Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100101, China.
School of Information and Communication Engineering, Beijing Information Science and Technology University, Beijing 100101, China.
Sensors (Basel). 2021 Nov 18;21(22):7673. doi: 10.3390/s21227673.
Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao-Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.
针对假设模型推导的滤波器的性能在噪声的先验知识和二阶统计量不确定时会下降或后验模型推导的滤波器的时间成本会增加的问题，提出了一种新的滤波器。本文推导了一种基于后验噪声统计的贝叶斯稳健卡尔曼滤波器（KFPNS），该滤波器的递归方程与经典算法非常相似。需要注意的是，后验噪声分布通过过离散黑盒变分推断（O-BBVI）进行近似。更确切地说，我们引入了一个过离散分布，将更多的概率密度推向变分分布的尾部，并将重要性采样的思想融入控制变量和 Rao-Blackwellization 的两种策略中，以降低估计量的方差。结果，收敛过程将会加快。通过仿真，我们可以观察到，对于噪声不确定的模型，所提出的滤波器具有良好的性能。此外，我们通过使用实际的多输入多输出（MIMO）雷达系统来验证所提出的算法。
