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This paper considers a bearings-only tracking problem using noisymeasurements of unknown noise statistics from a passive sensor. It is assumedthat the process and measurement noise follows the Gaussian distribution wherethe measurement noise has an unknown non-zero mean and unknown covariance. Herean adaptive nonlinear filtering technique is proposed where the jointdistribution of the measurement noise mean and its covariance are considered tobe following normal inverse Wishart distribution (NIW). Using the variationalBayesian (VB) method the estimation technique is derived with optimized tuningparameters i.e, the confidence parameter and the initial degree of freedom ofthe measurement noise mean and the covariance, respectively. The proposedfiltering technique is compared with the adaptive filtering techniques based onmaximum likelihood and maximum aposteriori in terms of root mean square errorin position and velocity, bias norm, average normalized estimation errorsquared, percentage of track loss, and relative execution time. Both adaptivefiltering techniques are implemented using the traditional Gaussian approximatefilters and are applied to a bearings-only tracking problem illustrated withmoderately nonlinear and highly nonlinear scenarios to track a target followinga nearly straight line path. Two cases are considered for each scenario, onewhen the measurement noise covariance is static and another when themeasurement noise covariance is varying linearly with the distance between thetarget and the ownship. In this work, the proposed adaptive filters using theVB approach are found to be superior to their corresponding adaptive filtersbased on the maximum aposteriori and the maximum likelihood at the expense ofhigher computation cost.

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