This paper aims to provide the reader with a review of the main technologies explored in the literature to solve the indoor localization issue. Furthermore, some systems that use these enabling technologies in real-world scenarios are presented and discussed. This could deliver a better understanding of the state-of-the-art and motivate new research efforts in this promising field. Finally, focusing on one of the major challenges in the indoor localization field, i.e., the indoor animal tracking, existing indoor tracking systems have been reviewed and compared by analyzing advantages and drawbacks.

A survey on indoor positioning systems

1. Introduction to Probability 2. Conditional Probability 3. Random Variables and Distributions 4. Expectation 5. Special Distributions 6. Large Random Samples 7. Estimation 8. Sampling Distributions of Estimators 9. Testing Hypotheses 10. Categorical Data and Nonparametric Methods 11. Linear Statistical Models 12. Simulation

Probability and Statistics

Sensitivity Analysis in Linear Regression

Availability of two overlapping frequencies L1/E1 and L5/E5a of the signals transmitted by GPS and Galileo systems offers the possibility of tightly combining observations from both systems in a single observational model. A tightly combined observational model assumes a single reference satellite for all observations from both Galileo and GPS systems. However, when inter-system double-differenced observations are created, receiver inter-system bias is introduced. This study presents the results and the methodology for estimation and accounting for phase and code GPS-Galileo inter-system bias in precise relative positioning. The research investigates the size and temporal stability of the estimated bias for different receiver pairs as well as examines the influence of accounting for the inter-system bias on the user position solution. The obtained numerical results are based on four experiments carried out at different locations and time periods using both real and simulated GNSS data.

/pdf/accounting-for-galileo-gps-inter-system-biases-in-precise-v6823m4g36.pdf

Accounting for Galileo-GPS inter-system biases in precise satellite positioning

The application of the theory of reliability has become a fundamental part of measurement analysis, whether in order to optimise measurement systems so that they are resistant to the influence of outliers or in the post-analysis identification of outliers. However, the current theory of reliability is based on the assumption of a single outlier—an assumption that may not necessarily be the case. This paper extends reliability theory so that it can be applied to multiple outliers through the derivation of appropriate measures of reliability for multiple outliers. The measures of reliability covered include minimal detectable biases, reliability numbers, controllability, and external reliability.

/pdf/generalised-measures-of-reliability-for-multiple-outliers-4o58z2p4ft.pdf

Generalised measures of reliability for multiple outliers

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.

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

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.

Outlier separability analysis with a multiple alternative hypotheses test

With the development of GPS, GLONASS, Galileo, Compass, QZSS and the IRNSS, there has been growing interest in the development of system independent receivers. However, one of the problems encountered in system independent receivers is in the different time systems employed by each of the satellite navigation systems. To overcome this problem it has become a standard practice to solve for the time differences within the receiver’s navigation solution via a combination of receiver clock corrections and/or time offsets. While this technique overcomes the problem of the different time systems, it is at the cost of a satellite from each additional time system. Despite this, the numerous studies that combine multiple satellite navigation systems this way have still found that there are significant benefits in improved accuracy, integrity, continuity and availability. To enhance interoperability though satellite navigation system providers are intending to measure and transmit the time offsets to other time systems. The subsequent use of these time offsets will provide a more accurate navigation solution than without them. However, the problem with using the time offsets is that they pose an additional integrity risk because they are also potential sources of faults. However, with the use of the time offsets for multiple constellation solution, a proper Receiver Autonomous Integrity Monitoring method has not been developed. Thus, mathematical models to account for the time differences with and without the time offsets are presented in this paper. Furthermore, the model that incorporates the time offset allows the application of Receiver Autonomous Integrity Monitoring to detect the presence of any faults within the time offsets. The reliability of the linear models is then compared using GPS and GLONASS geometry in terms of the Minimal Detectable Biases, Protection Levels and the correlation coefficients. The results of this analysis indicate that a more reliable solution can be obtained with the time offsets because they are additional measurements.

Impact of the GNSS Time Offsets on Positioning Reliability

With the increasing automation of measurement, adjustment, outlier detection and the consequential use of the results for real-time applications, reliable methods to detect and mitigate an outlier are required. However, it is frequently advised that the outlier test should not be used as a means to automatically reject an outlier. One of the reasons for this is that the outlier detection test at times can identify a wrong measurement. To address this issue, this paper proposes a new outlier separability test to confirm that the identified outlier, by the outlier test, can be confidently rejected as the outlier. In addition, the Minimally Separable Bias and the separability multiplying factor are also obtained for the proposed outlier separability test. With the initial comparisons between the proposed method with the reapplication of the global model test method and multiple hypothesis method, the advantages of the new outlier separability test are demonstrated.

Nathan L. Knight

Papers

Generalised measures of reliability for multiple outliers

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

Outlier separability analysis with a multiple alternative hypotheses test

Impact of the GNSS Time Offsets on Positioning Reliability

New Outlier Separability Test and Its Application in GNSS Positioning