Least squares algorithms for constant acceleration target tracking

A unified treatment of several least squares (LS) algorithms is presented for bearings-only tracking of a target moving at constant acceleration. The close link between the maximum likelihood (ML) estimator and other nonlinear and "linearized" LS algorithms is explored under the assumption of Gaussian bearing noise. In this context, a new asymptotically unbiased closed-form instrumental variables (IV) algorithm is derived. Reduced-bias total least squares (TLS) and constrained TLS (CTLS) algorithms are developed. The equivalence of the ML algorithm to the structured TLS (STLS) algorithm is established. Simulation examples are provided to demonstrate the improved performance of the IV and TLS estimators vis-a-vis the pseudolinear estimator.