Comparison of Two Kalman Filters: Classic and with the Signal Noise Delaying the Observation Noise

Abstract

Recently, it was justified that a linear state-observation system with the signal noise delaying the observation noise is more adequate in communication with considerably distanced spacecraft rather than the system with the ignored delay. However, the difference between the respective estimates may become negligible during some time duration. If so, taking a delay into account becomes inefficient because it does not provide any advantage after a certain time duration but makes calculations heavier. Therefore, it is important to know whether there are cases when the difference continues to stay valid and, thus, causes a nonrecoverable loss of information. In this paper, using numerical methods, we compare two Kalman filters—classic and with the signal noise delaying the observation noise. We demonstrate that there are cases when the mean square difference of the best estimates over these systems is asymptotically nonzero. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.