On the use of χ statistics of the Kalman Filter as contextual information in multisensor Kalman filtering

Multisensor data fusion has found widespread application in industry. The objective of data fusion is to provide an improved estimate of a state from a set of data provided by different sensors. Among the various multisensor approaches, Kalman filtering is one of the most significant. Reliability of the data provided by the sensor is a key factor for the integrity of the fusion process. Kalman filter being an IIR filter, burst are propagated into the next estimates causing long term damages. Techniques, based on χ statistical properties of the normalized innovation of the Kalman filter (KF), are used to detect such data failure: the value of the statistic is compared to a threshold in order to determine whether the sensor data should be used or not. However, to choose a threshold, i.e. using classical logic, to define validity of the sensor is quite arbitrary. Besides, Nimier at ONERA developed a theoretic framework to introduce contextual information, modelled by fuzzy subsets, into multisensor Kalman filter. This allows the improvement of the overall reliability of the fusion. Unfortunately, we generally dont get expert knowledge on the validity domains of sensors to determine fuzzy subsets. χ statistics of the KF will be used as contextual information to define fuzzy validity bounds of sensors. In section 2, basics of multisensor KF are recalled. Contextual Information is introduced in section 3 and derivations of contextual information into KF are given in section 4. An example of application based on the fusion of GPS and INS data is finally proposed in the last section.