Module primitives 

Estimation and detection primitives.

The primitives here are intentionally scalar, deterministic, and dependency-light. They are a direct implementation point for embedded and desktop callers.

Provenance

• Alpha-beta and equivalent scalar 2-state constant-velocity Kalman gains use the Bar-Shalom steady-state family relations.
• Innovation gating and NIS monitoring follow the standard chi-square gate construction.
• CFAR formulas use the cell-averaging exponential-tail model from Richards.
• MAD and EWMA are the canonical scalar definitions used in this repository’s robust-statistics layer, with the Gaussian consistency constant for MAD 1.482602....

Structs

AlphaBetaGains

Alpha-beta steady-state gain set for one scalar channel.

AlphaBetaState

State of a scalar level + rate estimator.

AlphaBetaStep

One alpha-beta update result.

NisGate

Result of an NIS gate test.

ScalarKalmanGains

Steady-state gains of the equivalent 2-state scalar Kalman model.

Enums

PrimitiveError

Public error for estimation/detection primitive validation failures.

Constants

MAD_GAUSSIAN_CONSISTENCY

MAD-Gaussian consistency factor 1 / Φ^{-1}(3/4).

Functions

alpha_beta_apply_measurement

Apply one measurement update on a predicted scalar alpha-beta state.

alpha_beta_filter_step

Run one alpha-beta predict/update step from prior state to posterior state.

alpha_beta_predict

Predict step for scalar alpha-beta.

alpha_beta_steady_state_gains

Compute steady-state alpha-beta gains from the tracking index λ.

cfar_ca_false_alarm_probability

CA-CFAR inverse map from absolute threshold to false-alarm probability.

cfar_ca_multiplier_from_pfa

CA-CFAR multiplier from target false-alarm probability.

cfar_ca_pfa_from_multiplier

CA-CFAR inverse map from threshold multiplier to false-alarm probability.

cfar_ca_threshold

CA-CFAR absolute threshold from noise level, search window, and false-alarm target.

ewma_update

EWMA update with generic gain alpha.

ewma_update_power_of_two

EWMA update with power-of-two denominator, alpha = 1 / 2^shift.

kalman_cv_steady_state_gains

Steady-state gains for a 2-state scalar constant-velocity Kalman filter.

mad_spread

Median absolute deviation spread estimate with Gaussian consistency scaling.

nis_expected_value

Bar-Shalom chi-square expectation E[NIS] = m.

nis_gate_test

Test a measurement residual against a chi-square gate.

nis_gate_threshold

Chi-square gate threshold for the requested confidence and DOF.

nis_statistic

Scalar normalized innovation squared statistic.

normalized_innovation

Scalar normalized innovation ν / sqrt(S).