A reduced order extended Kalman filter for sequential images containing a moving object

Abstract

The extended Kalman filter (EKF) is applied to the reduction of noise in sequential images containing a moving object and to the estimation of the object's velocity. A computationally tractable approximation of the EKF, called the parallel extended Kalman filter (PEKF), is generated. The PEKF consists of a parallel bank of third-order EKFs, operating on the Fourier coefficients of the image, followed by a finite impulse response filter. The PEKF is shown to converge to the optimal (in the mean square sense) algorithm in the limit as the velocity estimation errors approach zero. The performance of the PEKF is demonstrated for very low signal-to-noise ratio (SNR) images. The PEKF also provides a natural setting for tracking slow changes in the object (real or apparent) and its velocity, since these variations are included in the model. The relation of the PEKF to another frequency domain algorithm for velocity estimation is discussed. The algorithm is illustrated by application to an example and its performance is demonstrated in the presence of velocity estimation errors.