Efficient recursive state estimator for dynamic systems without knowledge of noise covariances

TLDR

The paper proposes an efficient recursive state estimator that operates without prior knowledge of noise covariances. The estimator, called extended forgetting factor recursive least squares (EFRLS), integrates the system dynamics and a forgetting factor into a least‑squares framework to compensate for unknown noise statistics. EFRLS achieves asymptotic performance comparable to a fully specified Kalman filter, outperforms existing methods when noise variance is misspecified, and remains robust to cross‑correlated or temporally dependent noise, as demonstrated by simulations that show it dominates standard FRLS and misspecified Kalman filtering.

Abstract

An efficient recursive state estimator for dynamic systems without knowledge of noise covariances is suggested. The basic idea for this estimator is to incorporate the dynamic matrix and the forgetting factor into the least squares (LS) method to remedy the lack of knowledge of noises. We call it the extended forgetting factor recursive least squares (EFRLS) estimator. This estimator is shown to have similar asymptotic properties to a completely specified Kalman filter state estimator. More importantly, the performance of EFRLS greatly exceeds that of existing filtering techniques when the noise variance is misspecified. In addition, EFRLS also performs well when there is cross-correlation between the process and measurement noise streams or temporal dependencies within those streams. Some discussions and a number of simulations are made to provide practical guidance on the choice of an optimal forgetting factor and evaluate the performance of the EFRLS algorithms, which strongly dominates that of the standard forgetting factor recursive least squares (FRLS) and some misspecified Kalman filtering.