BEARINGS-ONLY AND DOPPLER-BEARING TRACKING USING INSTRUMENTAL VARIABLES

Bearings-only tracking (BOT) or Doppler and bearing tracking (DBT) are common passive sonar problems. The measurement equations are nonlinear and in order to apply the Kalman filter, it is either necessary to linearize the equations or embed the nonlinearities into the noise terms. The former sometimes leads to filter divergence while the latter produces biased estimates. A new formulation of BOT and DBT is given which has a constant state vector, and simplifies the tracking problem to one of constant parameter estimation. The solution is by the instrumental variable method. The instrumental variables are obtained from predictions based on past measurements and are therefore independent of the present noisy measurements. The result is a recursive, unbiased estimator. The theoretical developments are verified by simulation, which also shows that the new formulation leads to near optimal estimators whose errors are close to the Cramer-Rao lower bound (CRLB).