Abstract
This paper develops a Rao-Blackwellized particle filter with variational inference for jointly estimating state and time-varying parameters in non-linear state-space models (SSM) with non-Gaussian measurement noise. Depending on the availability of the conjugate prior for the unknown parameters, the joint posterior distribution of the state and unknown parameters is approximated by using an auxiliary particle filter with a probabilistic changepoint model. The distribution of the SSM parameters conditionally on each particle is then updated by using variational Bayesian inference. Experiments are first conducted on a modified nonlinear benchmark model to compare the performance of the proposed approach with other state-of-the-art approaches. Finally, in the context of GNSS multipath mitigation, the proposed approach is evaluated based on data obtained from a measurement campaign conducted in a street urban canyon.
Highlights
State-space models (SSMs), composed of dynamic and measurement equations, are applied to a wide variety of signal processing problems, especially in positioning, tracking and navigation [1], [2]
interacting multiple model (IMM) Algorithm [1]: The models in the IMM differ by the choice of the parameter a where 10 spaced values of a are sampled in the range [−18, 18] and the measurement noise associated with each model is assumed to be distributed according to a N (0, 1) distribution
adaptive parameter estimation (APE) filter with known variance [31]: The APE filter is combined to the auxiliary particle filter (APF) with a changepoint model and the measurement noise model is assumed to be distributed according to a N (0, 1) distribution
Summary
State-space models (SSMs), composed of dynamic and measurement equations, are applied to a wide variety of signal processing problems, especially in positioning, tracking and navigation [1], [2]. A central problem when using these models is to recursively infer the state based on a sequence of measurements. In realistic contexts, these parameters can be time-varying due to abruptly changing environment, leading to the problem of state estimation in the presence of model uncertainty. Since the reliability of the IMM is dependent on the number and choice of models, some approaches for jointly estimating state and parameter for SSMs have been proposed.
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