An unbiased estimator for bearings-only tracking and Doppler-bearing tracking

The objective of both bearings-only tracking (BOT) and Doppler-bearing tracking (DBT) is to obtain the target trajectory based on bearings, and Doppler and bearing measurements respectively, from an observer to the target. The BOT and DBT problems are nontrivial because the measurement equations are nonlinear. The pseudo linear formulation allows a linear estimator to solve for the solution, but the solution obtained is biased. This paper proposes an estimator based on the pseudo linear equations that produce an unbiased solution. The proposed method applies least-squares minimization on the pseudo linear equations with appropriate constraints on the unknown parameters. Simulations are included to illustrate the performance of the proposed estimator. The proposed estimator achieves the Cramer-Rao lower bound (CRLB) for Gaussian noise around small error region.