Iterative Method of Maximum Likelihood for State Estimation with Inequality Constraints

An iterative method of incorporating state inequality constraints in kalman filter is proposed. The constrained filter is derived as the maximum posteriori solution to the constraints, a penalty function is used to transform the inequality constraints, and the solution to the set of estimates is obtained by using Gaussian Newton method. At each time step the unconstrained kalman filter solution is projected onto the state Constraint surface. A target tracking example is presented demonstrating the efficiency of the algorithm.