A TLS-Motivated Non-Iterative Robust Square-Root Cubature Kalman Filter for Bearings-Only Tracking

Measurement outliers remain a major source of performance degradation in nonlinear bearings-only target tracking, where a few corrupted observations can produce large innovations and even trigger filter divergence. This paper proposes a non-iterative robust square-root cubature Kalman filter (RSCKF) for bearings-only tracking with measurement outliers. Motivated by a TLS-type errors-in-variables interpretation of the pseudo-linear bearings-only measurement model, robustness is introduced through a closed-form equivalent weighting and rejection mechanism within the square-root cubature Kalman filtering framework. The proposed method preserves the derivative-free square-root filtering structure in implementation and avoids inner fixed-point or variational iterations. For the scalar bearing update considered in this paper, the weighting thresholds are determined from a normalized innovation statistic using prescribed confidence levels, so that moderate outliers are down-weighted, and extreme ones are rejected. Simulations under nominal, moderately contaminated, and severely contaminated measurement conditions show that the proposed RSCKF achieves accuracy comparable to the standard square-root cubature Kalman filter (SCKF) in the Gaussian case, while providing improved robustness and only a small computational overhead under the measurement outliers. Under the most severe contamination setting, where 15% of the bearings are corrupted by outliers with a standard deviation 30 times the nominal noise level, RSCKF limits the position-MSE increase to 8.4% relative to the nominal case and achieves the lowest position MSE among the seven compared filters, whereas the standard SCKF deteriorates by more than two orders of magnitude. It is also the only filter whose time-averaged ANEES remains within the consistency band used in the Monte Carlo evaluation, with a computation time close to that of the baseline CKF.