Integrity-Directed Sensor Fusion by Robust Risk Assessment of Fault-Tolerant Interval Functions

This study is concerned with the problem of static parameter estimation by robust sensor fusion in the context of applications requiring, for safety reasons, a high guarantee on the reliability of the results. The integrity certification process consists of providing confidence intervals for the unknown parameter with extremely low risks of error. The concept of integrity certification is formalized for robust sensor fusion methods based on interval arithmetics, including the widely-used fault-tolerant interval functions introduced by K. Marzullo and U. Schmid. Random Boolean variables with given bounds on their a priori probabilities are first considered in the Boolean logic setting. Worst-case reasoning leads to the robust derivation of integrity bounds on logical combinations of these variables. Next, integrity bounds on the Marzullo and Schmid functions are derived from the properties of a non-connex Boolean extension of Marzullo´s function