Joint State Estimation and Noise Identification Based on Variational Optimization
This work addresses adaptive filtering for systems with unknown noise, which is incremental as it builds on existing variational inference methods by optimizing in a different parameter space.
The paper tackled state estimation with unknown noise covariances in linear and nonlinear systems by proposing CVIAKF, a novel adaptive Kalman filter method based on variational optimization, which demonstrated effectiveness on synthetic and real-world datasets for maneuvering target tracking.
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.