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In this paper, the problem of parallel implementation of the square-root Kalman filters is addressed. In the system level, our approach is to apply systolic type processor arrays as basic building blocks to speed up the matrix operations required in each iteration. Specifically, by utilizing a sparse matrix structure, we derive a simple systolic array configuration which is able to solve a rotation operation very efficiently. To maximize the parallelism, we also exploit an inter-array pipelining scheme through the overlapping of execution between successive processor arrays. As a result, several modules can be tightly coupled to form a dedicate Kalman Filter processor for real time applications. We estimate that with O(n2) processors, it would take O(4n+3r-3) time units to complete one Kalman filter iteration, where n is number of states and r is number of inputs.