CRC32 avoids redownloading it if it's cached.
    };
    // And let's download it if we don't have it yet.
    jggrx_meta.process(true)?;

    // Build the spherical harmonics.
    // The harmonics must be computed in the body fixed frame.
    // We're using the long term prediction of the Moon principal axes frame.
    let moon_pa_frame = MOON_PA_FRAME.with_orient(31008);
    let sph_harmonics = Harmonics::from_stor(
        almanac.frame_from_uid(moon_pa_frame)?,
        HarmonicsMem::from_shadr(&jggrx_meta.uri, 80, 80, true)?,
    );

    // Include the spherical harmonics into the orbital dynamics.
    orbital_dyn.accel_models.push(sph_harmonics);

    // We define the solar radiation pressure, using the default solar flux and accounting only
    // for the eclipsing caused by the Earth and Moon.
    // Note that by default, enabling the SolarPressure model will also enable the estimation of the coefficient of reflectivity.
    let srp_dyn = SolarPressure::new(vec![EARTH_J2000, MOON_J2000], almanac.clone())?;

    // Finalize setting up the dynamics, specifying the force models (orbital_dyn) separately from the
    // acceleration models (SRP in this case). Use `from_models` to specify multiple accel models.
    let dynamics = SpacecraftDynamics::from_model(orbital_dyn, srp_dyn);

    println!("{dynamics}");

    // Now we can build the propagator.
    let setup = Propagator::default_dp78(dynamics.clone());

    // For reference, let's build the trajectory with Nyx's models from that LRO state.
    let (sim_final, traj_as_sim) = setup
        .with(*traj_as_flown.first(), almanac.clone())
        .until_epoch_with_traj(traj_as_flown.last().epoch())?;

    println!("SIM INIT:  {:x}", traj_as_flown.first());
    println!("SIM FINAL: {sim_final:x}");
    // Compute RIC difference between SIM and LRO ephem
    let sim_lro_delta = sim_final
        .orbit
        .ric_difference(&traj_as_flown.last().orbit)?;
    println!("{traj_as_sim}");
    println!(
        "SIM v LRO - RIC Position (m): {:.3}",
        sim_lro_delta.radius_km * 1e3
    );
    println!(
        "SIM v LRO - RIC Velocity (m/s): {:.3}",
        sim_lro_delta.velocity_km_s * 1e3
    );

    traj_as_sim.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_sim_truth_error.parquet",
        ExportCfg::default(),
    )?;

    // ==================== //
    // === OD SIMULATOR === //
    // ==================== //

    // After quite some time trying to exactly match the model, we still end up with an oscillatory difference on the order of 150 meters between the propagated state
    // and the truth LRO state.

    // Therefore, we will actually run an estimation from a dispersed LRO state.
    // The sc_seed is the true LRO state from the BSP.
    let sc_seed = *traj_as_flown.first();

    // Load the Deep Space Network ground stations.
    // Nyx allows you to build these at runtime but it's pretty static so we can just load them from YAML.
    let ground_station_file: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "dsn-network.yaml",
    ]
    .iter()
    .collect();

    let devices = GroundStation::load_named(ground_station_file)?;

    // Typical OD software requires that you specify your own tracking schedule or you'll have overlapping measurements.
    // Nyx can build a tracking schedule for you based on the first station with access.
    let trkconfg_yaml: PathBuf = [
        env!("CARGO_MANIFEST_DIR"),
        "examples",
        "04_lro_od",
        "tracking-cfg.yaml",
    ]
    .iter()
    .collect();

    let configs: BTreeMap<String, TrkConfig> = TrkConfig::load_named(trkconfg_yaml)?;

    // Build the tracking arc simulation to generate a "standard measurement".
    let mut trk = TrackingArcSim::<Spacecraft, GroundStation>::new(
        devices.clone(),
        traj_as_flown.clone(),
        configs,
    )?;

    trk.build_schedule(almanac.clone())?;
    let arc = trk.generate_measurements(almanac.clone())?;
    // Save the simulated tracking data
    arc.to_parquet_simple("./04_lro_simulated_tracking.parquet")?;

    // We'll note that in our case, we have continuous coverage of LRO when the vehicle is not behind the Moon.
    println!("{arc}");

    // Now that we have simulated measurements, we'll run the orbit determination.

    // ===================== //
    // === OD ESTIMATION === //
    // ===================== //

    let sc = SpacecraftUncertainty::builder()
        .nominal(sc_seed)
        .frame(LocalFrame::RIC)
        .x_km(0.5)
        .y_km(0.5)
        .z_km(0.5)
        .vx_km_s(5e-3)
        .vy_km_s(5e-3)
        .vz_km_s(5e-3)
        .build();

    // Build the filter initial estimate, which we will reuse in the filter.
    let initial_estimate = sc.to_estimate()?;

    println!("== FILTER STATE ==\n{sc_seed:x}\n{initial_estimate}");

    // Build the SNC in the Moon J2000 frame, specified as a velocity noise over time.
    let process_noise = ProcessNoise3D::from_velocity_km_s(
        &[1.8e-9, 1.8e-9, 1.8e-9],
        1 * Unit::Hour,
        10 * Unit::Minute,
        None,
    );

    println!("{process_noise}");

    // We'll set up the OD process to reject measurements whose residuals are move than 3 sigmas away from what we expect.
    let odp = SpacecraftKalmanOD::new(
        setup,
        KalmanVariant::ReferenceUpdate,
        Some(ResidRejectCrit::default()),
        devices,
        almanac.clone(),
    )
    .with_process_noise(process_noise);

    let od_sol = odp.process_arc(initial_estimate, &arc)?;

    let ric_err = traj_as_flown
        .at(od_sol.estimates.last().unwrap().epoch())?
        .orbit
        .ric_difference(&od_sol.estimates.last().unwrap().orbital_state())?;
    println!("== RIC at end ==");
    println!("RIC Position (m): {}", ric_err.radius_km * 1e3);
    println!("RIC Velocity (m/s): {}", ric_err.velocity_km_s * 1e3);

    println!(
        "Num residuals rejected: #{}",
        od_sol.rejected_residuals().len()
    );
    println!(
        "Percentage within +/-3: {}",
        od_sol.residual_ratio_within_threshold(3.0).unwrap()
    );
    println!("Ratios normal? {}", od_sol.is_normal(None).unwrap());

    od_sol.to_parquet("./04_lro_od_results.parquet", ExportCfg::default())?;

    // In our case, we have the truth trajectory from NASA.
    // So we can compute the RIC state difference between the real LRO ephem and what we've just estimated.
    // Export the OD trajectory first.
    let od_trajectory = od_sol.to_traj()?;
    // Build the RIC difference.
    od_trajectory.ric_diff_to_parquet(
        &traj_as_flown,
        "./04_lro_od_truth_error.parquet",
        ExportCfg::default(),
    )?;

    Ok(())
}

Trait Implementations

impl<StateType, EstType, MsrSize, Trk> Clone for ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType> + Clone, EstType: Estimate<StateType> + Clone, MsrSize: DimName + Clone, Trk: TrackerSensitivity<StateType, StateType> + Clone, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

fn clone(&self) -> ODSolution<StateType, EstType, MsrSize, Trk>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<StateType, EstType, MsrSize, Trk> Debug for ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType> + Debug, EstType: Estimate<StateType> + Debug, MsrSize: DimName + Debug, Trk: TrackerSensitivity<StateType, StateType> + Debug, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<StateType, EstType, MsrSize, Trk> Display for ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>, EstType: Estimate<StateType>, MsrSize: DimName, Trk: TrackerSensitivity<StateType, StateType>, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<StateType, EstType, MsrSize, Trk> PartialEq for ODSolution<StateType, EstType, MsrSize, Trk>

where StateType: Interpolatable + Add<OVector<f64, <StateType as State>::Size>, Output = StateType>, EstType: Estimate<StateType>, MsrSize: DimName, Trk: TrackerSensitivity<StateType, StateType> + PartialEq, <DefaultAllocator as Allocator<<StateType as State>::VecLength>>::Buffer<f64>: Send, DefaultAllocator: Allocator<<StateType as State>::Size> + Allocator<<StateType as State>::VecLength> + Allocator<MsrSize> + Allocator<MsrSize, <StateType as State>::Size> + Allocator<MsrSize, MsrSize> + Allocator<<StateType as State>::Size, <StateType as State>::Size> + Allocator<<StateType as State>::Size, MsrSize>,

fn eq(&self, other: &Self) -> bool

Checks that the covariances are within 1e-8 in norm, the state vectors within 1e-6, the residual ratios within 1e-4, the gains and flight-smoother consistencies within 1e-8.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.