A Generalization of the Kalman Filter for Models With State-Dependent Observation Variance
将卡尔曼滤波推广到观测误差方差依赖于状态向量的模型，从线性贝叶斯和高斯-马尔可夫理论推导最小均方误差线性估计，并应用于泊松分布观测的模型，得到指数平滑的推广。
Abstract The Kalman filter is generalized to cover state-space models in which the variance of the observation error depends on the state vector. Derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints: linear Bayes theory and Gauss—Markov theory. The results are applied to a model for which {y t: t = 1, 2, …, n} follow a Poisson distribution with corresponding intensities {θt: t = 1, 2, …,n} that are assumed to follow an autoregressive process of order 1, namely . The steady-state generalized Kalman filter algorithm in the case for which ρ = 1 gives a generalization of exponential smoothing for a Poisson process with time-varying intensity.