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In Moving Horizon Estimation (MHE) the computed estimate is found by solvinga constrained finite-time optimal estimation problem in real-time at eachsample in a receding horizon fashion. The constrained estimation problem can besolved by, e.g., interior-point (IP) or active-set (AS) methods, where the maincomputational effort in both methods is known to be the computation of thesearch direction, i.e., the Newton step. This is often done using genericsparsity exploiting algorithms or serial Riccati recursions, but as parallelhardware is becoming more commonly available the need for parallel algorithmsfor computing the Newton step is increasing. In this paper a tailored,non-iterative parallel algorithm for computing the Newton step using theRiccati recursion is presented. The algorithm exploits the special structure ofthe Karush-Kuhn-Tucker system for the optimal estimation problem. As a resultit is possible to obtain logarithmic complexity growth in the estimationhorizon length, which can be used to reduce the computation time for IP and ASmethods when applied to what is today considered as challenging estimationproblems. Promising numerical results have been obtained using an ANSI-Cimplementation of the proposed algorithm running on true parallel hardware.Beyond MHE, due to similarities in the problem structure, the algorithm can beapplied to various forms of on-line and off-line smoothing problems.

An O(log N) Parallel Algorithm for Newton Step Computations with Applications to Moving Horizon Estimation