Abstract

Conservative sensor error modeling is of great significance in the field of safety-of-life. At present, the overbound method has been widely used in areas such as satellite-based augmentation systems (SBASs) and ground-based augmentation systems (GBASs) that provide integrity service. It can effectively solve the difficulties of non-Gaussian and non-zero mean error modeling and confidence interval estimation of user position error. However, there is still a problem in that the model is too conservative and leads to the lack of availability. In order to further improve the availability of SBASs, an improved paired overbound method is proposed in this paper. Compared with the traditional method, the improved algorithm no longer requires the overbound function to conform to the characteristics of the probability distribution function, so that under the premise of ensuring the integrity of the system, the real error characteristics can be more accurately modeled and measured. The experimental results show that the modified paired overbound method can improve the availability of the system with a probability of about 99%. In view of the fact that conservative error modeling is more sensitive to large deviations, this paper analyzes the robustness of the improved algorithm in the case of abnormal data loss. The maximum deviation under a certain integrity risk is used to illustrate the effectiveness of the improved paired overbound method compared with the original method.

Highlights

  • Error modeling is the basis of sensor system design

  • The error data obtained from the real ephemeris are analyzed, and the results show that the modified method plays a positive role in improving availability when compared with the traditional paired overbound method

  • satellite-based augmentation systems (SBASs) integrity is usually defined by the indicator of integrity risk, which is the probability that the real positioning error of the user exceeds the calculated protection level but does not provide alarm within the specified time (TTA) [22]

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Summary

Introduction

Error modeling is the basis of sensor system design. In many fields that emphasize safety, reliability, and integrity, error modeling tends to pay more attention to the tail characteristics of error. For the specific form of the overbound function, in addition to the most basic Gaussian distribution, some scholars have proposed Gauss–Laplace [12], NIG (Normal Inverse Gaussian) [13], multi-Gauss [14], and so on The purpose of their design is to solve the problem of the Gaussian distribution being too conservative in dealing with heavy-tailed characteristics and to improve the availability of the system. A modified paired overbound method is proposed, which still uses the left and right functions to overbound the distribution characteristics of the real error but relaxes the requirements of the overbound function, which no longer has to meet the properties of the probability distribution function It reduces the calculated protection level while meeting the requirements of integrity and improving the availability of the system. The main work of this paper is summarized

SBAS Integrity
Conservatism of Broadcast Error Model
Remaining Conservatism after Convolution
Simplicity of User Calculation
High Efficiency of Broadcasting
Previous Overbounding Methods
Tail Overbound
PDF Overbound
CDF Overbound
Paired Overbound
Modified Paired Overbound Method
Overbound Property for a Single Error Source
Overbound Property after Convolution
Trade-off between Mean and Standard Deviation
The relationship between the overbound and the actual error afterfunctions
Data Collection
Generation of Overbound Parameters
Hypothesis test of the obtained results
Overbound Property in the Position Domain
Robustness for Large Errors
Findings
Conclusions

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