Kalman filter for discrete implicit systems

For an implicitly defined discrete system, a new implicit form of the Kalman filter is developed and an efficient numerical approach for its implementation is given. Unlike the traditional explicit approach, the implicit filter can be applied to ill-conditioned systems. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement than the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments