Inverse Filtering for Linear Gaussian State-Space Models

This paper considers inverse filtering problems for linear Gaussian state-space systems. We consider three problems of increasing generality in which the aim is to reconstruct the measurements and/or certain unknown sensor parameters, such as the observation likelihood, given posteriors (i. e., the sample path of mean and covariance). The paper is motivated by applications where one wishes to calibrate a Bayesian estimator based on remote observations of the posterior estimates, e. g., determine how accurate an adversary's sensors are. We propose inverse filtering algorithms and evaluate their robustness with respect to noise (e. g., measurement or quantization errors) in numerical simulations.