Ryan Malloy
87ab81e7d0
Batch weighted least-squares differential correction using equinoctial elements, LAPACK dgelss_() for SVD solve, vendored SGP4/SDP4 as the propagation engine. Per Vallado & Crawford (2008) AIAA 2008-6770. New SQL functions: - tle_from_eci(): fit TLE from ECI position/velocity ephemeris - tle_from_topocentric(): fit TLE from az/el/range observations - tle_fit_residuals(): per-observation position residuals diagnostic Solver features: 6-state (orbital) or 7-state (+ B*) fitting, equinoctial elements for singularity-free optimization, tiered step limiting, Brouwer/Kozai Newton-Raphson conversion, auto initial guess from first ECI observation when no seed TLE provided. Tested: 8 regression tests (LEO/MEO/near-circular round-trips, B* recovery, topocentric, seedless, error handling, diagnostics), 67 standalone math unit tests, all 14 suites pass.
240 lines
8.1 KiB
SQL
240 lines
8.1 KiB
SQL
-- od_fit.sql -- Regression tests for TLE fitting (orbit determination)
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--
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-- Tests tle_from_eci(), tle_from_topocentric(), and tle_fit_residuals().
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-- Uses round-trip methodology: propagate known TLE → fit from obs → compare.
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CREATE EXTENSION IF NOT EXISTS pg_orrery;
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-- ============================================================
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-- Test 1: ECI round-trip (ISS-like LEO orbit)
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--
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-- Generate 20 observations over 90 minutes from ISS TLE,
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-- then fit a TLE from those observations.
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-- Expected: RMS < 1 km, convergence.
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-- ============================================================
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WITH iss_tle AS (
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SELECT E'1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9025\n2 25544 51.6400 208.9163 0006703 30.1694 61.7520 15.50100486 00001'::tle AS t
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),
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obs AS (
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SELECT
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array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
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array_agg(ts ORDER BY ts) AS times
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FROM iss_tle,
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generate_series(
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'2024-01-01 12:00:00+00'::timestamptz,
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'2024-01-01 13:30:00+00'::timestamptz,
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'5 minutes'::interval
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) AS ts
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),
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result AS (
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SELECT (tle_from_eci(positions, times, t)).* FROM obs, iss_tle
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)
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SELECT
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iterations > 0 AS has_iterations,
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rms_final < 1.0 AS rms_under_1km,
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status = 'converged' AS did_converge
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FROM result;
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-- ============================================================
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-- Test 2: ECI round-trip (GPS-like MEO orbit)
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--
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-- Higher altitude, lower mean motion.
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-- ============================================================
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WITH gps_tle AS (
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SELECT E'1 28874U 05038A 24001.50000000 .00000003 00000-0 00000+0 0 9999\n2 28874 55.4000 200.0000 0057000 250.0000 110.0000 2.00567486 00001'::tle AS t
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),
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obs AS (
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SELECT
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array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
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array_agg(ts ORDER BY ts) AS times
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FROM gps_tle,
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generate_series(
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'2024-01-01 00:00:00+00'::timestamptz,
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'2024-01-01 12:00:00+00'::timestamptz,
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'30 minutes'::interval
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) AS ts
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),
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result AS (
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SELECT (tle_from_eci(positions, times, t)).* FROM obs, gps_tle
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)
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SELECT
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iterations > 0 AS has_iterations,
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rms_final < 1.0 AS rms_under_1km,
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status = 'converged' AS did_converge
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FROM result;
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-- ============================================================
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-- Test 3: 7-state with B* fitting
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--
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-- Fit ISS with B* as a free parameter.
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-- Verify B* is recovered within 50% of original.
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-- ============================================================
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WITH iss_tle AS (
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SELECT E'1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9025\n2 25544 51.6400 208.9163 0006703 30.1694 61.7520 15.50100486 00001'::tle AS t
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),
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obs AS (
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SELECT
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array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
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array_agg(ts ORDER BY ts) AS times
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FROM iss_tle,
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generate_series(
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'2024-01-01 12:00:00+00'::timestamptz,
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'2024-01-01 14:00:00+00'::timestamptz,
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'5 minutes'::interval
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) AS ts
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),
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result AS (
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SELECT (tle_from_eci(positions, times, t, true, 20)).* FROM obs, iss_tle
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)
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SELECT
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status = 'converged' AS did_converge,
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rms_final < 1.0 AS rms_under_1km
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FROM result;
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-- ============================================================
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-- Test 4: Topocentric round-trip (ISS via observe())
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--
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-- Observe ISS from MIT ground station, then fit TLE from
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-- the topocentric data. Wider tolerance (5 km) due to
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-- the topo→ECI information loss.
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-- ============================================================
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WITH iss_tle AS (
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SELECT E'1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9025\n2 25544 51.6400 208.9163 0006703 30.1694 61.7520 15.50100486 00001'::tle AS t
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),
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mit AS (
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SELECT '(42.36,-71.09,20)'::observer AS obs
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),
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topo_obs AS (
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SELECT
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array_agg(observe(t, obs, ts) ORDER BY ts) AS observations,
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array_agg(ts ORDER BY ts) AS times
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FROM iss_tle, mit,
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generate_series(
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'2024-01-01 12:00:00+00'::timestamptz,
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'2024-01-01 13:30:00+00'::timestamptz,
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'5 minutes'::interval
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) AS ts
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),
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result AS (
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SELECT (tle_from_topocentric(observations, times, obs, t, false, 20)).*
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FROM topo_obs, mit, iss_tle
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)
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SELECT
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iterations > 0 AS has_iterations,
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rms_final < 10.0 AS rms_under_10km,
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status = 'converged' AS did_converge
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FROM result;
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-- ============================================================
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-- Test 5: No seed (auto initial guess from first observation)
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--
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-- For ECI mode, the solver can derive an initial guess from
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-- the first observation without needing a seed TLE.
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-- ============================================================
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WITH iss_tle AS (
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SELECT E'1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9025\n2 25544 51.6400 208.9163 0006703 30.1694 61.7520 15.50100486 00001'::tle AS t
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),
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obs AS (
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SELECT
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array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
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array_agg(ts ORDER BY ts) AS times
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FROM iss_tle,
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generate_series(
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'2024-01-01 12:00:00+00'::timestamptz,
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'2024-01-01 13:30:00+00'::timestamptz,
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'5 minutes'::interval
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) AS ts
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),
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result AS (
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SELECT (tle_from_eci(positions, times)).* FROM obs
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)
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SELECT
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iterations > 0 AS has_iterations,
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rms_final < 5.0 AS rms_under_5km
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FROM result;
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-- ============================================================
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-- Test 6: Error - insufficient observations
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--
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-- Less than 6 observations should raise an error.
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-- ============================================================
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DO $$
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BEGIN
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PERFORM tle_from_eci(
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ARRAY[
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sgp4_propagate(
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E'1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9025\n2 25544 51.6400 208.9163 0006703 30.1694 61.7520 15.50100486 00001'::tle,
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'2024-01-01 12:00:00+00'::timestamptz
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)
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],
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ARRAY['2024-01-01 12:00:00+00'::timestamptz]
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);
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RAISE NOTICE 'ERROR: should have raised exception';
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EXCEPTION
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WHEN data_exception THEN
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RAISE NOTICE 'OK: insufficient observations error caught';
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WHEN invalid_parameter_value THEN
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RAISE NOTICE 'OK: insufficient observations error caught';
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END $$;
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-- ============================================================
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-- Test 7: tle_fit_residuals() diagnostic output
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--
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-- Verify the residual function returns per-observation data.
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-- ============================================================
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WITH iss_tle AS (
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SELECT E'1 25544U 98067A 24001.50000000 .00016717 00000-0 10270-3 0 9025\n2 25544 51.6400 208.9163 0006703 30.1694 61.7520 15.50100486 00001'::tle AS t
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),
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obs AS (
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SELECT
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array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
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array_agg(ts ORDER BY ts) AS times
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FROM iss_tle,
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generate_series(
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'2024-01-01 12:00:00+00'::timestamptz,
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'2024-01-01 12:30:00+00'::timestamptz,
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'5 minutes'::interval
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) AS ts
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)
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SELECT
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count(*) AS n_residuals,
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count(*) = 7 AS correct_count,
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max(pos_err_km) < 0.001 AS residuals_near_zero
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FROM iss_tle, obs, tle_fit_residuals(t, positions, times);
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-- ============================================================
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-- Test 8: Nearly circular orbit (equinoctial singularity-free)
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--
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-- Very low eccentricity tests that equinoctial elements handle
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-- the e→0 case without blowing up.
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-- ============================================================
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WITH circ_tle AS (
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SELECT E'1 00001U 24001A 24001.50000000 .00000000 00000-0 00000+0 0 9999\n2 00001 0.0100 000.0000 0000100 000.0000 000.0000 15.00000000 00001'::tle AS t
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),
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obs AS (
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SELECT
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array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
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array_agg(ts ORDER BY ts) AS times
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FROM circ_tle,
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generate_series(
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'2024-01-01 12:00:00+00'::timestamptz,
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'2024-01-01 13:30:00+00'::timestamptz,
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'5 minutes'::interval
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) AS ts
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),
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result AS (
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SELECT (tle_from_eci(positions, times, t)).* FROM obs, circ_tle
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)
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SELECT
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rms_final < 2.0 AS rms_under_2km,
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status = 'converged' AS did_converge
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FROM result;
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