Replacing the state vector of a linear state‐space model by any one‐to‐one linear transformation does not alter maximum likelihood estimation. We extend this invariance property to more general settings, with possibly diffuse initialization of the Kalman filter and injective affine transformations of the state vector. Our results hold for both direct maximization of the likelihood function and the EM algorithm. We offer two real examples that illustrate how one may employ our results to handle a variety of affine‐transformed state‐space models in the literature.

中文翻译：

---

仿射变换状态空间模型的最大似然估计不变性的扩展

用任何一对一的线性变换代替线性状态空间模型的状态向量不会改变最大似然估计。我们将这种不变性扩展到更一般的设置，可能使用卡尔曼滤波器的弥散初始化以及状态向量的射入仿射变换。我们的结果适用于似然函数的直接最大化和EM算法。我们提供了两个真实的例子，这些例子说明了如何利用我们的结果来处理文献中各种仿射变换的状态空间模型。