Kalman filtering : With a radar tracking implementation

Abstract: The Kalman filter algorithm can be applied as a recursive estimator of the state of a dynamic system described by a linear difference equation. Given discrete measurements linearly related to the state of the system, but corrupted by white Gaussian noise, the Kalman filter estimate of the system is statistically optimal with respect to a quadratic function of the estimate error. The first objective of this paper is to give deep enough insight into the mathematics of the Kalman filter algorithm to be able to choose the correct type of algorithm and to set all the parameters correctly in a basic application. This description also includes several examples of different approaches to derive and to explain the Kalman filter algorithm. In addition to the mathematical description of the Kalman filter algorithm this paper also provides an implementation written in MATLAB. The objective of this part is to correctly replicate the target tracker used in the surveillance radar PS-90. The result of the implementation is evaluated using a simulated target programmed to have an aircraft-like behaviour and done without access to the actual source code of the tracker in the PS-90 radar