An Analysis of the Kalman, Extended Kalman, Uncented Kalman and Particle Filters with Application to DOA Tracking

摘要

Tracking the Direction of Arrival (DOA) Estimation of a multiple moving sources is a significant taskwhich has to be performed in the field of navigation, RADAR, SONAR, Wireless Sensor Networks (WSNs)etc. DOA of the moving source is estimated first, later the estimated DOA using Estimation of SignalParameters via Rotational Invariance Technique (ESPRIT) is used as an initial value and will be providedto any of the Kalman filter (KF), Extended Kalman filter (EKF), Uncented Kalman filter (UKF) andParticle filter (PF) algorithms to track the moving source based on the motion model governing the motionof the source. ESPRIT algorithm used for the estimation of the DOA is accurate but computationallycomplex. The present comparative study deals with analysis of tracking the DOA Estimation Of Noncoherent,Narrowband moving sources under different scenarios. The KF (Kalman Filter) is used when thelinear motion model corrupted by Gaussian noise, The Extended Kalman Filter (EKF), an approximatedand non-linear version of the KF is used whenever the motion model is slightly non-linear but corrupted byGaussian noise. The process of linearization involves the explicit computation of Jacobian andapproximation using Taylor’s series is computationally complex and expensive. The computationallycomplex and expensive procedures of EKF viz explicit computation of Jacobian and approximation usingTaylor series are disadvantageous. In order to minimize the disadvantages of EKF are overcomed by theusage of UKF, which uses a transform technique viz Unscented Transform to linearize the non-linearmodel corrupted by Gaussian noise and Particle Filter (PF) Algorithms are used when the resultant modelis highly non-linear and is corrupted by non-Gaussian noise. Further the literature is concluded withappropriate findings based on the results of the studies of different algorithms in different scenarios carriedout.