Moving horizon estimation for staged QP problems

Abstract

Abstract-This paper considers moving horizon estimation (MHE) approach to solution of staged quadratic programming (QP) problems. Using an insight into the constrained solution structure for the growing horizon, we develop a very accurate iterative update of the arrival cost in the MHE solution. The update uses a quadratic approximation of the arrival cost and information about the previously active or inactive constraints. In the absence of constraints, the update is the familiar Kalman filter in information form. In the presence of the constraints, the update requires solving a sequence of linear systems with varying size. The proposed MHE update provides very good performance in numerical examples. This includes problems with ℓ1 regularization where optimal estimation allows us to perform online segmentation of streaming data.

Metamorphic moving horizon estimation

“…For (6), we have x e k ∈ X , w k ∈ W, where X = X ×E , W = W × V. The variables (x e k , w k , y k , ν k ) in (6) represent the parameters of the real augmented process, and we denote (χ e k , ω k , η k , υ k ) and ( x e k , w k , y k , ν k ) as the corresponding decision variables and the optimal solutions in the optimization, respectively. For notational ease, we still use y k and ν k to denote the optimal output prediction and fitting error for (6) as for (1). For system (6), consider the constrained estimation problem…”

“…Different from [3], the heading of the vehicle is assumed to be unknown. Assume the input is zero and the sampling period T = 0.5 s. We design a pre-estimator with Firstly, for system (6), we compare the metamorphic MHE in Section II (with λ taking the value of 0.1, 0.5) with the the unbiased FIR filter in [13]. As such, we choose Q = I 4 ; R = 0.5I 3 ; M = 10I 7 , and the rolling horizon length to be 20 in both metamorphic MHE and FIR.…”

Moving horizon fault-tolerant traffic state estimation for the Cell Transmission Model

“…Such constraints include physical model limitations, e.g. lower and upper bounds on the state variables, or artificially added constraints that aim to capture some insights regarding the dynamics such as state transition smoothness or sparse state changes [15]. In this work we exploit the MHE approach to incorporate additional constraints that provide sensor-fault tolerance.…”

“…[15], [16]). However, under a linear model with Gaussian noise and no constraints the AC is derived in closed form as:…”

Multiple window moving horizon estimation

“…The development will be in terms of general causal descriptor systems, which includes the standard state space representation as a special case. The potential of the new estimation algorithm will be demonstrated with an example showing a significant reduction in both computation time and numerical errors compared to conventional MHE.Recently in [11] an approximation hypothesis was used to derive a simple arrival cost update for general staged QP problems with sufficiently large horizon lengths by assuming that the active and inactive state constraints of the last state in the moving horizon window remain respectively active or…”