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Title: Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs

Abstract

This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.

Authors:
 [1];  [2];  [3];  [1];  [4]
  1. Southwest Jiaotong University
  2. Virginia Polytechnic Institute
  3. Virginia Tech
  4. BATTELLE (PACIFIC NW LAB)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1532528
Report Number(s):
PNNL-SA-144186
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
IEEE Signal Processing Letters
Additional Journal Information:
Journal Volume: 26; Journal Issue: 8
Country of Publication:
United States
Language:
English
Subject:
Unscented Kalman filter, unbiased minimumvariance estimation, unknown inputs

Citation Formats

Zheng, Zongsheng, Zhao, Junbo, Mili, Lamine, Liu, Zhigang, and Wang, Shaobu. Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs. United States: N. p., 2019. Web. doi:10.1109/LSP.2019.2922620.
Zheng, Zongsheng, Zhao, Junbo, Mili, Lamine, Liu, Zhigang, & Wang, Shaobu. Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs. United States. doi:10.1109/LSP.2019.2922620.
Zheng, Zongsheng, Zhao, Junbo, Mili, Lamine, Liu, Zhigang, and Wang, Shaobu. Thu . "Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs". United States. doi:10.1109/LSP.2019.2922620.
@article{osti_1532528,
title = {Unscented Kalman Filter-based Unbiased Minimum-Variance Estimation for Nonlinear Systems with Unknown Inputs},
author = {Zheng, Zongsheng and Zhao, Junbo and Mili, Lamine and Liu, Zhigang and Wang, Shaobu},
abstractNote = {This paper proposes an unscented Kalman filter (UKF)-based unbiased minimum-variance estimation (UMV) method for the nonlinear system with unknown inputs. By utilizing the statistical linerization, the nonlinear system and measurement functions are transformed into a “linear-like” regression form. The latter preserves the nonlinearity of the system and the measurement models. To this end, the unknown inputs can be estimated by the weighted least-squares. This “linear-like” regression form also allows us to resort to the UMV state estimation framework for the development of new nonlinear filter to handle unknown inputs. Specifically, two approaches have been developed: 1) given the estimated inputs, we derive a filter by minimizing the trace of the state error covariance matrix; 2) without input estimation, we derive the filter by minimizing the trace of the state error covariance matrix subject to a constraint imposed on the gain matrix. We prove that these two approaches provide the same results. Numerical results validate the effectiveness of the proposed method.},
doi = {10.1109/LSP.2019.2922620},
journal = {IEEE Signal Processing Letters},
number = 8,
volume = 26,
place = {United States},
year = {2019},
month = {8}
}