Module track 

Constant-velocity track filtering and fixed-interval RTS smoothing.

This module is a no-IMU position-domain estimator. The state vector is [position, velocity] in a caller-selected Cartesian frame. Position-only updates use H = [I, 0]; position-and-velocity updates use H = I.

Prediction uses the white-noise-acceleration constant-velocity model

F = [[I, dt I], [0, I]]

Q = q [[dt^3 / 3 I, dt^2 / 2 I], [dt^2 / 2 I, dt I]]

where q is the acceleration variance spectral density in m^2 / s^3.

Measurement correction uses the linear Kalman equations

nu = z - H x

S = H P H' + R

K = P H' S^-1

x = x + K nu

P = P - K H P.

The update methods also expose nu, S, K, and normalized innovation squared, nu' S^-1 nu, so callers can gate fixes before applying them.

The backward smoother follows the Rauch-Tung-Striebel recursion:

G_k = P_k F_{k+1}' (P_{k+1|k})^-1

x_k^s = x_k + G_k (x_{k+1}^s - x_{k+1|k})

P_k^s = P_k + G_k (P_{k+1}^s - P_{k+1|k}) G_k'.

Structs

SmoothedTrack

Smoothed track returned by rts_smooth.

SmoothedTrackEpoch

One epoch in a smoothed track.

TrackFilter

No-IMU constant-velocity Kalman filter over a Cartesian position track.

TrackFilterConfig

Configuration for TrackFilter.

TrackGatedUpdate

Gated update result.

TrackInnovation

Innovation report for a pending or applied track update.

TrackPrediction

Prediction result returned by TrackFilter::predict.

TrackRtsEpoch

One epoch in a recorded forward pass for track RTS smoothing.

TrackRtsHistory

Recorded history accepted by rts_smooth.

TrackRtsHistoryBuilder

Builder for recording a forward track-filter pass for RTS smoothing.

TrackState

State of a no-IMU constant-velocity track filter.

TrackUpdate

Update result returned after a covariance-weighted correction.

Enums

TrackCoordinateFrame

Cartesian frame used by a track filter.

TrackError

Error returned by no-IMU track filtering and smoothing.

Functions

rts_smooth

Apply a fixed-interval RTS smoother to a recorded no-IMU track history.

smooth_track_rts

Alias for rts_smooth with the track domain in the function name.