Estimation of System Parameters Using Kalman Filter and Extended Kalman Filter

In 1960, Sir R E Kalman published his famous paper describing a solution to discrete data linear filtering problem. Since then there has been advances in digital computing and Kalman filter has been subjected to extensive research and application, particularly in the area of autonomous or assisted navigation. This paper gives a brief introduction on Kalman filter, the equations that can be used for discrete stochastic systems which has additive white Gaussian noise present that models ‘unpredictable disturbances’ of the system. We then have simulation results of a system considered. However in real time scenarios we might also encounter non-linear systems and Kalman filter is not a good choice for such systems. So we go in for extended Kalman filter that linearizes the non-linear parameters about its mean and covariance using Jacobian matrices, and then using the same algorithm as of Kalman Filter. This algorithm is implemented on a target moving with a known trajectory with Gaussian noise introduced in the measurements. With the help of this algorithm we have tried to minimize the error in the measurements which is shown in the simulation results. We have also explained about various tuning factors that affect the estimation part and showed how these values stabilise after few iterations.