Outlier-Robust Autocovariance Least-Squares Estimation via Iteratively Reweighted Least Squares

Accurate process and measurement noise covariances are indispensable for Kalman filtering, yet they are difficult to identify when the innovation used for calibration is intermittently corrupted by sensor outliers. Conventional autocovariance least-squares (ALS) estimates the noise covariances by matching empirical and theoretical innovation autocovariances, but its quadratic criterion can convert a few impulsive autocovariance entries into large covariance bias. This paper develops an outlier-robust ALS estimator, ALS-IRLS, for covariance identification under such contamination. ALS-IRLS casts ALS as a structured Huber M-estimation problem on the stacked multi-lag autocovariance equations and solves the induced weighted least-squares subproblems by iteratively reweighted least squares (IRLS) within the Riccati/gain fixed-point loop. This design preserves the information that separates process and measurement noise while bounding the influence of contaminated equations. Bounded-influence, threshold-sensitivity, local-convergence, admissibility, and amortized-complexity analyses are provided. Simulations under 15% contamination show that ALS-IRLS reduces covariance-estimation errors by over two orders of magnitude relative to ALS and yields downstream filtering accuracy close to the oracle Kalman filter, including against adaptive robust-filter baselines.