An Unbiased Filtering Scheme Applied in the Underwater Passive Target

Bearing-only or time difference of arrival and bearing tracking are common passive target tracking problems. The problem of how to track underwater target using bearings and time difference of arrival is presented and analyzed. It is well known that the measurement equations are nonlinear and in order to apply the Kalman filter, the equations are linearized or embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence while the latter produces biased estimates. Therefore, an unbiased staged filtering scheme in which an instrumental variable is put forward to eliminate the bias of least squares estimator is presented. The instrumental variables are obtained from predictions based on past measurements. The result is a recursive, unbiased. The theoretical developments are verified by simulation, which also shows that the new formulation leads to near optimal filtering scheme whose estimate states are very close to the target true states