Adaptive Unscented Kalman Filter for Target Tracking with Unknown Time-Varying Noise Covariance

TLDR

The unscented Kalman filter is widely used for nonlinear target tracking but its performance degrades when the noise covariance is mismatched. This paper proposes a new adaptive UKF scheme to address time‑varying noise covariance problems and overcome limitations of existing adaptive UKFs. The method derives a linear matrix equation from the cross‑correlation of innovation and residual sequences to estimate process noise covariance in real time, and uses redundant measurements to estimate measurement noise covariance independently of the state estimate. Simulations show that the proposed adaptive UKF outperforms both the standard UKF and current adaptive UKFs under time‑varying noise covariances, yielding higher tracking accuracy and stability.

Abstract

The unscented Kalman filter (UKF) is widely used to address the nonlinear problems in target tracking. However, this standard UKF shows unstable performance whenever the noise covariance mismatches. Furthermore, in consideration of the deficiencies of the current adaptive UKF algorithm, this paper proposes a new adaptive UKF scheme for the time-varying noise covariance problems. First of all, the cross-correlation between the innovation and residual sequences is given and proven. On this basis, a linear matrix equation deduced from the innovation and residual sequences is applied to resolve the process noise covariance in real time. Using the redundant measurements, an improved measurement-based adaptive Kalman filtering algorithm is applied to estimate the measurement noise covariance, which is entirely immune to the state estimation. The results of the simulation indicate that under the condition of time-varying noise covariances, the proposed adaptive UKF outperforms the standard UKF and the current adaptive UKF algorithm, hence improving tracking accuracy and stability.