带不确定混合噪声系统的变分贝叶斯期望最大滤波算法

Variational Bayesian expectation-maximization filter for systems with uncertain hybrid noises

卡尔曼滤波器假设量测噪声为已知统计特性的高斯白噪声,然而系统可能受到不确定随机噪声以及未知有界噪声共同影响,若采用单一滤波策略,则估计结果易出现较大偏差。将两种不确定噪声运用未知参数的高斯混合模型进行表示,提出变分贝叶斯期望最大滤波算法。所提方法采用变分贝叶斯最大化方法对量测噪声模型中的超参数进行更新,在得到模型超参数后,利用变分贝叶斯期望算法计算噪声模型的隐变量。对上述过程反复迭代,最终获得系统的状态和协方差。仿真结果表明,相比于传统的卡尔曼滤波算法和联合滤波算法,变分贝叶斯期望最大滤波算法在出现混合不确定噪声时,经纬度定位精度均提高60%以上,提高了导航系统的精确性。

The Kalman filter relies upon the hypothesis of known white noises.However,in some cases,the measurements are interrupted by the uncertain stochastic noises and unknown-but-bounded noises simultaneously.The estimated results have a larger bias by using only one single filtering algorithm.A variational Bayesian expectation-maximization(VBEM)filter is proposed which model the uncertain hybrid noises model by using the Gaussian mixture model.In the variational Bayesian expectation step,the hyper-parameter of the measurement noises model is calculated.The hidden variables of the noise model are updated in the variational Bayesian maximization step.Through repeated iteration,the state and covariance of the system can be obtained.Simulation results show that compared with the traditional Kalman filter and combined filter algorithms,the variational Bayesian expectation-maximization filter can improve the latitude and longitude accuracy by more than 60% with uncertain hybrid noises,and improve the accuracy of the navigation system.