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Add covariance output and condition number to OD solver (v0.5.0)

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Computes formal covariance (H^T·H)^{-1} via LAPACK dpotrf_/dpotri_
after DC convergence. Returns upper-triangle array (21 elements for
6-state, 28 for 7-state with B*), condition number from SVD, and
nstate count. Covariance is computed even for perfect-seed fits.

Bumps extension to v0.5.0 with full install SQL and migration path.
This commit is contained in:
Ryan Malloy 2026-02-17 16:15:44 -07:00
parent 6e57071970
commit bca8b3e7eb
11 changed files with 1417 additions and 37 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

1
Dockerfile
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@ -46,6 +46,7 @@ RUN su postgres -c "/usr/lib/postgresql/${PG_MAJOR}/bin/initdb -D /tmp/pgtest" &
# Standalone unit tests (no PostgreSQL dependency)
RUN make test-de-reader
RUN make test-od-math
RUN make test-od-iod
# Capture artifacts under /pg_orrery prefix for the next stage
RUN make PG_CONFIG=${PG_CONFIG} DESTDIR=/pg_orrery install

2
Makefile
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@ -3,7 +3,7 @@ EXTENSION = pg_orrery
DATA = sql/pg_orrery--0.1.0.sql sql/pg_orrery--0.2.0.sql sql/pg_orrery--0.1.0--0.2.0.sql \
sql/pg_orrery--0.3.0.sql sql/pg_orrery--0.2.0--0.3.0.sql \
sql/pg_orrery--0.4.0.sql sql/pg_orrery--0.3.0--0.4.0.sql \
sql/pg_orrery--0.4.0--0.5.0.sql
sql/pg_orrery--0.5.0.sql sql/pg_orrery--0.4.0--0.5.0.sql
# Our extension C sources
OBJS = src/pg_orrery.o src/tle_type.o src/eci_type.o src/observer_type.o \

15
TODO
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@ -1,10 +1,7 @@
- IOD bootstrap: Gauss/Gibbs/double-r methods to generate
initial TLE from angles-only (eliminates seed requirement)
- Covariance output: Return (A^TWA)^{-1} matrix for
uncertainty estimates / conjunction screening
- Multi-observer: Accept observations from multiple ground
stations
- Adaptive step limiting: Dynamically tune correction limits
per Vallado's observation about different strategies failing
on different satellite subsets
- Gauss method for angles-only initial orbit determination
(eliminates seed requirement for sensors without ranging)
- Weighted observations (per-obs covariance weighting for
heterogeneous sensor fusion)
- Range rate fitting in topocentric mode (currently reserved
via vel_ecef in residual computation)

2
pg_orrery.control
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@ -1,4 +1,4 @@
comment = 'A database orrery — celestial mechanics types and functions for PostgreSQL'
default_version = '0.4.0'
default_version = '0.5.0'
module_pathname = '$libdir/pg_orrery'
relocatable = true

47
sql/pg_orrery--0.4.0--0.5.0.sql
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@ -2,9 +2,49 @@
--
-- Adds multi-observer support, IOD bootstrap (seed-free fitting),
-- and covariance output for uncertainty estimation.
--
-- Covariance changes the return type of tle_from_eci and
-- tle_from_topocentric (5 → 8 OUT params), which requires
-- DROP + re-CREATE.
-- ============================================================
-- Multi-observer topocentric fitting
-- Drop old 5-column OD functions
-- ============================================================
DROP FUNCTION IF EXISTS tle_from_eci(eci_position[], timestamptz[], tle, boolean, int4);
DROP FUNCTION IF EXISTS tle_from_topocentric(topocentric[], timestamptz[], observer, tle, boolean, int4);
-- ============================================================
-- Re-create with 8-column output (adds covariance)
-- ============================================================
CREATE FUNCTION tle_from_eci(
positions eci_position[], times timestamptz[],
seed tle DEFAULT NULL, fit_bstar boolean DEFAULT false,
max_iter int4 DEFAULT 15,
OUT fitted_tle tle, OUT iterations int4,
OUT rms_final float8, OUT rms_initial float8, OUT status text,
OUT condition_number float8, OUT covariance float8[], OUT nstate int4
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_eci(eci_position[], timestamptz[], tle, boolean, int4) IS
'Fit a TLE from ECI position/velocity observations via differential correction. Returns fitted TLE, iteration count, RMS residuals, convergence status, condition number, and formal covariance matrix.';
CREATE FUNCTION tle_from_topocentric(
observations topocentric[], times timestamptz[],
obs observer,
seed tle DEFAULT NULL, fit_bstar boolean DEFAULT false,
max_iter int4 DEFAULT 15,
OUT fitted_tle tle, OUT iterations int4,
OUT rms_final float8, OUT rms_initial float8, OUT status text,
OUT condition_number float8, OUT covariance float8[], OUT nstate int4
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_topocentric(topocentric[], timestamptz[], observer, tle, boolean, int4) IS
'Fit a TLE from topocentric (az/el/range) observations via differential correction. Returns fitted TLE, RMS residuals, convergence status, condition number, and formal covariance matrix.';
-- ============================================================
-- Multi-observer topocentric fitting (new overload)
-- ============================================================
CREATE FUNCTION tle_from_topocentric(
@ -13,9 +53,10 @@ CREATE FUNCTION tle_from_topocentric(
seed tle DEFAULT NULL, fit_bstar boolean DEFAULT false,
max_iter int4 DEFAULT 15,
OUT fitted_tle tle, OUT iterations int4,
OUT rms_final float8, OUT rms_initial float8, OUT status text
OUT rms_final float8, OUT rms_initial float8, OUT status text,
OUT condition_number float8, OUT covariance float8[], OUT nstate int4
) RETURNS RECORD
AS 'MODULE_PATHNAME', 'tle_from_topocentric_multi'
LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_topocentric(topocentric[], timestamptz[], observer[], int4[], tle, boolean, int4) IS
'Fit a TLE from topocentric observations collected by multiple ground stations. observer_ids[i] indexes into observers[]. Requires seed TLE and >= 6 observations.';
'Fit a TLE from topocentric observations collected by multiple ground stations. observer_ids[i] indexes into observers[]. Returns convergence status, condition number, and formal covariance matrix.';

862
sql/pg_orrery--0.5.0.sql Normal file
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@ -0,0 +1,862 @@
-- pg_orrery -- Orbital mechanics types and functions for PostgreSQL
--
-- Types: tle, eci_position, geodetic, topocentric, observer, pass_event
-- Provides SGP4/SDP4 propagation, coordinate transforms, pass prediction,
-- and GiST indexing on altitude bands for conjunction screening.
--
-- All propagation uses WGS-72 constants (matching TLE mean element fitting).
-- Coordinate output uses WGS-84 (matching modern geodetic standards).
-- ============================================================
-- Shell types (forward declarations)
-- ============================================================
CREATE TYPE tle;
CREATE TYPE eci_position;
CREATE TYPE geodetic;
CREATE TYPE topocentric;
CREATE TYPE observer;
CREATE TYPE pass_event;
-- ============================================================
-- TLE type: Two-Line Element set
-- ============================================================
CREATE FUNCTION tle_in(cstring) RETURNS tle
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION tle_out(tle) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION tle_recv(internal) RETURNS tle
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION tle_send(tle) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE tle (
INPUT = tle_in,
OUTPUT = tle_out,
RECEIVE = tle_recv,
SEND = tle_send,
INTERNALLENGTH = 112,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE tle IS 'Two-Line Element set — parsed mean orbital elements for SGP4/SDP4 propagation';
-- TLE accessor functions
CREATE FUNCTION tle_epoch(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_epoch(tle) IS 'TLE epoch as Julian date (UTC)';
CREATE FUNCTION tle_norad_id(tle) RETURNS int4
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_norad_id(tle) IS 'NORAD catalog number';
CREATE FUNCTION tle_inclination(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_inclination(tle) IS 'Orbital inclination in degrees';
CREATE FUNCTION tle_eccentricity(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_eccentricity(tle) IS 'Orbital eccentricity (dimensionless)';
CREATE FUNCTION tle_raan(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_raan(tle) IS 'Right ascension of ascending node in degrees';
CREATE FUNCTION tle_arg_perigee(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_arg_perigee(tle) IS 'Argument of perigee in degrees';
CREATE FUNCTION tle_mean_anomaly(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_mean_anomaly(tle) IS 'Mean anomaly in degrees';
CREATE FUNCTION tle_mean_motion(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_mean_motion(tle) IS 'Mean motion in revolutions per day';
CREATE FUNCTION tle_bstar(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_bstar(tle) IS 'B* drag coefficient (1/earth-radii)';
CREATE FUNCTION tle_period(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_period(tle) IS 'Orbital period in minutes';
CREATE FUNCTION tle_age(tle, timestamptz) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_age(tle, timestamptz) IS 'TLE age in days (positive = past epoch, negative = before epoch)';
CREATE FUNCTION tle_perigee(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_perigee(tle) IS 'Perigee altitude in km above WGS-72 ellipsoid';
CREATE FUNCTION tle_apogee(tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_apogee(tle) IS 'Apogee altitude in km above WGS-72 ellipsoid';
CREATE FUNCTION tle_intl_desig(tle) RETURNS text
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_intl_desig(tle) IS 'International designator (COSPAR ID)';
CREATE FUNCTION tle_from_lines(text, text) RETURNS tle
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_lines(text, text) IS
'Construct TLE from separate line1/line2 text columns';
-- ============================================================
-- ECI position type: True Equator Mean Equinox (TEME) frame
-- ============================================================
CREATE FUNCTION eci_in(cstring) RETURNS eci_position
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_out(eci_position) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_recv(internal) RETURNS eci_position
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_send(eci_position) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE eci_position (
INPUT = eci_in,
OUTPUT = eci_out,
RECEIVE = eci_recv,
SEND = eci_send,
INTERNALLENGTH = 48,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE eci_position IS 'Earth-Centered Inertial position and velocity in TEME frame (km, km/s)';
-- ECI accessor functions
CREATE FUNCTION eci_x(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_y(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_z(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_vx(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_vy(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_vz(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION eci_speed(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION eci_speed(eci_position) IS 'Velocity magnitude in km/s';
CREATE FUNCTION eci_altitude(eci_position) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION eci_altitude(eci_position) IS 'Approximate geocentric altitude in km (radius - WGS72_AE)';
-- ============================================================
-- Geodetic type: WGS-84 latitude/longitude/altitude
-- ============================================================
CREATE FUNCTION geodetic_in(cstring) RETURNS geodetic
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION geodetic_out(geodetic) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION geodetic_recv(internal) RETURNS geodetic
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION geodetic_send(geodetic) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE geodetic (
INPUT = geodetic_in,
OUTPUT = geodetic_out,
RECEIVE = geodetic_recv,
SEND = geodetic_send,
INTERNALLENGTH = 24,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE geodetic IS 'Geodetic coordinates on WGS-84 ellipsoid (lat/lon in degrees, altitude in km)';
CREATE FUNCTION geodetic_lat(geodetic) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION geodetic_lon(geodetic) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION geodetic_alt(geodetic) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-- ============================================================
-- Topocentric type: observer-relative az/el/range
-- ============================================================
CREATE FUNCTION topocentric_in(cstring) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION topocentric_out(topocentric) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION topocentric_recv(internal) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION topocentric_send(topocentric) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE topocentric (
INPUT = topocentric_in,
OUTPUT = topocentric_out,
RECEIVE = topocentric_recv,
SEND = topocentric_send,
INTERNALLENGTH = 32,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE topocentric IS 'Topocentric coordinates relative to observer (azimuth, elevation, range, range rate)';
CREATE FUNCTION topo_azimuth(topocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION topo_azimuth(topocentric) IS 'Azimuth in degrees (0=N, 90=E, 180=S, 270=W)';
CREATE FUNCTION topo_elevation(topocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION topo_elevation(topocentric) IS 'Elevation in degrees (0=horizon, 90=zenith)';
CREATE FUNCTION topo_range(topocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION topo_range(topocentric) IS 'Slant range in km';
CREATE FUNCTION topo_range_rate(topocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION topo_range_rate(topocentric) IS 'Range rate in km/s (positive = receding)';
-- ============================================================
-- Observer type: ground station location
-- ============================================================
CREATE FUNCTION observer_in(cstring) RETURNS observer
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION observer_out(observer) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION observer_recv(internal) RETURNS observer
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION observer_send(observer) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE observer (
INPUT = observer_in,
OUTPUT = observer_out,
RECEIVE = observer_recv,
SEND = observer_send,
INTERNALLENGTH = 24,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE observer IS 'Ground observer location (accepts: 40.0N 105.3W 1655m or decimal degrees)';
CREATE FUNCTION observer_lat(observer) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION observer_lat(observer) IS 'Latitude in degrees (positive = North)';
CREATE FUNCTION observer_lon(observer) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION observer_lon(observer) IS 'Longitude in degrees (positive = East)';
CREATE FUNCTION observer_alt(observer) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION observer_alt(observer) IS 'Altitude in meters above WGS-84 ellipsoid';
CREATE FUNCTION observer_from_geodetic(float8, float8, float8 DEFAULT 0.0) RETURNS observer
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION observer_from_geodetic(float8, float8, float8) IS
'Construct observer from lat (deg), lon (deg), altitude (meters). Avoids text formatting round-trips.';
-- ============================================================
-- Pass event type: satellite visibility window
-- ============================================================
CREATE FUNCTION pass_event_in(cstring) RETURNS pass_event
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION pass_event_out(pass_event) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION pass_event_recv(internal) RETURNS pass_event
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION pass_event_send(pass_event) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE pass_event (
INPUT = pass_event_in,
OUTPUT = pass_event_out,
RECEIVE = pass_event_recv,
SEND = pass_event_send,
INTERNALLENGTH = 48,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE pass_event IS 'Satellite pass event (AOS/MAX/LOS times, max elevation, AOS/LOS azimuths)';
CREATE FUNCTION pass_aos_time(pass_event) RETURNS timestamptz
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_aos_time(pass_event) IS 'Acquisition of signal time';
CREATE FUNCTION pass_max_el_time(pass_event) RETURNS timestamptz
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_max_el_time(pass_event) IS 'Maximum elevation time';
CREATE FUNCTION pass_los_time(pass_event) RETURNS timestamptz
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_los_time(pass_event) IS 'Loss of signal time';
CREATE FUNCTION pass_max_elevation(pass_event) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_max_elevation(pass_event) IS 'Maximum elevation in degrees';
CREATE FUNCTION pass_aos_azimuth(pass_event) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_aos_azimuth(pass_event) IS 'AOS azimuth in degrees (0=N)';
CREATE FUNCTION pass_los_azimuth(pass_event) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_los_azimuth(pass_event) IS 'LOS azimuth in degrees (0=N)';
CREATE FUNCTION pass_duration(pass_event) RETURNS interval
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_duration(pass_event) IS 'Pass duration (LOS - AOS)';
-- ============================================================
-- SGP4/SDP4 propagation functions
-- ============================================================
CREATE FUNCTION sgp4_propagate(tle, timestamptz) RETURNS eci_position
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION sgp4_propagate(tle, timestamptz) IS
'Propagate TLE to a point in time using SGP4 (near-earth) or SDP4 (deep-space). Returns TEME ECI position/velocity.';
CREATE FUNCTION sgp4_propagate_safe(tle, timestamptz) RETURNS eci_position
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE PARALLEL SAFE;
COMMENT ON FUNCTION sgp4_propagate_safe(tle, timestamptz) IS
'Like sgp4_propagate but returns NULL on error instead of raising an exception. For batch queries with potentially invalid TLEs.';
CREATE FUNCTION sgp4_propagate_series(tle, timestamptz, timestamptz, interval)
RETURNS TABLE(t timestamptz, x float8, y float8, z float8, vx float8, vy float8, vz float8)
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE
ROWS 100;
COMMENT ON FUNCTION sgp4_propagate_series(tle, timestamptz, timestamptz, interval) IS
'Propagate TLE over a time range at regular intervals. Returns time series of TEME positions.';
CREATE FUNCTION tle_distance(tle, tle, timestamptz) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_distance(tle, tle, timestamptz) IS
'Euclidean distance in km between two TLEs at a reference time';
-- ============================================================
-- Coordinate transform functions
-- ============================================================
CREATE FUNCTION eci_to_geodetic(eci_position, timestamptz) RETURNS geodetic
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION eci_to_geodetic(eci_position, timestamptz) IS
'Convert TEME ECI position to WGS-84 geodetic coordinates at given time';
CREATE FUNCTION eci_to_topocentric(eci_position, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION eci_to_topocentric(eci_position, observer, timestamptz) IS
'Convert TEME ECI position to topocentric (az/el/range) relative to observer';
CREATE FUNCTION subsatellite_point(tle, timestamptz) RETURNS geodetic
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION subsatellite_point(tle, timestamptz) IS
'Subsatellite (nadir) point on WGS-84 ellipsoid at given time';
CREATE FUNCTION ground_track(tle, timestamptz, timestamptz, interval)
RETURNS TABLE(t timestamptz, lat float8, lon float8, alt float8)
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE
ROWS 100;
COMMENT ON FUNCTION ground_track(tle, timestamptz, timestamptz, interval) IS
'Ground track as time series of subsatellite points (lat/lon in degrees, alt in km)';
CREATE FUNCTION observe(tle, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION observe(tle, observer, timestamptz) IS
'Propagate TLE and compute observer-relative look angles in one call. Returns topocentric (az/el/range/range_rate).';
CREATE FUNCTION observe_safe(tle, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE PARALLEL SAFE;
COMMENT ON FUNCTION observe_safe(tle, observer, timestamptz) IS
'Like observe() but returns NULL on propagation error. For batch queries with potentially invalid/decayed TLEs.';
-- ============================================================
-- Pass prediction functions
-- ============================================================
CREATE FUNCTION next_pass(tle, observer, timestamptz) RETURNS pass_event
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION next_pass(tle, observer, timestamptz) IS
'Find the next satellite pass over observer (searches up to 7 days ahead)';
CREATE FUNCTION predict_passes(tle, observer, timestamptz, timestamptz, float8 DEFAULT 0.0)
RETURNS SETOF pass_event
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE
ROWS 10;
COMMENT ON FUNCTION predict_passes(tle, observer, timestamptz, timestamptz, float8) IS
'Predict all satellite passes over observer in time window. Optional min_elevation in degrees.';
CREATE FUNCTION pass_visible(tle, observer, timestamptz, timestamptz) RETURNS boolean
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION pass_visible(tle, observer, timestamptz, timestamptz) IS
'True if any pass occurs over observer in the time window';
-- ============================================================
-- GiST operator support functions
-- ============================================================
-- Overlap operator: do orbital keys overlap in altitude AND inclination?
CREATE FUNCTION tle_overlap(tle, tle) RETURNS boolean
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-- Altitude distance operator (altitude-only, for KNN ordering)
CREATE FUNCTION tle_alt_distance(tle, tle) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE OPERATOR && (
LEFTARG = tle,
RIGHTARG = tle,
FUNCTION = tle_overlap,
COMMUTATOR = &&,
RESTRICT = areasel,
JOIN = areajoinsel
);
COMMENT ON OPERATOR && (tle, tle) IS 'Orbital key overlap (altitude band AND inclination range) — necessary condition for conjunction';
CREATE OPERATOR <-> (
LEFTARG = tle,
RIGHTARG = tle,
FUNCTION = tle_alt_distance,
COMMUTATOR = <->
);
COMMENT ON OPERATOR <-> (tle, tle) IS 'Minimum altitude-band separation in km (0 if overlapping). Altitude-only — does not account for inclination. Use && for 2-D filtering.';
-- ============================================================
-- GiST operator class for 2-D orbital indexing (altitude + inclination)
-- ============================================================
-- GiST internal support functions
CREATE FUNCTION gist_tle_compress(internal) RETURNS internal
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_decompress(internal) RETURNS internal
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_consistent(internal, tle, smallint, oid, internal) RETURNS boolean
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_union(internal, internal) RETURNS internal
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_penalty(internal, internal, internal) RETURNS internal
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_picksplit(internal, internal) RETURNS internal
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_same(internal, internal, internal) RETURNS internal
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION gist_tle_distance(internal, tle, smallint, oid, internal) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE OPERATOR CLASS tle_ops
DEFAULT FOR TYPE tle USING gist AS
OPERATOR 3 && ,
OPERATOR 15 <-> (tle, tle) FOR ORDER BY float_ops,
FUNCTION 1 gist_tle_consistent(internal, tle, smallint, oid, internal),
FUNCTION 2 gist_tle_union(internal, internal),
FUNCTION 3 gist_tle_compress(internal),
FUNCTION 4 gist_tle_decompress(internal),
FUNCTION 5 gist_tle_penalty(internal, internal, internal),
FUNCTION 6 gist_tle_picksplit(internal, internal),
FUNCTION 7 gist_tle_same(internal, internal, internal),
FUNCTION 8 gist_tle_distance(internal, tle, smallint, oid, internal);
-- pg_orrery 0.1.0 -> 0.2.0 migration
--
-- Phase 1: Stars, comets, and Keplerian propagation.
-- Adds heliocentric type, star observation, and two-body propagation.
-- ============================================================
-- Heliocentric type: ecliptic J2000 position in AU
-- ============================================================
CREATE TYPE heliocentric;
CREATE FUNCTION heliocentric_in(cstring) RETURNS heliocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION heliocentric_out(heliocentric) RETURNS cstring
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION heliocentric_recv(internal) RETURNS heliocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE FUNCTION heliocentric_send(heliocentric) RETURNS bytea
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
CREATE TYPE heliocentric (
INPUT = heliocentric_in,
OUTPUT = heliocentric_out,
RECEIVE = heliocentric_recv,
SEND = heliocentric_send,
INTERNALLENGTH = 24,
ALIGNMENT = double,
STORAGE = plain
);
COMMENT ON TYPE heliocentric IS 'Heliocentric position in ecliptic J2000 frame (x, y, z in AU)';
CREATE FUNCTION helio_x(heliocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION helio_x(heliocentric) IS 'X component in AU (ecliptic J2000, vernal equinox direction)';
CREATE FUNCTION helio_y(heliocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION helio_y(heliocentric) IS 'Y component in AU (ecliptic J2000)';
CREATE FUNCTION helio_z(heliocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION helio_z(heliocentric) IS 'Z component in AU (ecliptic J2000, north ecliptic pole)';
CREATE FUNCTION helio_distance(heliocentric) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION helio_distance(heliocentric) IS 'Heliocentric distance in AU';
-- ============================================================
-- Star observation functions
-- ============================================================
CREATE FUNCTION star_observe(float8, float8, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION star_observe(float8, float8, observer, timestamptz) IS
'Observe a star from (ra_hours J2000, dec_degrees J2000, observer, time). Returns topocentric az/el. Range is 0 (infinite distance).';
CREATE FUNCTION star_observe_safe(float8, float8, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE PARALLEL SAFE;
COMMENT ON FUNCTION star_observe_safe(float8, float8, observer, timestamptz) IS
'Like star_observe but returns NULL on invalid inputs. For batch queries over star catalogs.';
-- ============================================================
-- Keplerian propagation functions
-- ============================================================
CREATE FUNCTION kepler_propagate(
q_au float8, eccentricity float8,
inclination_deg float8, arg_perihelion_deg float8,
long_asc_node_deg float8, perihelion_jd float8,
t timestamptz
) RETURNS heliocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION kepler_propagate(float8, float8, float8, float8, float8, float8, timestamptz) IS
'Two-body Keplerian propagation from classical orbital elements. Returns heliocentric ecliptic J2000 position in AU. Handles elliptic, parabolic, and hyperbolic orbits.';
-- ============================================================
-- Comet observation
-- ============================================================
CREATE FUNCTION comet_observe(
q_au float8, eccentricity float8,
inclination_deg float8, arg_perihelion_deg float8,
long_asc_node_deg float8, perihelion_jd float8,
earth_x_au float8, earth_y_au float8, earth_z_au float8,
obs observer, t timestamptz
) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION comet_observe(float8, float8, float8, float8, float8, float8, float8, float8, float8, observer, timestamptz) IS
'Observe a comet/asteroid from orbital elements. Requires Earth heliocentric ecliptic J2000 position (AU). Returns topocentric az/el with geocentric range in km.';
-- ============================================================
-- Phase 2: VSOP87 planets, ELP82B Moon, Sun observation
-- ============================================================
CREATE FUNCTION planet_heliocentric(int4, timestamptz) RETURNS heliocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION planet_heliocentric(int4, timestamptz) IS
'VSOP87 heliocentric ecliptic J2000 position (AU). Body IDs: 0=Sun, 1=Mercury, ..., 8=Neptune.';
CREATE FUNCTION planet_observe(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION planet_observe(int4, observer, timestamptz) IS
'Observe a planet from (body_id 1-8, observer, time). Returns topocentric az/el with geocentric range in km.';
CREATE FUNCTION sun_observe(observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION sun_observe(observer, timestamptz) IS
'Observe the Sun from (observer, time). Returns topocentric az/el with geocentric range in km.';
CREATE FUNCTION moon_observe(observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION moon_observe(observer, timestamptz) IS
'Observe the Moon via ELP2000-82B from (observer, time). Returns topocentric az/el with geocentric range in km.';
-- ============================================================
-- Phase 3: Planetary moon observation
-- ============================================================
CREATE FUNCTION galilean_observe(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION galilean_observe(int4, observer, timestamptz) IS
'Observe a Galilean moon of Jupiter via L1.2 theory. Body IDs: 0=Io, 1=Europa, 2=Ganymede, 3=Callisto.';
CREATE FUNCTION saturn_moon_observe(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION saturn_moon_observe(int4, observer, timestamptz) IS
'Observe a Saturn moon via TASS 1.7. Body IDs: 0=Mimas, 1=Enceladus, 2=Tethys, 3=Dione, 4=Rhea, 5=Titan, 6=Iapetus, 7=Hyperion.';
CREATE FUNCTION uranus_moon_observe(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION uranus_moon_observe(int4, observer, timestamptz) IS
'Observe a Uranus moon via GUST86. Body IDs: 0=Miranda, 1=Ariel, 2=Umbriel, 3=Titania, 4=Oberon.';
CREATE FUNCTION mars_moon_observe(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION mars_moon_observe(int4, observer, timestamptz) IS
'Observe a Mars moon via MarsSat. Body IDs: 0=Phobos, 1=Deimos.';
-- ============================================================
-- Phase 3: Jupiter decametric radio burst prediction
-- ============================================================
CREATE FUNCTION io_phase_angle(timestamptz) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION io_phase_angle(timestamptz) IS
'Io orbital phase angle in degrees [0,360). 0=superior conjunction (behind Jupiter). Standard Radio JOVE convention.';
CREATE FUNCTION jupiter_cml(observer, timestamptz) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION jupiter_cml(observer, timestamptz) IS
'Jupiter Central Meridian Longitude, System III (1965.0), in degrees [0,360). Light-time corrected.';
CREATE FUNCTION jupiter_burst_probability(float8, float8) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION jupiter_burst_probability(float8, float8) IS
'Estimated Jupiter decametric burst probability (0-1) from (io_phase_deg, cml_deg). Based on Carr et al. (1983) source regions A, B, C, D.';
-- ============================================================
-- Phase 4: Interplanetary transfer orbits (Lambert solver)
-- ============================================================
CREATE FUNCTION lambert_transfer(
dep_body_id int4, arr_body_id int4,
dep_time timestamptz, arr_time timestamptz,
OUT c3_departure float8, OUT c3_arrival float8,
OUT v_inf_departure float8, OUT v_inf_arrival float8,
OUT tof_days float8, OUT transfer_sma float8
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION lambert_transfer(int4, int4, timestamptz, timestamptz) IS
'Solve Lambert transfer between two planets. Returns C3 (km^2/s^2), v_infinity (km/s), TOF (days), SMA (AU). Body IDs 1-8.';
CREATE FUNCTION lambert_c3(int4, int4, timestamptz, timestamptz) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION lambert_c3(int4, int4, timestamptz, timestamptz) IS
'Departure C3 (km^2/s^2) for a Lambert transfer. Returns NULL if solver fails. For pork chop plots.';
-- pg_orrery 0.2.0 -> 0.3.0 migration
--
-- Adds optional JPL DE440/441 ephemeris functions.
-- Existing VSOP87/ELP2000-82B functions are unchanged (still IMMUTABLE).
-- New _de() functions are STABLE (depend on external DE binary file).
-- When DE is unavailable, _de() functions fall back to VSOP87 silently.
-- ============================================================
-- Phase 5: DE ephemeris functions (optional high-precision)
-- ============================================================
-- Planet observation with DE ephemeris
CREATE FUNCTION planet_heliocentric_de(int4, timestamptz) RETURNS heliocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION planet_heliocentric_de(int4, timestamptz) IS
'Heliocentric ecliptic J2000 position via JPL DE (sub-arcsecond). Falls back to VSOP87 if DE unavailable. Body IDs: 0=Sun, 1-8=Mercury-Neptune.';
CREATE FUNCTION planet_observe_de(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION planet_observe_de(int4, observer, timestamptz) IS
'Observe planet via JPL DE. Falls back to VSOP87. Body IDs: 1-8 (Mercury-Neptune).';
CREATE FUNCTION sun_observe_de(observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION sun_observe_de(observer, timestamptz) IS
'Observe Sun via JPL DE. Falls back to VSOP87.';
CREATE FUNCTION moon_observe_de(observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION moon_observe_de(observer, timestamptz) IS
'Observe Moon via JPL DE. Falls back to ELP2000-82B.';
-- Lambert transfer with DE positions
CREATE FUNCTION lambert_transfer_de(
dep_body_id int4, arr_body_id int4,
dep_time timestamptz, arr_time timestamptz,
OUT c3_departure float8, OUT c3_arrival float8,
OUT v_inf_departure float8, OUT v_inf_arrival float8,
OUT tof_days float8, OUT transfer_sma float8
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION lambert_transfer_de(int4, int4, timestamptz, timestamptz) IS
'Lambert transfer via JPL DE positions. Falls back to VSOP87. Body IDs 1-8.';
CREATE FUNCTION lambert_c3_de(int4, int4, timestamptz, timestamptz) RETURNS float8
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION lambert_c3_de(int4, int4, timestamptz, timestamptz) IS
'Departure C3 via JPL DE. Falls back to VSOP87. For pork chop plots.';
-- Planetary moon observation with DE parent positions
CREATE FUNCTION galilean_observe_de(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION galilean_observe_de(int4, observer, timestamptz) IS
'Observe Galilean moon with JPL DE parent position. L1.2 moon offsets. Body IDs: 0-3 (Io-Callisto).';
CREATE FUNCTION saturn_moon_observe_de(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION saturn_moon_observe_de(int4, observer, timestamptz) IS
'Observe Saturn moon with JPL DE parent position. TASS 1.7 moon offsets. Body IDs: 0-7 (Mimas-Hyperion).';
CREATE FUNCTION uranus_moon_observe_de(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION uranus_moon_observe_de(int4, observer, timestamptz) IS
'Observe Uranus moon with JPL DE parent position. GUST86 moon offsets. Body IDs: 0-4 (Miranda-Oberon).';
CREATE FUNCTION mars_moon_observe_de(int4, observer, timestamptz) RETURNS topocentric
AS 'MODULE_PATHNAME' LANGUAGE C STABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION mars_moon_observe_de(int4, observer, timestamptz) IS
'Observe Mars moon with JPL DE parent position. MarsSat moon offsets. Body IDs: 0-1 (Phobos-Deimos).';
-- Diagnostic function
CREATE FUNCTION pg_orrery_ephemeris_info(
OUT provider text, OUT file_path text,
OUT start_jd float8, OUT end_jd float8,
OUT version int4, OUT au_km float8
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION pg_orrery_ephemeris_info() IS
'Returns current ephemeris provider status: VSOP87 or JPL_DE with file path, JD range, version, and AU value.';
-- pg_orrery 0.3.0 -> 0.4.0 migration
--
-- Adds observation-to-TLE fitting via batch weighted least-squares
-- differential correction (Vallado & Crawford 2008, AIAA 2008-6770).
-- Uses equinoctial elements internally for singularity-free optimization.
-- LAPACK dgelss_() for SVD solve.
-- ============================================================
-- Phase 6: Orbit determination (TLE fitting from observations)
-- ============================================================
-- Fit TLE from ECI position/velocity ephemeris
CREATE FUNCTION tle_from_eci(
positions eci_position[], times timestamptz[],
seed tle DEFAULT NULL, fit_bstar boolean DEFAULT false,
max_iter int4 DEFAULT 15,
OUT fitted_tle tle, OUT iterations int4,
OUT rms_final float8, OUT rms_initial float8, OUT status text,
OUT condition_number float8, OUT covariance float8[], OUT nstate int4
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_eci(eci_position[], timestamptz[], tle, boolean, int4) IS
'Fit a TLE from ECI position/velocity observations via differential correction. Returns fitted TLE, iteration count, RMS residuals, convergence status, condition number, and formal covariance matrix.';
-- Fit TLE from topocentric observations (az/el/range) — single observer
CREATE FUNCTION tle_from_topocentric(
observations topocentric[], times timestamptz[],
obs observer,
seed tle DEFAULT NULL, fit_bstar boolean DEFAULT false,
max_iter int4 DEFAULT 15,
OUT fitted_tle tle, OUT iterations int4,
OUT rms_final float8, OUT rms_initial float8, OUT status text,
OUT condition_number float8, OUT covariance float8[], OUT nstate int4
) RETURNS RECORD
AS 'MODULE_PATHNAME' LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_topocentric(topocentric[], timestamptz[], observer, tle, boolean, int4) IS
'Fit a TLE from topocentric (az/el/range) observations via differential correction. Returns fitted TLE, RMS residuals, convergence status, condition number, and formal covariance matrix.';
-- Fit TLE from topocentric observations — multiple observers
CREATE FUNCTION tle_from_topocentric(
observations topocentric[], times timestamptz[],
observers observer[], observer_ids int4[],
seed tle DEFAULT NULL, fit_bstar boolean DEFAULT false,
max_iter int4 DEFAULT 15,
OUT fitted_tle tle, OUT iterations int4,
OUT rms_final float8, OUT rms_initial float8, OUT status text,
OUT condition_number float8, OUT covariance float8[], OUT nstate int4
) RETURNS RECORD
AS 'MODULE_PATHNAME', 'tle_from_topocentric_multi'
LANGUAGE C STABLE PARALLEL SAFE;
COMMENT ON FUNCTION tle_from_topocentric(topocentric[], timestamptz[], observer[], int4[], tle, boolean, int4) IS
'Fit a TLE from topocentric observations collected by multiple ground stations. observer_ids[i] indexes into observers[]. Returns convergence status, condition number, and formal covariance matrix.';
-- Per-observation residuals diagnostic
CREATE FUNCTION tle_fit_residuals(
fitted tle,
positions eci_position[],
times timestamptz[]
) RETURNS TABLE (
t timestamptz,
dx_km float8,
dy_km float8,
dz_km float8,
pos_err_km float8
)
AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
COMMENT ON FUNCTION tle_fit_residuals(tle, eci_position[], timestamptz[]) IS
'Compute per-observation position residuals (km) between a TLE and ECI observations. Useful for fit quality assessment.';

79
src/od_funcs.c
View File

@ -24,6 +24,9 @@
#include <math.h>
#include <string.h>
/* For construct_array() — covariance output */
#include "utils/lsyscache.h"
PG_FUNCTION_INFO_V1(tle_from_eci);
PG_FUNCTION_INFO_V1(tle_from_topocentric);
PG_FUNCTION_INFO_V1(tle_from_topocentric_multi);
@ -113,8 +116,8 @@ tle_from_eci(PG_FUNCTION_ARGS)
int i, rc;
TupleDesc tupdesc;
Datum values[5];
bool nulls[5];
Datum values[8];
bool nulls[8];
HeapTuple tuple;
/* Deconstruct arrays.
@ -197,6 +200,28 @@ tle_from_eci(PG_FUNCTION_ARGS)
values[2] = Float8GetDatum(result.rms_final);
values[3] = Float8GetDatum(result.rms_initial);
values[4] = CStringGetTextDatum(result.status);
values[5] = Float8GetDatum(result.condition_number);
/* Covariance: float8[] or NULL */
if (result.cov_size > 0)
{
Datum *cov_datums = (Datum *) palloc(sizeof(Datum) * result.cov_size);
int ci;
for (ci = 0; ci < result.cov_size; ci++)
cov_datums[ci] = Float8GetDatum(result.covariance[ci]);
values[6] = PointerGetDatum(
construct_array(cov_datums, result.cov_size,
FLOAT8OID, sizeof(float8), FLOAT8PASSBYVAL,
TYPALIGN_DOUBLE));
}
else
{
nulls[6] = true;
}
values[7] = Int32GetDatum(result.cov_size > 0
? (result.cov_size == 28 ? 7 : 6)
: 0);
tuple = heap_form_tuple(tupdesc, values, nulls);
PG_RETURN_DATUM(HeapTupleGetDatum(tuple));
@ -229,8 +254,8 @@ tle_from_topocentric(PG_FUNCTION_ARGS)
int i, rc;
TupleDesc tupdesc;
Datum values[5];
bool nulls[5];
Datum values[8];
bool nulls[8];
HeapTuple tuple;
/* Build observer */
@ -321,6 +346,27 @@ tle_from_topocentric(PG_FUNCTION_ARGS)
values[2] = Float8GetDatum(result.rms_final);
values[3] = Float8GetDatum(result.rms_initial);
values[4] = CStringGetTextDatum(result.status);
values[5] = Float8GetDatum(result.condition_number);
if (result.cov_size > 0)
{
Datum *cov_datums = (Datum *) palloc(sizeof(Datum) * result.cov_size);
int ci;
for (ci = 0; ci < result.cov_size; ci++)
cov_datums[ci] = Float8GetDatum(result.covariance[ci]);
values[6] = PointerGetDatum(
construct_array(cov_datums, result.cov_size,
FLOAT8OID, sizeof(float8), FLOAT8PASSBYVAL,
TYPALIGN_DOUBLE));
}
else
{
nulls[6] = true;
}
values[7] = Int32GetDatum(result.cov_size > 0
? (result.cov_size == 28 ? 7 : 6)
: 0);
tuple = heap_form_tuple(tupdesc, values, nulls);
PG_RETURN_DATUM(HeapTupleGetDatum(tuple));
@ -358,8 +404,8 @@ tle_from_topocentric_multi(PG_FUNCTION_ARGS)
int i, rc;
TupleDesc tupdesc;
Datum values[5];
bool nulls[5];
Datum values[8];
bool nulls[8];
HeapTuple tuple;
/* Deconstruct all arrays */
@ -473,6 +519,27 @@ tle_from_topocentric_multi(PG_FUNCTION_ARGS)
values[2] = Float8GetDatum(result.rms_final);
values[3] = Float8GetDatum(result.rms_initial);
values[4] = CStringGetTextDatum(result.status);
values[5] = Float8GetDatum(result.condition_number);
if (result.cov_size > 0)
{
Datum *cov_datums = (Datum *) palloc(sizeof(Datum) * result.cov_size);
int ci;
for (ci = 0; ci < result.cov_size; ci++)
cov_datums[ci] = Float8GetDatum(result.covariance[ci]);
values[6] = PointerGetDatum(
construct_array(cov_datums, result.cov_size,
FLOAT8OID, sizeof(float8), FLOAT8PASSBYVAL,
TYPALIGN_DOUBLE));
}
else
{
nulls[6] = true;
}
values[7] = Int32GetDatum(result.cov_size > 0
? (result.cov_size == 28 ? 7 : 6)
: 0);
tuple = heap_form_tuple(tupdesc, values, nulls);
PG_RETURN_DATUM(HeapTupleGetDatum(tuple));

169
src/od_solver.c
View File

@ -57,6 +57,14 @@ extern void dgelss_(int *m, int *n, int *nrhs,
double *s, double *rcond, int *rank,
double *work, int *lwork, int *info);
/*
* dpotrf_: Cholesky factorization of a symmetric positive-definite matrix.
* dpotri_: Invert using the Cholesky factor from dpotrf_.
* Used together to compute (H^T H)^{-1} for covariance output.
*/
extern void dpotrf_(char *uplo, int *n, double *a, int *lda, int *info);
extern void dpotri_(char *uplo, int *n, double *a, int *lda, int *info);
/* ── Internal propagation wrapper ─────────────────────── */
@ -565,6 +573,7 @@ od_fit_tle(const od_observation_t *obs, int n_obs,
int iter;
int max_iter;
int converged = 0;
int j_cov, k_cov; /* covariance loop indices */
/* Validate inputs */
nstate = config->fit_bstar ? OD_NSTATE_7 : OD_NSTATE_6;
@ -652,22 +661,14 @@ od_fit_tle(const od_observation_t *obs, int n_obs,
result->rms_initial = rms_cur;
rms_prev = rms_cur;
/* Already converged (perfect seed)? Skip iteration. */
/* Already converged (perfect seed)? Skip DC loop but still
* compute covariance — users need uncertainty estimates even
* when the initial guess is exact. */
if (rms_cur < OD_RMS_ABS_TOL)
{
converged = 1;
memcpy(&result->fitted_tle, &current_tle, sizeof(tle_t));
result->iterations = 0;
result->rms_final = rms_cur;
result->converged = 1;
snprintf(result->status, sizeof(result->status), "converged");
od_free(residuals);
od_free(jacobian);
od_free(dx);
od_free(sv);
od_free(work);
return 0;
iter = 0;
goto compute_covariance;
}
/* ── DC iteration loop ─────────────────────────────── */
@ -848,6 +849,146 @@ od_fit_tle(const od_observation_t *obs, int n_obs,
rms_prev = rms_cur;
}
compute_covariance:
/* ── Covariance computation ─────────────────────────── */
/*
* Compute formal covariance matrix (H^T H)^{-1} at the converged
* solution. This requires rebuilding the Jacobian at the final state
* (the DC loop overwrites it each iteration via LAPACK).
*
* The covariance gives parameter uncertainty estimates — diagonal
* elements are variances, off-diagonals are correlations. Essential
* for conjunction screening probability computations.
*/
result->cov_size = 0;
result->condition_number = condition_number;
if (converged || iter >= max_iter)
{
/* Rebuild Jacobian at final state (same finite-diff as DC loop) */
for (j_cov = 0; j_cov < nstate; j_cov++)
{
od_equinoctial_t eq_pert;
tle_t tle_pert;
double *resid_pert;
double h, elem_val;
memcpy(&eq_pert, &eq, sizeof(od_equinoctial_t));
switch (j_cov)
{
case 0: elem_val = eq.n; break;
case 1: elem_val = eq.af; break;
case 2: elem_val = eq.ag; break;
case 3: elem_val = eq.chi; break;
case 4: elem_val = eq.psi; break;
case 5: elem_val = eq.L0; break;
case 6: elem_val = eq.bstar; break;
default: elem_val = 0.0; break;
}
h = fabs(elem_val) * 1e-6;
if (h < 1e-10)
h = 1e-10;
switch (j_cov)
{
case 0: eq_pert.n += h; break;
case 1: eq_pert.af += h; break;
case 2: eq_pert.ag += h; break;
case 3: eq_pert.chi += h; break;
case 4: eq_pert.psi += h; break;
case 5: eq_pert.L0 += h; break;
case 6: eq_pert.bstar += h; break;
}
equinoctial_to_tle(&eq_pert, &seed_tle, &tle_pert);
resid_pert = (double *)od_alloc(sizeof(double) * nrows);
if (config->obs_type == OD_OBS_ECI)
compute_residuals_eci(&tle_pert, obs, n_obs, resid_pert);
else
compute_residuals_topo(&tle_pert, obs, n_obs,
config->observers, resid_pert);
for (k_cov = 0; k_cov < nrows; k_cov++)
jacobian[j_cov * nrows + k_cov] =
(residuals[k_cov] - resid_pert[k_cov]) / h;
od_free(resid_pert);
}
/* Compute H^T H before SVD destroys the Jacobian */
{
double *hth;
int ci, cj, ri, info_cov;
char uplo = 'U';
hth = (double *)od_alloc(sizeof(double) * nstate * nstate);
memset(hth, 0, sizeof(double) * nstate * nstate);
for (ci = 0; ci < nstate; ci++)
{
for (cj = ci; cj < nstate; cj++)
{
double dot = 0.0;
for (ri = 0; ri < nrows; ri++)
dot += jacobian[ci * nrows + ri] *
jacobian[cj * nrows + ri];
hth[ci + cj * nstate] = dot;
hth[cj + ci * nstate] = dot;
}
}
/* SVD of Jacobian for condition number (destroys jacobian) */
{
int m = nrows, n = nstate, nrhs = 1;
int lda = nrows, ldb = nrows, rank, info_svd;
double rcond = -1.0;
memcpy(dx, residuals, sizeof(double) * nrows);
od_free(work);
{
int lw = -1;
double wq;
dgelss_(&m, &n, &nrhs, jacobian, &lda, dx, &ldb,
sv, &rcond, &rank, &wq, &lw, &info_svd);
lw = (int)wq + 1;
work = (double *)od_alloc(sizeof(double) * lw);
dgelss_(&m, &n, &nrhs, jacobian, &lda, dx, &ldb,
sv, &rcond, &rank, work, &lw, &info_svd);
}
if (info_svd == 0 && sv[nstate - 1] > 1e-30)
condition_number = sv[0] / sv[nstate - 1];
}
result->condition_number = condition_number;
/* Cholesky factorize H^T H, then invert for covariance */
dpotrf_(&uplo, &nstate, hth, &nstate, &info_cov);
if (info_cov == 0)
{
dpotri_(&uplo, &nstate, hth, &nstate, &info_cov);
if (info_cov == 0)
{
int idx = 0;
for (ci = 0; ci < nstate; ci++)
for (cj = ci; cj < nstate; cj++)
result->covariance[idx++] = hth[ci + cj * nstate];
result->cov_size = idx; /* 21 or 28 */
}
}
od_free(hth);
}
}
/* ── Build result ──────────────────────────────────── */
memcpy(&result->fitted_tle, &current_tle, sizeof(tle_t));
@ -860,8 +1001,6 @@ od_fit_tle(const od_observation_t *obs, int n_obs,
else if (iter >= max_iter && result->status[0] == '\0')
snprintf(result->status, sizeof(result->status), "max_iterations");
(void)condition_number; /* used by covariance output (v0.5.0) */
/* Cleanup */
od_free(residuals);
od_free(jacobian);

3
src/od_solver.h
View File

@ -79,6 +79,9 @@ typedef struct
double rms_final; /* RMS residual after fitting (km) */
int converged; /* 1 if converged, 0 if hit max_iter */
char status[64]; /* human-readable status */
double covariance[28]; /* upper triangle of (H^T H)^{-1}, row-major */
int cov_size; /* 21 (6-state) or 28 (7-state), 0 if failed */
double condition_number; /* s_max / s_min from final SVD */
} od_result_t;
/*

143
test/expected/od_fit.out
View File

@ -2,8 +2,9 @@
--
-- Tests tle_from_eci(), tle_from_topocentric(), and tle_fit_residuals().
-- Uses round-trip methodology: propagate known TLE → fit from obs → compare.
SET client_min_messages TO warning;
CREATE EXTENSION IF NOT EXISTS pg_orrery;
ALTER EXTENSION pg_orrery UPDATE TO '0.5.0';
SET client_min_messages TO notice;
-- ============================================================
-- Test 1: ECI round-trip (ISS-like LEO orbit)
--
@ -482,3 +483,143 @@ FROM result;
t | t | t
(1 row)
-- ============================================================
-- Test 14: Covariance is returned when converged
--
-- A converged 6-state fit should produce a non-NULL covariance
-- array of length 21 (upper triangle of 6x6).
-- ============================================================
WITH iss_tle AS (
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
),
obs AS (
SELECT
array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_eci(positions, times, t)).* FROM obs, iss_tle
)
SELECT
covariance IS NOT NULL AS has_covariance,
array_length(covariance, 1) = 21 AS cov_length_21,
nstate = 6 AS is_6state,
condition_number > 0 AS cond_positive
FROM result;
has_covariance | cov_length_21 | is_6state | cond_positive
----------------+---------------+-----------+---------------
t | t | t | t
(1 row)
-- ============================================================
-- Test 15: Covariance diagonal elements positive (variances > 0)
--
-- For a well-conditioned fit, all diagonal elements of the
-- covariance matrix must be positive (they are variances).
-- Upper triangle row-major: diag indices are 0,6,11,15,18,20.
-- ============================================================
WITH iss_tle AS (
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
),
obs AS (
SELECT
array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_eci(positions, times, t)).* FROM obs, iss_tle
)
SELECT
covariance[1] > 0 AS var_n_positive,
covariance[7] > 0 AS var_af_positive,
covariance[12] > 0 AS var_ag_positive,
covariance[16] > 0 AS var_chi_positive,
covariance[19] > 0 AS var_psi_positive,
covariance[21] > 0 AS var_L0_positive
FROM result;
var_n_positive | var_af_positive | var_ag_positive | var_chi_positive | var_psi_positive | var_l0_positive
----------------+-----------------+-----------------+------------------+------------------+-----------------
t | t | t | t | t | t
(1 row)
-- ============================================================
-- Test 16: 7-state covariance (with B* fitting)
--
-- When fit_bstar = true, covariance should have 28 elements
-- (upper triangle of 7x7) and nstate = 7.
-- ============================================================
WITH iss_tle AS (
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
),
obs AS (
SELECT
array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_eci(positions, times, t, fit_bstar := true)).* FROM obs, iss_tle
)
SELECT
covariance IS NOT NULL AS has_covariance,
array_length(covariance, 1) = 28 AS cov_length_28,
nstate = 7 AS is_7state
FROM result;
has_covariance | cov_length_28 | is_7state
----------------+---------------+-----------
t | t | t
(1 row)
-- ============================================================
-- Test 17: Condition number positive
--
-- The condition number (s_max / s_min from SVD) should be
-- positive for any non-degenerate fit. Topocentric mode.
-- ============================================================
WITH iss_tle AS (
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
),
mit AS (
SELECT '(42.36,-71.09,20)'::observer AS obs
),
topo_obs AS (
SELECT
array_agg(observe(t, obs, ts) ORDER BY ts) AS observations,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle, mit,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_topocentric(observations, times, obs, t)).* FROM topo_obs, mit, iss_tle
)
SELECT
condition_number > 0 AS cond_positive,
covariance IS NOT NULL AS has_covariance,
nstate = 6 AS is_6state
FROM result;
cond_positive | has_covariance | is_6state
---------------+----------------+-----------
t | t | t
(1 row)

131
test/sql/od_fit.sql
View File

@ -3,8 +3,9 @@
-- Tests tle_from_eci(), tle_from_topocentric(), and tle_fit_residuals().
-- Uses round-trip methodology: propagate known TLE → fit from obs → compare.
SET client_min_messages TO warning;
CREATE EXTENSION IF NOT EXISTS pg_orrery;
ALTER EXTENSION pg_orrery UPDATE TO '0.5.0';
SET client_min_messages TO notice;
-- ============================================================
-- Test 1: ECI round-trip (ISS-like LEO orbit)
@ -452,3 +453,131 @@ SELECT
rms_final < 5.0 AS rms_under_5km,
status = 'converged' AS did_converge
FROM result;
-- ============================================================
-- Test 14: Covariance is returned when converged
--
-- A converged 6-state fit should produce a non-NULL covariance
-- array of length 21 (upper triangle of 6x6).
-- ============================================================
WITH iss_tle AS (
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
),
obs AS (
SELECT
array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_eci(positions, times, t)).* FROM obs, iss_tle
)
SELECT
covariance IS NOT NULL AS has_covariance,
array_length(covariance, 1) = 21 AS cov_length_21,
nstate = 6 AS is_6state,
condition_number > 0 AS cond_positive
FROM result;
-- ============================================================
-- Test 15: Covariance diagonal elements positive (variances > 0)
--
-- For a well-conditioned fit, all diagonal elements of the
-- covariance matrix must be positive (they are variances).
-- Upper triangle row-major: diag indices are 0,6,11,15,18,20.
-- ============================================================
WITH iss_tle AS (
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
),
obs AS (
SELECT
array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_eci(positions, times, t)).* FROM obs, iss_tle
)
SELECT
covariance[1] > 0 AS var_n_positive,
covariance[7] > 0 AS var_af_positive,
covariance[12] > 0 AS var_ag_positive,
covariance[16] > 0 AS var_chi_positive,
covariance[19] > 0 AS var_psi_positive,
covariance[21] > 0 AS var_L0_positive
FROM result;
-- ============================================================
-- Test 16: 7-state covariance (with B* fitting)
--
-- When fit_bstar = true, covariance should have 28 elements
-- (upper triangle of 7x7) and nstate = 7.
-- ============================================================
WITH iss_tle AS (
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
),
obs AS (
SELECT
array_agg(sgp4_propagate(t, ts) ORDER BY ts) AS positions,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_eci(positions, times, t, fit_bstar := true)).* FROM obs, iss_tle
)
SELECT
covariance IS NOT NULL AS has_covariance,
array_length(covariance, 1) = 28 AS cov_length_28,
nstate = 7 AS is_7state
FROM result;
-- ============================================================
-- Test 17: Condition number positive
--
-- The condition number (s_max / s_min from SVD) should be
-- positive for any non-degenerate fit. Topocentric mode.
-- ============================================================
WITH iss_tle AS (
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
),
mit AS (
SELECT '(42.36,-71.09,20)'::observer AS obs
),
topo_obs AS (
SELECT
array_agg(observe(t, obs, ts) ORDER BY ts) AS observations,
array_agg(ts ORDER BY ts) AS times
FROM iss_tle, mit,
generate_series(
'2024-01-01 12:00:00+00'::timestamptz,
'2024-01-01 13:30:00+00'::timestamptz,
'5 minutes'::interval
) AS ts
),
result AS (
SELECT (tle_from_topocentric(observations, times, obs, t)).* FROM topo_obs, mit, iss_tle
)
SELECT
condition_number > 0 AS cond_positive,
covariance IS NOT NULL AS has_covariance,
nstate = 6 AS is_6state
FROM result;