We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with state and observation noises of possibly unequal intensities. It is shown that both estimators are consistent, asymptotically normal with convergent moments and asymptotically efficient. This model has an unusual feature: larger noise in the state equation yields smaller estimation error. The proofs are based on asymptotic analysis of the Kalman-Bucy filter and the associated Riccati equation in particular.

翻译：我们在一个部分观测到的线性高斯系统中考虑参数估计问题,该系统在状态和观察方程式中有小噪音,我们用可能不平等强度的状态和观测振动来描述MLE和Bayes测算器的微量特性,我们描述在设置时,MLE和Bayes测算器的微量和观测振动可能存在不均匀强度的状态和观测振动。我们发现,这两个测算器是一致的,与趋同的瞬间和无静态效率无异。这个模型有一个不寻常的特征:州方程式中较大的噪音产生较小的估计误差。证据基于对Kalman-Bcy过滤器以及特别是相关的Riccati等式的微量分析,特别是基于对Kalman-Bcy过滤器和相关的Riccati等式的微量分析。