Approaches to Obtaining Beidou Hazardous Pseudorange Bias with the Ordered Weighted Aggregation Operators

S. Qian, Y. Yuan

Abstract:	GNSS navigation technologies are in their highway developing which implies great improvements in the number as well as the quality of available measurements. Though the redundancy of navigation sources may bring prosperity to some extent, pseudorange measurements from different constellations have to be researched as precisely as possible. Moreover, the most important step is to study the hazardous bias that leads to possible positioning failure in individual measurement from different constellations in order to obtain better Interoperability and performance. The study of this paper focuses on the Beidou positioning performance evaluation using its history observation data of 2012, and mainly on the hazardous pseudorange bias with statistical method. Based on precisely model and analysis of the measurements error resources, the calculation algorithm of nominal bias and hazardous bias depending on Ordered Weighted Aggregation operators are studied. Adopt Beidou as the research objectives in the OWA method and the promising contribution can be used to design the fault detection algorithm. This paper includes fifth sections and the corresponding contents are as follows: Firstly, research environments and assumptions are detailed. Individual pseudorange naturally carries bias caused by noise, propagation path and other factors that can be divided into two types, which are fault free bias and faulty bias. Definition of the type for the bias research is presented firstly according to the positioning model using different radio navigation satellite signals. The fault free bias which leads the error distribution radius in the operation scale is seen as the normal condition of the system that the position tolerance is acceptable according to the performance requirements. On the other hands the faulty bias which leads the error distribution overbounding is regarded as one positioning failure. Secondly, measurements error resources and model from Beidou are studied based on the concept proposed above. Most of the fault free case models assume that the pseudorange error components have a normal distribution with a known variance and a zero mean and that the pseudorange error components are combined by convolving their error distributions. The resulting pseudorange error distribution is set as the normal distribution with 0 mean, where the variance is defined by the root-sum-square of the component variances. But some error components are not well characterized by a normal distribution, in this part the details are addressed here. Thirdly, geometric characteristic combined error model are studied. When various sources of the radio navigation signals are available to function the positioning, the all in view satellites have special effects on the measurements performance, especially for the geometric characteristic. That is to say there is a function between the geometric and the positioning performance, furthermore, there is a relationship between the available satellites and the hazardous bias which may lead to positioning failure. In this part, geometric characteristic of different constellation for all in view satellites at the same time are studied to get a function of two variables which are bias and the elevation angle. Fourthly, the hazardous pseudorange bias method with the ordered weighted aggregation operators is proposed. Referred to the GNSS positioning performance assessment, one of the most import factors is the projection matrix, which are calculated based on the error model and the selected type such as fault free or faulty mode. In order to get the ordered weighted matrix, the worst-case based on the geometric which are researched in the above section must be specified. The approaches to determining the weights of two of the most important ordered weighted aggregating operators (the ordered weighted averaging (OWA) and the ordered weighted geometric averaging (OWGA) operators) are studied. By using the known arguments of samples and the relevant aggregated values derived from different constellations, two linear objective programming models for obtaining the weights of OWA and OWGA operators under partial weight information are given. Fifthly, an illustrative example is provided to illustrate the developed models based on different constellation. Some experimental results referred to the adaptive weighted operators are given and the numerical results show that the models are feasible and effective. The goal of this paper is to identify the key pseudorange biases that lead to a positioning failure or not, that is say to propose an effective and adaptive algorithm to define and calculate the hazardous bias for each available pseudorange, manifest the smallest bias on this pseudorange that will lead to a positioning failure. These smallest biases correspond to the worst case detection/exclusion situation, the OWA method can be used to design fault detection algorithm and/or to estimate their statistical properties.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	403 - 407
Cite this article:	Qian, S., Yuan, Y., "Approaches to Obtaining Beidou Hazardous Pseudorange Bias with the Ordered Weighted Aggregation Operators," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 403-407.
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