THRESHOLD DETERMINATION DEVICE, THRESHOLD DETERMINATION METHOD AND PROGRAM
INCORPORATION BY REFERENCE This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2010-254526, file on November 15, 2010, the disclosure of which is incorporated herein in its entirely by reference.
BACKGROUND OF THE INVENTION Field of the Invention
The present invention relates to a threshold determination device that determines a threshold for selecting a Global Positioning System (GPS) satellite that is providing normal ephemeris data and can be used for measuring from a plurality of GPS satellites, and a threshold determination method and program for determining a threshold for selecting a GPS satellite that is providing normal ephemeris data and can be used for measuring from a plurality of GPS satellites.
Description of Related Art
In aircraft approach systems, the differential GPS of a narrow covered region near an airport is termed a GBAS. GBAS standards and recommended practises (SARPS) are determined by the International Civil Aviation Organization (ICAO), and stipulate requirements for accuracy, completeness, availability, continuity, etc.
In the GBAS system, a DGPS ground equipment (hereinafter 'GBAS ground station') receives a measurement signal from a GPS satellite and measures the distance to the satellite, creates GBAS correction information based on that measurement, and uses a
very high frequency (VHF) band data link to transmit the GB AS correction information to an aircraft (GBAS user).
In the GBAS system, when there is a large difference between the true orbital position of the GPS satellite and the orbital position calculated from orbit information being broadcasted from the GPS satellite, if approach control is performed using the broadcast from that satellite, there is a possibility of accident. To prevent this, the GBAS system includes a monitor for evaluating the size of error in the orbit pos calculated from the orbit information being broadcast from the GPS satellite.
The GPS satellite transmits a measuring signal that is needed to calculate the position of the aircraft, and the GBAS ground station uses the measuring signal from the GPS satellite to create GBAS correction information for increasing the accuracy and safety of the trajectory of the aircraft. The aircraft includes a receiver for receiving the measuring signal from the GPS satellite, and a reception equipment for receiving the GBAS correction information.
When using a measuring signal from the GPS satellite in navigation in the manner described above, a satellite position calculated from ephemeris data (orbit calendar), which is orbit information broadcast from the GPS satellite, is used in calculating the position of the aircraft. The ephemeris data is normally updated approximately once every two hours. However, if erroneous orbit information is broadcast at the time of updating, the measuring error of the aircraft increases, leading to a danger that it may become impossible to guarantee a safe trajectory.
As a method of detecting errors in orbit information and judging whether orbit information can be used, Sam Pullen, et al., 'Ephemeris Protection Level Equations and Monitor Algorithms for GBAS' ION GPS 2001, September 11 to 14, 2001, discloses a method that uses an algorithm described in GPS Interface Specification IS-GPS-200E to
calculate a three-dimensional position of a satellite expressed in an earth-fixed coordinate system in time series from an initial value of an orbit element of ephemeris data, compares two types of three-dimensional positions calculated from new and old ephemeris (updated ephemeris data and pre-update ephemeris data), and, when the positional error exceeds a predetermined threshold, judges that the updated ephemeris data is too much in error and cannot be used.
Japanese Unexamined Patent Application, First Publication, No. (JP-A) 2000-275320, JP-A 2003-21672, and JP-A 2009-68927 disclose methods that compare a value obtained from data from a satellite with a predetermined threshold and thereby determine whether the data from the satellite can be used, such as a method of comparing the quality of observational data with a predetermined threshold and determining whether to discard the observational data, and a method of determining the validity of ephemeris data based on whether the difference between an estimated value of a Doppler shift and a detected value exceeds a threshold.
In setting a threshold for determining whether data from a satellite can be used, if the acceptable error with respect to data from the satellite (an acceptable range of error between positional information of a satellite calculated using data from the satellite and the actual position of the satellite) is made large, there is a danger that error in the measuring data of the aircraft calculated using the data from the satellite will increase, reducing the safety of the trajectory of the aircraft.
On the other hand, if the acceptable error with respect to data from the satellite is made small, the probability that the data from the satellite will be judged to be unusable will rise, leading to an increased probability that there will be insufficient data that can be used in measuring of the aircraft, and it will become impossible to perform the measuring.
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Thus, although the process of setting the threshold for judging whether data from a satellite (ephemeris data) can be used is important for ensuring the safety of the trajectory of the aircraft (the health of the measuring system) and the measuring capability (the continuity of the measuring system), none of the Prior Art Documents described above discloses a method of setting the threshold.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a threshold determination device, a threshold determination method, and a program that can solve the problems described above.
The present invention has been realized to solve the problems mentioned above. A threshold determination device according to the invention determines a threshold for selecting a GPS satellite transmitting ephemeris data that will be used in measuring from among a plurality of GPS satellites, and includes a threshold determination unit that determines a threshold for selecting a GPS satellite based on a maximum acceptable detection failure probability and a maximum acceptable detection false alarm probability that are set.
A threshold determination method according to an aspect of the invention determines a threshold for selecting a GPS satellite transmitting ephemeris data that will be used in measuring from among a plurality of GPS satellites, and includes a threshold determination step of determining a threshold for selecting a GPS satellite based on a maximum acceptable detection failure probability and a maximum acceptable detection false alarm probability that are set.
A program according to an aspect of the invention is a program for making a computer, functioning as a threshold determination device that determines a threshold for
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selecting a GPS satellite transmitting ephemeris data that will be used in measuring from among a plurality of GPS satellites, execute a threshold determination step of determining a threshold for selecting a GPS satellite based on a maximum acceptable detection failure probability and a maximum acceptable detection false alarm probability that are set.
According to the invention, it is possible to obtain a threshold that can ensure both the health and the continuity of a measuring system.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of an example of a schematic configuration of a GBAS ground station in a first embodiment of the invention.
FIG. 2 is a flowchart of a sequence of processes whereby a threshold determination computer determines a threshold in the same embodiment.
FIG 3 is an explanatory diagram of variables indicating the relationship between a GBAS ground station (base station), a GPS satellite, and an aircraft.
FIG. 4 is an explanatory diagram of variables indicating the relationship between a GPS satellite position obtained using a new ephemeris, a GPS satellite position obtained using an old ephemeris, and a true GPS satellite position.
FIG. 5 is an explanatory diagram showing an image of the relationship between distribution of the scale of normalized three-dimensional error and a range in which a threshold can be set.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS An embodiment of the invention will now be explained with reference to the drawings. The applicable range of the invention is not limited to a GBAS ground
station as described in this embodiment, and the invention can be applied in various kinds of GPS equipment that receive ephemeris data from a plurality of GPS satellites.
FIG. 1 is a block diagram of an example of a schematic configuration of a GBAS ground station in a first embodiment of the invention. In FIG. 1, a GBAS ground station 1 includes a reference station 100, a GPS satellite selection computer 200, a threshold determination computer 300, and a VHF data broadcast equipment 400 including an antenna. The reference station 100 includes an antenna for GPS reception 110 and a GPS receiver 200. The threshold determination computer 300 includes an integrity threshold calculation unit 310, a continuity threshold calculation unit 320, and a threshold determination unit 330.
The GBAS ground station 1 receives wireless signals from GPS satellites 801 to 805 provided inside an airport base or near an airport, and transmits a wireless signal containing data for correction (GBAS correction information) when an aircraft 901, which is a GBAS user, performs measuring. The reference station 100, the GPS satellite selection computer 200, the threshold determination computer 300, and the VHF data broadcast equipment 400 can be installed inside and around the same building, or they can be installed in and around a plurality of buildings.
The applicable range of the invention is not limited to five GPS satellites as shown in FIG. 1. The invention can be applied in various kinds of GPS equipment that receive ephemeris data from a plurality of GPS satellites, and select a GPS satellite for measuring based on old and new ephemeris data (pre-update ephemeris data and updated ephemeris data) and a threshold. Furthermore, the number of aircrafts is not limited to one as in FIG. 1, and can be a plurality.
The antenna for GPS reception 110 receives wireless signals (GPS signals) transmitted from the GPS satellites 801 to 805, and outputs the received wireless signals
to the GPS receiver 120. The wireless signals that the antenna for GPS reception 110 receives from the GPS satellites 801 to 805 contain ephemeris data as orbit information broadcast from the GPS satellites.
The GPS receiver 120 extracts data by performing a process such as demodulation to the wireless signals received by the antenna for GPS reception 110, and transmits it to the GPS satellite selection computer 200.
From the plurality of GPS satellites 801 to 805, the GPS satellite selection computer 200 selects four GPS satellites for the aircraft 901 to use in measuring, and creates augmentation information (data for correction and virtual distance correction values for when the aircraft 901 performs measuring) relating to the selected GPS satellites.
The threshold determination computer 300 determines a threshold used as a reference when the GPS satellite selection computer 200 selects the GPS satellites (hereinafter 'threshold for selecting GPS satellite').
The integrity threshold calculation unit 310 calculates an integrity threshold THi. The integrity threshold THi is for satisfying the safety of navigation of the aircraft (the health of the measuring system).
The continuity threshold calculation unit 320 calculates a continuity threshold THc. The continuity threshold THc is for satisfying the measuring possibility (the continuity of the measuring system).
The threshold determination unit 330 determines a threshold for selecting GPS satellite within the range of the continuity threshold THc and the integrity threshold THi.
The VHF data broadcast equipment 400 transmits a wireless signal containing the augmentation information created by the GPS satellite selection computer 200.
Subsequently, a process whereby the threshold determination computer 300
determines a threshold will be explained. As described above, the threshold determination computer 300 determines a threshold to be used when the GPS satellite selection computer 200 selects the GPS satellites. Every time the ephemeris data of one of the GPS satellites 801 to 805 is updated, the GPS satellite selection computer 200 calculates a test statistic R shown in equation (1) for the GPS satellite whereof the ephemeris data was updated.
where (x0, y0, Zo) are positional coordinates of the GPS satellite in a earth-fixed coordinate system (WGS-84ECEF) calculated from pre-update ephemeris data (hereinafter 'old ephemeris'), and (xn, yn, Zn) are positional coordinates of the GPS satellite in an earth-fixed coordinate system (WGS-84ECEF) calculated from updated ephemeris data (hereinafter 'new ephemeris').
Vector R is a vector from a GPS satellite position (x0, y0, Zo) calculated from the old ephemeris to a GPS satellite position (xn, yn, z„) calculated from the new ephemeris. The test statistic R expresses the size of vector R, i.e. the linear distance between the GPS satellite position calculated from the old ephemeris and the GPS satellite position calculated from the new ephemeris. A publicly known method described in GPS Interface Specification IS-GPS-200E can be used to calculate the positional coordinates of the GPS satellite in the earth-fixed coordinate system (WGS-84ECEF) based on ephemeris data, and will not be explained here.
The GPS satellite selection computer 200 judges that a GPS with a test statistic R greater than a predetermined threshold is unsuitable, and deletes it from the GPS satellites that the aircraft 901 uses when measuring. The GPS satellite selection
computer 200 judges that a GPS with a test statistic R equal to or less than a predetermined threshold is suitable, and selects it as a GPS satellite that the aircraft 901 uses when measuring. When the ephemeris data of one of the GPS satellites is updated, the threshold determination computer 300 determines a threshold for judging whether to delete the GPS satellite whereof the ephemeris data has been updated.
FIG. 2 is a flowchart of a sequence of processes whereby a threshold determination computer determines a threshold. The data values shown below are examples to facilitate explanation. Therefore, values other than those shown below can be used for the data values.
Firstly, the threshold determination computer 300 sets a maximum acceptable detection failure probability (the probability that a GPS satellite that should be deleted from the measuring objects of the aircraft 901 will not be deleted) PMD (Step S101).
For example, a manager of the GBAS ground station 1 determines the maximum acceptable detection failure probability PMD by performing a fault tree analysis (FTA) of an integrity malfunction (a malfunction where the GBAS ground station supplies data containing error that exceeds a predetermined tolerance to the aircraft 901). In performing fault tree analysis of the integrity malfunction, it creates a fault tree with the integrity risk demanded of the GBAS ground station 1 (e.g. 0.00001 percent) set at the top, and determines a maximum acceptable detection failure probability PMD that satisfies this integrity risk. A maximum acceptable detection failure probability PMD of, for example, 5.71E-4 (0.0571 percent) is determined.
The manager of the GBAS ground station 1 then inputs the determined maximum acceptable detection failure probability PMD to the threshold determination computer 300, which sets (stores) the inputted maximum acceptable detection failure probability PMD.
The threshold determination computer 300 then sets a maximum acceptable false alarm probability PFA (the probability that a GPS satellite will be deleted from the measuring objects of the aircraft 901 even though its data is normal) (Step S102).
For example, in a manner similar to the integrity malfunction fault tree analysis, the manager of the GBAS ground station 1 determines the maximum acceptable false alarm probability PFA by performing a fault tree analysis of a continuity malfunction (a malfunction where the GBAS ground station 1 becomes incapable of supplying data to the aircraft). A maximum acceptable false alarm probability PFA of, for example, 0.02E-6 (0.000002 percent) is determined.
The manager of the GBAS ground station 1 then inputs the determined maximum acceptable false alarm probability PFA to the threshold determination computer 300, which sets (stores) the inputted maximum acceptable false alarm probability PFA-
The threshold determination computer 300 then determines the maximum acceptable error ∆ PMERR in the range domain (the distance measured from the aircraft 901 to each GPS satellite) (Step S103).
For example, the threshold determination computer 300 sets APMERR = 0.6 meters (m). A publicly known method can be used to determine the maximum acceptable error APMERR, and will not be explained here.
The threshold determination computer 300 then sets a bound model for standard deviation of ephemeris error in a fault-free state for each orbit in the satellite-fixed coordinate system (Step S104). For example, the manager of the GBAS ground station 1 inputs values determined by offline analysis of previously broadcast ephemeris data to the threshold determination computer 300, and the threshold determination computer 300 sets (stores) the inputted values.
'Ephemeris data' is error in positional information indicated by ephemeris data
transmitted from a GPS satellite. A fault-free state is one where the ephemeris error is within a predetermined tolerance.
The following coordinate system is used as the satellite-fixed coordinate system. The X-axis is the along-track direction of the satellite orbit (the direction along which it travels), and oa represents a bound model of standard deviation of ephemeris error in the along-track direction. The Y-axis is the cross-track direction of the satellite orbit (the direction orthogonal to the along-track direction and parallel to the earth surface), and ac represents a bound model of standard deviation of ephemeris error in the cross-track direction. The Z-axis is the radial direction of the satellite orbit (the vertical (perpendicular to the earth's surface) direction), and σ k represents a bound model of standard deviation of ephemeris error in the radial direction.
A bound model is a normal distribution with the smallest standard deviation that can cover the probability distribution of error when it differs from normal distribution. To 'cover' signifies that a comparison of the cumulative error probability distribution with the cumulative normal distribution reveals that the cumulative error probability distribution is smaller than the cumulative normal distribution.
A publicly known method can be used to determine the bound models of standard deviation of fault-free ephemeris error, and will not be explained here.
By way of example, let us suppose that the threshold determination computer 300 determines the bound models as follows: bound model of standard deviation of ephemeris error in the radial direction σk = 3 meters, bound model of standard deviation of ephemeris error in the along-track direction σa = 14 meters, and bound model of standard deviation of ephemeris error in the cross-track direction σ 0 = 6 meters.
The threshold determination computer 300 (continuity threshold calculation unit 320) determines the continuity threshold THc based on the fault-free ephemeris error
distribution and on the maximum acceptable false alarm probability PFA that was set in Step S102 (Step S105).
Equation (2) below express the probability density P(r) of the scale of normalized three-dimensional error (a value obtained by normalizing the size of the ephemeris error) r.
where % is the circumference ratio, and exp is an exponential function.
The continuity threshold calculation unit 320 determines a value for r such that the cumulative probability of P(r) integrated in the positive direction of r from r = 0 is 1-PFA (hereinafter termed r0). This value rc indicates the minimum value of the scale (normalized size) of error that should be deemed acceptable to satisfy the maximum acceptable false alarm probability PFA-
The bound model of test statistic distribution Rbound can be expressed using the bound model of standard deviation of ephemeris error in the along-track direction aa, which has the maximum value (14 meters) among the bound models of standard deviation ak, aa, and ac in step S105, as Rbound = (V2)aar. Accordingly, the continuity threshold calculation unit 320 determines the continuity threshold THc by inserting the values of oa and r0 into the equation THc = (V2)oar.
By using the bound model with the maximum value among the bound models of standard deviation σk, σa, and σc (in this example, σa) to determine the continuity threshold THc in this manner, it becomes possible to reduce the calculation amount of the continuity threshold calculation unit 320 by simplifying the calculation equation, while
obtaining a continuity threshold THc that satisfies the maximum acceptable false alarm probability PFA that was set.
That is, since the continuity threshold calculation unit 320 determines the continuity threshold THc by substituting the bound models of standard deviation σk and σc with the bound model of standard deviation σa which indicates a larger error, it can obtain a continuity threshold THc that satisfies the maximum acceptable false alarm probability PFA that was set. In addition, by substituting the bound models of standard deviation Ok and ac with the bound model of standard deviation aa, the calculation equation is simplified and the calculation amount can be reduced.
The threshold determination computer 300 then calculates the maximum acceptable ephemeris error; MAEE) TMAEE (Step S106).
The maximum acceptable ephemeris error TMAEE indicates the maximum value of acceptable error in the position of a GPS satellite calculated from a new ephemeris from the true position of that GPS satellite.
A calculation equation for the maximum acceptable ephemeris error TMAEE will be explained.
FIG. 3 is an explanatory diagram of variables indicating the relationship between a GBAS ground station (reference station 100), a GPS satellite, and the aircraft 901. As shown in FIG. 3, D represents the distance between the reference station 100 and the true position of the GPS satellite, and "D represents the distance between the reference station 100 and a GPS satellite position calculated using a new ephemeris (" represents a hat. Likewise hereinafter).
Vector rs represents a satellite orbit error vector (a vector from the true position TP of a GPS satellite to a GPS satellite position NEP calculated using a new ephemeris), and vector rsT represents a transpose vector thereof. Vector ls represents a unit vector
from the GBAS ground station 1 in the direction of the GPS satellite that is the determination object, and vector 1ST represents a transpose vector thereof. Vector represents a unit vector from the GBAS ground station 1 in the direction of the GPS satellite that is the determination object, estimated from ephemeris data, and vector 1ST represents a transpose vector thereof. Vector Als represents an error vector of vector ls and vector \ and vector A1ST represents a transpose vector thereof
Vector Xair represents a base line vector (a vector from the reference station 100 to the aircraft 901).
0 represents the angle between the satellite orbit error vector rs and the base line vector xair (0°<8<180°), a represents the angle between the vector ls and the base line vector Xair (0°< a<180°, since the aircraft 901 is higher (in the sky) than the horizon when seen from the GBAS ground station, a=180° is not included), and p represents the angle between the satellite orbit error vector rs and the vector ls (0°
THi, the threshold determination unit 330 judges that a threshold cannot be set, and the threshold determination computer 300 performs an error process. For example, the threshold determination computer 300 performs an error process with respect to the manager of the GBAS ground station 1. In this case, the manager of the GBAS ground station conceivably responds by checking whether a device at the GBAS ground station 1 (especially the reference station 100) has malfunctioned.
FIG. 5 is an explanatory diagram showing an image of the relationship between
distribution of the scale r of normalized three-dimensional error and a range in which a threshold can be set. Here, rc is expressed by Equation (16), and n is expressed by Equation (17).
In FIG. 5, the distribution L12 obtained by inverting the fault-free distribution Lll from the position of r shown in Equation (18) represents a worst-case integrity.
The threshold determination computer 300 determines n from this distribution and the PMD set in Step S101. This obtains a threshold that can detect error greater than TMAEE at a detection failure probability lower than PMD
As described above, since the threshold determination unit determines the threshold for selecting a GPS satellite based on the maximum acceptable detection failure probability and the maximum acceptable detection false alarm probability, it can obtain a threshold that can ensure both the health and the continuity of the measuring system.
The continuity threshold calculation unit sets bound models for standard deviation of ephemeris error in the along-track direction, the cross-track direction, and the radial direction of the orbit of the GPS satellite, and calculates a continuity threshold based on a bound model of the distribution of test statistic obtained using the largest bound model among these bound models. Therefore, while simplifying the calculation
equation, it is possible to determine a maximum acceptable ephemeris error TMAEE that satisfies the maximum error in range ∆ PMERR of the measuring error of the aircraft 901.
When the ephemeris data is updated, the integrity threshold determination unit calculates the integrity threshold for a case where the vector rfault _ free from a position of a GPS satellite obtained based on updated ephemeris data to a position of the GPS satellite obtained based on pre-update ephemeris data, and the vector TMAEE from a position of the GPS satellite obtained based on an updated ephemeris data estimation value estimated from previous ephemeris data to the position of the GPS satellite obtained based on said pre-updated ephemeris data, are facing in the same direction. Therefore, the calculation equation can be simplified, and an integrity threshold TH1 that satisfies the integrity risk demand can be determined.
A program for realizing some or all of the functions of the threshold determination computer 300 can be stored on a computer-readable recording medium, and the processes of the various units can then be performed by making a computer system read the program stored in the recording medium. 'Computer system' includes an OS and hardware such as peripheral devices. If using a www system, 'computer system' also includes a webpage provision environment (or a display environment).
A 'computer-readable recording medium' includes portable media such as a flexible disk, a magneto-optical disk, a ROM, and a CD-ROM, and storage devices such as hardware built into the computer system. Furthermore, 'computer-readable recording medium' also includes media that dynamically store the program for a short period of time, such as a communication line used when transmitting a program via a network such as the Internet or a communication line such as a telephone line, and media that store the program for a fixed time, such as a volatile memory in a computer system that is a client or a server in such a case. The program can acceptably realize some of the functions
described above, or can realize the functions described above in combination with a program already stored in the computer system.
While preferred embodiments of the invention have been described with reference to the drawings, the specific configuration is not limited to these embodiments, and can be modified in various ways without departing from the spirit or scope of the present invention.
What is claimed is:
1. A threshold determination device that determines a threshold for selecting a GPS
satellite transmitting ephemeris data that will be used in measuring from among a
plurality of GPS satellites, comprising:
a threshold determination unit that determines a threshold for selecting a GPS satellite based on a maximum acceptable detection failure probability and a maximum acceptable detection false alarm probability that are set.
2. The threshold determination device according to claim 1, comprising
an integrity threshold calculation unit that calculates an integrity threshold that satisfies said maximum acceptable detection failure probability; and
a continuity threshold calculation unit that calculates a continuity threshold that satisfies said maximum acceptable detection false alarm probability;
and wherein said threshold determination unit determines a threshold for selecting said GPS satellite such that it is greater than said continuity threshold and lower than said integrity threshold.
3. The threshold determination device according to claim 2, wherein said
continuity threshold determination unit sets a bound model of standard deviation of
ephemeris error in each of an along-track direction which is the along-track direction of
said GPS satellite, a cross-track direction which is orthogonal to said along-track
direction and lies in a horizontal direction), and a radial direction which is vertical, and
calculates said continuity threshold based on a bound model of the distribution of test
statistic obtained using the largest one of said bound models.
4. The threshold determination device according to claims 2 or 3, wherein, when said ephemer is data has been updated, the integrity threshold determination unit calculates said integrity threshold for a case where a vector from a position of said GPS satellite obtained based on updated ephemeris data to a position of said GPS satellite obtained based on pre-update ephemeris data, and a vector from a position of said GPS satellite obtained based on an updated ephemeris data estimation value estimated from previous ephemeris data to the position of said GPS satellite obtained based on said pre-updated ephemeris data, are facing in the same direction.
5. A threshold determination method of determining a threshold for selecting a GPS satellite transmitting ephemeris data that will be used in measuring from among a plurality of GPS satellites, comprising:
a threshold determination step of determining a threshold for selecting a GPS satellite based on a maximum acceptable detection failure probability and a maximum acceptable detection false alarm probability that are set.
6. A program for making a computer, functioning as a threshold determination
device that determines a threshold for selecting a GPS satellite transmitting ephemeris
data that will be used in measuring from among a plurality of GPS satellites, execute a
threshold determination step of determining a threshold for selecting a GPS satellite
based on a maximum acceptable detection failure probability and a maximum acceptable
detection false alarm probability that are set.