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.

通过将系统状态和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 - 计算变分推理（CVIAKF）的新型自适应卡尔曼滤波器方法，用于近似潜变量的联合后验概率密度函数。与现有的自适应卡尔曼滤波器方法不同的是，CVIAKF 在期望参数空间中进行优化，从而实现更快且更简单的解决方案。同时，CVIAKF 将优化目标分为非线性动力模型的共轭部分和非共轭部分，并分别应用共轭计算和随机镜像下降。值得注意的是，重参数化技巧用于降低非共轭部分的随机梯度方差。通过合成和真实世界的机动目标跟踪数据集验证了 CVIAKF 的有效性。