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

Journal Article · Thu Aug 01 04:00:00 EDT 2019 · IEEE Signal Processing Letters

DOI:https://doi.org/10.1109/LSP.2019.2922620· OSTI ID:1532528

Zheng, Zongsheng ^[1]; Zhao, Junbo ^[2]; Mili, Lamine ^[3]; Liu, Zhigang ^[1]; Wang, Shaobu ^[4]

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1. Southwest Jiaotong University
2. Virginia Polytechnic Institute
3. Virginia Tech
4. BATTELLE (PACIFIC NW LAB)

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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1532528
• Report Number(s): PNNL-SA-144186
• Journal Information: IEEE Signal Processing Letters, Journal Name: IEEE Signal Processing Letters Journal Issue: 8 Vol. 26
• Country of Publication: United States
• Language: English

Related Subjects

Unscented Kalman filter
unbiased minimumvariance estimation
unknown inputs