Ill-conditioned problems improvement adapting Joseph covariance formula to non-linear Bayesian filters

Integration of Unmanned Aerial Vehicles (UAVs) into civil airspace is becoming a fundamental requirement to satisfy the even more consumer growing demand. The limiting issues for this integration are related to the development of a reliable Sense and Avoid (SAA) system able to equate the human eye performances. Multisensor data fusion techniques are generally used in order to overcome single sensor shortcomings. Although much research addresses toward the realisation of better performing sensors, system degradation could arise from bad numerical behaviours injected by the specific fusion algorithm. Bayesian estimators are the most widely used techniques to perform this task but they could be affected by round-off errors. To improve filter instabilities, induced by ill-conditioned matrices, an alternative numerical approach, based on the Joseph form of the state covariance matrix update applied to non-linear systems is presented. The novelty of this technique lies on taking advantage from the higher order accuracy ensured by Sigma-Point Kalman Filters for solving non-linear inference problems, and using the more numerically robust Joseph update equation.