State estimation with nonlinear inequality constraints based on unscented transformation

The state of some practical dynamic systems satisfies constraints, which can be utilized to improve the performance of state estimation. State estimation with nonlinear inequality constraints is a challenging problem. Projection methods are widely used to solve this problem. In this paper, a projection method is formulated as a special nonlinear function. Based on this formulation, unconstrained estimated states can be easily projected into the feasible constraint region through unscented transformation (UT), and both the constrained mean and co-variance can be obtained. An approach is proposed to reduce the complexity of this projection process and a closed-form solution is derived for one-dimensional constraints. To solve the problem that the constrained covariance may be ill-conditioned in UT-based approaches, a modification of the covariance is also proposed to account for necessary uncertainties. Two illustrative scenarios for ground moving target tracking are simulated to demonstrate the effectiveness and the efficiency of the proposed approaches.