Constrained Kalman Filtering: A Compensating Approach

Kalman filtering can produce unrealistic values and can prevent accurate convergence as the technique does not naturally include safeguards that exclude unphysical states. It can be demonstrated that without implementing constraints, or even some existing constraint strategies, that the filter could converge incorrectly. Currently available approaches to constraining the estimated state variables are arbitrary. For example, a simple way to constrain a violating state variable, is to reset its value to the constraint limit, the effect of which is a reduction of the importance of the measurement. The proposed constraining method attempts to preserve the importance of the observation/measurement in the fused estimate. This method compensates the changes in the constrained state variables by adjusting the non-constrained state variables in order to force the net change in measurement estimate to zero.