The traditional Kalman filter assumes that all measurements can be obtained in real time, which is invalid in practical engineering. Therefore, a variational Bayesian- (VB-) based Gaussian sum cubature Kalman filter is proposed to solve the nonlinear tracking problem of multistep random measurement delay and loss (MRMDL) with unknown probability. First, the measurement model with MRMDL is modified by Bernoulli random variables. Then, the expression of the likelihood function is reformulated as a mixture of multiple Gaussian distributions, and the cubature rule is used to improve the estimation accuracy under the framework of Gaussian sum filter in the process of time update. Finally, by constructing a hierarchical Gaussian model, the unknown and time-varying measurement delay and loss probability are estimated in real time with the state jointly using the VB method in the measurement update stage. The algorithm does not need to calculate the equivalent noise covariance matrix so as to avoid the possible division by zero operation, which improves the stability of the algorithm. Simulation results for a target tracking problem show that the proposed algorithm has a better performance in the presence of MRMDL and can estimate the unknown measurement delay and loss probability accurately.

中文翻译：

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基于 VB 的高斯和体积卡尔曼滤波器用于未知延迟和丢失概率的自适应估计

传统的卡尔曼滤波器假设所有测量值都能实时获得，这在实际工程中是无效的。因此，提出一种基于变分贝叶斯（VB）的高斯和立方卡尔曼滤波器来解决未知概率的多步随机测量延迟和损耗（MRMDL）的非线性跟踪问题。首先，利用伯努利随机变量修改 MRMDL 测量模型。然后，将似然函数的表达式重新表述为多个高斯分布的混合，并在时间更新过程中在高斯和滤波器的框架下利用体积规则来提高估计精度。最后，通过构建分层高斯模型，在测量更新阶段利用VB方法联合状态实时估计未知的时变测量延迟和丢失概率。该算法不需要计算等效噪声协方差矩阵，避免了可能出现的除零运算，提高了算法的稳定性。针对目标跟踪问题的仿真结果表明，该算法在存在MRMDL的情况下具有更好的性能，并且能够准确估计未知的测量延迟和丢失概率。