It is well known that the optimality of the Kalman filter relies on the Gaussian distribution of process and observation model errors, which in many situations is well justified [1]–[3]. However, this optimality is useless in applications where the distribution assumptions of the model errors do not hold in practice. Even minor deviations from the assumed (or nominal) distribution may cause the Kalman filter’s performance to drastically degrade or completely break down. In particular, when dealing with perceptually important signals, such as speech, image, medical, campaign, and ocean engineering, measurements have confirmed the presence of non-Gaussian impulsive (heavy-tailed) and Laplace noises [4]. Therefore, the classical Kalman filter, which is derived under the nominal Gaussian probability model, is biased and even fails in such situations.

中文翻译：

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非高斯模型误差中的卡尔曼滤波：新视角 [提示与技巧]


众所周知，卡尔曼滤波器的最优性依赖于过程和观测模型误差的高斯分布，这在许多情况下都是合理的[1]-[3]。然而，这种最优性在模型误差的分布假设在实践中不成立的应用中是无用的。即使与假设（或标称）分布的微小偏差也可能导致卡尔曼滤波器的性能急剧下降或完全崩溃。特别是，在处理感知上重要的信号（例如语音、图像、医疗、运动和海洋工程）时，测量已证实非高斯脉冲（重尾）和拉普拉斯噪声的存在[4]。因此，在标称高斯概率模型下推导的经典卡尔曼滤波器在这种情况下是有偏差的，甚至失效的。