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An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints

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Abstract

In this paper, an improved recursive non-linear dynamic data reconciliation (IRNDDR) algorithm is proposed to estimate the state variables of non-linear system subject to bound constraints. In the original RNDDR formulation, the predicted state estimate does not satisfy the bound constraints and in the computation of prediction error covariance matrix and updated error covariance matrix, the bound constraints have not been respected, whereas in the computation of updated state estimate, the state constraints are complied by explicitly solving a constrained optimization problem. However, this has introduced incomparability between the point estimate and its covariance estimate. Since RNDDR is a recursive algorithm, this inconsistency can propagate through each iteration causing a problem in the constraint state estimation. Hence, in this paper, we propose improvements which enable the RNDDR algorithm to account for constraints in the prediction step as well as update step, for both point estimate and covariance estimate. Extensive Monte Carlo simulation studies on the benchmark examples such as gas-phase reactor and iso-thermal batch reactor reveal that the proposed modifications resulted in a significant improvement in the RNDDR performance.

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Acknowledgements

This work is supported by All India Council for Technical Education New Delhi under the Research Promotion Scheme (8-250/RFID/RPS(Policy-1)/18-19 dated 22/11/2019) and RUSA project.

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  1. Department of Instrumentation Engineering, Madras Institute of Technology Campus, Anna University, Chennai, 600044, India

    J. Prakash & P. Anbumalar

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  1. J. Prakash
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  2. P. Anbumalar
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Appendix 1

Appendix 1

See Table 5.

Table 5 Comparison of RNDDR, modified extended Kalman filter(M-EKF), constrained ensemble Kalman filter and constrained unscented Kalman filter based state estimation schemes in handling bound constraints during prediction and updated steps
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Prakash, J., Anbumalar, P. An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints. Int J Adv Eng Sci Appl Math 15, 15–23 (2023). https://doi.org/10.1007/s12572-023-00326-7

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