In this article, the state estimation problems with unknown process noise and measurement noise covariances for both linear and nonlinear systems are considered. By formulating the joint estimation of system state and noise parameters into an optimization problem, a novel adaptive Kalman filter method based on conjugate-computation variational inference, referred to as CVIAKF, is proposed to approximate the joint posterior probability density function of the latent variables. Unlike the existing adaptive Kalman filter methods utilizing variational inference in natural-parameter space, CVIAKF performs optimization in expectation-parameter space, resulting in a faster and simpler solution. Meanwhile, CVIAKF divides optimization objectives into conjugate and non-conjugate parts of nonlinear dynamical models, whereas conjugate computations and stochastic mirror-descent are applied, respectively. Remarkably, the reparameterization trick is used to reduce the variance of stochastic gradients of the non-conjugate parts. The effectiveness of CVIAKF is validated through synthetic and real-world datasets of maneuvering target tracking.

翻译：本文研究了线性与非线性系统中过程噪声与量测噪声协方差未知时的状态估计问题。通过将系统状态与噪声参数的联合估计转化为优化问题，提出了一种基于共轭计算变分推断的新型自适应卡尔曼滤波方法（称为CVIAKF），用于逼近隐变量的联合后验概率密度函数。与现有在自然参数空间中利用变分推断的自适应卡尔曼滤波方法不同，CVIAKF在期望参数空间中执行优化，从而获得更快速、更简洁的解。同时，CVIAKF将优化目标划分为非线性动力学模型中的共轭部分与非共轭部分，并分别采用共轭计算与随机镜像下降法进行处理。值得注意的是，通过重参数化技巧降低了非共轭部分随机梯度的方差。基于机动目标跟踪的合成数据集与真实数据集验证了CVIAKF的有效性。