To solve the problem of high-order moment Gaussian distribution (HGD) noise in state estimation, a fusion filter for Markov jump linear systems (MJLSs) with high-order moment information obtained from sensor data is designed. To obtain high-order moment information, the multi-sensor MJLS is converted to a single-mode system composed of high-order moment components by using a cumulant generating function. Next, a filter design based on Bayesian theory is established to achieve state estimation with a high-order moment information form according to the transformed single-mode deterministic system. Subsequently, a high-order moment fusion technique based on entropy theory is proposed to obtain a more accurate estimation result of the state by using the high-order moment information obtained from various sensors. Comparing the first- and second-order moment information obtained by traditional Gaussian distribution, the HGD introduces higher-order moment information and makes the fusion process more reasonable. In this way, a more precise and reasonable performance of the state estimation is achieved, depending on the sensor fusion technique. To confirm the effectiveness and advantages of the proposed method, a numerical simulation example is provided with various fusion methods. Thus, the performance of the proposed fusion filter design is verified.

中文翻译：

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马尔可夫跳跃线性系统的高阶矩多传感器融合滤波器设计

为了解决状态估计中高阶矩高斯分布（HGD）噪声的问题，设计了一种马尔可夫跳跃线性系统（MJLSs）的融合滤波器，该融合滤波器具有从传感器数据获得的高阶矩信息。为了获得高阶矩信息，通过使用累积量生成功能，将多传感器MJLS转换为由高阶矩分量组成的单模系统。接下来，根据变换后的单模确定性系统，建立基于贝叶斯理论的滤波器设计，以高阶矩信息形式实现状态估计。随后，提出了一种基于熵理论的高阶矩融合技术，以通过使用从各种传感器获得的高阶矩信息来获得更准确的状态估计结果。通过比较传统高斯分布获得的一阶和二阶矩信息，HGD引入了高阶矩信息，使融合过程更加合理。以这种方式，取决于传感器融合技术，实现了状态估计的更精确和合理的性能。为了确认所提方法的有效性和优势，提供了一种数值模拟示例，其中包含各种融合方法。因此，验证了所提出的融合滤波器设计的性能。为了确认所提方法的有效性和优势，提供了一种数值模拟示例，其中包含各种融合方法。因此，验证了所提出的融合滤波器设计的性能。为了确认所提方法的有效性和优势，提供了一种数值模拟示例，其中包含各种融合方法。因此，验证了所提出的融合滤波器设计的性能。