Abstract
For the integration of global navigation satellite system (GNSS) and inertial navigation system (INS), real-time and accurate fault detection is essential to enhance the reliability and precision of the system. Among the existing methods, the residual chi-square detection is still widely used due to its good real-time performance and sensibility of fault detection. However, further investigation on the performance of fault detection for different observational conditions and fault models is still required. In this paper, the principle of chi-square detection based on the predicted residual and least-squares residual is analyzed and the equivalence between them is deduced. Then, choosing the chi-square detection based on the predicted residual as the research object, the influence of satellite configuration and fault duration time on the performance of fault detection is analyzed in theory. The influence of satellite configuration is analyzed from the number and geometry of visible satellites. Several numerical simulations are conducted to verify the theoretical analysis. The results show that, for a single-epoch fault, the location of faulty measurement and the geometry have little effect on the performance of fault detection, while the number of visible satellites has greater influence on the fault detection performance than the geometry. For a continuous fault, the fault detection performance will decrease with the increase of fault duration time when the value of the fault is near the minimal detectable bias (MDB), and faults occurring on different satellite’s measurement will result in different detection results.
Highlights
Due to the good complementary characteristics, the integration of the inertial navigation system (INS) and the global navigation satellite system (GNSS) can achieve superior performance to either of them operating alone [1,2], and is widely applied on unmanned aerial vehicles (UAVs)
The performance of multiple solution separation (MSS) and autonomous integrity monitoring by extrapolation (AIME) for gradual fault were tested and the analysis revealed that both methods had advantages and disadvantages [24]
To analyze the performance of fault detection when fault occurs on the same satellite’s measurement in different geometries, a concept called relative differential precision of positioning (RDPOP) is introduced, and it can be expressed as j=7
Summary
Due to the good complementary characteristics, the integration of the inertial navigation system (INS) and the global navigation satellite system (GNSS) can achieve superior performance to either of them operating alone [1,2], and is widely applied on unmanned aerial vehicles (UAVs). In order to apply the related methods of GNSS receiver autonomous integrity monitoring (RAIM) into GNSS/INS integration, Hewitson proposed an extended RAIM (eRAIM) through adopting least-squares principles for the state estimation in a Kalman filter [27] This method formed the test statistic basing on the least-squares residual obtained by integrating the measurements with one-step prediction of the state parameters, and it can detect faults in the dynamic model and isolate them from the measurement model. There is a need to analyze the influence of measurement conditions and fault duration time on the performance of abrupt fault detection In this contribution, to have an overall understanding of the performance of the residual chi-square detection method and deepen the application of it in GNSS/INS integration, we analyze the principle of two residual chi-square detection methods and give the equivalence deduction of them in theory. Hρ1 and Hρ2 are matrices that denote the relationship between measurements and state vector [25]
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