τ ‐EKF: Extended Kalman Filter With Sparse On‐Demand Residual Correction for Radar Manoeuvring Target Tracking

ABSTRACT

Conventional extended Kalman filters (EKFs) suffer from degraded performance in radar manoeuvring target tracking due to fixed noise covariances and accumulated linearisation errors. This paper proposes a τ ‐EKF integrating a sparse on‐demand residual correction guided by the Mahalanobis distance of the innovation vector. Unlike full‐time deep learning‐enhanced Kalman filters, the proposed method maintains a lightweight backbone EKF and activates a deep residual network only at high‐uncertainty moments, following Tao's Law: reserve capacity during stable periods and activate correction on demand. A bounded noise adaptation layer dynamically adjusts noise matrices with hard constraints to prevent divergence. The method is evaluated against five baselines—EKF, UKF, CKF, IMM‐EKF and a full‐time CNN‐based adaptive EKF—on a simulated radar dataset. The τ ‐EKF achieves a position root‐mean‐square error (RMSE) of 2.005 m, improving by 27.5% over the baseline EKF and 1.1% over the full‐time adaptive EKF, while requiring only 59.4% network activation. Ablation studies confirm that adaptive noise estimation contributes the most significant accuracy gain and the Mahalanobis trigger achieves 95.6% of the full‐time correction accuracy while activating the correction network for only about 60% of the time steps. PCRLB analysis validates near‐optimal performance. With sub‐ms inference, the τ ‐EKF is suited for embedded real‐time radar systems.