An Online Performance Index for the Kalman Filter

In this article, we propose a performance index (PI) on the point rather than batches to quantify the real-time performance of the Kalman filter (KF). To avoid the problem of describing KF performance that may require actual values, we attempt to find a new index that does not require actual values. The uncertainty is the main factor that makes the KF deviate from the optimal estimate. Uncertainty information is extracted from the observations, the effect of uncertainty is projected onto the KF, and the degree of deviation from the optimal estimate is then obtained, which is unitized to reflect the performance. The main advantage of the proposed PI is the ability to quantify the KF performance in real time without the need for actual values and without the need to know the type and source of uncertainty. Two numerical examples and a practice-oriented case study are given to illustrate the effectiveness of the proposed approach. The results show that the PI provides a good representation of the performance.