Quantitative verification of Kalman filters

Kalman filters are widely used for estimating the state of a system based on noisy or inaccurate sensor readings, example in control and navigation vehicles robots. However, numerical instability modelling errors may lead to divergence filter, leading erroneous estimations. Establishing robustness against such issues can be challenging. We propose novel formal verification techniques software perform rigorous quantitative analysis effectiveness filters. present general framework filter implementations operating linear discrete-time stochastic systems, systematically construct Markov model filter's operation using truncation discretisation noise model. Numerical stability properties then verified probabilistic checking. evaluate scalability accuracy our approach two distinct kinematic models four implementations.