Tracking an Underwater Target with Unknown Measurement Noise Statistics Using Variational Bayesian Filters

This paper considers a bearings-only tracking problem using noisy measurements of unknown noise statistics from a passive sensor. It is assumed that the process and measurement noise follows the Gaussian distribution where the measurement noise has an unknown non-zero mean and unknown covariance. Here an adaptive nonlinear filtering technique is proposed where the joint distribution of the measurement noise mean and its covariance are considered to be following normal inverse Wishart distribution (NIW). Using the variational Bayesian (VB) method the estimation technique is derived with optimized tuning parameters i.e, the confidence parameter and the initial degree of freedom of the measurement noise mean and the covariance, respectively. The proposed filtering technique is compared with the adaptive filtering techniques based on maximum likelihood and maximum aposteriori in terms of root mean square error in position and velocity, bias norm, average normalized estimation error squared, percentage of track loss, and relative execution time. Both adaptive filtering techniques are implemented using the traditional Gaussian approximate filters and are applied to a bearings-only tracking problem illustrated with moderately nonlinear and highly nonlinear scenarios to track a target following a nearly straight line path. Two cases are considered for each scenario, one when the measurement noise covariance is static and another when the measurement noise covariance is varying linearly with the distance between the target and the ownship. In this work, the proposed adaptive filters using the VB approach are found to be superior to their corresponding adaptive filters based on the maximum aposteriori and the maximum likelihood at the expense of higher computation cost.