Abstract We propose a novel estimation procedure for linear time-varying pairwise Markov models (PMM), that is robust to system parameter uncertainties occurring in real-world applications. In order to cope with mismodeling errors and ignorance of noise/initial state statistics, we solve a finite-horizon state estimation problem. The resulting unbiased finite impulse response filter for PMMs (PMM-UFIR) is first derived in batch form and then converted to a recursive Kalman-like form for the sake of complexity reduction. Closed forms for the error covariance matrix of the state estimate are also provided for analytical performance assessment. Numerical results illustrate the effectiveness of the proposed estimation method over Gaussian processes, by showing that the PMM-UFIR is nearly as accurate as (resp. more robust than) optimal filtering under perfect (resp. uncertain) system parameters after tuning the horizon size.

中文翻译：

---

使用无偏 FIR 滤波提高鲁棒性的成对马尔可夫模型中的状态估计

摘要 我们为线性时变成对马尔可夫模型 (PMM) 提出了一种新的估计程序，它对现实世界应用中发生的系统参数不确定性具有鲁棒性。为了应对建模错误和对噪声/初始状态统计的无知，我们解决了有限范围状态估计问题。用于 PMM 的无偏有限脉冲响应滤波器 (PMM-UFIR) 首先以批处理形式导出，然后为了降低复杂性而转换为递归卡尔曼式形式。状态估计的误差协方差矩阵的闭合形式也被提供用于分析性能评估。数值结果说明了所提出的估计方法对高斯过程的有效性，通过表明 PMM-UFIR 几乎与 (resp.