Performance-Specified Moving-Horizon State Estimation With Minimum Risk

Aghapour, Elahe; Farrell, A.

doi:10.23919/ecc.2018.8550605

Cited by 2 publications

(5 citation statements)

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“…The single‐epoch RAPS approach was proposed to choose a subset of measurements to estimate the state vector x k , where a subset is selected to have minimum risk of containing an outlier while achieving a specified accuracy. RAPS for the problem of state estimation in the presence of outliers within a fixed‐lag sliding window considers the performance constrained optimization problem:

\begin{matrix} right & left X^{⋆}, b^{⋆} = \underset{X, b}{argmin} C (X, b) \\ right & left subject to: J_{b} \geq J_{l} \\ right & left b_{i j} \in {0, 1}, \forall i = 1, …, L, j = 1, …, m, \end{matrix}

where J l is an user‐defined lower bound specified for the accuracy, as quantified by the Fisher information matrix for the trajectory X corresponding to the selected measurements:

J_{b} = {\bar{D}}^{⊤} Ψ {(b)}^{⊤} Ψ (b) \bar{D} .

The choice of J l is discussed in Section 5.2.…”

Section: Problem Formulation: Moving Horizon With Outliersmentioning

confidence: 99%

“…MH‐RAPS is closely related to MHE and SLAM, which also work within an optimization framework over a window of measurements, but MHE and SLAM do not include a measurement selection vector or a performance specification. A shorter and less comprehensive presentation of MH‐RAPS is presented in the work of Aghapour and Farrell . Relative to the work of Aghapour and Farrell, this paper makes several new contributions.…”

Section: Introductionmentioning

confidence: 99%

“…A shorter and less comprehensive presentation of MH‐RAPS is presented in the work of Aghapour and Farrell . Relative to the work of Aghapour and Farrell, this paper makes several new contributions. It has tutorial content explaining the interrelationships between the MHE, SLAM, and MH‐RAPS.…”

Section: Introductionmentioning

confidence: 99%

“…It includes a thorough discussion and analysis of MH‐RAPS. This paper presents a modified RAPS solution, applicable when only the diagonal elements of the information matrix are of interest for the performance specification, which is faster than the MH‐RAPS approach of Aghapour and Farrell . Finally, Aghapour and Farrell evaluated MH‐RAPS using simulated MATLAB data.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents a modified RAPS solution, applicable when only the diagonal elements of the information matrix are of interest for the performance specification, which is faster than the MH‐RAPS approach of Aghapour and Farrell . Finally, Aghapour and Farrell evaluated MH‐RAPS using simulated MATLAB data. This article includes experimental results for state estimation on a car utilizing real‐world GNSS Doppler and differential pseudorange data.…”

Section: Introductionmentioning

confidence: 99%

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Outlier accommodation in moving‐horizon state estimation: A risk‐averse performance‐specified approach

Aghapour

Farrell

2019

Adaptive Control & Signal

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Summary This paper presents a novel state estimation approach for linear dynamic systems when measurements are corrupted by outliers. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The standard approach combines outlier detection utilizing Neyman‐Pearson (NP) type tests with a Kalman filter (KF). This approach ignores all residuals greater than a designer‐specified threshold. When measurements with outliers are used (ie, missed detections), both the state estimate and the error covariance matrix become corrupted. This corrupted state and covariance estimate are then the basis for all subsequent outlier decisions. When valid measurements are rejected (ie, false alarms), potentially using the corrupted state estimate and error covariance, measurement information is lost. Either using invalid information or discarding too much valid information can result in divergence of the KF. An alternative approach is moving‐horizon (MH) state estimation, which maintains all recent measurement data within a moving window with a time horizon of length L. In MH approaches, the number of measurements available for state estimation is affected by both the number of measurements per time step and the number of time steps L over which measurements are retained. Risk‐averse performance‐specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This paper derives and formulates the MH‐RAPS solution for outlier accommodation. The paper also presents implementation results. The MH‐RAPS application uses Global Navigation Satellite Systems measurements to estimate the state of a moving platform using a position, velocity, and acceleration model. In this application, MH‐RAPS performance is compared with MH‐NP state estimation.

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\begin{matrix} right & left X^{⋆}, b^{⋆} = \underset{X, b}{argmin} C (X, b) \\ right & left subject to: J_{b} \geq J_{l} \\ right & left b_{i j} \in {0, 1}, \forall i = 1, …, L, j = 1, …, m, \end{matrix}

where J l is an user‐defined lower bound specified for the accuracy, as quantified by the Fisher information matrix for the trajectory X corresponding to the selected measurements: