On Robustness of Pairwise Kalman Filters

We consider the problem of pairwise Kalman filter (PKF) robustness in the context of Gaussian homogeneous Markov pairwise models (GH-PMMs). We provide a fast and accurate sequential calculation of the mean square error increase for the pairwise Kalman filter when the parameters of the model used deviate from the actual parameters. We illustrate the relevance of the theoretical results by studying filter deterioration in a specific situation, where one replaces the real PMM model by the classical homogeneous Gaussian state-space model (GH-SSM). We also present an application to the real-world problem of estimating soil moisture by filtering the temperature sequence.