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TRACK FITTING WITH LONG-TAILED NOISE - A BAYESIAN APPROACH

机译：长尾噪声的轨道拟合-贝叶斯方法

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摘要

If the measurement noise in a linear dynamic system is non-Gaussian, the optimal linear filter (Kalman filter) is not necessarily the one with minimum variance. We describe a non-linear filter, based on a Bayesian approach, which performs better than the linear filter. The relative efficiency of the non-linear filter in the context of track reconstruction is determined in a simulation study. As the filter presupposes a Gaussian mixture model of the measurement noise, we address the problem of approximating the distribution of the measurement errors by a Gaussian mixture. We also study the performance of the filter on some types of long-tailed distributions other than Gaussian mixtures. Finally, the filter is extended to cope with long-tailed process noise, for example a Gaussian mixture model of multiple scattering. [References: 7]
机译：如果线性动态系统中的测量噪声不是高斯噪声，则最佳线性滤波器（卡尔曼滤波器）不一定是方差最小的滤波器。我们基于贝叶斯方法描述了一种非线性滤波器，其性能优于线性滤波器。在模拟研究中确定了在轨道重构的情况下非线性滤波器的相对效率。由于滤波器预设了测量噪声的高斯混合模型，因此我们解决了用高斯混合来近似测量误差分布的问题。我们还研究了除高斯混合以外的某些类型的长尾分布滤波器的性能。最后，扩展滤波器以应对长尾过程噪声，例如多重散射的高斯混合模型。 [参考：7]

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