State estimation for equality-constrained linear systems

We address the state-estimation problem for linear systems in a context where prior knowledge, in addition to the model and the measurements, is available in the form of an equality constraint. First, we investigate from where an equality constraint arises in a dynamic system. Then, the equality-constrained Kalman filter (ECKF) is derived as the solution to the equality-constrained state-estimation problem and compared to alternative algorithms. These methods are investigated in an example. In addition to exactly satisfying an equality constraint on the system, ECKF produce more accurate and more informative estimates than the unconstrained estimates.