Gain-constrained Kalman filtering for linear and nonlinear systems

This paper considers the state-estimation problem with it constraint on the data-injection gain. Special cases of this problem include the enforcing of a linear equality constraint in the state vector, the enforcing of unbiased estimation for systems with unknown inputs, and simplification of the estimator structure for large-scale systems. Both the one-step gain-constrained Kalman predictor and the two-step gain-constrained Kalman filter are presented. The latter is extended to the nonlinear case, yielding the gain-constrained unscented Kalman filter. Two illustrative examples are presented.