A novel unbiased algorithm for two-station bearings-only passive location and tracking

The Extended Kalman Filter (EKF) algorithm is easy to be affected by the initial state value and the pseudo linear equation based algorithm will result in biased solution. A new asymptotically unbiased location and tracking algorithm with bearings-only measurements by two stations is proposed to solve these problems. The proposed algorithm introduces the correlation matrix of the observation error matrix into constraint condition. It uses constraint least squares minimization on the pseudo linear equation which includes quadratic constraint about the state vector and the state estimate can be got by taking a generalized eigen-decomposition to a pair of matrix pencil.