Abstract
Although moving horizon estimation (MHE) is a very efficient technique for estimating parameters and states of constrained dynamical systems, however, the approximation of the arrival cost remains a major challenge and therefore a popular research topic. The importance of the arrival cost is such that it allows information from past measurements to be introduced into current estimates. In this paper, using an adaptive estimation algorithm, we approximate and update the parameters of the arrival cost of the moving horizon estimator. The proposed method is based on the least-squares algorithm but includes a variable forgetting factor which is based on the constant information principle and a dead zone which ensures robustness. We show by this method that a fairly good approximation of the arrival cost guarantees the convergence and stability of estimates. Some simulations are made to show and demonstrate the effectiveness of the proposed method and to compare it with the classical MHE.
Highlights
Since the 1960s, the state estimation of systems by a moving horizon approach has been highlighted. e dazzling success of this estimation technique is based on its ability to explicitly take into account the constraints on the estimate of variables of a dynamic system [1,2,3]
In [7], the authors focus on distributed moving horizon estimation (DMHE) for a class of two-time-scale nonlinear systems described in the Journal of Control Science and Engineering framework of singularly perturbed systems
The moving horizon estimation was developed to take into account a certain amount of data and possibly to make dynamic updates of certain parameters in an estimation window moving in time
Summary
Since the 1960s, the state estimation of systems by a moving horizon approach has been highlighted. e dazzling success of this estimation technique is based on its ability to explicitly take into account the constraints on the estimate of variables of a dynamic system [1,2,3]. In [13], the authors proposed to use the Kalman filter approach for updating the term of the arrival cost (in particular the weighting matrix) for the case of linear systems, leading to an inadequate approximation of the weighting matrix leading to relatively poor estimates due to a Gaussian distribution of the Kalman filter. To overcome this problem, the authors in [14] proposed an iterative scheme for updating the arrival cost using the information on the active or inactive constraints from the previous iteration and a quadratic approximation.
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