JP2021015002A - Estimation method of relative position between antennas and estimation program of relative position between antennas - Google Patents

Abstract

To realize an estimation method of a relative position between antennas and an estimation program of a relative position between antennas capable of easily estimating relative positions between the antennas.SOLUTION: A frequency deviation based on Doppler effects between each of a first antenna 12A and a second antenna 12B and a positioning satellite is detected from positioning information received by each of the first antenna 12A and the second antenna 12B, a velocity difference A between the first antenna 12A and the second antenna 12B in the ENU coordinate system is calculated based on the frequency deviation, an azimuth angle θ of a moving object 20 is calculated, a yaw rate ω of the moving object 20 is calculated, and the relative positions of the first antenna 12A and the second antenna 12B on planes whose axes are a direction and a width of the moving object 20 are estimated based on a difference between the velocity difference B between the antenna 12A and the second antenna 12B that is calculated based on the azimuth angle θ and the yaw rate ω and the velocity difference A in the ENU coordinate system.SELECTED DRAWING: Figure 3

Description

The present invention relates to an antenna-to-antenna relative position estimation method and an antenna-to-antenna relative position estimation program in GNSS (Global Navigation Satellite System).

In GNSS, which estimates the position by using radio waves transmitted from a positioning satellite (hereinafter abbreviated as "satellite") as positioning information, in order to realize highly accurate positioning, a plurality of moving objects such as vehicles to be positioned are used. May be equipped with an antenna. When a moving body is equipped with a plurality of antennas, it is necessary to accurately grasp the relative positions between the antennas. If the relative position between the antennas is inaccurate, the consistency between the positioning result when using one antenna and the positioning result when using another antenna cannot be guaranteed, and as a result, the positioning of the moving body becomes difficult. It will be inaccurate.

When a moving body is equipped with a plurality of antennas, it is conceivable to measure the relative positions between the antennas including the distance between the antennas in advance when mounting the antennas on the moving body at the time of manufacturing the moving body. However, manually measuring the relative positions between the antennas in advance causes an increase in the manufacturing cost of the moving body.

GNSS equipment may be mounted at a dealer or a maintenance shop after the mobile body is manufactured, but when installing multiple antennas, it is necessary to manually measure the relative position between the antennas at the dealer and. There was a problem that it was difficult at maintenance shops.

Patent Document 1 discloses an invention of a measuring device and a measuring method for calculating the relative positions of two antennas based on carrier phase positioning that estimates the position based on the phase of the carrier wave.

In Patent Document 2, the vector of the difference between the two antenna velocities that occurs when the moving body turns is calculated, and the tangential contact point that coincides with the above-mentioned vector direction on the circumference of the radius L from the reference antenna is the other antenna position. As such, the invention of a side slip measuring device for a moving body that calculates the relative positions of two antennas is disclosed.

Japanese Unexamined Patent Publication No. 2013-170903 JP-A-2007-225408

The carrier phase positioning adopted by the measuring device and the measuring method described in Patent Document 1 is complicated in processing, and a corresponding receiver is required. Therefore, there is a problem that it cannot be realized by an existing receiver that supports only general code positioning, which is a positioning method based on pseudo distances observed from four or more satellites.

The skid measuring device described in Patent Document 2 is based on a general code positioning-based method rather than carrier phase positioning. However, when the two antennas are not aligned in the vehicle traveling direction, there is a problem that the deviation angle between the antennas needs to be measured in advance.

The present invention has been made in view of the above problems, and an object of the present invention is to realize an antenna-to-antenna relative position estimation method and an antenna-to-antenna relative position estimation program that can easily estimate the relative positions between antennas.

In order to achieve the above object, the inter-antenna relative position estimation method according to claim 1 is provided on a moving body and is a Doppler of each of a plurality of receiving antennas for receiving positioning information from a plurality of positioning satellites and the positioning satellite. The frequency deviation detection step of detecting the frequency deviation due to the effect from the positioning information received by each of the plurality of receiving antennas, and the first velocity difference between the plurality of antennas in the ENU coordinate system based on the frequency deviation. The speed difference calculation step to be calculated, the posture angle calculation step to calculate the posture angle of the moving body, the angular velocity calculation step to calculate the angular velocity of the moving body, and the calculation based on the posture angle and the angular velocity. Relative positions between the plurality of antennas on a plane centered on the traveling direction and the width direction of the moving body based on the difference between the second velocity difference between the plurality of antennas in the ENU coordinate system and the first velocity difference. It is provided with a relative position estimation process between antennas for estimating.

Further, the inter-antenna relative position estimation method according to claim 2 is the inter-antenna relative position estimation method according to claim 1, wherein the inter-antenna relative position estimation step is a frequency deviation detection step and a speed difference calculation step. To the minimum value of each difference between the plurality of first speed differences and the second speed difference obtained by executing a series of steps including the posture angle calculation step and the angular velocity calculation step a plurality of times in a time series. Based on this, the relative position between the plurality of antennas is estimated.

The method for estimating the relative position between antennas according to claim 3 is the method for estimating the relative position between antennas according to claim 2, and the step for estimating the relative position between antennas is the first speed difference using the minimum square method. The minimum value of each difference between the second speed difference and the second speed difference is extracted.

Further, in the method for estimating the relative position between antennas according to claim 4, in the method for estimating the relative position between antennas according to claim 2, the absolute value of each difference between the first speed difference and the second speed difference is The inter-antenna relative position estimation step when the dispersion value of each value indicating the relative position between the antennas estimated in time series in the inter-antenna relative position estimation step is equal to or less than the predetermined threshold value. It includes a reliability determination step of determining that the reliability of the value indicating the relative position between the plurality of antennas estimated in is high.

In order to achieve the above object, the inter-antenna relative position estimation program according to claim 5 is provided with a computer on a moving body, each of a plurality of receiving antennas for receiving positioning information from a plurality of positioning satellites, and a positioning satellite. A frequency deviation detection unit that detects the frequency deviation due to the Doppler effect with and from the positioning information received by each of the plurality of receiving antennas, and the first velocity between the plurality of antennas in the ENU coordinate system based on the frequency deviation. The speed difference calculation unit for calculating the difference, the posture angle calculation unit for calculating the posture angle of the moving body, the angular velocity calculation unit for calculating the angular velocity of the moving body, and the above-mentioned calculated based on the posture angle and the angular velocity. Relative positions between the plurality of antennas on a plane centered on the traveling direction and the width direction of the moving body based on the difference between the second velocity difference between the plurality of antennas in the ENU coordinate system and the first velocity difference. It functions as a relative position estimation unit between antennas to estimate.

According to the present invention, it is possible to realize an antenna-to-antenna relative position estimation method and an antenna-to-antenna relative position estimation program that can easily estimate the relative position between antennas.

It is a block diagram which showed an example of the moving body provided with the position estimation system which concerns on 1st Embodiment of this invention. This is an example of a functional block diagram of the position estimation system according to the first embodiment of the present invention. It is explanatory drawing of the relative position estimation between antennas which concerns on 1st Embodiment of this invention. It is a flowchart which showed an example of the process of the relative distance estimation between antennas in 1st Embodiment of this invention. This is an example of a functional block diagram of the position estimation system according to the second embodiment of the present invention. It is a flowchart which showed an example of the process of the relative distance estimation between antennas in the 2nd Embodiment of this invention.

[First Embodiment]
Hereinafter, the position estimation system 100 using the inter-antenna relative position estimation method and the inter-antenna relative position estimation program according to the embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing an example of a moving body 20 provided with a position estimation system 100 according to the present embodiment.

The mobile body 20 includes a first antenna 12A and a first receiver 14A, a second antenna 12B and a second receiver 14B, respectively, which receive radio waves which are positioning information from satellites, and further, a first receiver 14A and a second receiver 14A. The relative position between the first antenna 12A and the second antenna 12B antenna is estimated based on the information obtained from each of the receivers 14B, and the position of the moving body 20 is estimated. The estimation device 10 is provided. In the present embodiment, the detailed description of the position estimation by GNSS will be omitted, and the estimation of the relative position between the first antenna 12A and the second antenna 12B antenna will be described.

As shown in FIG. 1, the first antenna 12A and the second antenna 12B antenna are separated by a distance L1 in the front-rear direction of the moving body 20 and a distance L2 in the width direction of the moving body 20. In the present embodiment, the distances L1 and L2 are relative positions of the first antenna 12A and the second antenna 12B antenna on a plane about the traveling direction and the width direction of the moving body 20.

Each of the first receiver 14A and the second receiver 14B is a circuit that detects the Doppler frequency of the radio wave received from the satellite by each of the first antenna 12A and the second antenna 12B. Since the GNSS satellite is constantly moving, the frequency of the radio waves received by each of the first antenna 12A and the second antenna 12B fluctuates due to the Doppler effect. Each of the first receiver 14A and the second receiver 14B detects the Doppler frequency, which is the deviation of the frequency caused by the Doppler effect.

The position estimation device 10 is a kind of computer, and estimates the relative position between the antennas and estimates the position of the moving body 20 based on the program stored in the storage device or the like.

As will be described later, the position estimation device 10 has a speed difference between the first antenna 12A and the second antenna 12B from the Doppler frequencies detected by each of the first receiver 14A and the second receiver 14B while the moving body 20 is traveling. (Hereinafter referred to as "velocity difference A") is calculated, and the posture angle (azimuth angle) of the moving body 20 and the angular velocity (yaw rate) of the moving body 20 detected by the IMU (Inertial Measurement Unit) or the like are used. The distances L1 and L2 that minimize the difference between the speed difference between the first antenna 12A and the second antenna 12B (hereinafter referred to as “speed difference B”) and the speed difference A, which are calculated based on the above, are estimated.

Since the calculation of the velocity vector based on the Doppler frequency is less affected by multipath than the calculation of the position based on the pseudo distance, it is expected that the velocity difference A is basically calculated with high accuracy. .. On the other hand, the speed difference B obtained based on the direction and the yaw rate is not always obtained with higher accuracy than the above speed difference A because the direction estimation error, the yaw rate estimation error, and the like are not necessarily small. Further, the velocity difference B is obtained as a variable including unknown numbers (L1, L2). On the other hand, as the speed difference A, a value expected to have high accuracy can be obtained as described above. In the present embodiment, L1 and L2 can be estimated with high accuracy by comparing the speed difference A and the speed difference B and estimating L1 and L2 that minimize the difference between the two. However, as described above, there is a high possibility that the speed difference B includes an error, so it is necessary to perform processing such as reliability determination to improve the accuracy of the estimation results of L1 and L2.

FIG. 2 is an example of a functional block diagram of the position estimation system 100 according to the present embodiment. As shown in FIG. 2, in the position estimation device 10, the Doppler frequency detected by the first receiver 14A from the radio waves received by the first antenna 12A and the second receiver 14B from the radio waves received by the second antenna 12B The antenna speed difference calculation unit 30 for calculating the speed difference A by the method described in the following documents and the like using the detected Doppler frequency is provided.
Y. Kojima, "Proposal for a new localization method using tightly coupled integration based on a precise estimation of trajectory from GPS Doppler", Proceedings of AVEC2010, Loughborough UK, 2010

Further, the position estimation device 10 includes a posture angle calculation device 32 for calculating the azimuth angle θ which is the posture angle of the moving body 20, and an angular velocity calculation device 34 for calculating the yaw rate ω of the moving body 20. As an example, the attitude angle calculation device 32 calculates the azimuth angle θ based on the detection value of the magnetic sensor or the velocity vector of each of the first antenna 12A or the second antenna 12B described later. As an example, the angular velocity calculation device 34 calculates the yaw rate ω from the detection value of the gyro sensor. Further, the angular velocity calculation device 34 may be the above-mentioned IMU or the like.

The position estimation device 10 has a speed difference B calculated based on the azimuth angle θ calculated by the attitude angle calculation device 32 and the yaw rate ω calculated by the angular velocity calculation device 34, and a speed difference calculated by the antenna speed difference calculation unit 30. The antenna-to-antenna relative position calculation unit 36 that estimates the relative position between the first antenna 12A and the second antenna 12B based on the difference from A is provided.

FIG. 3 is an explanatory diagram of the relative position estimation between antennas according to the present embodiment. The arrow E shown in FIG. 3 indicates the east, that is, the longitude direction in the ENU coordinate system, and the arrow N indicates the north, that is, the latitude direction in the ENU coordinate system. In the present embodiment, the velocity vector of the first antenna 12A and the velocity vector of the second antenna 12B are defined as velocity vectors in the ENU coordinate system.

As shown in FIG. 3, the speed difference between the first antenna 12A and the second antenna 12B in the traveling direction of the moving body 20 is given by the product of the distance L2 and the yaw rate ω. Further, the speed difference in the lateral direction of the moving body 20 between the first antenna 12A and the second antenna 12B is given by the product of the distance L1 and the yaw rate ω.

Further, the velocity vector difference D _{EY in the} E direction based on the yaw rate ω and the azimuth angle θ is calculated by the following equation (1).
D _EY = L1 x ω x cos θ + L2 x ω x sin θ ... (1)

The velocity vector difference D _{NY in the} N direction based on the yaw rate ω and the azimuth angle θ is calculated by the following equation (2).
D _NY = -1 x L1 x ω x sinθ + L2 x ω x cosθ ... (2)

Here, the velocity vector difference in the E direction based on the GNSS Doppler is D _Edp , and the velocity vector difference in the N direction based on the GNSS Doppler is D _Ndp .

The velocity vector difference D _Edp is the velocity vector in the E direction of the first antenna 12A calculated from the Doppler frequency detected by the first receiver 14A from the radio waves received by the first antenna 12A by a known method, and the second antenna 12B. This is the difference from the speed vector in the E direction of the second antenna 12B calculated from the Doppler frequency detected by the second receiver 14B from the radio wave received in.

Further, the velocity vector difference D _Ndp is the velocity vector in the N direction of the first antenna 12A calculated from the Doppler frequency detected by the first receiver 14A from the radio wave received by the first antenna 12A by a known method, and the second. This is the difference from the N-direction velocity vector of the second antenna 12B calculated from the Doppler frequency detected by the second receiver 14B from the radio wave received by the antenna 12B. Further, the angular velocity calculation device 34 has described above that the azimuth angle θ is calculated based on the respective velocity vectors of the first antenna 12A or the second antenna 12B, but the azimuth angle θ is the velocity vector in the E direction of the first antenna 12A. (Or the velocity vector in the E direction of the second antenna 12B) and the velocity vector in the N direction of the first antenna 12A (or the velocity vector in the N direction of the second antenna 12B) can be calculated.

The following equation (3) can be defined as the square of the difference between the velocity difference A and the velocity difference B by the above-mentioned velocity vector differences D _EY , D _NY , D _Edp , and D _Ndp .
F (L1, L2) = (D _Edp −D _EY ) ² + (D _Ndp −D _NY ) ² … (3)

In the present embodiment, F (L1, L2), which is the square of the difference between the speed difference A and the speed difference B, represented by the formula (3), is calculated. Since the velocity vector differences D _EY and D _{NY in} the E and N directions include the distances L1 and L2 between the first antenna 12A and the second antenna 12B, the calculated F (L1, L2) is also included. The distances L1 and L2 between the first antenna 12A and the second antenna 12B are included.

The calculation of F (L1, L2) is performed a plurality of times in a time series, and the calculated F (L1, L2) is stored in a storage device such as a memory. Then, the distances L1 and L2 that minimize F (L1, L2) are estimated from the accumulated plurality of F (L1, L2). Various methods can be considered for extracting the minimum value of F (L1, L2), but in the present embodiment, the least squares method is used as an example. At this time, if the approximate distance between the first antenna 12A and the second antenna 12B is known, it may be used as a tentative value of the distances L1 and L2.

FIG. 4 is a flowchart showing an example of processing for estimating the relative distance between antennas in the present embodiment. In step 400, each of the first receiver 14A and the second receiver 14B detects the Doppler frequency from the radio waves received from the satellite.

In step 402, the velocity vector in the ENU coordinate system at each position of the first antenna 12A and the second antenna 12B is calculated. Specifically, the velocity vector in the E direction of the first antenna 12A calculated from the Doppler frequency detected by the first receiver 14A and the E direction of the second antenna 12B calculated from the Doppler frequency detected by the second receiver 14B. The velocity vector in the N direction of the first antenna 12A calculated from the Doppler frequency detected by the first receiver 14A, and the N direction of the second antenna 12B calculated from the Doppler frequency detected by the second receiver 14B. And the velocity vector of, respectively.

In step 404, the speed difference between the antennas is calculated. Specifically, the above-mentioned velocity vector differences D _Edp and D _Ndp are calculated.

In step 406, the azimuth angle θ, which is the posture angle of the moving body 20, is calculated. The azimuth angle θ may be calculated based on the velocity vector calculated in step 402, or may be calculated based on the azimuth detected by the magnetic sensor.

In step 408, the yaw rate ω, which is the angular velocity, is calculated. The yaw rate ω is calculated using a gyro sensor or an IMU.

In step 410, equations (1), (2), and (3) are used to calculate F (L1, L2), which is the square of the difference between the speed difference A and the speed difference B.

In step 412, the calculated F (L1, L2) is accumulated. Then, in step 414, the distances L1 and L2, which are relative positions between the antennas, are estimated from the minimum values of F (L1, L2), and the process ends.

As described above, according to the present embodiment, the velocity calculated based on the velocity difference A between the antennas calculated from the Doppler frequency, the attitude angle (azimuth angle θ) and the angular velocity (yaw rate ω) of the moving body 20. The distances L1 and L2 that minimize the difference from the difference B are estimated, and the distances L1 and L2 are adopted as the relative positions between the antennas that improve the accuracy of code positioning.

In the present embodiment, the speed difference at each position of the first antenna 12A and the second antenna 12B is calculated by using the reception information of GNSS, the azimuth angle θ of the moving body 20, and the yaw rate ω are used. The relative positional relationship between the antennas is estimated by comparing with the calculated value. Such estimation can be handled by an existing general-purpose receiver, and when the antenna-to-antenna relative position estimation method and the antenna-to-antenna relative position estimation program according to the present embodiment are performed, the GNSS device mounted on the moving body 20 is used. No need to change hardware.

Further, the antenna-to-antenna relative position estimation method and the antenna-to-antenna relative position estimation program according to the present embodiment do not require any manual measurement in advance and can grasp the relative positional relationship between the antennas.

In the present embodiment, the relative positions between the two antennas of the first antenna 12A and the second antenna 12B are estimated, but the relative positions between the three or more GNSSS antennas are estimated by the same method as in the present embodiment. It is also possible to estimate.

[Second Embodiment]
Subsequently, a second embodiment of the present invention will be described. The present embodiment is different from the first embodiment in that the reliability of the relative position between the antennas is determined, but the other configurations are the same as those of the first embodiment, so that is the first embodiment. The same components as those in the above are designated by the same reference numerals, and detailed description thereof will be omitted.

FIG. 5 is an example of a functional block diagram of the position estimation system 200 according to the present embodiment. As shown in FIG. 5, the position estimation system 200 according to the present embodiment is different from the first embodiment in that the position estimation device 40 includes the reliability determination unit 38.

The reliability determination unit 38 estimates that the absolute value of the residual between the velocity difference A and the velocity difference B, which are the square roots of F (L1, L2) calculated using the equation (3), is equal to or less than a predetermined threshold value. When the variances of the distances L1 and L2 in each time series are equal to or less than the predetermined variance threshold, it is determined that the distances L1 and L2, which are the estimated relative positions between the antennas, have high reliability.

The predetermined threshold value and the predetermined variance threshold value are specifically determined, for example, through an experiment using an actual machine or the like.

FIG. 6 is a flowchart showing an example of processing for estimating the relative distance between antennas in the present embodiment. In the process shown in FIG. 6, since the procedure of steps 400 to 412 is the same as that of the first embodiment, detailed description thereof will be omitted.

In the first embodiment, in step 414, the distances L1 and L2, which are the relative positions between the antennas, were estimated from the minimum values of F (L1, L2), but in the present embodiment, the speed difference A and the speed are estimated. All the samples in which the square root of F (L1, L2) which is the residual with the difference B is equal to or less than a predetermined threshold are extracted, and a plurality of distances L1 and L2 are used as measurement results using the extracted F (L1, L2). ..

In step 416, the square root of F (L1, L2), which is the residual between the speed difference A and the speed difference B, is equal to or less than a predetermined threshold value, and the variance of the estimated distances L1 and L2 in each time series is predetermined. It is determined whether or not it is equal to or less than the variance threshold value of. If the square root of F (L1, L2) is less than or equal to the predetermined threshold value in step 414, the variance of the estimated distances L1 and L2 in each time series is less than or equal to the predetermined variance threshold value in step 416. It suffices to determine whether or not it is. If the determination in step 416 is that the square root of F (L1, L2) is less than or equal to the predetermined threshold value and the variance of the estimated distances L1 and L2 in each time series is less than or equal to the predetermined variance threshold value, F. The distances L1 and L2 estimated from the minimum values of (L1, L2) are adopted as the relative positions between the antennas that improve the accuracy of code positioning, and the process ends. If the determination in step 416 is that the square root of F (L1, L2) is not less than or equal to the predetermined threshold value, or the variance of the estimated distances L1 and L2 in each time series is not less than or equal to the predetermined variance threshold value, the procedure is performed. The process proceeds to step 400, and the process of estimating the relative position between the antennas is performed again.

As described above, according to the present embodiment, the square root of F (L1, L2), which is the residual between the speed difference A and the speed difference B, is equal to or less than a predetermined threshold value, and the estimated distances L1 and L2. By determining that the variance in each time series of is less than or equal to a predetermined variance threshold, it can be ensured that the plurality of values of the estimated relative positions between the antennas converge within a predetermined range, and the measurement can be performed. The accuracy of the value can be improved.

Further, the first embodiment is performed by extracting the minimum value of F (L1, L2) from the sample whose reliability is guaranteed and estimating the distances L1 and L2 which are the relative positions between the antennas from the minimum value. The relative position between the antennas can be estimated with even higher accuracy.

10 Position estimation device 12A 1st antenna 12B 2nd antenna 14A 1st receiver 14B 2nd receiver 20 Moving object 30 Antenna speed difference calculation unit 32 Attitude angle calculation device 34 Angular velocity calculation device 36 Inter-antenna relative position calculation unit 38 Reliability Judgment unit 40 Position estimation device 100, 200 Position estimation system θ _Aspect angle ω _Yaw rate D _EY , D _NY , D _Edp , D _Ndp Velocity vector difference L1, L2 Distance

Claims (5)

The frequency deviation due to the Doppler effect between each of the plurality of receiving antennas provided on the moving body and receiving the positioning information from the plurality of positioning satellites and the positioning satellite is detected from the positioning information received by each of the plurality of receiving antennas. Frequency deviation detection process and
A speed difference calculation step of calculating the first speed difference between the plurality of antennas in the ENU coordinate system based on the frequency deviation, and
The posture angle calculation step of calculating the posture angle of the moving body and
An angular velocity calculation step for calculating the angular velocity of the moving body, and
The traveling direction and width direction of the moving body are determined based on the difference between the second speed difference between the plurality of antennas in the ENU coordinate system and the first speed difference calculated based on the posture angle and the angular velocity. An antenna-to-antenna relative position estimation step for estimating the relative position between the plurality of antennas on a plane as an axis,
A method for estimating the relative position between antennas. The inter-antenna relative position estimation step is obtained by executing a series of steps including the frequency deviation detection step, the speed difference calculation step, the attitude angle calculation step, and the angular velocity calculation step a plurality of times in a time series. The method for estimating the relative position between antennas according to claim 1, wherein the relative position between the plurality of antennas is estimated based on the minimum value of each difference between the first speed difference and the second speed difference. The method for estimating the relative position between antennas according to claim 2, wherein the step of estimating the relative position between antennas is the method of estimating the relative position between antennas according to claim 2, wherein the minimum value of each difference between the first speed difference and the second speed difference is extracted by using the least squares method. Each of the absolute values of the difference between the first speed difference and the second speed difference is equal to or less than a predetermined threshold value and indicates the relative position between the antennas estimated in the time series in the relative position estimation step between the antennas. A claim including a reliability determination step of determining that the reliability of the value indicating the relative position between the plurality of antennas estimated in the relative position estimation step between antennas is high when the dispersion value of the value is equal to or less than a predetermined dispersion threshold value. Item 2. The method for estimating the relative position between antennas according to Item 2. Computer,
The frequency deviation due to the Doppler effect between each of the plurality of receiving antennas provided on the moving body and receiving the positioning information from the plurality of positioning satellites and the positioning satellite is detected from the positioning information received by each of the plurality of receiving antennas. Frequency deviation detection unit, velocity difference calculation unit that calculates the first velocity difference between the plurality of antennas in the ENU coordinate system based on the frequency deviation, attitude angle calculation unit that calculates the attitude angle of the moving body, the movement The angular velocity calculation unit that calculates the angular velocity of the body, and the difference between the second velocity difference between the plurality of antennas in the ENU coordinate system and the first velocity difference calculated based on the attitude angle and the angular velocity. An inter-antenna relative position estimation program that functions as an inter-antenna relative position estimation unit that estimates the relative positions between the plurality of antennas on a plane centered on the traveling direction and the width direction of the moving body.