Generalized bias compensated pseudolinear Kalman filter for colored noisy bearings-only measurements

Bias compensated pseudolinear Kalman filter (BC-PLKF) has been shown to solve the bias problem of pseudolinear Kalman filter (PLKF) and outperform Extended Kalman Filter (EKF) and many others in bearings-only target estimation applications with a low computational cost. However, BC-PLKF assumes that measurement noise is white, which is not a valid approximation for some applications such as weather-vane-used guided missiles where wind disturbance appears as a strongly time-correlated measurement noise, estimators performing high-frequency measurement updates, or cascaded Kalman filter-based algorithms. When the well-known noise augmentation method is applied to BC-PLKF, no straightforward solution for the bias compensation is available. First, process noise and observer matrix become coupled leading to unique bias. Second, the measurement autocovariance turns into zero whose inverse is used at the bias compensation step of BC-PLKF. Therefore, a bias analysis is performed for PLKF where the measurement noise is colored. Moreover, the generalized BC-PLKF algorithm (GBC-PLKF) for colored noise-corrupted measurements is derived. Simulations are performed to compare performances of GBC-PLKF, EKF, Cubature Kalman Filter (CKF), BC-PLKF, and colored noise augmented EKF and CKF (C-EKF and C-CKF) with typical air-to-surface missile engagement scenarios. Results verify that GBC-PLKF outperforms all comparison filters with a low computational cost for bearings-only estimation applications.