Constrained Kalman Filtering: Improving Fused Information Retention During Constraining

Abstract

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. The approach is implemented for the extended Kalman filters. The method is using a gas phase reaction in a Continuously Stirred Tank Reactor, with the state variables consisting of three species concentrations and the measurement is a pressure measurement with a known relationship to the state variables. The performance of the method is compared to currently available constraining techniques.