Effects of modeling errors on the stability and innovations moments of kalman filters

The effects of modeling errors on the performance of Kalman filters are classified and analyzed for the scalar time-invariant continuous-time case. Sufficient conditions for filter divergence are presented showing that process instability and unbounded deterministic control inputs usually cause the filter to go unstable if the dynamic parameters are incorrect. For stable processes and bounded control inputs errors in the dynamic parameters normally cause the filter innovations process to cease being zero mean. Errors in the noise covariances normally have no effect on the filter stability or the innovations mean, but such errors have impact on the innovations "whiteness" and covariance. The paper results may be applied for development of practical guidelines for Failure Detection and Diagnosis problems in dynamic systems.