Nathan L. Knight

A Comparison of Outlier Detection Procedures and Robust Estimation Methods in GPS Positioning

With more satellite systems becoming available there is currently a need for Receiver Autonomous Integrity Monitoring (RAIM) to exclude multiple outliers. While the single outlier test can be applied iteratively, in the field of statistics robust methods are preferred when multiple outliers exist. This study compares the outlier test and numerous robust methods with simulated GPS measurements to identify which methods have the greatest ability to correctly exclude outliers. It was found that no method could correctly exclude outliers 100% of the time. However, for a single outlier the outlier test achieved the highest rates of correct exclusion followed by the MM-estimator and the L 1 -norm. As the number of outliers increased MM-estimators and the L 1 -norm obtained the highest rates of normal exclusion, which were up to ten percent higher than the outlier test.

Outlier separability analysis with a multiple alternative hypotheses test

Outlier separability analysis is a fundamental component of modern geodetic measurement analysis, positioning, navigation, and many other applications. The current theory of outlier separability is based on using two alternative hypotheses—an assumption that may not necessarily be valid. In this paper, the current theory of outlier separability is statistically analysed and then extended to the general case, where there are multiple alternative hypotheses. Taking into consideration the complexity of the critical region and the probability density function of the outlier test, the bounds of the associated statistical decision probabilities are then developed. With this theory, the probabilities of committing type I, II, and III errors can be controlled so that the probability of successful identification of an outlier can be guaranteed when performing data snooping. The theoretical findings are then demonstrated using a simulated GPS point positioning example. Detailed analysis shows that the larger the correlation coefficient, between the outlier statistics, the smaller the probability of committing a type II error and the greater the probability of committing a type III error. When the correlation coefficient is greater than 0.8, there is a far greater chance of committing a type III error than committing a type II error. In addition, to guarantee successful identification of an outlier with a set probability, the minimal detectable size of the outlier (often called the Minimal Detectable Bias or MDB) should dramatically increase with the correlation coefficient.

Indoor positioning within a single camera and 3D maps

In this paper, we propose a method of vision-based positioning with the use of single camera and newly defined 3D maps for indoor localization and navigation purposes. Our work here is to address the accuracy and reliability concerns of an indoor navigation system. The main contribution will be the adoption of photogrammetric 6DOF pose estimation method to improve the positioning accuracy. DOPs are introduced to evaluate positioning precision within vision-based domain. Quality control strategies are also applied to detect outliers in the observation and strengthen system reliability. Besides, only natural landmarks are required in the proposed method to provide absolute position and orientation information.

Optimal Fault Detection and Exclusion Applied in GNSS Positioning

In Global Navigation Satellite System (GNSS) positioning, it is standard practice to apply the Fault Detection and Exclusion (FDE) procedure iteratively, in order to exclude all faulty measurements and then ensure reliable positioning results. Since it is often only necessary to consider a single fault in a Receiver Autonomous Integrity Monitoring (RAIM) procedure, it would be ideal if a fault could be correctly identified. Thus, fault detection does not need to be applied in an iterative sense. One way of evaluating whether fault detection needs to be reapplied is to determine the probability of a wrong exclusion. To date, however, limited progress has been made in evaluating such probabilities. In this paper the relationships between different parameters are analysed in terms of the probability of correct and incorrect identification. Using this knowledge, a practical strategy for incorporating the probability of a wrong exclusion into the FDE procedure is developed. The theoretical findings are then demonstrated using a GPS single point positioning example.

Optimising Fault Detection and Exclusion in positioning

Reliability and integrity has become increasingly important in ubiquitous positioning systems, and particularly in critical applications. To implement reliability and integrity measures, Fault Detection and Exclusion (FDE) procedures should be used. However, the current FDE procedures in the chi-square test and the outlier test are suboptimal in terms of continuity and availability. This is due to the assumption that the bias always corresponds with the measurement that has the largest Protection Level (PL), and in the setting of the continuity probability to a predefined value rather than being maximised.