Description of an alpha-beta Filter in Cartesian Coordinates

Abstract : A procedure for determining the mean and covariance errors in an alpha-beta filter operating in cartesian coordinates was found. The results obtained from this procedure were compared to an alpha-beta filter operating in polar coordinates. Assuming that the input measurements in polar coordinates were Gaussian distributed, it was shown that at the output of the coordinate transformations the noise could be approximated accurately by a Gaussian distribution for typical radar data. Closed-form solutions under steady-state conditions were found for the output covariances for the polar coordinate filter and for the cartesian coordinate filter when the target is stationary. These covariances depended upon alpha, beta, and the measurement variances. For moving targets, the cartesian coordinate filter yielded output covariances which were nonstationary. Their values depended upon alpha, beta, measurement variances, target trajectory, target speed, and sampling time. The mean errors were discussed. Under fading conditions both the mean and covariance errors increased during the fading time.