Development of a Robust Receding-Horizon Nonlinear Kalman Filter Using M-Estimators,Industrial & Engineering Chemistry Research

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Development of a Robust Receding-Horizon Nonlinear Kalman Filter Using M-Estimators
Industrial & Engineering Chemistry Research ( IF 3.8 ) Pub Date : 2022-01-18 , DOI: 10.1021/acs.iecr.1c03830
Pavanraj H. Rangegowda ₁ , Jayaram Valluru ₂ , Sachin C. Patwardhan ₃ , Lorenz T. Biegler ₄ , Siddhartha Mukhopadhyay ₅

Affiliation

The majority of Bayesian methods for the state estimation are based on the assumption that the measurements are corrupted only with random errors. In practice, however, the measurements are often corrupted with gross errors or biases, which leads to biased state estimates when the conventional Bayesian estimators are used. This, in turn, deteriorates the performance of model based process monitoring or control schemes that rely on the state estimator. In this work, to minimize the effects of gross errors on state estimates, two robust versions of the receding-horizon nonlinear Kalman filter (RNK) are developed by integrating M-estimators with the conventional RNK. In the first approach, referred to as Explicit M-RNK, the update step is recast as an optimization problem and further modified by explicitly including an M-estimator. Using the Taylor series approximation, a recursive update step is derived analytically and further used to arrive at a recursive rule for the associated covariance update. The second approach, referred to as the Implicit M-RNK, uses the gradient of the influence function of the chosen M-estimator for adaptive modification of the measurement model used in the update step. This approach facilities the use of the update step in conventional RNK without requiring explicit use of the M-estimator. The proposed robust RNK state estimation formulation is further used to develop a robust state and parameter estimation scheme. The efficacies of the proposed estimation schemes have been demonstrated by conducting simulation studies on some benchmark systems and experimental data sets. The simulation studies reveal that the proposed robust RNK estimators can estimate states and drifting parameter(s) accurately even with the gross errors in the measurements.

中文翻译：

使用 M 估计器开发稳健的后退水平非线性卡尔曼滤波器

用于状态估计的大多数贝叶斯方法都基于这样的假设，即测量值仅因随机误差而损坏。然而，在实践中，测量结果经常被严重的错误或偏差所破坏，当使用传统的贝叶斯估计器时，这会导致有偏差的状态估计。这反过来又降低了依赖于状态估计器的基于模型的过程监控或控制方案的性能。在这项工作中，为了尽量减少粗差对状态估计的影响，通过将 M 估计器与传统 RNK 相结合，开发了两个稳健版本的后退水平非线性卡尔曼滤波器 (RNK)。在第一种方法中，称为显式 M-RNK，更新步骤被重铸为优化问题，并通过显式包含 M 估计器进一步修改。使用泰勒级数近似，递归更新步骤被解析推导并进一步用于得出相关协方差更新的递归规则。第二种方法，称为隐式 M-RNK，使用所选 M 估计器的影响函数的梯度来自适应修改更新步骤中使用的测量模型。这种方法便于在传统 RNK 中使用更新步骤，而不需要显式使用 M 估计器。所提出的稳健 RNK 状态估计公式进一步用于开发稳健的状态和参数估计方案。通过对一些基准系统和实验数据集进行模拟研究，证明了所提出的估计方案的有效性。

更新日期：2022-02-02

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