Joint State Estimation and Noise Identification Based on Variational
  Optimization
Hua Lan Shijie Zhao Jinjie Hu Zengfu Wang Jing Fu
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.