MATLAB TCL parity inventory

A function-level comparison of pytcl against the MATLAB library at commit 593ce51 of the U.S. Naval Research Laboratory’s Tracker Component Library, produced by walking every directory of the MATLAB repository rather than by asserting a percentage.

Why this document exists

Earlier documentation claimed “full feature parity” and “100% MATLAB parity”. Those claims were scoped to a tier-1/tier-2 component list that was never published alongside them, and one of their checkmarks — NRLMSISE-00 — proved to be a placeholder shipped under the model’s name (gh-79). This inventory replaces assertion with enumeration.

Method

The MATLAB public surface was counted under MATLAB’s actual visibility rules: a regular .m file exposes exactly its first function (later declarations are file-local subfunctions), and classdef files expose their methods except those in Access = private blocks. Third-party code, sample code and compiled artifacts are excluded. That yields 2,549 public names across 1,843 files — against 1,899 public names in pytcl.

Automated name matching is a lower bound only: MATLAB ships one file per variant where pytcl uses a keyword argument, and the port renamed systematically (KalmanUpdate → kf_update). The verdicts below come from reading each area’s function list against pytcl’s modules.

Summary

pytcl ports the core tracking workflow comprehensively and validates it against independent references, but the MATLAB library’s full surface is substantially broader. By function count, coverage is roughly a third of the MATLAB public surface. By workflow — filter, associate, track, evaluate, in Earth-referenced coordinates — coverage is near-complete, and in several places pytcl exceeds the original (OSPA/MOT metrics, ionosphere models, R-trees and cover trees, STFT/wavelet transforms and matched filtering, SQL/HDF5 track storage, GPU backends). Min-cost flow is not among them: MATLAB ships Mathematical_Functions/Graph_Algorithms/minCostFlow.m.

MATLAB area	Public	Coverage	Notes
Dynamic_Estimation	113	Core strong	KF/EKF/UKF/CKF, square-root and UD forms, SRIF, information filter, H-infinity, IMM, particle filters, RBPF, and RTS/two-filter/fixed-lag smoothers all ported (fixed_interval_smoother is a documented alias for the RTS smoother, not a fourth algorithm); v2.9.0 added EnKF, ESRIF, the quasi-Monte-Carlo Kalman variants, BLUE polar/spherical measurement updates, batch least-squares estimators, and the PCRLB/Riccati performance-prediction tools. Missing: progressive Gaussian update, pure-propagation filter, reduced-state filters. Also absent, and larger than that list suggests: the entire Measurement_Update/Update_Parts tree (30 files, 27% of the area – separate gain, measurement-prediction and update-with-prediction entry points, which pytcl does not decompose its updates into), continuous-discrete propagation (State_Propagation/Continuous_Time, 6 files), divided-difference filters, one/two-point initialization, and batch/FIR smoothers. By counterpart count roughly 20 of the 113 MATLAB functions have a pytcl equivalent; “Core strong” describes the KF family’s depth, not breadth across the area.
Dynamic_Models	62	Partial	CV/CA (arbitrary polynomial order, via f_poly_kal/q_poly_kal), coordinated turn (2D/3D/polar) and Singer F and Q matrices ported. Missing: Gauss-Markov at orders other than 2 – MATLAB’s FGaussMarkov/QGaussMarkov are arbitrary-order (order 0 is Ornstein-Uhlenbeck, 1 is integrated OU, 2 is Singer) and pytcl ports only the order-2 Singer case, with no order argument; also weave/spiral maneuver models, flat-to-curved-Earth dynamics, geodesic Brownian motion, trajectory generators with constrained endpoints, process-noise suggestion tooling.
Assignment_Algorithms	45	Core strong	2D assignment (Hungarian, auction, Murty k-best), 3D assignment, JPDA with gating, min-cost flow all ported and oracle-validated. Missing: bottleneck assignment, knapsack, transportation problem, stable-matching family, missed-detection LR matrix builders, assignment-probability calculators beyond JPDA.
Coordinate_Systems	331	Partial	Cartesian/spherical/polar/geodetic/ENU/NED/SEZ conversions, rotations, quaternions, r-u-v (range plus direction cosines, cart2ruv/ ruv2cart) and the standard projections ported; UTM is validated to sub-mm against pyproj/EPSG, but stereographic and azimuthal_equidistant are spherical approximations that diverge from PROJ by kilometres away from the projection centre (their own docstrings tabulate this; gh-25). The angle-only direction-cosine UV measurement system’s core conversions are ported (coordinate_systems.conversions.uv, v2.8.0: u-v <-> spherical, full bistatic r-u-v, camera-to-uv), its cubature/Taylor covariance conversions in v2.9.0, and the measurement Jacobians in v2.10.0: the component gradients (range, range rate, spherical/polar angles, u-v(-w) direction cosines, TDOA) and the full bistatic spherical/polar/r-u-v measurement Jacobians with range-rate and converted variants (coordinate_systems/jacobians/, validated against MATLAB fixtures at 1e-12). The relativistic/dynamical time scales (TDB/TCB/TCG, Besselian epochs, local sidereal time) are ported in astronomical/time_scales (v2.10.0). The measurement Hessians and cross gradients/Hessians (u-v <-> spherical angle, 2-D u <-> polar) are ported in coordinate_systems/hessians/ (v2.10.0, same fixture validation). Missing: the calendar/timezone utilities of the time suite, the ellipsoidal azimuthal-equidistant family (pytcl’s azimuthal_equidistant is a spherical approximation) and its Jacobians, other exotic projections (bipolar, gnomonic), ellipsoidal-harmonic coordinates, RF transform-parameter estimation.
Mathematical_Functions	1,440	Selective	The largest area and the largest gap, though much of it is generic numerics rather than tracking. Ported well: the CFAR family (pytcl adds GO/SO/2-D beyond MATLAB’s CA and OS), core statistics (12 distribution classes vs MATLAB’s 54), interpolation, special functions. Note that pytcl’s STFT/CWT/DWT and matched filtering are not ports – the MATLAB library contains no STFT, wavelet or matched-filter code at all, so they belong under “what pytcl adds” below, not under parity. Signal processing overall is thin against the original: roughly 6 of 51 MATLAB names, with the entire 17-file Array_Processing subtree (tapering, beam patterns, subarray weights) unported. Basic matrix operations likewise: about 10 of 99, with the Joint_Matrix_Diagonalization and Tensors subtrees absent. The cubature-point library (~148 files – a signature strength of the MATLAB TCL) is now well covered: the degree-5/7 Gaussian rules including the full seventh_order_cubature_points algorithm surface, spherical-radial points (with the beta generalization), Genz-Keister nested rules, the 14th-order and 2nd-order (Julier) rules, Student-t cubature points, Smolyak sparse grids over the Genz-Keister sequences, and tensor Gauss-Hermite. Gaussian LCD samples (gaussian_lcd_samples) and the general-dimension uniform region-cubature rules (Cube/Simplex/Sphere/Spherical-Surface) have since shipped. Remaining: the 48 dimension-specialized subdirectory files within that same region-cubature subset (fixed 2D/3D formulas in Cube/, Square/, Tetrahedra/, Triangles/), three 1-D quadrature building blocks, and the region types outside that subset (Prism, Pyramid, Cross_Polytope, Exp_Weight, Weighted_Ellipse, Hexagon, Spherical_Shell – 33 files – plus loose torus and n-dimensional-shell rules; see Development Roadmap). There is no cone or wedge rule anywhere in the MATLAB library. Also thin or absent: combinatorics (113 vs 18), polynomials (55 files; pytcl covers the multivariate-system solvers in polynomials/multivariate.py, the rest is thin), geometry beyond basics (81), continuous optimization (37), most specific integrals/derivatives (the Carlson symmetric and incomplete elliptic integrals are ported, in special_functions/elliptic.py), graph algorithms other than min-cost flow, accurate-arithmetic helpers.
Astronomical_Code	28	Partial	SGP4 (validated against the official library), Kepler propagation, orbital elements, Lambert solvers, JPL ephemerides via jplephem. Missing: Hipparcos catalog access, aberration and light-deflection corrections, EOP acquisition, angles-only initial orbit determination, two-point velocity determination, equinoctial Kepler solver.
Atmosphere_and_Refraction	34	Partial	U.S. Standard Atmosphere 1976/ISA validated; barometric thermosphere with documented limits (gh-79); all 10 humidity conversions, both dew-point functions, the refractivity helpers and the astronomical-refraction group (SinclairAtmos, removeAstroRefrac/addAstroRefrac with all three algorithms, simpAstroRefParam transcribed from the in-tree SOFA source) and the complete Standard_Exponential_Model suite (bistatic r-u-v ray tracing, bias approximation, cubature conversions, refractivity reduction) ported and validated against MATLAB fixtures; speed of sound (all three algorithms, including the gas-table mixture computation with its Constants.gasProp thermophysical data); NRLMSISE-00 proper (the reference C compiled into pytcl.atmosphere._nrlmsise00_c with a validated pure-Python fallback) and its wrapper API. Jacchia 1971 shipped in v2.11.0 as pytcl.atmosphere.jacchia (the MATLAB original is unrunnable as shipped – undefined EOP variables – so the oracle captures the model physics with the solar geometry as explicit inputs; see the capture script). pytcl adds ionosphere models (Klobuchar, TEC) that the MATLAB area lacks.
Gravity	14	Good	EGM coefficient loading, geoid height, normal gravity, tide offsets (solid/pole/ocean) ported; v2.11.0 added the ellipsoidal parameter conversions (alt_ellips_param_to_flattening, ellips_grav_coeffs). Missing: lunar gravity coefficients, polar-motion/drift coefficient adjustments, and ellipsParam2Grav (needs the ellipsoidal-harmonic coordinate conversions as prerequisites).
Magnetism	12	Split	Coefficient loading and field evaluation for WMM/IGRF/EMM ported and validated to sub-nT. The coordinate-system half is ported in magnetism/coordinates (v2.10.0): centered-dipole transforms, magnetic-heading conversions, and apex/quasi-dipole coordinates by field-line tracing, validated against MATLAB fixtures and a pure-dipole closed form. (The MATLAB CD functions’ default-model call form errors in R2026a – ClusterSet 2-argument indexing – and its data directory ships a 2024-11-13 pre-release WMM2025 coefficient file.)
Navigation	21	Good	Direct/indirect geodesic, great-circle and rhumb problems ported, validated against GeographicLib; rhumb intersection is ported as rhumb_intersect. (The invented great_circle_tdoa_loc was removed in v2.11.0: it was not a port and its reliability was self-documented as poor.) Great-circle intersection is ported too, as great_circle_intersect (plus a path-endpoint form, great_circle_path_intersect). Missing: the geodesic (ellipsoidal) intersection, surface angles, the at-a-fixed-height *ProbGen generalizations of the direct/indirect geodesic and rhumb problems, geodesic midpoint, and standalone pseudorange localization (pseudoRangeLoc) – pytcl has only the filter-component pieces of the last.
Static_Estimation	11	Split	Nine of the 11 localization estimators are ported in static_estimation.localization (v2.8.0): TDOAOnlyStaticLocEst, rangeOnlyStaticLocEstNP, RROnlyStaticVelEst, getAdHocCartCov, directionOnlyStaticLocEst (with two upstream defects fixed and documented: an RInv-discarding overwrite that also crashed 2D, and a range-refinement typo) and computePolyMeasFIM, plus — via the polyRootsMultiDim port — TDOA2Cart, rangeRate2StaticPos and rangeRateRatio2StaticPos2D, all validated against MATLAB fixtures. Missing: only the two Uses_External_Solver files, which build 6-7-variable polynomial systems and require an external homotopy-continuation solver (Bertini/PHCpack/Macaulay2), not SCS as earlier stated here. pytcl’s static_estimation also ports the general estimators (OLS/TLS/robust/MLE) that MATLAB keeps elsewhere; RANSAC and recursive least squares are pytcl originals with no MATLAB counterpart anywhere in the library.
Clustering_and_Mixture_Reduction	14	Good	Runnalls and West mixture reduction, k-means(++) ported; pytcl adds DBSCAN and hierarchical clustering. Missing: ISE-based reduction and its gradients, brute-force reduction, windowed grid centroiding.
Container_Classes	265	Different emphasis	k-d tree and metric tree ported (as KDTree/BallTree/VPTree), ClusterSet ported; pytcl adds R-trees, cover trees and the whole track/measurement container layer. Missing: AVL tree, binary heaps, disjoint sets, linked lists, interval class, B-spline class — largely idiomatic-Python non-goals, but absent nonetheless.
Performance_Evaluation	12	Split	NEES (with confidence bounds), RMSE ported; pytcl adds the standard OSPA metric and CLEAR-MOT metrics. The MOSPA/MMOSPA family (calcMOSPAError, MMOSPA2Tar2D, MMOSPAApprox) is ported in performance_evaluation/mospa (v2.10.0). Missing: AEE/GAE, jitter, MERF, non-credibility index, calcMSE, identVarGauss.
Terrain	3	Partial	The Earth2014 dataset is read (plus GEBCO, which MATLAB lacks), but not MATLAB’s function: getEarth2014TerrainCoeffs returns degree-2160 spherical-harmonic coefficients from .bshc files, while pytcl parses the 1-arcmin geodetic grid products and has no .bshc parser. Solid-tide shift ported. So of the three public functions, one (solidTideShift) has a genuine equivalent and both coefficient-returning functions – Earth2014 and EGM2008 terrain – are unported.
Misc	52	Mostly N/A	Bit manipulation, MATLAB plotting, file utilities — superseded by numpy/matplotlib/stdlib. Substantive absences: GSHHG coastline data access and pointIsOnLand.
Transponders	3	Partial	MATLAB’s Transponders directory holds exactly three functions: decodeAISString (parse an NMEA sentence to a struct, wrapping libais, a C library), decodeAISPosReports2Mat (extract position reports into a matrix), and NMEAChecksum (compute/validate an NMEA sentence’s trailing *hh checksum, usable whether decoding or constructing one). pytcl (v2.2.0) ports the first two as pytcl.transponders.ais’s decode_ais and ais_position_reports, which reassemble multipart !AIVDM/!AIVDO sentences and extract position reports (message types 1/2/3/18/19), normalizing ITU-R M.1371 “not available” sentinels to NaN – via pyais, a pure-Python decoder, rather than a libais binding, so the two are functionally equivalent but not the same implementation. Validated against 6,808 real position reports from 299 ships off Norway (see Results I/O). NMEAChecksum is ported too, as nmea_checksum; decode_ais and ais_position_reports validate the trailing *hh by default (validate_checksum=True, NMEA 4.10 TAG blocks handled). Missing: NMEA sentence construction in either direction (encoding a message back to !AIVDM text) – neither is ported.
Scheduling	4	Ported	All four interval scheduling algorithms ported in pytcl/scheduling (v2.10.0): greedy maximum-cardinality selection, minimum partitioning, minimum-lateness sequencing and the weighted-interval dynamic program, validated against MATLAB fixtures and brute-force enumeration.
Physical_Values	14	Partial	Physical constants partially ported: 43 module-level constants against Constants.m’s 92 properties (Constant), with the WGS72, EGM96/EGM2008 and lunar (GL0900C/JPL) constant families and the atomic/electromagnetic set (electron and proton mass, fine structure, Rydberg, Faraday) all absent. Radar bands, water permittivity, reflection-coefficient models, elementAMU and gasProp absent.

What pytcl has that the MATLAB library does not

The comparison runs both ways. pytcl adds: the standard OSPA metric and CLEAR-MOT evaluation, ionospheric delay models, R-trees and cover trees, DBSCAN and hierarchical clustering, min-cost-flow assignment, SQL and HDF5 track storage with migration tooling, dual-backend GPU acceleration, and a test suite of 8,000+ cases that includes 80+ validation files checking against independent references — the MATLAB library distributes no test suite at all.

Honest bottom line

The defensible claim is not “full feature parity”. It is: the core tracking workflow is ported, oracle-validated, and in places extended; the MATLAB library’s long tail — its cubature collection, refraction suite, time-scale zoo, localization estimators and specialized coordinate systems — is substantially unported, at roughly a third of the full public surface by function count. Areas above marked Absent, Weak or Divergent are the honest priority list for anyone who needs them.