Variational Nonlinear Kalman Filtering with Unknown Process Noise
  Covariance
Hua Lan Jinjie Hu Zengfu Wang Qiang Cheng
Motivated by the maneuvering target tracking with sensors such as radar and
sonar, this paper considers the joint and recursive estimation of the dynamic
state and the time-varying process noise covariance in nonlinear state space
models. Due to the nonlinearity of the models and the non-conjugate prior, the
state estimation problem is generally intractable as it involves integrals of
general nonlinear functions and unknown process noise covariance, resulting in
the posterior probability distribution functions lacking closed-form solutions.
This paper presents a recursive solution for joint nonlinear state estimation
and model parameters identification based on the approximate Bayesian inference
principle. The stochastic search variational inference is adopted to offer a
flexible, accurate, and effective approximation of the posterior distributions.
We make two contributions compared to existing variational inference-based
noise adaptive filtering methods. First, we introduce an auxiliary latent
variable to decouple the latent variables of dynamic state and process noise
covariance, thereby improving the flexibility of the posterior inference.
Second, we split the variational lower bound optimization into conjugate and
non-conjugate parts, whereas the conjugate terms are directly optimized that
admit a closed-form solution and the non-conjugate terms are optimized by
natural gradients, achieving the trade-off between inference speed and
accuracy. The performance of the proposed method is verified on radar target
tracking applications by both simulated and real-world data.