nyx_space/od/noise/
white.rs

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
/*
    Nyx, blazing fast astrodynamics
    Copyright (C) 2018-onwards Christopher Rabotin <christopher.rabotin@gmail.com>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU Affero General Public License as published
    by the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Affero General Public License for more details.

    You should have received a copy of the GNU Affero General Public License
    along with this program.  If not, see <https://www.gnu.org/licenses/>.
*/

use std::ops::{Mul, MulAssign};

use anise::constants::SPEED_OF_LIGHT_KM_S;
use hifitime::{Duration, Epoch};
use rand::Rng;
use rand_distr::Normal;
use serde_derive::{Deserialize, Serialize};

use super::Stochastics;

/// White noise is an uncorrelated random variable.
#[derive(Copy, Clone, Debug, Default, PartialEq, Serialize, Deserialize)]
pub struct WhiteNoise {
    /// Mean value of this white noise
    pub mean: f64,
    /// Process noise as a one-sigma of the Normal distribution.
    pub sigma: f64,
}

impl WhiteNoise {
    /// Initializes a new random walk stochastic noise model from the process noise and the integration time.
    /// This will compute the process noise per second automatically.
    pub fn new(process_noise: f64, integration_time: Duration) -> Self {
        Self {
            sigma: process_noise / integration_time.to_seconds(),
            ..Default::default()
        }
    }

    /// Initializes a new random walk stochastic noise model from the provided process noise, assuming that the noise level
    /// is fixed regardless of the integration time.
    pub fn constant_white_noise(process_noise: f64) -> Self {
        Self {
            sigma: process_noise,
            ..Default::default()
        }
    }

    // Initializes a new time-uncorrelated white noise process, using only the Pr/N0 value and the bandwidth.
    // This returns a white noise sigma in kilometers.
    //
    // # Equation
    // σ = c / (2 * B * √(Pr/N0))
    //
    // Where c is the speed of light, B is the bandwidth in Hz, and the Pr/N0 is the signal-to-noise ratio.
    pub fn from_pr_n0(pr_n0: f64, bandwidth_hz: f64) -> Self {
        Self {
            sigma: SPEED_OF_LIGHT_KM_S / (2.0 * bandwidth_hz * (pr_n0).sqrt()),
            mean: 0.0,
        }
    }
}

impl Stochastics for WhiteNoise {
    fn covariance(&self, _epoch: Epoch) -> f64 {
        self.sigma.powi(2)
    }

    fn sample<R: Rng>(&mut self, _epoch: Epoch, rng: &mut R) -> f64 {
        rng.sample(Normal::new(self.mean, self.sigma).unwrap())
    }
}

impl Mul<f64> for WhiteNoise {
    type Output = Self;

    /// Scale the white noise sigmas by a constant.
    fn mul(mut self, rhs: f64) -> Self::Output {
        self.sigma *= rhs;
        self
    }
}

impl MulAssign<f64> for WhiteNoise {
    fn mul_assign(&mut self, rhs: f64) {
        *self = *self * rhs;
    }
}

#[cfg(test)]
mod ut_wn {
    use hifitime::{Epoch, TimeUnits};
    use rand_pcg::Pcg64Mcg;

    use super::{Stochastics, WhiteNoise};

    #[test]
    fn white_noise_test() {
        let sigma = 10.0_f64;
        let mut wn = WhiteNoise { mean: 0.0, sigma };

        let mut larger_wn = WhiteNoise {
            mean: 0.0,
            sigma: sigma * 10.0,
        };

        let epoch = Epoch::now().unwrap();

        let mut rng = Pcg64Mcg::new(1000);
        let mut cnt_above_3sigma = 0;
        let mut cnt_below_3sigma = 0;
        let mut larger_cnt_above_3sigma = 0;
        let mut larger_cnt_below_3sigma = 0;
        for seconds in 0..1000_i64 {
            let bias = wn.sample(epoch + seconds.seconds(), &mut rng);

            if bias > 3.0 * sigma {
                cnt_above_3sigma += 1;
            } else if bias < -3.0 * sigma {
                cnt_below_3sigma += 1;
            }

            let larger_bias = larger_wn.sample(epoch + seconds.seconds(), &mut rng);
            if larger_bias > 30.0 * sigma {
                larger_cnt_above_3sigma += 1;
            } else if larger_bias < -30.0 * sigma {
                larger_cnt_below_3sigma += 1;
            }
        }

        assert!(dbg!(cnt_above_3sigma) <= 3);
        assert!(dbg!(cnt_below_3sigma) <= 3);

        assert!(dbg!(larger_cnt_above_3sigma) <= 3);
        assert!(dbg!(larger_cnt_below_3sigma) <= 3);
    }
}