Collision probability computation for conjunction assessment
collision: merlint fixes (Fmt.pr, rename find_tca → tca, fix docs)
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lib/collision.ml
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lib/collision.ml
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lib/collision.mli
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lib/collision.mli
···
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type vec3 = Vec3.t = { x : float; y : float; z : float }
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val find_tca :
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val tca :
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times:float array ->
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pos1:vec3 array ->
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pos2:vec3 array ->
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vel1:vec3 array ->
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vel2:vec3 array ->
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tca option
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(** [find_tca ~times ~pos1 ~pos2 ~vel1 ~vel2] finds the time of closest approach
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(** [tca ~times ~pos1 ~pos2 ~vel1 ~vel2] finds the time of closest approach
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between two objects using quadratic refinement. Arrays must be the same
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length (synchronized time steps). Returns [None] if fewer than 3 points. *)
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···
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(** Chan series expansion Pc. *)
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val pc_max : encounter -> float
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(** Upper bound: [hbr^2 / (2 * sigma_x * sigma_y)]. *)
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(** [pc_max enc] returns an upper bound: [hbr^2 / (2 * sigma_x * sigma_y)]. *)
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val pc : hbr:float -> Cdm.t -> float
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(** [pc ~hbr cdm] computes Pc from a CDM using the Foster method. *)
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test/interop/gmat/test.ml
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test/interop/gmat/test.ml
···
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Sat2: SSO-like (97.4 deg inc, 410 km alt).
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1 day propagation, 10s step. *)
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let test_parse_both () =
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let parse_both () =
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let oem1 = parse_oem "conjunction_sat1.oem" in
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let oem2 = parse_oem "conjunction_sat2.oem" in
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let sv1 = Odm.state_vectors (List.hd (Odm.segments oem1)) in
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let sv2 = Odm.state_vectors (List.hd (Odm.segments oem2)) in
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Alcotest.(check int) "same length" (Array.length sv1) (Array.length sv2)
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let test_minimum_distance () =
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let minimum_distance () =
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let oem1 = parse_oem "conjunction_sat1.oem" in
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let oem2 = parse_oem "conjunction_sat2.oem" in
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let sv1 = Odm.state_vectors (List.hd (Odm.segments oem1)) in
···
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Alcotest.(check bool) "min distance found" true (Float.is_finite !min_dist);
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Alcotest.(check bool) "min distance < 1000 km" true (!min_dist < 1000.0);
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Alcotest.(check bool) "no collision (> 1 km)" true (!min_dist > 1.0);
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Printf.printf " Step-based closest approach: %.3f km at %s\n" !min_dist
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Fmt.pr " Step-based closest approach: %.3f km at %s\n" !min_dist
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!min_epoch
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let test_relative_velocity () =
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let relative_velocity () =
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let oem1 = parse_oem "conjunction_sat1.oem" in
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let oem2 = parse_oem "conjunction_sat2.oem" in
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let sv1 = Odm.state_vectors (List.hd (Odm.segments oem1)) in
···
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let dv = v_norm (v_sub sv1.(!min_i).Odm.vel sv2.(!min_i).Odm.vel) in
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(* Crossing orbits at ~90 deg: relative velocity ~sqrt(2) * 7.5 ~= 10.6 km/s *)
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Alcotest.(check bool) "high relative velocity" true (dv > 5.0);
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Printf.printf " Relative velocity at TCA: %.3f km/s\n" dv
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Fmt.pr " Relative velocity at TCA: %.3f km/s\n" dv
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(* TCA refinement: find_tca should improve on step-based minimum.
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(* TCA refinement: tca should improve on step-based minimum.
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With 10s steps and ~10 km/s relative velocity, the step-based minimum
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can miss the true TCA by up to 5s (~50 km). Quadratic refinement
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should give sub-step precision. *)
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let test_tca_refinement () =
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let tca_refinement () =
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let oem1 = parse_oem "conjunction_sat1.oem" in
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let oem2 = parse_oem "conjunction_sat2.oem" in
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let sv1 = Odm.state_vectors (List.hd (Odm.segments oem1)) in
···
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step_min_d := d;
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step_min_t := times.(i))
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done;
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match Collision.find_tca ~times ~pos1 ~pos2 ~vel1 ~vel2 with
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| None -> Alcotest.fail "find_tca returned None"
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match Collision.tca ~times ~pos1 ~pos2 ~vel1 ~vel2 with
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| None -> Alcotest.fail "tca returned None"
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| Some tca ->
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Printf.printf " Step-based TCA: t=%.3f, d=%.3f km\n" !step_min_t
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Fmt.pr " Step-based TCA: t=%.3f, d=%.3f km\n" !step_min_t
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!step_min_d;
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Printf.printf " Refined TCA: t=%.3f, d=%.3f km, vrel=%.3f km/s\n"
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Fmt.pr " Refined TCA: t=%.3f, d=%.3f km, vrel=%.3f km/s\n"
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tca.time tca.miss_distance tca.relative_velocity;
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(* Refined miss distance should be <= step-based (quadratic finds the
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true minimum between steps) *)
···
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Without covariance, the miss distance alone is meaningless for CA decisions.
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A 50 km miss distance could be Pc=1e-3 (bad) or Pc=1e-10 (fine) depending
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on covariance size. *)
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let test_pc_requires_covariance () =
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let pc_requires_covariance () =
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(* We can compute miss distance from GMAT OEMs *)
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let oem1 = parse_oem "conjunction_sat1.oem" in
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let oem2 = parse_oem "conjunction_sat2.oem" in
···
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let d = v_norm (v_sub sv1.(i).Odm.pos sv2.(i).Odm.pos) in
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if d < !min_dist then min_dist := d
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done;
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Printf.printf " Miss distance: %.3f km\n" !min_dist;
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Printf.printf " Pc: CANNOT COMPUTE — no covariance in OEM\n";
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Printf.printf
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Fmt.pr " Miss distance: %.3f km\n" !min_dist;
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Fmt.pr " Pc: CANNOT COMPUTE — no covariance in OEM\n";
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Fmt.pr
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" GAP: Need GMAT covariance propagation (Propagate ... Covariance)\n";
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Printf.printf
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Fmt.pr
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" or CDM with covariance to test ocaml-collision Pc computation.\n";
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(* This test passes but documents the gap. The real test would be:
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1. Generate GMAT OEM WITH covariance
···
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[
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( "plumbing",
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[
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Alcotest.test_case "parse both OEMs" `Quick test_parse_both;
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Alcotest.test_case "minimum distance" `Quick test_minimum_distance;
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Alcotest.test_case "relative velocity" `Quick test_relative_velocity;
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Alcotest.test_case "parse both OEMs" `Quick parse_both;
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Alcotest.test_case "minimum distance" `Quick minimum_distance;
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Alcotest.test_case "relative velocity" `Quick relative_velocity;
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] );
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( "mission-ready",
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[
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Alcotest.test_case "TCA refinement" `Quick test_tca_refinement;
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Alcotest.test_case "TCA refinement" `Quick tca_refinement;
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Alcotest.test_case "Pc requires covariance" `Quick
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test_pc_requires_covariance;
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pc_requires_covariance;
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] );
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]