A Closed-Form Estimator for Bearings-Only Fusion of Heterogeneous Passive Sensors

Bearings-only target motion analysis with fusion of heterogeneous passive sensors with and without propagation delay attempts to estimate a target trajectory by fusing bearings from two sensors: a sensor whose measurements have negligible propagation delay and a sensor with measurements that have non-negligible propagation delay. This problem is highly nonlinear and challenging, particularly due to the fact that the propagation delay is unknown and is highly coupled with the unknown target states. This paper proposes a novel closed-form instrumental variable based batch estimator for this problem that is computationally fast. The estimator is derived by writing pseudolinear type equations for the error vector—difference between the true target state and a nominal solution. A theoretical bias and mean square error analysis of the proposed estimator is carried out which provides insight into the performance of this estimator. Results indicate that this is a computationally efficient algorithm that is able to produce comparable performance to the maximum likelihood estimator and achieves the Cramer Rao lower bound.