A Kalman filtering for linear discrete-time system with unknown inputs

Weiran Li, Jie Pan, Yanjun Li, Shuwen Pan, Yan Liu

Research output: Chapter in Book/Conference paperConference paper

Abstract

This paper focuses on the joint input and state estimation for linear stochastic discrete-time systems. To obtain unique estimators that are optimal in the sense of being both least-squares and minimum-variance unbiased (MVU) and their recursive solution, an objective function of the sum of squared errors of outputs is first minimized with respect to an extended state vector including states and unknown inputs. A recursive solution of the extended state vector is then derived with the aid of matrix manipulations. Finally, appropriate matrix decomposition and transformation are used to extract the recursive solutions only involving the current states and unknown inputs from the recursive solution obtained in the previous step. This approach avoids excessive computation due to the dimensions of the matrices that increase with time. As a result, the resulting recursive solution is referred to as a general Kalman filter with unknown inputs (GKF-UI), which covers the most general case of unknown inputs so far in the literature without resorting to transforming the outputs and/or unknown inputs. The unknown inputs to be estimated by the proposed GKF-UI could be arbitrary signals without any prior information and the properties of the proposed GKF-UI are also examined. A numerical example with partial feedthrough from three unknown inputs is used to demonstrate the effectiveness and accuracy of the proposed algorithm.

Original languageEnglish
Title of host publicationProceedings of the 30th Chinese Control and Decision Conference, CCDC 2018
Place of PublicationChina
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages5423-5428
Number of pages6
ISBN (Electronic)9781538612439
DOIs
Publication statusPublished - 6 Jul 2018
Event30th Chinese Control and Decision Conference, CCDC 2018 - Shenyang, China
Duration: 9 Jun 201811 Jun 2018

Conference

Conference30th Chinese Control and Decision Conference, CCDC 2018
CountryChina
CityShenyang
Period9/06/1811/06/18

Fingerprint

Unknown Inputs
Discrete-time Linear Systems
Kalman Filtering
Kalman filters
Kalman Filter
State estimation
Kalman filtering
Discrete-time
Matrix Transformation
Matrix Decomposition
Decomposition
Minimum Variance
Output
State Estimation
Prior Information
Discrete-time Systems
Stochastic Systems
Least Squares
Manipulation
Objective function

Cite this

Li, W., Pan, J., Li, Y., Pan, S., & Liu, Y. (2018). A Kalman filtering for linear discrete-time system with unknown inputs. In Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018 (pp. 5423-5428). China: IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CCDC.2018.8408075
Li, Weiran ; Pan, Jie ; Li, Yanjun ; Pan, Shuwen ; Liu, Yan. / A Kalman filtering for linear discrete-time system with unknown inputs. Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018. China : IEEE, Institute of Electrical and Electronics Engineers, 2018. pp. 5423-5428
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Li, W, Pan, J, Li, Y, Pan, S & Liu, Y 2018, A Kalman filtering for linear discrete-time system with unknown inputs. in Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018. IEEE, Institute of Electrical and Electronics Engineers, China, pp. 5423-5428, 30th Chinese Control and Decision Conference, CCDC 2018, Shenyang, China, 9/06/18. https://doi.org/10.1109/CCDC.2018.8408075

A Kalman filtering for linear discrete-time system with unknown inputs. / Li, Weiran; Pan, Jie; Li, Yanjun; Pan, Shuwen; Liu, Yan.

Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018. China : IEEE, Institute of Electrical and Electronics Engineers, 2018. p. 5423-5428.

Research output: Chapter in Book/Conference paperConference paper

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N2 - This paper focuses on the joint input and state estimation for linear stochastic discrete-time systems. To obtain unique estimators that are optimal in the sense of being both least-squares and minimum-variance unbiased (MVU) and their recursive solution, an objective function of the sum of squared errors of outputs is first minimized with respect to an extended state vector including states and unknown inputs. A recursive solution of the extended state vector is then derived with the aid of matrix manipulations. Finally, appropriate matrix decomposition and transformation are used to extract the recursive solutions only involving the current states and unknown inputs from the recursive solution obtained in the previous step. This approach avoids excessive computation due to the dimensions of the matrices that increase with time. As a result, the resulting recursive solution is referred to as a general Kalman filter with unknown inputs (GKF-UI), which covers the most general case of unknown inputs so far in the literature without resorting to transforming the outputs and/or unknown inputs. The unknown inputs to be estimated by the proposed GKF-UI could be arbitrary signals without any prior information and the properties of the proposed GKF-UI are also examined. A numerical example with partial feedthrough from three unknown inputs is used to demonstrate the effectiveness and accuracy of the proposed algorithm.

AB - This paper focuses on the joint input and state estimation for linear stochastic discrete-time systems. To obtain unique estimators that are optimal in the sense of being both least-squares and minimum-variance unbiased (MVU) and their recursive solution, an objective function of the sum of squared errors of outputs is first minimized with respect to an extended state vector including states and unknown inputs. A recursive solution of the extended state vector is then derived with the aid of matrix manipulations. Finally, appropriate matrix decomposition and transformation are used to extract the recursive solutions only involving the current states and unknown inputs from the recursive solution obtained in the previous step. This approach avoids excessive computation due to the dimensions of the matrices that increase with time. As a result, the resulting recursive solution is referred to as a general Kalman filter with unknown inputs (GKF-UI), which covers the most general case of unknown inputs so far in the literature without resorting to transforming the outputs and/or unknown inputs. The unknown inputs to be estimated by the proposed GKF-UI could be arbitrary signals without any prior information and the properties of the proposed GKF-UI are also examined. A numerical example with partial feedthrough from three unknown inputs is used to demonstrate the effectiveness and accuracy of the proposed algorithm.

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Li W, Pan J, Li Y, Pan S, Liu Y. A Kalman filtering for linear discrete-time system with unknown inputs. In Proceedings of the 30th Chinese Control and Decision Conference, CCDC 2018. China: IEEE, Institute of Electrical and Electronics Engineers. 2018. p. 5423-5428 https://doi.org/10.1109/CCDC.2018.8408075