A novel approach is proposed to $H_2$ finite impulse response (FIR) prediction in discrete-time state-space. The biased-constrained $H_2$ optimal unbiased FIR ($H_2$-OUFIR) predictor derived under disturbances and measurement errors is shown to have the maximum likelihood form and be equivalent to the OUFIR predictor under Gaussian noise. The derivation is provided using the backward Euler method by minimizing the squared weighted Frobenius norm. A bias-constrained suboptimal $H_2$ FIR filtering algorithm using the linear matrix inequality is also designed. The $H_2$-OUFIR predictor performance is investigated by simulations and experimentally in a comparison with the Kalman and unbiased FIR predictors.

中文翻译：

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一种在干扰和测量误差下进行 FIR 预测的新型 H2 方法

提出了一种新颖的方法 $H_2$离散时间状态空间中的有限脉冲响应 (FIR) 预测。有偏见的约束$H_2$ 最优无偏FIR（$H_2$-OUFIR) 在干扰和测量误差下导出的预测器被证明具有最大似然形式，并且等效于高斯噪声下的 OUFIR 预测器。通过最小化平方加权 Frobenius 范数，使用后向欧拉方法提供推导。偏置约束次优$H_2$还设计了使用线性矩阵不等式的FIR滤波算法。这$H_2$-OUFIR 预测器性能通过模拟和实验与卡尔曼和无偏 FIR 预测器进行比较来研究。