Linear Quadratic Recursive Estimation Scheme Using Bayesian Inference for Navigation Systems

In the ocean environment, two dimensional Range & Bearings Target Motion Analysis (TMA) is generally used. In the underwater scenario, the active sonar, positioned on a observer, is capable of sensing the sound waves reflected from the target in water. The sonar sensors in the water pick up the target reflected signal in the active mode. The observer is assumed to be moving in straight line and the target is assumed to be moving mostly in straight line with maneuver occasionally. The observer processes the measurements and estimates the target motion parameters, viz., Range, Bearing, Course and Speed of the target. It also generates the validity of each of these parameters. Here we try to apply Kalman Filter for the sea scenario using the input estimation technique to detect target maneuver, estimate target acceleration and correct the target state vector accordingly.     There are mainly two versions of Kalman Filter – a Linearised Kalman Filter (LKF) in which polar measurements are converted into Cartesian coordinates and the well-known Extended Kalman Filter (EKF). Recently S. T. Pork and L. E. Lee presented a detailed theoretical comparative study of the above two methods and stated that both the methods perform well. Here, EKF is used throughout.