Abstract: The stability of a recursive estimator process (e.g., a Kalman filter is assured for long time periods by periodically resetting an error covariance P(tn) of the system to a predetermined reset value Pr. The recursive process is thus repetitively forced to start from a selected covariance and continue for a time period that is short compared to the system's total operational time period. The time period in which the process must maintain its numerical stability is significantly reduced as is the demand on the system's numerical stability. The process stability for an extended operational time period To is verified by performing the resetting step at the end of at least one reset time period Tr whose duration is less than the operational time period To and then confirming stability of the process over the reset time period Tr.