Target Location Using the Extended Kalman Filter

Abstract

The Kalman filter has earned its fame through its elegance, its compatibility with digital simulation, and its reasonable performance even when the somewhat restrictive assumptions on which it is based are not all met. Extensions of the Kalman filter are varied, and not all estimators dubbed Extended Kalman Filter (EKF) are equivalent. This chapter develops some filter extensions appropriate to target tracking, classification, and command architectures. These include estimation of essentially nonlinear and non-Gaussian motion models for targets, nonlinear conversion of range-bearing measurements into position measurements, and lack of true independence between target state and observation system errors. In target tracking, using models of target motion and a stream of measurements or observations, the Kalman filter provides the conditional distribution of the location of a target following an unpredictable path. From distribution we can not only accurately estimate the location of the target, but we can also place a capture region about the estimate that will contain the target with any pre-specified probability. The Kalman algorithm is based upon a linear-Gauss–Markov (LGM) model of the engagement. Even when there are nonlinearities in the engagement model, an expanded version of the Kalman filter (the EKF) generates plausible position estimates and capture regions. We will contrast realized performance with that predicted by the EKF. The shortcomings of the Kalman filter when used in command architectures are important, but in many cases they can be mitigated. In others alternative approaches like the GWE, explored in later chapters, are much more effective.