612 lines
22 KiB
Rust
612 lines
22 KiB
Rust
//! Tests for the access window finder.
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//!
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//! The reference case is a circular equatorial orbit at 550 km altitude seen
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//! from a station on the equator with a ten degree mask. For that geometry
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//! the elevation is a function of the orbital position alone, so the rise,
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//! peak, and set times have a closed form:
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//!
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//! <div>
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//! $$
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//! \begin{aligned}
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//! \theta_c &= 90^\circ - \text{mask} - \arcsin\!\left(\frac{\text{Re} \cos(\text{mask})}{\text{Rs}}\right) \\
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//! t &= \frac{\theta - \theta_0}{n}
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//! \end{aligned}
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//! $$
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//! </div>
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//!
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//! with `theta` the orbital position measured from the station and `n` the
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//! mean motion. The values used below are computed from those expressions.
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//!
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//! 可见性窗口查找器的测试。
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//!
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//! 参考用例是自赤道上、遮蔽十度的一座站看 550 km 高度的圆赤道轨道。对该几何，
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//! 仰角只依赖于轨道位置，故升起、峰值与降落时刻有闭式：
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//!
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//! <div>
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//! $$
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//! \begin{aligned}
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//! \theta_c &= 90^\circ - \text{mask} - \arcsin\!\left(\frac{\text{Re} \cos(\text{mask})}{\text{Rs}}\right) \\
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//! t &= \frac{\theta - \theta_0}{n}
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//! \end{aligned}
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//! $$
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//! </div>
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//!
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//! 其中 `theta` 是自站量起的轨道位置，`n` 是平运动。下面所用的值即由这些表达式
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//! 计算。
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use apsis_access::{AccessErrorKind, AccessFinder, OrbitSample, Pass, PassSummary};
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use apsis_coverage::GroundPoint;
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use apsis_geodesy::Geodetic;
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use apsis_math::Vec3;
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use core::f64::consts::{FRAC_PI_2, PI};
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/// The Earth equatorial radius, in kilometers.
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///
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/// 地球赤道半径，单位为千米。
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const BODY_RADIUS: f64 = 6_378.137;
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/// The orbit radius for a 550 km circular orbit, in kilometers.
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///
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/// 550 km 圆轨道的轨道半径，单位为千米。
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const ORBIT_RADIUS: f64 = BODY_RADIUS + 550.0;
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/// The mean motion of the reference orbit, in radians per second.
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///
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/// This is `sqrt(mu / a^3)` with the WGS 84 gravitational parameter.
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///
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/// 参考轨道的平运动，单位为弧度每秒。
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///
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/// 这是使用 WGS 84 引力参数的 `sqrt(mu / a^3)`。
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const MEAN_MOTION: f64 = 0.001_094_823_692_885_802;
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/// A station on the equator with a ten degree mask.
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///
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/// 赤道上、遮蔽十度的一座站。
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fn station() -> GroundPoint {
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GroundPoint::new(Geodetic::new(0.0, 0.0, 0.0), 10.0_f64.to_radians())
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}
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/// A finder with a one second step and a millisecond tolerance.
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///
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/// 一秒步长、毫秒容差的查找器。
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fn finder() -> AccessFinder {
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AccessFinder {
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station: station(),
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sample_step_seconds: 1.0,
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crossing_tolerance_seconds: 0.001,
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}
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}
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/// The orbital position measured from the station at the start of the
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/// search, in radians.
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///
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/// The reference closed form solves for the crossing times relative to an
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/// initial position of minus one radian, so the track starts there.
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///
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/// 搜索开始时自站量起的轨道位置，单位为弧度。
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///
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/// 参考闭式是相对初始位置负一弧度求解穿越时刻，故轨迹从那里开始。
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const INITIAL_ANGLE: f64 = -1.0;
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/// Returns the satellite position for a reference orbit that passes over the
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/// station.
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///
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/// The orbit is circular and equatorial, so the position depends only on the
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/// angular position at the given time. The angle is measured from the station
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/// and increases at the mean motion, so the elevation is a function of that
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/// angle alone.
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///
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/// 返回一条自该站正上方经过的参考轨道的卫星位置。
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///
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/// 轨道是圆形的且位于赤道面，故位置只依赖于给定时刻的角位置。该角自站量起并以平
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/// 运动增大，故仰角只是该角的函数。
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fn reference_position(seconds: f64) -> Vec3 {
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let angle = INITIAL_ANGLE + MEAN_MOTION * seconds;
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Vec3::new(ORBIT_RADIUS * angle.cos(), ORBIT_RADIUS * angle.sin(), 0.0)
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}
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/// Returns the samples of the reference orbit over a window around one pass.
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///
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/// 返回参考轨道在一次过境附近窗口上的样本。
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fn reference_samples(step: f64, start: f64, end: f64) -> Vec<OrbitSample> {
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let mut samples = Vec::new();
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let mut seconds = start;
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while seconds <= end {
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samples.push(OrbitSample::new(seconds, reference_position(seconds)));
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seconds += step;
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}
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samples
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}
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/// The half angle of the footprint for the reference geometry, in radians.
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///
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/// This is `90 - mask - asin(Re cos(mask) / Rs)`, which for the reference
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/// case is 14.9566 degrees.
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///
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/// 参考几何的覆盖区半角，单位为弧度。
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///
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/// 这是 `90 - mask - asin(Re cos(mask) / Rs)`，对参考用例为 14.9566 度。
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const FOOTPRINT_HALF_ANGLE: f64 = 0.261_042_364_648_894_9;
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/// The rise time of the reference pass from the start of the search, in
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/// seconds.
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///
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/// 参考过境自搜索起点起的升起时刻，单位为秒。
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const REFERENCE_RISE: f64 = 674.955_681_770_3;
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/// The peak time of the reference pass, in seconds.
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///
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/// 参考过境的峰值时刻，单位为秒。
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const REFERENCE_PEAK: f64 = 913.389_074_878_5;
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/// The set time of the reference pass, in seconds.
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///
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/// 参考过境的降落时刻，单位为秒。
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const REFERENCE_SET: f64 = 1_151.822_467_986_6;
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#[test]
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fn the_finder_settings_are_validated() {
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assert!(finder().is_valid());
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let coarse = AccessFinder {
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sample_step_seconds: 0.0,
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..finder()
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};
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assert!(!coarse.is_valid());
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assert_eq!(
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coarse
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.find(&reference_samples(1.0, 0.0, 10.0))
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.expect_err("zero step")
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.kind(),
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AccessErrorKind::InvalidSampleStep
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);
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let loose = AccessFinder {
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crossing_tolerance_seconds: 10.0,
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..finder()
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};
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assert!(!loose.is_valid());
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assert_eq!(
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loose
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.find(&reference_samples(1.0, 0.0, 10.0))
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.expect_err("tolerance exceeds the step")
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.kind(),
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AccessErrorKind::InvalidTolerance
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);
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let bad_station = AccessFinder {
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station: GroundPoint::new(Geodetic::new(0.0, 0.0, 0.0), PI),
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..finder()
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};
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assert!(!bad_station.is_valid());
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assert_eq!(
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bad_station
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.find(&reference_samples(1.0, 0.0, 10.0))
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.expect_err("invalid station")
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.kind(),
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AccessErrorKind::InvalidStation
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);
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}
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#[test]
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fn the_reference_pass_matches_the_closed_form() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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assert_eq!(summary.count(), 1, "expected exactly one pass");
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let pass = &summary.passes[0];
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assert!(
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(pass.rise_seconds - REFERENCE_RISE).abs() < 0.5,
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"rise {} against {REFERENCE_RISE}",
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pass.rise_seconds
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);
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assert!(
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(pass.peak_seconds - REFERENCE_PEAK).abs() < 1.0,
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"peak {} against {REFERENCE_PEAK}",
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pass.peak_seconds
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);
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assert!(
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(pass.set_seconds - REFERENCE_SET).abs() < 0.5,
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"set {} against {REFERENCE_SET}",
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pass.set_seconds
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);
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}
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#[test]
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fn the_peak_of_an_overhead_pass_is_a_right_angle() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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let pass = &summary.passes[0];
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// The reference geometry passes directly over the station, so the
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// greatest elevation is a right angle.
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// 参考几何自该站正上方经过，故最大仰角是直角。
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assert!(
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(pass.peak_elevation - FRAC_PI_2).abs() < 0.01,
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"peak elevation {}",
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pass.peak_elevation
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);
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}
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#[test]
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fn the_pass_is_symmetric_about_the_peak() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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let pass = &summary.passes[0];
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let rise_to_peak = pass.rise_to_peak();
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let peak_to_set = pass.set_seconds - pass.peak_seconds;
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assert!(
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(rise_to_peak - peak_to_set).abs() < 1.0,
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"{rise_to_peak} against {peak_to_set}"
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);
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}
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#[test]
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fn the_duration_matches_the_geometry() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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let pass = &summary.passes[0];
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// The orbital position spans twice the footprint half angle, so the
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// duration is 2 theta_c / n.
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// 轨道位置跨越覆盖区半角的两倍，故时长为 2 theta_c / n。
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let expected = 2.0 * FOOTPRINT_HALF_ANGLE / MEAN_MOTION;
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assert!(
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(pass.duration() - expected).abs() < 1.0,
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"{} against {expected}",
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pass.duration()
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);
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}
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#[test]
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fn the_refinement_is_independent_of_the_sample_step() {
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// The crossing times are found by interpolating the satellite position
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// between samples, so the result approaches the true crossing as the
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// step falls. The residual difference between two steps is second order
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// in the step, because the chord between two samples departs from the
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// arc by that order.
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// 穿越时刻通过样本之间插值卫星位置求得，故结果随步长减小而趋近真穿越。两个步长
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// 之间的残余差是步长的二阶量，因为两样本之间的弦与弧的偏差为该阶。
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let coarse = finder()
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.find(&reference_samples(10.0, 0.0, 2_000.0))
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.expect("valid");
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let fine = finder()
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.find(&reference_samples(1.0, 0.0, 2_000.0))
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.expect("valid");
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assert_eq!(coarse.count(), 1);
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assert_eq!(fine.count(), 1);
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let coarse_pass = &coarse.passes[0];
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let fine_pass = &fine.passes[0];
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// A ten second step gives a crossing within about a tenth of a second
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// of the one found with a one second step, because the chord error is
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// second order.
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// 十秒步长给出的穿越与一秒步长所得相差约十分之一秒，因为弦误差是二阶的。
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assert!(
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(coarse_pass.rise_seconds - fine_pass.rise_seconds).abs() < 0.1,
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"rise {} against {}",
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coarse_pass.rise_seconds,
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fine_pass.rise_seconds
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);
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assert!(
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(coarse_pass.set_seconds - fine_pass.set_seconds).abs() < 0.1,
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"set {} against {}",
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coarse_pass.set_seconds,
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fine_pass.set_seconds
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);
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}
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#[test]
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fn the_tolerance_controls_the_crossing_accuracy() {
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let loose = AccessFinder {
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crossing_tolerance_seconds: 1.0,
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..finder()
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};
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let tight = AccessFinder {
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crossing_tolerance_seconds: 1e-6,
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..finder()
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};
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let loose_pass = loose.find(&samples).expect("valid").passes[0];
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let tight_pass = tight.find(&samples).expect("valid").passes[0];
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// The two agree to within the looser tolerance.
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// 二者在较宽松的容差内一致。
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assert!((loose_pass.rise_seconds - tight_pass.rise_seconds).abs() <= 1.0);
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assert!((loose_pass.set_seconds - tight_pass.set_seconds).abs() <= 1.0);
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}
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#[test]
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fn a_full_orbit_finds_exactly_one_pass() {
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// The reference geometry gives one overhead pass per revolution, so a
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// window of one period contains one pass.
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// 参考几何每圈给出一次过顶，故一个周期的窗口含一次过境。
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let period = 2.0 * PI / MEAN_MOTION;
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let samples = reference_samples(1.0, 0.0, period);
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let summary = finder().find(&samples).expect("valid");
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assert_eq!(summary.count(), 1);
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}
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#[test]
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fn the_summary_reports_the_access_fraction() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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let fraction = summary.access_fraction().expect("a positive interval");
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let expected = summary.total_access_seconds() / 2_000.0;
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assert!((fraction - expected).abs() < 1e-12);
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// One overhead pass in a two thousand second window is about a quarter
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// of the time.
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// 两千秒窗口中的一次过顶约占四分之一时间。
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assert!(fraction > 0.2 && fraction < 0.3, "fraction {fraction}");
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}
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#[test]
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fn the_summary_finds_the_longest_and_highest_pass() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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assert!(summary.longest().is_some());
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assert!(summary.highest().is_some());
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assert!(summary.mean_duration_seconds().is_some());
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}
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#[test]
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fn a_pass_that_starts_before_the_window_is_clipped() {
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// Starting the search after the rise means the pass is reported from
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// the first sample rather than extrapolated backwards.
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// 在升起之后开始搜索意味着过境自第一个样本起报告，而不向后外推。
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let samples = reference_samples(1.0, 800.0, 1_400.0);
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let summary = finder().find(&samples).expect("valid");
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assert_eq!(summary.count(), 1);
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let pass = &summary.passes[0];
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assert!((pass.rise_seconds - 800.0).abs() < 1e-9);
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assert!((pass.set_seconds - REFERENCE_SET).abs() < 1.0);
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}
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#[test]
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fn a_pass_that_ends_after_the_window_is_clipped() {
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let samples = reference_samples(1.0, 0.0, 1_000.0);
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let summary = finder().find(&samples).expect("valid");
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assert_eq!(summary.count(), 1);
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let pass = &summary.passes[0];
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assert!((pass.rise_seconds - REFERENCE_RISE).abs() < 1.0);
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assert!((pass.set_seconds - 1_000.0).abs() < 1e-9);
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}
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#[test]
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fn a_window_with_no_pass_is_empty() {
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// A window before the satellite comes into view contains no pass.
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// 在卫星进入视野之前的窗口不含过境。
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let samples = reference_samples(1.0, -2_000.0, -1_000.0);
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let summary = finder().find(&samples).expect("valid");
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assert_eq!(summary.count(), 0);
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assert_eq!(summary.total_access_seconds(), 0.0);
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assert_eq!(summary.longest(), None);
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assert_eq!(summary.mean_duration_seconds(), None);
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assert_eq!(summary.longest_gap_seconds(), None);
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}
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#[test]
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fn the_gap_between_passes_is_reported() {
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// Two orbits give two passes, and the gap between them is the period
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// less the pass duration.
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// 两个轨道给出两次过境，其间的间隙是周期减去过境时长。
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let period = 2.0 * PI / MEAN_MOTION;
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let samples = reference_samples(1.0, 0.0, 2.0 * period);
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let summary = finder().find(&samples).expect("valid");
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assert!(summary.count() >= 2, "count {}", summary.count());
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let gap = summary.gap_seconds(0, 1).expect("consecutive passes");
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let expected = period - summary.passes[0].duration();
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assert!((gap - expected).abs() < 2.0, "{gap} against {expected}");
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// The largest gap is at least that one.
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// 最大间隙至少是该值。
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let longest = summary.longest_gap_seconds().expect("at least two passes");
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assert!(longest >= gap - 1e-9);
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}
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#[test]
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fn a_non_consecutive_gap_query_is_rejected() {
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let samples = reference_samples(1.0, 0.0, 2_000.0);
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let summary = finder().find(&samples).expect("valid");
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assert_eq!(summary.gap_seconds(0, 2), None);
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assert_eq!(summary.gap_seconds(1, 0), None);
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assert_eq!(summary.gap_seconds(0, 99), None);
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}
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#[test]
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fn the_pass_reports_containment() {
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let pass = Pass {
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rise_seconds: 100.0,
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set_seconds: 200.0,
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peak_seconds: 150.0,
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peak_elevation: 1.0,
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mask_elevation: 0.1,
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peak_position: Vec3::new(ORBIT_RADIUS, 0.0, 0.0),
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};
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assert!(pass.contains(100.0));
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assert!(pass.contains(150.0));
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assert!(pass.contains(200.0));
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assert!(!pass.contains(99.9));
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assert!(!pass.contains(200.1));
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assert!((pass.duration() - 100.0).abs() < 1e-12);
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assert!((pass.rise_to_peak() - 50.0).abs() < 1e-12);
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|
assert!((pass.maximum_elevation() - 1.0).abs() < 1e-12);
|
|
}
|
|
|
|
#[test]
|
|
fn too_few_samples_are_rejected() {
|
|
let error = finder()
|
|
.find(&[OrbitSample::new(0.0, Vec3::new(ORBIT_RADIUS, 0.0, 0.0))])
|
|
.expect_err("one sample is not enough");
|
|
assert_eq!(error.kind(), AccessErrorKind::InvalidInterval);
|
|
assert_eq!(
|
|
finder().find(&[]).expect_err("no samples").kind(),
|
|
AccessErrorKind::InvalidInterval
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn an_unordered_sample_sequence_is_rejected() {
|
|
let samples = reference_samples(1.0, 1_000.0, 0.0);
|
|
assert!(samples.is_empty());
|
|
// The ends run backwards.
|
|
// 两端是倒序的。
|
|
let backwards = [
|
|
OrbitSample::new(100.0, reference_position(100.0)),
|
|
OrbitSample::new(50.0, reference_position(50.0)),
|
|
];
|
|
let error = finder().find(&backwards).expect_err("time runs backwards");
|
|
assert_eq!(error.kind(), AccessErrorKind::UnorderedSamples);
|
|
|
|
// The ends are in order but the middle is not. This is the case that a
|
|
// check of the ends alone misses: the interpolation binary searches the
|
|
// list, and a binary search over an unordered list returns a wrong index
|
|
// without failing, so the search would refine a crossing against the
|
|
// wrong pair of positions and report a pass that never happened.
|
|
// 两端有序但中间无序。这正是只检查两端会漏掉的情形：插值对该列表做二分查找，而
|
|
// 对无序列表的二分查找会返回错误下标而不报错，故搜索会针对错误的位置对细化穿越，
|
|
// 并报告一个从未发生过的过境。
|
|
let mut shuffled = reference_samples(60.0, 0.0, 1_200.0);
|
|
assert!(shuffled.len() > 6, "the reference track is long enough");
|
|
shuffled.swap(2, 4);
|
|
let error = finder()
|
|
.find(&shuffled)
|
|
.expect_err("the middle is out of order");
|
|
assert_eq!(error.kind(), AccessErrorKind::UnorderedSamples);
|
|
}
|
|
|
|
#[test]
|
|
fn an_invalid_position_is_rejected() {
|
|
let samples = [
|
|
OrbitSample::new(0.0, reference_position(0.0)),
|
|
OrbitSample::new(1.0, Vec3::splat(f64::NAN)),
|
|
];
|
|
let error = finder()
|
|
.find(&samples)
|
|
.expect_err("the position is not finite");
|
|
assert_eq!(error.kind(), AccessErrorKind::InvalidPosition);
|
|
}
|
|
|
|
#[test]
|
|
fn the_finder_can_drive_a_propagator_directly() {
|
|
// The convenience entry point must agree with building the samples by
|
|
// hand.
|
|
// 该便利入口必须与手工构建样本一致。
|
|
let via_samples = finder()
|
|
.find(&reference_samples(1.0, 0.0, 2_000.0))
|
|
.expect("valid");
|
|
let via_propagator = finder()
|
|
.find_with(0.0, 2_000.0, |seconds| Some(reference_position(seconds)))
|
|
.expect("valid");
|
|
assert_eq!(via_samples.count(), via_propagator.count());
|
|
let first = &via_samples.passes[0];
|
|
let second = &via_propagator.passes[0];
|
|
assert!((first.rise_seconds - second.rise_seconds).abs() < 1e-6);
|
|
assert!((first.set_seconds - second.set_seconds).abs() < 1e-6);
|
|
}
|
|
|
|
#[test]
|
|
fn a_failing_propagator_is_reported() {
|
|
let error = finder()
|
|
.find_with(0.0, 100.0, |_| None)
|
|
.expect_err("the propagator failed");
|
|
assert_eq!(error.kind(), AccessErrorKind::InvalidPosition);
|
|
}
|
|
|
|
#[test]
|
|
fn an_invalid_search_interval_is_rejected() {
|
|
let error = finder()
|
|
.find_with(100.0, 0.0, |seconds| Some(reference_position(seconds)))
|
|
.expect_err("the interval runs backwards");
|
|
assert_eq!(error.kind(), AccessErrorKind::InvalidInterval);
|
|
assert_eq!(
|
|
finder()
|
|
.find_with(0.0, f64::NAN, |seconds| Some(reference_position(seconds)))
|
|
.expect_err("the interval is not finite")
|
|
.kind(),
|
|
AccessErrorKind::InvalidInterval
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn a_higher_mask_shortens_the_pass() {
|
|
let low = AccessFinder {
|
|
station: GroundPoint::new(Geodetic::new(0.0, 0.0, 0.0), 5.0_f64.to_radians()),
|
|
..finder()
|
|
};
|
|
let high = AccessFinder {
|
|
station: GroundPoint::new(Geodetic::new(0.0, 0.0, 0.0), 30.0_f64.to_radians()),
|
|
..finder()
|
|
};
|
|
let samples = reference_samples(1.0, 0.0, 2_000.0);
|
|
let low_duration = low.find(&samples).expect("valid").passes[0].duration();
|
|
let high_duration = high.find(&samples).expect("valid").passes[0].duration();
|
|
assert!(
|
|
low_duration > high_duration,
|
|
"{low_duration} against {high_duration}"
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn the_summary_is_constructible_directly() {
|
|
let pass = Pass {
|
|
rise_seconds: 0.0,
|
|
set_seconds: 10.0,
|
|
peak_seconds: 5.0,
|
|
peak_elevation: 1.0,
|
|
mask_elevation: 0.1,
|
|
peak_position: Vec3::ZERO,
|
|
};
|
|
let summary = PassSummary::new(vec![pass], 10.0);
|
|
assert_eq!(summary.count(), 1);
|
|
assert!((summary.total_access_seconds() - 10.0).abs() < 1e-12);
|
|
assert!((summary.access_fraction().expect("valid") - 1.0).abs() < 1e-12);
|
|
assert_eq!(PassSummary::new(Vec::new(), 0.0).access_fraction(), None);
|
|
}
|
|
|
|
#[test]
|
|
fn the_propagator_entry_point_reaches_the_tolerance_regardless_of_step() {
|
|
// When the propagator is available the refinement evaluates the true
|
|
// position at each bisection point rather than interpolating, so the
|
|
// crossing is accurate to the tolerance however coarse the sampling.
|
|
// 当传播器可用时，细化在每个二分点求真实位置而非插值，故无论采样多粗，穿越都
|
|
// 精确到容差。
|
|
let coarse = AccessFinder {
|
|
sample_step_seconds: 30.0,
|
|
crossing_tolerance_seconds: 1e-6,
|
|
..finder()
|
|
};
|
|
let fine = AccessFinder {
|
|
sample_step_seconds: 1.0,
|
|
crossing_tolerance_seconds: 1e-6,
|
|
..finder()
|
|
};
|
|
let via_coarse = coarse
|
|
.find_with(0.0, 2_000.0, |seconds| Some(reference_position(seconds)))
|
|
.expect("valid");
|
|
let via_fine = fine
|
|
.find_with(0.0, 2_000.0, |seconds| Some(reference_position(seconds)))
|
|
.expect("valid");
|
|
|
|
assert_eq!(via_coarse.count(), 1);
|
|
assert_eq!(via_fine.count(), 1);
|
|
let first = &via_coarse.passes[0];
|
|
let second = &via_fine.passes[0];
|
|
assert!(
|
|
(first.rise_seconds - second.rise_seconds).abs() < 1e-5,
|
|
"rise {} against {}",
|
|
first.rise_seconds,
|
|
second.rise_seconds
|
|
);
|
|
assert!(
|
|
(first.set_seconds - second.set_seconds).abs() < 1e-5,
|
|
"set {} against {}",
|
|
first.set_seconds,
|
|
second.set_seconds
|
|
);
|
|
// The crossing matches the closed form to the tolerance.
|
|
// 该穿越在容差内与闭式一致。
|
|
assert!(
|
|
(first.rise_seconds - REFERENCE_RISE).abs() < 1e-5,
|
|
"rise {} against {REFERENCE_RISE}",
|
|
first.rise_seconds
|
|
);
|
|
}
|