The performance of the conventional bearings-only tracking (BOT) from a single passive sensor hinges on the sensor platform maneuvers. This paper presents a new BOT approach based on fusion from two heterogenous bearings-only sensors residing on the same moving or stationary platform. The two sensors are an ESM/EO with negligible propagation delay and an acoustic sensor with significant propagation delay. The time difference between the reception times of the two sensors (corresponding to the same emission time) is the acoustic propagation delay. Since target range information is contained in the acoustic propagation delay (which is not known but can be estimated), the target state is shown to be completely observable even when the platform is stationary. The observability is studied in this paper via the Fisher information matrix (FIM).

Two estimators are developed. They are the maximum likelihood (ML) estimator for batch estimation and the out-of-sequence measurements fusion from acoustic and ESM/EO sensors (OOSM-AE) for recursive estimation. It shows that the ML estimator for batch estimation attains the Cramer´-Rao lower bound (CRLB)– it is statistically efficient–except in cases with a small number of measurements and the target heading close to the bearing from the sensor platform. The OOSM-AE is developed to handle out-of-sequence measurements (OOSM) due to the acoustic propagation delay. It consists of an unscented Kalman filter (UKF) to handle the in-sequence ESM/EO measurements and an OOSM unscented Gauss-Helmert filter (OOSM-UGHF) to handle the out-of-sequence acoustic measurements. Simulation results are presented to demonstrate the performance of this new BOT approach.