Smoothly Constrained Unscented Kalman Filter

For the uncertainty and nonlinearity of the nonlinear dynamic system, by implementing the measurement constraints into the unscented Kalman filtering routine, the smoothly constrained unscented Kalman filter (SCUKF) is proposed in this paper. To deal with the soft constraints, the statistics of the modified prior probability density function (PDF) is approximated via the numerical method. The sampled sigma points is restricted into the feasible area by the global optimal solution. Hence, the posterior PDF of interest can be characterized well with a heavier tailor. Finally, the filtering performance is compared and analyzed in the two simulated scenarios: the univariate nonstationary growth model and the bearings only maneuvering target tracking. Simulation results demonstrate the superiority in respect of the accuracy and robustness.