Note on Autocorrelation of the Residuals of the NCV Kalman Filter Tracking a Maneuvering Target - Part 2
Paul A. Miceli, William Dale Blair, Peter Willett · 2022 25th International Conference on Information Fusion (FUSION) · 2022
When a target is not maneuvering, the residuals from the nearly constant velocity (NCV) Kalman filter are inde-pendent, zero mean, and Gaussian. When the target maneuvers, the residuals are no longer independent, unbiased or Gaussian. A chi-squared (χ2) test is a common method to detect maneuvering targets, however, the correlation between consecutive residuals is lost by the calculation of the χ2statistic. In this work, two methods that utilize the correlation between consecutive residuals are explored for the purpose of detecting weak maneuvers. First, a recursion is developed to compute the full cross correlation for an arbitrary number of residuals under the hypothesis that the target is maneuvering. This result is compared in a hypothesis test to the null hypothesis that the target is not maneuvering. Second, an arbitrary size window of residual errors is used to form a least squares estimate of the bias (i.e. acceleration), and the significance of that estimate is tested against the corresponding covariance. Both methods are shown to be an improvement over a standard χ2test.