Analysis of Range and Position Comparison Methods as a Means to Provide Gps Integrity in the User Receiver

Integrity is the ability of a system to let its users know whether the system is operating out of its specified performance limits. This paper analyzes two receiver-based methods for assuring the integrity of Global Positioning System (GPS) signals-in-space for the purpose of determining whether the methods can do the job satisfactorily. These methods are called the range comparison method and the position comparison method. Equations relating unknown satellite range errors to the quantity measured in each method are analyzed. The equations reveal important characteristics of the methods, including their mathematical equivalence. The performance of the two methods is then derived as a function of the range error magnitude of the failed satellite. Finally, numerical results for the performance of the methods are shown, both alone and in combination with monitoring of the receiver clock bias estimate. INTRODUCTION Integrity is the ability of a system to let its users know whether the system is operating out of its specified performance limits. The integrity of GPS signals-in-space is essential if the system is to be used by civil aviation for nonprecision approach guidance. One alternative, probably the simplest, is to perform the integrity function in the user receiver. This would obviate the need for any communication links from ground monitoring station(s) that would be necessary in other methods. This paper analyzes two such self-contained integrity evaluation methods, which are called the range comparison (RCM) and position comparison (PCM) methods. It also evaluates the detection performance of these methods, both alone and in combination with monitoring of the receiver clock bias estimate. For both of the above methods, it is assumed that five satellites are in view of the user. This assumption is influenced by a coverage study [1] showing that five or more satellites are in view to the user in the conterminous U.S. 98 percent of the time. The current study is motivated by a surmise that while four satellites are needed for a navigation solution, the additional satellite might give an indication on the state (normal and abnormal) of the GPS signals-in-space and even perhaps indicate which satellite signal(s) may not be useable. In the RCM method, illustrated in Figure 1, the user receiver first estimates user position and clock bias based on four satellites at a time. Each of the five 4-satellite navigation solutions is then used to predict the pseudorange to the fifth satellite not included in that particular solution. The differences between predicted pseudoranges and the corresponding measured pseudoranges are used as the basis for detecting an abnormal state. In the PCM method, illustrated in Figure 2, the user receiver estimates position and clock bias using all five satellites at once and then using sets of four satellites one set at a time. The differences between the five possible 4-satellite solutions and the 5-satellite solution are used as the basis for detecting an abnormal state. ∗ This paper is based upon navigation system studies performed by The MITRE Corporation for the Systems Engineering Service, Federal Aviation Administration under Contract No. DTFA01-84-C-00001. The data presented herein do not necessarily reflect the official views or policy of the FAA.