State estimation with a destination constraint using pseudo-measurements

The problem of state estimation with a destination constraint, in which only one point on a straight line is known, is considered. The existing estimation methods with linear equality constraint cannot be applied to produce constrained estimates due to the lack of full information of the straight line. Here, two pseudo-measurements are constructed to formulate the destination constraint. One, a noisy pseudo-measurement, uses the measured position as another point on the constraint line. In that case, the implicit constraint on the velocity components is approximated. The other, a noiseless pseudo-measurement, describes directly the deterministic relationship among position and velocity components, based on the constraint. These two measurements are augmented into the measurement vector and result in two different destination constraint Kalman filters (DCKF), both of which utilize the unscented Kalman filter (UKF) to handle measurement nonlinearities. In the DCKF with noisy pseudo-measurement, the unscented transform (UT) is applied to obtain the statistical properties of the augmented measurements before utilizing the UKF. In the DCKF with noiseless pseudo-measurement, both block and sequential processing methods are presented. Additionally, the constraint error is defined as a new measure to evaluate estimation performances with equality constraints. Simulations illustrate the effectiveness of the proposed methods.