In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed observations results in an asymptotically optimal filter. In the current paper, we study the convergence rate of Goggin's filter in a pre-limit setting that allows us to study a range of signal-to-noise regimes which includes, as a special case, Goggin's setting. Our guarantees are explicit in the level of observation noise, and unlike most other works in filtering, we do not assume Gaussianity of the noises. Our proofs build on combining simple tools from two separate literature streams. One is a general posterior Cramér-Rao lower bound for filtering. The other is convergence-rate bounds in the Fisher information central limit theorem. Along the way, we also study filtering regimes for linear state-space models, characterizing clearly degenerate regimes -- where trivial filters are nearly optimal -- and a {\em balanced} regime, which is where Goggin's filter has the most value. \footnote{This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

翻译：本文重新审视了文献[1]中针对非高斯噪声提出的非线性滤波器。Goggin证明了通过分数函数对观测值进行变换，再对变换后的观测值应用卡尔曼滤波器(KF)，可得到渐近最优的滤波器。本文在预设极限条件下研究了Goggin滤波器的收敛速率，该框架允许我们分析包括Goggin设定作为特例在内的多种信噪比机制。我们的性能保证明确表达了观测噪声水平的影响，且与大多数滤波研究不同，本文不假设噪声的高斯性。证明过程融合了两个独立文献体系中的基础工具：其一是滤波问题的通用后验克拉美-罗下界，其二是费希尔信息中心极限定理中的收敛速率界限。在研究过程中，我们还分析了线性状态空间模型的滤波机制，清晰刻画了退化机制（此时平凡滤波器接近最优）与平衡机制（该机制下Goggin滤波器最具应用价值）。\footnote{本研究成果已提交IEEE审议出版。版权可能未经通知即发生转移，届时当前版本可能无法继续访问。}