Efficient Reformulation of Moving Horizon Approach for Nonlinear Constrained State Estimation

One of the open problems in the area of state estimation is nonlinear state estimation. Several approaches have been proposed to solve this problem. Moving Horizon Estimation (MHE) is one possible approach and has been shown to provide the most reliable estimates in several example problems; albeit at a high computational price. In this paper, an alternate formulation for moving window estimation is provided. In the proposed formulation, the states are used as decision variables instead of the noise variables that are used in a MHE formulation. This removes the use of an integrator inside the optimizer and results in much better computational properties than the MHE approach.

There are a number of computationally efficient approaches for addressing estimation using nonlinear process models. The most commonly cited reason for using moving window formulation is the ability to incorporate constraints in the estimation problem. Recursive estimation approaches that are able to incorporate constraints have started to appear in the literature. The most important advantage of using a large window size is that this mitigates problems due to poor initialization in constrained state estimation. However, the price that one usually pays for this robustness is large computational cost. The proposed approach provides a possible direction for addressing both the robustness and computational concerns.

A series of simulation examples from the literature are used to benchmark the proposed estimator. It is shown that the proposed estimator is robust to poor initialization and provides improved estimates with increasing window size. It is also shown that the improved estimates are achieved with small window sizes compared to results reported in the literature. Attributes of the algorithm that are important in reducing the window size when compared to MHE are discussed in detail.