Yet another FDE for multiple outliers

A new fault detection and exclusion (FDE) algorithm for multiple outliers is presented in this paper. Its idea is in iterative exclusion of observations that correspond to large test statistics and recalculation of weighted leastsquares (WLS) solution over remaining observations. During each iteration, M observations are excluded consecutively and are used to construct different subsets of observations. In this way, the presented FDE constructs an M-wide "exclusion tree" from subsets of the observation epoch and performs breadth-first walkabout of this tree. Considering more than one observation as a potential outlier in each iteration allows the algorithm to perform better than other FDEs for multiple outliers that check only one observation to be an outlier. In addition, redundancy check is used to decrease the probability of a wrong exclusion. Calculating redundancy numbers allows to check the degree of relation between the suspected observation and corresponding test statistic . If it is not strong enough, then solution is marked is unreliable. The performance of the presented FDE algorithm - probabilities of successful and wrong exclusion was measured using simulated outliers added to data from International GPS Service (IGS) reference stations. This approach - running "synthetic" tests on FDE algorithms - allows direct numeric estimation of the characteristics of FDE algorithms (probabilities of wrong exclusion, missed detection and false alarm), separated from the performance of the receiver hardware and environmental conditions during recording experimental data. The performance was compared to two other FDE algorithms (forward-backward FDE and FDE with extended w-test). The comparison shows that the presented FDE provides probability of wrong exclusion as low as 10^-3 when the magnitudes of outliers are higher than minimum detectible bias (MDB) for given variance of the observations.