| Popis: |
Conventional first order approximations used in extended Kalman filters (EKFs) do not accurately describe the statistics of the estimate error vector when measurement faults are present. This paper shows that run-to-run variations in the estimator gain matrix are the primary cause of inaccuracy. In response, we derive new, generalized expressions for the mean and covariance matrix of the EKF estimate error vector that account for matrix variations. The results of this work are relevant to integrity analysis of fault detection algorithms, specifically, false alarm and missed detection probability assessments. In addition, they provide an analytical alternative to Monte Carlo simulation for performing trade studies and sensitivity analysis of faulted systems. The new methods are compared against Monte Carlo simulation for a two-dimensional navigation problem. |
