JP2012047496A - Gps satellite position calculation method and apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technology capable of improving a position detection accuracy of a GPS satellite as a result by improving a calculation precision while simplifying a calculation method of a pseudo distance.SOLUTION: A GPS satellite position calculation apparatus 10 calculates a position B of a GPS satellite at a time tr when a signal is received at a position O of a reference point from a trajectory velocity v contained in a signal transmitted from the GPS satellite and a time tb; calculates an angle α of a horizon line with respect to a line segment connecting the position B of the GPS satellite and the position O of the reference point (S106); calculates a distance cs from the position O of the reference point to a position A of the GPS satellite at a time when a signal is transmitted as a pseudo distance on the basis of a distance ct from the position O of the reference point to the calculated position B of the GPS satellite, an acquired height h and the calculated angle α (S107); and calculates the position A of the GPS satellite using the pseudo distance (S108).

Description

  The present invention relates to a GPS satellite position calculation method and apparatus for receiving a signal transmitted from a GPS (Global Positioning System) satellite and calculating the position of the GPS satellite from a reference point whose position on the horizon is known.

  Usually, in order for the GPS receiver to detect the position, it is necessary to know the distance to the GPS satellite and the position of the GPS satellite. In the signal sent from the GPS satellite, data called a navigation message (hereinafter referred to as navigation data) is modulated, and the navigation data includes orbit information.

  A GPS receiver receives navigation data from a plurality of GPS satellites, and measures the position of the GPS satellite and the distance from the GPS satellite to a reference point, for example, an automobile, a ship, an aircraft, a work vehicle, a portable terminal For example, the position of the moving body as a reference point is detected.

  By the way, in the GPS receiver, a time difference Δt is generated between a transmission time when a signal is transmitted from a GPS satellite and a reception time when the signal is received. In this case, if the time completely matches between the clock provided to the GPS receiver and the atomic clock provided to the GPS satellite, the navigation data is received with a delay of the radio wave propagation time. . Therefore, the GPS receiver can calculate the distance to the GPS satellite by multiplying the propagation time of the radio wave by the speed of light (the propagation speed of the electromagnetic field).

  However, in many cases, the time is not exactly the same between both watches. For this reason, the GPS receiver calculates the distance to the GPS satellite as a “pseudo-range”. Here, the “pseudo distance” is measured by adding an error due to the advance of the clock of the GPS receiver to an accurate distance from the GPS satellite to the GPS receiver. That is, the GPS receiver calculates the pseudo distance by multiplying the propagation time obtained by subtracting the time when the GPS satellite transmits the signal from the time when the signal is received, by the speed of light. The position of each GPS satellite is calculated by receiving the ephemeris of the navigation data, and the position of the reference point is calculated in three dimensions from the position of the GPS satellite at the transmission time and the calculated pseudo distance. (For example, refer to Patent Document 1).

  The ephemeris of navigation data used in GPS is, for example, as shown in FIG. Determined based on the above. Since the position of the measurement point is calculated from the position of the GPS satellite 101, the position of the GPS satellite 101 is very important, and is currently updated about every two hours. The GPS receiver included in the measurement point calculates the current position in three dimensions from the position when the GPS satellite 101 is transmitted and the pseudorange.

  By the way, if the above-mentioned time error Δt is small, the GPS receiver should be able to calculate the position of the reference point using the three-dimensional xyz three variables based on the signal from the GPS satellite. However, since the time error Δt is very large, a technique for calculating the current position of the measurement point using four variables obtained by adding one variable of the time error Δt to three variables of the three-dimensional xyz is known. For example, as shown in FIG. 8, the GPS receiver 105 needs to receive navigation data from at least four GPS satellites 101 to 104.

  There is also a method using navigation data from four or more GPS satellites (see, for example, Patent Document 2). According to these techniques, since a large error occurs in the calculated pseudo distance, there is a limit in improving the positioning accuracy. Therefore, as shown in FIG. 9, there are various methods for improving accuracy, such as a method of estimating an error in pseudorange from differential data that is a positioning result at a reference base station (fixed station receiver 110). Proposed. However, these methods have disadvantages such as increasing the complexity of the system and increasing the calculation time and cost.

  Possible causes of errors include clock errors and orbit errors in GPS satellites, ionospheric refraction and tropospheric refraction in signal propagation, and changes in antenna phase center, clock errors, and multipaths in GPS receivers. In addition, the clock error includes a time error due to the error of the clock itself, a special relativity called a relativistic effect, and a general relativity. Furthermore, the influence of random noise can be considered.

Many attempts have been made to suppress the influence of these errors. However, at present, there are no decisive measures, and there is still trial and error. Therefore, as described above, a method is used in which data is acquired from four or more GPS satellites, or a pseudo distance is estimated from a positioning result at a reference ground base station.
Further, for example, as shown in FIG. 10, the relationship between the elevation angle and the distance measurement error is shown in a graph, and the dependence characteristic on the elevation angle (or zenith angle) is clarified as a factor of the error. For this reason, it is common to preferentially use GPS satellite data with a relatively small distance measurement error and a large elevation angle, and these errors complicate the pseudorange calculation method and system.

International Publication No. 2005/017552 Pamphlet Japanese Patent No. 3524018

  It is an object of the present invention to provide a technique capable of improving the calculation accuracy while simplifying the pseudo distance calculation method and consequently improving the GPS satellite position detection accuracy.

  In the invention according to claim 1, a signal transmitted from at least three GPS satellites is received by the receiver, and the position A of the GPS satellite at the signal transmission time tb is calculated based on a reference point where the position O on the horizon is known. A GPS satellite position calculation method for calculating by a satellite, a first step of acquiring orbit information including a signal transmission time tb, an orbital velocity v and an altitude h from a signal, and a GPS at a reception time tr The position B of the satellite is calculated from the time difference between the reception time tr and the transmission time tb and the orbital velocity v, and an angle α formed by the line segment connecting the position B of the GPS satellite and the position O of the reference point with respect to the horizon is obtained. Based on the second step to be calculated, the distance ct from the reference point O to the GPS satellite position B, the altitude h, and the angle α, the position A at the transmission time tb of the GPS satellite signal from the reference point position O. Ma A third step of calculating a distance cs at the first position, and a first step of calculating the position A of the GPS satellite from each of the distances cs from the reference point position O to the position A at the time of signal transmission of at least three GPS satellites. And 4 steps.

  In the invention according to claim 2, the signal received by at least three GPS satellites is received by the receiver, and the position B of the GPS satellite at the signal reception time tr is calculated based on the reference point where the position O on the horizon is known. A GPS satellite position calculation method for calculating by a satellite, a first step of acquiring orbit information including a signal transmission time tb, an orbital velocity v and an altitude h from a signal, and a GPS at a reception time tr A second step of calculating the satellite position B from the time difference between the reception time tr and the transmission time tb and the orbital velocity, and the distance ct from the reference point position O to the position B at the GPS satellite signal reception time tr And a fourth step of calculating the GPS satellite position B from the respective distances ct from the reference point position O to the positions B of at least three GPS satellites. And having a flop, a.

  In the invention according to claim 3, a GPS satellite position that receives a signal transmitted from at least three GPS satellites and calculates a position A of the GPS satellite at a signal transmission time tb from a reference point whose position O on the horizon is known. A calculation device that receives a navigation data acquisition unit that acquires orbit information including a signal transmission time tb, an orbital velocity v, and an altitude h from a signal, and a GPS satellite position B at the reception time tr An elevation angle calculation unit for calculating an angle α formed by a line segment connecting the position B of the GPS satellite and the position O of the reference point with respect to the horizon, calculated from the time difference between the time tr and the transmission time tb and the orbital velocity v; Based on the distance ct from the reference point O to the position B of the GPS satellite, the altitude h, and the angle α, a pseudo value for calculating the distance cs from the position O of the reference point to the position A at the GPS satellite signal transmission time tb. Distance calculation And a satellite position calculation unit that calculates the position A of the GPS satellite from each of the distances cs from the position O of the reference point to the position A at the transmission time tb of at least three GPS satellite signals. And

  In the invention according to claim 4, a GPS satellite position that receives a signal transmitted from at least three GPS satellites and calculates a position B of the GPS satellite at a signal reception time tb from a reference point whose position O on the horizon is known. A calculation device that receives a navigation data acquisition unit that acquires orbit information including a signal transmission time tb, an orbital velocity v, and an altitude h from a signal, and a GPS satellite position B at the reception time tr A pseudo distance calculation unit that calculates a distance ct from the position O of the reference point to the position B at the reception time of the GPS satellite signal, calculated from the time difference between the time tr and the transmission time tb and the orbital velocity v; A satellite position calculating unit that calculates the position B of the GPS satellite from each distance ct from the position O to the position B of at least three GPS satellites.

  According to the first aspect of the present invention, since the distance connecting the position A of the GPS satellite and the position O of the reference point at the time tb when the signal is transmitted is used as the pseudo distance, the position A of the GPS satellite is calculated. Compared to the conventional method of calculating the GPS satellite position A using the distance ct between the GPS satellite position B and the reference point position O at tr as the pseudo distance, the calculation method of the pseudo distance is simplified. The accuracy can be improved, and as a result, the position detection accuracy of the GPS satellite can be improved. In addition, when calculating the position A of the GPS satellite at the transmission time tr, observation data from a plurality of existing stations on the ground is not required, so that the calculation method is simplified.

  According to the second aspect of the present invention, the GPS satellite position B is calculated by using the distance ct between the GPS satellite position B and the reference point position O at the time tr when the signal is received as the pseudo distance. Compared to the conventional method of calculating the GPS satellite position B using the distance cs between the GPS satellite position A and the reference point position O at the time tb as a pseudo distance, the pseudo distance calculation method is simplified. The calculation accuracy can be improved, and as a result, the position detection accuracy of the GPS satellite can be improved. In addition, in calculating the position B of the GPS satellite signal reception time tr, observation data from a plurality of existing stations on the ground is not required, so that the calculation method is simplified.

  According to the third aspect of the invention, the satellite position calculation unit uses the distance cs between the position A of the GPS satellite and the position O of the reference point at the time tb when the signal is transmitted as a pseudo distance, and the signal of the GPS satellite In order to calculate the position A at the transmission time tb, the conventional GPS that calculates the position A of the GPS satellite using the distance ct between the position B of the GPS satellite and the position O of the reference point at the signal reception time tr as a pseudo distance. As compared with the satellite position calculation device, it is possible to provide a GPS satellite position calculation device that can improve the calculation accuracy while simplifying the pseudo distance calculation method, and consequently improve the position detection accuracy of the GPS satellite. . In addition, since the observation data from a plurality of ground stations on the ground is not necessary for calculating the position A at the signal transmission time tb of the GPS satellite, it is possible to provide a GPS satellite position calculation device that reduces the calculation load. .

  According to the invention of claim 4, the satellite position calculation unit uses the distance ct between the GPS satellite position B and the reference point position O at the time tr when the signal is received as a pseudo-range, Compared with the conventional GPS satellite position calculation device that calculates the position B of the GPS satellite using the distance cs between the position A of the GPS satellite at the time of signal transmission and the position O of the reference point as a pseudo distance in order to calculate B. Thus, it is possible to provide a GPS satellite position calculation device that can improve the calculation accuracy while simplifying the calculation method of the pseudo distance, and consequently improve the position detection accuracy of the GPS satellite. In addition, when calculating the position B of the GPS satellite signal reception time tr, observation data from a plurality of existing stations on the ground is not required, so the calculation load is reduced.

It is a figure which shows the structure of the GPS satellite position calculation apparatus which concerns on Example 1 of this invention. It is the figure which expressed the basic idea of GPS positioning with two inertia systems. FIG. 3 is a diagram illustrating a relationship between angles α and β between a GPS satellite having a base point as a base in the inertial system of FIG. 2. It is a flowchart which shows operation | movement of the GPS satellite position calculation apparatus which concerns on Example 1 of this invention. It is the figure which expressed the basic idea of GPS positioning with the rotation inertia system. It is a flowchart which shows operation | movement of the GPS satellite position calculation apparatus which concerns on Example 2 of this invention. It is the figure quoted in order to demonstrate the conventional GPS satellite position calculation method. It is the figure quoted in order to demonstrate the conventional GPS positioning. It is the figure quoted in order to demonstrate the GPS positioning using the differential data by the conventional fixed station receiver. It is the figure which showed the relationship between an elevation angle and the ranging error by GPS positioning with the graph.

  Embodiments of the present invention will be described below with reference to the accompanying drawings.

First, Embodiment 1 of the present invention will be described with reference to the drawings.
(Configuration of Example 1)
As shown in FIG. 1, a GPS satellite position calculation apparatus 10 according to Embodiment 1 of the present invention includes a receiver 11, an analog / digital converter 12 (A / D (analog / digital) converter 12), and a correlation. The unit 13, the arithmetic unit 14, the control unit 15, and the storage unit 16 are configured. The receiver 11 includes an antenna 11a and a high frequency circuit 11b (hereinafter referred to as an RF (Radio Frequency Circuit) circuit 11b).

  The RF circuit 11b receives signals (radio waves) emitted from at least three GPS satellites 21 to 23 via the antenna 11a, down-converts the signals into intermediate frequency (IF) signals, and performs A / D. Output to the converter 12.

  The A / D converter 12 converts the analog signal output from the RF circuit 11 b into a digital signal and outputs the digital signal to the correlator 13 and the control unit 15.

  The correlator 13 detects the reception frequency based on the input digital signal. Specifically, the correlator 13 demodulates the digital signal output from the A / D converter 12 from the C / A (Coarse and Access) code of the GPS satellite, and calculates the radio wave propagation delay.

  The control unit 15 acquires navigation data from the digital signal output from the A / D converter 12 and outputs the navigation data to the computing unit 14, and issues a positioning command including calculation of a pseudo distance to the computing unit 14. The calculator 14 has a function of performing pseudo distance calculation and positioning calculation.

  By the way, the navigation data used for GPS positioning includes “almanac data” and “ephemeris data”.

  “Almanac data” describes parameters that indicate the approximate positions of all GPS satellites, and can be used for about two weeks. This time limit is a limit due to the GPS satellite orbit shifting with time, and corresponds to the valid period of data. “Ephemeris data” is data describing detailed parameters of each satellite orbit information, and is used when the control unit 15 calculates the position of each GPS satellite. The time limit for the ephemeris data is about 2 hours.

  The computing unit 14 performs the following first to fourth steps under program control by the control unit 15.

  Specifically, in the first step, from the navigation data included in the signal received by the RF circuit 11b, the positions A1, A2, A3 (hereinafter referred to as the three GPS satellites 21-23 at the time tb when the signal is transmitted). Collectively referred to as position A), times tb1, tb2, and tb3 (hereinafter collectively referred to as tb) when the GPS satellites 21 to 23 transmit signals, and orbital speeds v1 of the GPS satellites 21 to 23, Orbital information including v2, v3 (hereinafter collectively referred to as v) and altitudes h1, h2, and h3 (hereinafter collectively referred to as h) at the time when the GPS satellites 21 to 23 transmit signals. get.

  In the next second step, the positions B1, B2, and B3 (hereinafter collectively referred to as position B) of the GPS satellites 21 to 23 at the reception time tr acquired in the first step are referred to as the reception time tr. Is calculated from the time difference (t = tr−tb) between the transmission time tb and the orbital velocity v, and the angles α1, α2 formed by the line segment connecting the position B of the GPS satellite and the position O of the reference point with respect to the horizon. , Α3 (hereinafter collectively referred to as α). Here, the reference point position O is a fixed station position O whose position on the horizon is known.

  In the next third step, distances ct1, ct2, and ct3 (hereinafter collectively referred to as ct) from the reference point O calculated in the second step to the position B of the GPS satellite are acquired in the first step. Based on the altitude h of each of the GPS satellites 21 to 23 and the angle α calculated in the second step, between the position A of each GPS satellite 21 to 23 and the reference point position O at the signal transmission time tb. The pseudo distance is calculated by calculating the distance cs.

  In the next fourth step, the position A at the GPS satellite transmission time tb is calculated from the distance cs between the position A of the three GPS satellites 21 to 23 calculated in the third step and the position O of the reference point.

  The first to fourth steps described above are programmed in advance and stored in the storage unit 16. The control unit 15 is configured by, for example, a microprocessor, and causes the calculator 14 to calculate the angle α and the distance cs (pseudo distance) by sequentially reading and executing the program stored in the storage unit 16. Finally, the position A at the GPS satellite transmission time tb is calculated.

  In addition, the storage unit 16 also stores information such as the center position and radius r of the earth, the frequencies of the GPS satellites 21 to 23 that are GPS signal reception targets, and the speed of light c, which are referred to by the control unit 15. Yes.

  The calculation of the angle α, the distance cs (pseudo distance), and the position A at the GPS satellite transmission time tb will all be described as being performed by the computing unit 14 under the control of the control unit 15. The control unit 15 may execute instead of the computing unit 14.

(Operation of Example 1)
Hereinafter, the operation of the GPS satellite position calculation apparatus 10 according to the first embodiment of the present invention will be described. Before that, the basic concept of GPS positioning calculation for explaining the embodiment will be described with reference to FIGS. This will be briefly explained using.

  Here, as shown in FIG. 2A, a case where a GPS satellite position calculation device 10 located at a reference point receives a signal emitted from a GPS satellite at position A at time 0 (Time = 0). Suppose. At the time when the GPS satellite position calculation device 10 receives the signal, the GPS satellite has already moved to position B instead of position A. In FIG. 2 (a), the GPS satellite is indicated by the symbol S.

  This state will be described with reference to a K coordinate indicated by a square (parallelogram) dotted line in FIG. 2B and a Q coordinate indicated by a rectangular dotted line in FIG.

  According to FIG. 2B, there are an O point and a B point on the diagonal of the K coordinate. Further, according to FIG. 2C, there is a point A on the right side of the upper side of the Q coordinate. The K coordinate moves in the right direction at a velocity v with respect to the Q coordinate. Here, the GPS satellite S is always at the B point of the K coordinate. FIG. 2D shows a state in which these two inertia systems (a coordinate system in which the law of inertia is established) are overlapped at Time = 0.

  In FIG. 2 (d), position A and position B overlap. In this state, if a GPS satellite emits a signal at a radio wave propagation speed (light velocity c) from time A to point O of the K inertial system at time 0, at time t (Time = t). The signal reaches point O. Thus, the distance between point B and point O is set to be ct. The distance between the O point and the P point is set to be vt.

  FIG. 2 (e) shows the situation when the point O and the point P overlap when Time = t. According to FIG.2 (e), the signal transmitted from the B point by the GPS satellite reaches the O point. The GPS satellite position calculation device 10 located in another Q inertial system appears as if the signal emitted from the point A has reached the point P. At this time, since the signal propagates at the speed of light even in the Q inertial system, the distance from the point A to the point P is cs.

  FIG. 3 shows an angle reflected in the relationship between the signal and the motion shown by the inertial system in FIG. Here, the elevation angle at the time of signal transmission of the GPS satellite (the angle of the line segment connecting the reference position A of the GPS satellite S and the position O of the reference point with respect to the horizon e) is β, and the GPS satellite position calculation device 10 uses the signal as the signal. The elevation angle at the time of reception (the angle of the line segment connecting the current position B of the GPS satellite and the position O of the reference point with respect to the horizon e) is α. Note that the altitude of the GPS satellite S is h, and the altitude h and other information regarding the orbital speed v and the time t are all included in the navigation data transmitted from the GPS satellite S.

  From FIG. 3, the distance cs can be expressed by the following arithmetic expression (1) from the three-square theorem based on the right triangle ΔOAC.

  Here, ct · sin α is equal to the height h. Then, by substituting the above equation (1) into ct · sin α = cs · sin β, which is the relational expression between the two right triangles ΔOBD and ΔOAC, the following relational expression (2) is derived. The When this is further modified, the following angular relational expression (3) is derived. Subsequently, when the above length relational expression is considered with respect to this angular relational expression (3), the following time change expression (4) is derived.

  In accordance with the above angle relation (3), the angle α with respect to the horizon e of the line segment connecting the position B of the GPS satellite S and the position O of the reference point and the reference position A of the GPS satellite and the position O of the reference point are connected. An angle β with respect to the horizon e of the line segment can be calculated. Then, the pseudo distance cs between the reference point and the GPS satellite S at the time of signal reception from the GPS satellite S is obtained from the angle α calculated by the angle relational expression (3) by the following relational expression (5).

By the way, in the above-described angular relational expression (3), when β = π / 2, α = cos ⁻¹ (v / c), and the time variation expression (4) at this time is expressed by the following arithmetic expression (6) Deformed.

  The above arithmetic expression (6) coincides with the time delay due to the special relativity. That is, the special relativity indicates that the relationship between the angle α and the angle β cannot be considered. For this reason, conventionally, as shown in the graph of FIG. 8, the error tends to increase unless the pseudorange is calculated based on a signal from a satellite having a large elevation angle. This tendency is similar to the amount of zenith angle delay that has been reported as a conventional error. That is, as the zenith angle increases, the amount of delay increases at a rate of approximately 1 / cos, so the error increases.

  On the other hand, in the first embodiment of the present invention, the relationship between the angle α and the angle β is reflected in the calculation of the pseudo distance, thereby making it possible to calculate the pseudo distance with high accuracy independent of the zenith angle. Further, it is not necessary to delay the GPS satellite clock with respect to the clock of the receiving station in consideration of special relativity. That is, the GPS satellite clock and the receiving station clock may be synchronized. The above is the idea that is the basis for the pseudorange calculation of two inertial systems that perform relative motion.

  Next, the operation of the GPS satellite position calculation apparatus 10 according to the first embodiment of the present invention shown in FIG. 1 will be described in detail with reference to the processing flowchart of the control unit 15 shown in FIG.

  First, in step S101, the controller 15 inputs 0 to the counter value i assigned to the program. The counter counts the number of GPS satellites that are the targets of signal reception. Here, the counter position is detected using n (for example, three) GPS satellites 21 to 23. explain.

  Next, in step S102, the control unit 15 determines whether or not the RF circuit 11b has received a high-frequency analog signal transmitted from the GPS satellite 21 that is a signal reception target, and confirms that it has been received. In step S103, the signal is down-converted to an IF signal and output to the A / D converter 12.

  Next, the control unit 15 starts a signal conversion operation by the A / D converter 12. In response to this, the A / D converter 12 converts the I / F signal into a digital signal and outputs it to the correlator 13 and the control unit 15 in step S104.

  Next, the control unit 15 acquires navigation data (orbital velocity v, transmission time tb, altitude h) from the digital signal A / D converted in step S105 and outputs the navigation data to the calculator 14. At the same time, a pseudo distance calculation command is issued to the computing unit 14.

  When the computing unit 14 receives the pseudo distance calculation command from the control unit 15, the time tr at which the signal is received at the receiving station (reference point position O) from the orbital velocity v and the transmission time tb acquired in step S 105. The position B of the GPS satellite at is calculated. Here, the position B of the GPS satellite is calculated from the time difference t (t = tr−tb) between the reception time tr when the receiving station receives the signal and the transmission time tb of the navigation data and the orbital velocity v of the navigation data.

  Subsequently, the angle α of the line segment connecting the position B of the GPS satellite S and the position O of the reference point with respect to the horizon is calculated based on the above angle relational expression (3). Then, based on the angle α calculated here and the orbital velocity v of the acquired GPS satellite, the position A of the GPS satellite at the transmission time tb and the reference point of the horizon e based on the angular relational expression (3). The angle β of the line segment connecting the position O is calculated.

  Next, in step S107, the computing unit 14 obtains information on the angle α calculated in step S106, the distance ct between the position B of the GPS satellite and the position O of the reference point whose position is known, and the altitude h. Based on this, the distance cs between the position A of the GPS satellite and the position O of the reference point is calculated as the pseudo distance. The calculation of the pseudo distance cs is obtained when the computing unit 14 calculates the above-described relational expression (5).

  Subsequently, in step S108, the computing unit 14 determines the position Ai of the GPS satellite at the transmission time tb from the distance cs (pseudo distance) between the position A of the GPS satellite which is a pseudo distance and the position O of the reference point whose position is known. (Si (xi, yi, zi)) is calculated by solving the following arithmetic expression (7). Then, the calculation unit 14 delivers the calculation result to the control unit 15.

  When receiving the information on the position A of the GPS satellite from the computing unit 14, the control unit 15 stores it in a predetermined area of the storage unit 16 in step S109, and increments the counter value i by 1 in step S110.

  In step S111, the control unit 15 compares the counter value i with the number n of GPS satellites to be received. If the number of GPS satellites that have received the signal is less than n (step S111 “NO”), the process returns to the GPS signal reception determination process in step S102. The same processing (steps S102 to S110) as the reception of the signal 21 is repeatedly executed. That is, the computing unit 14 calculates the distance cs between the reference points where the position A and the position O of each GPS satellite at the signal transmission time tb are known, and determines the pseudo distance from the pseudo distance cs. Simultaneous equations (5) showing the position A (S1 (x1, y1, z1), S2 (x2, y2, z2), S3 (x3, y3, z3)) at the transmission time tb by the above equation (7) Is calculated by solving

  Finally, in step S111, the control unit 15 confirms that the counter value i has reached the number n of GPS satellites to be received (step S111 "YES"), and calculates the GPS satellite position A described above. A series of processes for is completed.

(Effect of Example 1)
According to the GPS satellite position calculation apparatus 10 according to the first embodiment described above, the distance between the position A at the time when the GPS satellite transmits a signal and the position O of the reference point is used as a pseudo distance, and the position of the GPS satellite is calculated. Compared to the conventional method in which the GPS satellite position A is calculated using the distance ct between the GPS satellite position B and the reference point position O at the time of receiving the signal as a pseudo-range, The calculation accuracy can be improved while simplifying the distance calculation method, and as a result, the position detection accuracy of the GPS satellite can be improved. According to the first embodiment, data on the speed v and the angle α of the GPS satellite is necessary to calculate the pseudo distance cs. However, the pseudo distance ct at the time of GPS satellite signal reception is set as the pseudo distance at the time of signal transmission. By simply replacing the distance cs, calculation with high accuracy can be easily performed.

  In the flowchart of FIG. 4, step S105 constitutes GPS satellite position calculation device 10 “acquisition of navigation data including signal transmission time tb, orbital velocity v and altitude h from the signal. Part.

  Further, the step S106 calculates “the position B of the GPS satellite at the reception time tr is calculated from the time difference between the reception time tr and the transmission time tb and the orbital velocity v, and the position B of the GPS satellite and the position O of the reference point are obtained. It corresponds to an “elevation angle calculating unit that calculates an angle α formed by a connecting line segment with respect to the horizon”.

  Further, the step S107 is “based on the distance ct from the reference point O to the GPS satellite position B, the altitude h, and the angle α, from the reference point position O to the position A at the GPS satellite signal transmission time. This corresponds to a “pseudo distance calculation unit that calculates the distance cs”.

  Step S108 corresponds to “a satellite position calculation unit that calculates the position A of the GPS satellite from each of the distances cs from the position O of the reference point to the position A at the transmission time tb of at least three GPS satellite signals”. To do.

  In Example 1 described above, calculation of the pseudorange was attempted using two inertial systems. However, in practice, the relationship between the GPS satellites 21 to 23 and the reference point on the ground is a relative circular orbit, so that it becomes a rotational inertia system. Hereinafter, the relationship between the rotational motion of the rotary inertia system and signal transmission will be described with reference to FIG.

In FIG. 5, the relationship between rotational motion and signal transmission as viewed from the K coordinate is shown in FIG. 5 (a), and the relationship between rotational motion and signal transmission as viewed from the Q coordinate is shown in FIG. 5 (b).
In FIG. 5A, when viewed from the K coordinate, the GPS satellite position calculation device 10 at the ground reference point moves from the position P to the position O by the angle ωt at time t. In FIG. 5B, when viewed from the Q coordinate, the GPS satellites 21 to 23 move from the position A to the position B by the angle ωt at time t.

  From this, by calculating the following relational expression (8) with the K coordinate, it is possible to calculate the relation between the movement and the time in the rotational movement, and also calculating the following relational expression (9) with respect to the Q coordinate. By doing so, it is possible to calculate the relationship between the motion and time in the rotational motion. Here, ω is the relative angular velocity of the GPS satellite position calculation device 10 and the GPS satellites 21 to 23 at the positioning point on the ground, r is the radius of the earth, and R is the radius of the orbit of the GPS satellite.

  Note that since the relationship between ct, cs, and vtr does not change for ellipses and satellites with more complicated orbits, the pseudo distance cs is calculated by drawing a similar triangular vector consisting of ct, cs, and vtr. Is possible. Accordingly, in calculating the pseudo distance cs in the GPS satellite position calculation device 10, except that the computing unit 14 calculates the relationship between the motion and the time in the rotational motion by the relational expressions (8) and (9) described above. Performs the same operation as in the first embodiment.

  As described above, the relationship between the GPS satellites 21 to 23 performing the circular orbit and the ground reference point can be expressed by the rotational inertia system, and the relational expressions (13) and (14) described above regarding the relationship between the rotational motion and the time at this time. In the case of taking a more complicated trajectory such as an ellipse, it is possible to calculate the pseudo distance cs with high accuracy without causing an error, as in the above-described embodiment.

  In calculating the pseudo distance cs, information on the velocity v and the angle α of the GPS satellites 21 to 23 is necessary. However, conventionally, ct used as the pseudo distance is simply replaced with cs, and calculation with high accuracy is possible. Is possible. Similarly, in the case of a circular orbit, it is possible to calculate a pseudo distance with high accuracy without causing an error.

  In addition, the GPS satellite position calculation method according to the first embodiment of the present invention is a calculation method that can take elevation angle-dependent characteristics into consideration, and this can greatly improve the calculation accuracy of the pseudorange. If the calculation accuracy of the pseudo distance is improved, the accuracy of the position detection of the reference point is consequently greatly improved. In addition, industrial effects such as simplification of the calculation method and reduction of the number of GPS satellites used are extremely large.

  In the first embodiment of the present invention described above, an example in which the position A of the GPS satellite is calculated using the distance cs between the position A of the GPS satellite and the position O of the reference point at the signal transmission time tb as a pseudo distance will be described. However, hereinafter, as the second embodiment, the GPS satellite position B is calculated using the distance ct between the GPS satellite position B and the reference point position O at the signal reception time tr as a pseudo distance. explain.

(Configuration of Example 2)
In the second embodiment described below, the GPS satellite position calculation device 10 uses the same configuration as that of the first embodiment shown in FIG. However, the computing unit 14 executes the processing from the first step to the fourth step shown below under program control by the control unit 15.

  Specifically, in the first step, from the navigation data included in the signal received by the RF circuit 11, the positions A1, A2, A3 (hereinafter referred to as the three GPS satellites 21 to 23) at the time when the signals are transmitted. Orbital information including each transmission time tb and each orbital velocity v is acquired.

  In the subsequent second step, the GPS satellite positions B1, B2, and B3 (hereinafter, generic names) at the reception time tr when the position O of the reference point received the signal from the orbital velocity v and the time tb acquired in the first step. And B) is calculated from the time difference t = tr−tb.

  In the third step, distances ct1, ct2, and ct3 (hereinafter collectively referred to as ct) between the position B of the GPS satellite calculated in the second step and the position O of the reference point are referred to as pseudo distances. calculate.

  Finally, in the fourth step, each GPS at the reception time tr of the signal from each distance ct between the position B and the position O of the three GPS satellites calculated in the third step is known. Calculate satellite position B

  The first to fourth steps are programmed in advance and stored in the storage unit 16. Then, the control unit 15 is constituted by, for example, a microprocessor, and sequentially reads out and executes a program stored in the storage unit 16, thereby causing the computing unit 14 to have the position of the GPS satellite based on the above-described distance ct (pseudorange). B is calculated.

(Operation of Example 2)
Hereinafter, a detailed operation will be described by paying attention to the difference from the first embodiment with reference to the flowchart shown in FIG. The processing (S201 to S204) from when the GPS satellite positioning operation device 10 receives a signal from a GPS satellite until it issues a pseudo distance calculation command to the computing unit 14 is the same as in the first embodiment (S101 to S104). Therefore, the navigation data acquisition process in step S205 will be described.

  When the computing unit 14 receives the pseudo distance calculation command from the control unit 15, in step S206, the reference point position O receives the signal from the orbital velocity v acquired in step S205 and the reception time tb. The position B of the GPS satellite at is calculated from the time difference t = tr−tb. In step S207, the time difference (t = tr−tb) between the transmission time tb when the GPS satellite transmits a signal and the reception time tr when the reference point receives the signal is multiplied by the speed of light c, so that the reference point becomes the signal. The distance ct between the GPS satellite and the reference point at the reception time tr when the signal is received is calculated as a pseudo distance.

  Subsequently, in step S208, the computing unit 14 determines the position at the reception time tr of the GPS satellite signal from the distance ct between the position B of the GPS satellite which is a pseudo distance and the position O of the reference point whose position is known. B (= Si (xi, yi, zi)) is calculated by the above-described arithmetic expression (7). Then, the calculation unit 14 delivers the calculation result to the control unit 15.

  When receiving the information on the position B of the GPS satellite from the computing unit 14, the control unit 15 stores it in a predetermined area of the storage unit 16 in step S209, and increments the counter value i by 1 in step S210.

  In step S211, the control unit 15 compares the counter value i with the number n of GPS satellites to be received. If the number of GPS satellites that have received the signal is less than n (step S211 “NO”), the process returns to the GPS signal reception determination process in step S202. The same processing (steps S202 to S210) as the reception of the signal 21 is repeatedly executed. That is, the calculator 14 calculates a pseudo distance by calculating a distance ct between the position B of each GPS satellite and the position O of a reference point whose position is known at the signal reception time tr, and calculates the pseudo distance from the pseudo distance ct. The position B (S1 (x1, y1, z1), S2 (x2, y2, z2), S3 (x3, y3, z3)) at the reception time tr of the GPS satellite is represented by the simultaneous expression shown by the above-described arithmetic expression (7). Calculation is performed by solving equation (7).

  Finally, in step S211, the control unit 15 confirms that the counter value i has reached the number n of GPS satellites to be received (step S211 “YES”), and calculates the GPS satellite position B described above. A series of processes for is completed.

(Effect of Example 2)
According to the GPS satellite position calculation device 10 according to the second embodiment of the present invention described above, the distance between the position B of the GPS satellite and the reference point where the position O is known at the time when the satellite position calculation unit receives the signal. In order to calculate the position B of the GPS satellite using ct as a pseudo distance, the position of the GPS satellite was calculated using the distance connecting the position of the GPS satellite and the reference point position O at the time of signal transmission as a pseudo distance. Compared with the method, it is possible to provide a GPS satellite position calculation device 10 that improves the calculation accuracy while simplifying the pseudo-range calculation method, and as a result, can improve the position detection accuracy of the GPS satellite. Further, in calculating the position B of the GPS satellite, observation data from a plurality of existing stations on the ground is not required, so that the calculation method is simplified.

  Here, the distance ct between the calculated GPS satellite position B and the reference point position O is a pseudo distance, but from the reference point position O, further, the GPS satellite position A and the reference point position. The distance cs connecting with O may be calculated, and the calculated distance cs of the line segment may be a pseudo distance. In this case, although the number of operation steps increases, the pseudo distance cs can be calculated without using the elevation angle, and the calculation using the existing GPS positioning system can be performed, thereby reducing the calculation load.

  Further, in the flowchart of FIG. 6, step S205 is “acquisition of navigation data that acquires the orbit information including the signal transmission time tb, the orbital velocity v, and the altitude h from the signal” constituting the GPS satellite position calculating device 10. Part.

  Steps S206 and S207 are as follows: “The position B of the GPS satellite at the signal reception time tr is calculated from the time difference between the reception time tr and the transmission time tb and the orbital velocity v, and the GPS satellite signal is calculated from the reference point position O. Corresponds to a “pseudo distance calculation unit that calculates the distance ct to the position B at the reception time tr”.

  Step S208 corresponds to “a satellite position calculation unit that calculates the position B of the GPS satellite from each distance ct from the position O of the reference point to the position B of at least three GPS satellites”.

  In Example 2 described above, calculation of the pseudorange was attempted using two inertial systems. However, in practice, the relationship between the GPS satellites 21 to 23 and the reference point on the ground becomes a relative circular or elliptical orbit, so that it becomes a rotational inertia system. Since the relationship between the rotational motion of this rotary inertia system and signal transmission is the same as that of the first embodiment described with reference to FIG. 5, the description thereof is omitted to avoid duplication.

  The GPS satellite position calculation apparatus of the present invention is not limited to a car navigation system, and can be used for detecting the position of a moving body serving as a reference point, such as a ship, an aircraft, a work vehicle, and a portable terminal. Further, if a method such as estimating the pseudo-range error from the differential data is adopted, the accuracy can be further improved. In addition to position detection, atmospheric delay, ionospheric delay, and the like can be calculated with high accuracy, so a dramatic improvement in weather observation can be expected.

  DESCRIPTION OF SYMBOLS 10 ... GPS satellite position calculation apparatus, 11 ... Receiver, 11a ... Antenna, 11b ... RF circuit, 12 ... A / D converter, 13 ... Correlator, 14 ... Calculator, 15 ... Control part, 16 ... Memory | storage part, 21-23 GPS satellites.

Claims (4)

A GPS satellite position in which a signal transmitted from at least three GPS satellites is received by a receiver, and a position A of the GPS satellite at the time of signal transmission is calculated by a calculator based on a reference point whose position O on the horizon is known. A calculation method,
A first step of acquiring trajectory information including a transmission time tb of the signal, a trajectory speed v, and an altitude h from the signal;
The position B of the GPS satellite at the reception time tr of the signal is calculated from the time difference between the reception time tr and the transmission time tb and the orbital velocity v, and the position B of the GPS satellite at the reception time tr A second step of calculating an angle α formed by a line segment connecting the position O of the reference point with respect to the horizon;
Based on the distance ct from the position O of the reference point to the position B of the GPS satellite at the reception time tr, the altitude h, and the angle α, the GPS at the transmission time tb from the position O of the reference point. A third step of calculating a distance cs to the position A of the satellite;
A fourth step of calculating the position A of the GPS satellite at the transmission time tb from each of the distances cs from the position O of the reference point to the position A of the at least three GPS satellites at the transmission time tb;
A GPS satellite position calculation method comprising: A GPS satellite position calculation method in which a signal transmitted from at least three GPS satellites is received by a receiver, and a position B of the GPS satellite at the reception time is calculated by a calculator based on a reference point whose position O on the horizon is known. Because
A first step of acquiring trajectory information including a transmission time tb of the signal and a trajectory velocity v from the signal;
A second step of calculating the position B of the GPS satellite at the reception time tr from the time difference between the reception time tr and the transmission time tb and the orbital speed;
A third step of calculating a distance ct from the position O of the reference point to the position B of the GPS satellite at the reception time tr;
A fourth step of calculating the position B of the GPS satellite at the reception time tr from each distance ct from the position O of the reference point to the position B of the at least three GPS satellites at the reception time tr; ,
A GPS satellite position calculation method comprising: A GPS satellite position calculation device that receives a signal transmitted by at least three GPS satellites and calculates a position A of the GPS satellite at a signal transmission time from a reference point where a position O on the horizon is known,
A navigation data acquisition unit for acquiring trajectory information including the signal transmission time tb, trajectory speed v, and altitude h from the signal;
The position B of the GPS satellite at the reception time tr is calculated from the time difference between the reception time tr and the transmission time tb and the orbital velocity v, and the position B of the GPS satellite at the reception time tr and the reference point An elevation angle calculation unit for calculating an angle α formed by a line segment connecting the position O to the horizon;
Based on the distance ct from the position O of the reference point to the position B of the GPS satellite at the reception time tr, the altitude h, and the angle α, the GPS at the transmission time tb from the position O of the reference point. A pseudo-range calculator for calculating a distance cs to the position A of the satellite;
A satellite position calculating unit that calculates the position A of the GPS satellite at the transmission time tb from each of the distances cs from the position O of the reference point to the position A of the at least three GPS satellites at the transmission time tb;
A GPS satellite position calculation device that executes the following. A GPS satellite position calculation device that receives a signal transmitted by at least three GPS satellites and calculates a position B of the GPS satellite at a reception time of the signal from a reference point where a position O on the horizon is known;
A navigation data acquisition unit for acquiring trajectory information including the signal transmission time tb, trajectory speed v, and altitude h from the signal;
The position B of the GPS satellite at the reception time tr is calculated from the time difference t between the reception time tr and the transmission time tb and the orbital velocity v, and the GPS satellite at the reception time tr is calculated from the reference point position O. A pseudo-range calculator for calculating a distance ct to the satellite position B;
A satellite position calculation unit that calculates the position B of the GPS satellite at the reception time tr from the distance ct from the position O of the reference point to the position B of the at least three GPS satellites at the reception time tr;
A GPS satellite position calculation device characterized by comprising:

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