Note on Autocorrelation of the Residuals of the NCV Kalman Filter Tracking a Maneuvering Target - Part 2

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 (χ
²
) test is a common method to detect maneuvering targets, however, the correlation between consecutive residuals is lost by the calculation of the χ
²
statistic. 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 χ
²
test.