Kalman filtering with multiple nonlinear-linear mixing state constraints

This paper is devoted to the problem of state estimation for a class of dynamic system with multiple nonlinear-linear (NL) mixing state constraints. A computational algorithm was developed by C. Yang and E. Blasch to incorporate a positive definite quadratic form equality constraint into the Kalman filtering for the ground vehicle tracking. However, when the target tracked in multidimensional space, a single positive definite quadratic form constraint is not enough due to the involvement of other surface such as hyperboloid, paraboloid, or even plane. A analytic method of incorporating multiple nonlinear-linear mixing state constraints into the Kalman filter is presented here, and a sufficient condition is obtained that guarantee the existence of solution. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraints surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a nonlinear-linear mixing spacecraft positioning problem.