A Confidence Statistic and an Outlier Detector for Difference Estimates in Sensor Arrays

Evaluating estimation errors with minimal prior information is a difficult problem, encountered in sensor systems that require outlier rejection and self-diagnosis. This work proposes a confidence statistic and an outlier detector for difference estimates in sensor arrays. The statistic is based on the configuration of the sensor array, and it is applicable to a variety of estimates from a generalized difference quantity model. For instance, differences of arrival times used in direction of arrival estimation and localization are compliant with the proposed model. The confidence statistic is used to detect the presence of outliers in data. An optimum detector and a description of detection accuracy are derived. Performance is examined within a case study, and it is demonstrated that the analytical results are useful also when the statistical assumptions are not met. Results show that the statistic is effective in measuring estimation reliability and identifying outliers, especially when errors are large and a majority of the data is corrupted.