Sequential Constraint Estimation: Implementation Modifications

In recent works, the first author has developed a constraint estimation technique that can be applied to the kinematic tracking problem. This a posteriori technique maintains an unconstrained estimate based solely on the measurements while the constrained estimate is computed, if necessary, at each time step. This technique has been expanded to incorporate nonlinear systems and time-varying systems. In this paper, we modify the original approach to accommodate several implementation issues that have arisen in the discussions about this work. The first modification of this approach is to utilize a probability-based estimator, the extended Kalman filter, as the unconstrained estimator as opposed to the deterministic unconstrained estimator in this work. By showing a minimal variation in performance of the algorithm, the constrained estimator can be shown to be a simple addition to standard tracking estimation routines.