Monitoring and evaluation algorithm of GNSS signal in space availability
Introduction
With the development of Global Navigation Satellite System (GNSS), nowadays the GNSS has been widely used in navigation and positioning on Earth’s surface (Jin et al., 2009, Jin et al., 2013, Jin et al., 2016a, Li et al., 2010, Hou et al., 2014). Meanwhile, the compatibility, interoperability and service performance of GNSS has become an important issue regarding to the system construction and the users’ requirements (Zhao et al., 2016, Li et al., 2013, Jin, 2014). Since there is not a unified standard for satellite navigation service, e.g., GPS of the United States, Galileo of the European Union, GLONASS of Russia and BeiDou of China (Steffen et al., 2011, Jin et al., 2011, Jin et al., 2016b), the name of indicators, the manner and the prescribed scope of indicators also have large differences. The GPS service performance has just referred to the official documents, such as GPS Standard Positioning Service (SPS) performance standard to civil users, GPS Precise Positioning Service (PPS) performance standard to the military and particular users, and GPS Wide Area Augmentation System (WAAS) performance standard. Also since 1993, on the basis of performance standards given by GPS SPS, the Federal Aviation Administration (FAA) has monitored GPS and constructed its augmentation system, and corresponding results were shown in its quarterly performance analysis report (Federal Aviation Administration, 2015). Amongst existing standards, the GPS SPS PS released by USA is more widely used to evaluate satellite navigation systems (John and Joseph, 2011).
Accuracy, integrity, continuity and availability are the four basic service performances of satellite navigation system. Accuracy is defined as the statistical value of errors (95% probability) for any healthy satellite in normal operation. Integrity is defined to be the trust which can be placed in the correctness of the information provided by the SPS SIS. The continuity for a healthy SPS SIS is the probability that the SPS SIS will continue to be healthy without unscheduled interruption over a specified time interval. Availability is the probability that the slots in the GPS constellation will be occupied by satellites transmitting a trackable and healthy SPS SIS. As one of this four basic service performances, availability has become a key indicator in the field of civil aviation and other navigation applications, evaluating whether a navigation system is reliable or not (Zhao and Sun, 2014). So far, there are four versions of GPS SPS performance standards (U.S. Department of Defense, 1993, U.S. Department of Defense, 1995, U.S. Department of Defense, 2001, U.S. Department of Defense, 2008). With the development of GPS SPS PS, the availability performance indicator is constantly improved. In the latest version, it is divided into SIS availability and service availability, respectively. SIS availability is gained more and more attention (Walter et al., 2010, Sun and Wang, 2016).
There are lots of researches of per-satellite availability and constellation availability. Ochieng et al. reported a per-satellite availability evaluation model, which calculated instantaneous availability based on failure rate and reliability, while the on-orbit restoration performance was not taken into account (Ochieng et al., 2001). In fact, most satellite failures can be restored by ground control segments or resolved by spare satellites. In addition, the previous constellation availability models (Clifford, 1999, Wu et al., 1999) were considered a specific constellation with a defined number (generally 24) of space vehicles, when more space vehicles than required for the constellation have actually been on orbit for most of the time since the declaration of Full Operational Capability (FOC). The constellation availability was based on per-satellite availability, and MTBF and MTTR of different per-satellite outages directly influenced the constellation availability in different states. U.S. Department of Defense refers that constellation availability model is based on binomial probability distribution (U.S. Department of Defense, 2008). To some extent, it reflects the constellation availability under different failure conditions, but it ignores that the satellite restoration condition and the spare satellites also have impact on constellation availability. So this model is a static analysis method of constellation availability. In order to improve the model of constellation availability, the per-satellite availability and spare satellites should be taken into account. Compared to the above model, the per-satellite availability model proposed in this paper is a combination of satellite failure and restoration. It is based on Markov process and reflects the overall availability of the satellite. To ensure more accurate evaluation, the per-satellite availability model and constellation availability model proposed in this paper are fully considered the impact of constellation status and satellite backup strategy. This paper also uses the most accurate MTBF and MTTR numbers, which measured from actual GPS experience.
The GPS SPS performance standard is more suitable to evaluate the performance of satellite navigation systems. This paper mainly aims at evaluating satellite availability and constellation availability of GPS SIS based on GPS SPS documents and other relevant data of the quarterly GPS performance analysis report released by the FAA (U.S. Department of Defense, 2008). BDS SIS is also evaluated based on BDS SIS ICD (China Satellite Navigation Office, 2013a, China Satellite Navigation Office, 2013b). The measured data of GPS and BDS are from the quarterly GPS performance analysis report released by FAA and International GNSS Service (IGS). Furthermore, the validity of the evaluation model and the conformity to the evaluation standards of the GPS and BDS SIS availability are presented. This paper is organized as follows: in Section 2 availability evaluation model based on Markov Process is presented, Per-Satellite Availability Evaluation of GPS and BDS are investigated by the measured data in Section 3, in Section 4 constellation availability evaluation is shown, and finally the conclusion is given.
Section snippets
Availability evaluation model based on Markov process
SIS availability includes per-slot availability and constellation availability. The per-slot availability is the fraction of time that a slot in the GPS constellation occupied by a satellite transmitting the trackable and healthy SPS SIS. It mainly depends on the satellite design together with the control segment procedure for on-orbit maintenance and failure response. The constellation availability is the fraction of time that a specified number of slots in the GPS constellation occupied by
Per-satellite availability evaluation of GPS
According to the Markov state transition model, it can be seen that the key to calculate satellite availability is to get satellite failure rate and restoration rate μ. So by analyzing GPS performance report from FAA, the MTBF and MTTR of different failure types can be gotten, then the per-satellite availability can be evaluated.
In order to guarantee the reliability of the evaluated results, this paper makes the statistics based on all outages according to the GPS failure report of FAA.
Constellation availability evaluation of GPS SIS
For all the operational GPS satellites, there are 27 satellites except the satellites that we haven’t got their satellite availability. These 27 satellites assign in the six orbital planes, respectively. The distribution of the 27 satellites is listed in Table 1.
In order to keep the status that four baseline slot satellites located on the same orbital plane, the satellites of SVN23, SVN46 and SVN67 are considered as spare satellites, and the rest of the 24 satellites as the baseline slot
Conclusions
In this paper, the evaluation method of GNSS SIS availability was presented. An evaluation model of per-satellite availability that based on Markov process was proposed, and the evaluation model of constellation availability that based on the baseline slot satellites and spare satellites was discussed. According to the GPS measured data and BDS measured data, the evaluation algorithms are investigated, the per-satellite availability results of GPS and BDS are obtained, and the constellation
Acknowledgment
This study is supported by the National Basic Research Program of China (No. 2010CB731805), National Natural Science Foundation of China (Nos. 61571309 and 61101161), and the Open Program of Key Laboratory of Intelligent Waterway Transport of Ministry of Transport and the Fundamental Research Funds for the Central Universities (No. 3132016317).
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