A new algorithm for filtering a correlated measurement sequence

One important assumption associated with the standard Kalman filter is that the measurement sequence is white noise and thus uncorrelated. In practice, there exists evidence that measurement sequences are correlated in time and significant discrepancies may arise if such correlation is neglected. Although some methods have been already proposed to solve this problem, some difficulty has been encountered when applying them to actual problems. In this paper, a new Kalman filter algorithm is presented. The major advantage of the algorithm is its concise form and its ease of implementation. The correlated measurement sequence is also given for Bayes filtering, an alternative form of the Kalman approach.