Signal processing device and signal processing method

Abstract

A signal processing device (3) is configured to comprise a signal acquiring unit (11) that, when electromagnetic waves are emitted from a target, acquires electromagnetic wave reception signals from three or more satellites that have received the electromagnetic waves, and a speed calculating unit (13) that calculates the speed of the target using: a first equation that relates to a frequency difference between a Doppler frequency included in the reception signal from a first satellite among the three or more satellites and a Doppler frequency included in the reception signal from a second satellite among the three or more satellites, and that includes a term relating to the speed difference between the first satellite (1-1) and the target and a term relating to the speed difference between the second satellite (1-2) and the target; a second equation that relates to a frequency difference between the Doppler frequency included in either the reception signal from the first satellite (1-1) or the reception signal from the second satellite (1-2) and a Doppler frequency included in the reception signal from a third satellite (1-3) among the three or more satellites, and that includes a term relating to the speed difference between either the first satellite (1-1) or the second satellite (1-2) and the target and a term relating to the speed difference between the third satellite (1-3) and the target; and position information indicating the position of the target.

Description

Signal processing device and signal processing method

[0001] This disclosure relates to a signal processing device and a signal processing method.

[0002] There is a signal processing device that calculates the position of a target. As an example of such a signal processing device, Non-Patent Literature 1 discloses a signal processing device in which, when electromagnetic waves are emitted from a target, multiple satellites receive the electromagnetic waves and transmit electromagnetic wave reception signals, and each of multiple passive sensors receives the electromagnetic wave reception signal transmitted from its respective satellite, and calculates the position of the target based on the reception signals received by the multiple passive sensors.

[0003] “INTERFERENCE LOCALIZATION FOR EUTELSAT SATELLITES-THE FIRST EUROPEAN TRANSMITTER LOCATION SYSTEM”, INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS, VOL. 15, 155-183 (1997)

[0004] The signal processing device disclosed in Non-Patent Document 1 has the problem that, although it can calculate the position of a target using a passive sensor, it cannot calculate the speed of the target.

[0005] This disclosure was made to solve the above-mentioned problems and aims to provide a signal processing device that can calculate a target speed using a passive sensor.

[0006] The signal processing device according to this disclosure includes: a signal acquisition unit that acquires received signals of electromagnetic waves from three or more satellites that receive electromagnetic waves when electromagnetic waves are emitted from a target; a first equation relating to the frequency difference between the Doppler frequency contained in the received signal from a first satellite among the three or more satellites and the Doppler frequency contained in the received signal from a second satellite among the three or more satellites, each including a term relating to the velocity difference between the first satellite and the target and a term relating to the velocity difference between the second satellite and the target; a second equation relating to the frequency difference between the Doppler frequency contained in either the received signal from the first satellite or the received signal from the second satellite and the Doppler frequency contained in the received signal from a third satellite among the three or more satellites, each including a term relating to the velocity difference between either the first satellite or the second satellite and the target and a term relating to the velocity difference between the third satellite and the target; and position information indicating the position of the target, which calculates the velocity of the target.

[0007] According to this disclosure, the target speed can be calculated using a passive sensor.

[0008] This is a configuration diagram showing a positioning system including a signal processing device 3 according to Embodiment 1. This is a hardware configuration diagram showing the hardware of the signal processing device 3 according to Embodiment 1. This is a hardware configuration diagram of a computer when the signal processing device 3 is implemented by software or firmware, etc. This is a flowchart showing the signal processing method, which is the processing procedure of the signal processing device 3. Target position p ｔａｒ This is an explanatory diagram showing the relationship between the positions of the first satellite 1-1, the second satellite 1-2, and the third satellite 1-3. This is an explanatory diagram showing that the target is moving in a direction perpendicular to the Earth's radial direction. This is a configuration diagram showing a positioning system including the signal processing device 3 according to Embodiment 2. This is a hardware configuration diagram showing the hardware of the signal processing device 3 according to Embodiment 2. This is a configuration diagram showing a positioning system including the signal processing device 3 according to Embodiment 3. This is a hardware configuration diagram showing the hardware of the signal processing device 3 according to Embodiment 3. The speed v of the target ｔａｒ The velocity v when it does not have a radial component of the Earth ｔａｒThis is an explanatory diagram showing the calculation results. Target speed v ｔａｒ The velocity v when it has a component in the Earth's radial direction ｔａｒ This is an explanatory diagram showing the calculation results.

[0009] To provide a more detailed explanation of this disclosure, the forms for implementing this disclosure will be described below with reference to the attached drawings.

[0010] Embodiment 1. Figure 1 is a configuration diagram showing a positioning system including a signal processing device 3 according to Embodiment 1. Figure 2 is a hardware configuration diagram showing the hardware of the signal processing device 3 according to Embodiment 1. The positioning system shown in Figure 1 comprises a first satellite 1-1, a second satellite 1-2, a third satellite 1-3, antennas 2-1, 2-2, 2-3, and a signal processing device 3. The target shown in Figure 1 is a radio wave source that repeatedly emits electromagnetic waves. The signal represented by the electromagnetic waves can be any signal, for example, a pulse signal. The target can be, for example, a ship or a vehicle.

[0011] The first satellite 1-1 receives each electromagnetic wave when it is repeatedly emitted from the target. The first satellite 1-1 transmits a first received signal, which is the received signal for each electromagnetic wave, to antenna 2-1. The second satellite 1-2 receives each electromagnetic wave when it is repeatedly emitted from the target. The second satellite 1-2 transmits a second received signal, which is the received signal for each electromagnetic wave, to antenna 2-2. The third satellite 1-3 receives each electromagnetic wave when it is repeatedly emitted from the target. The third satellite 1-3 transmits a third received signal, which is the received signal for each electromagnetic wave, to antenna 2-3.

[0012] Antennas 2-1, 2-2, and 2-3 each function as passive sensors. Antenna 2-1 receives a first received signal transmitted from the first satellite 1-1 and transmits the first received signal to the signal processing device 3. Antenna 2-2 receives a second received signal transmitted from the second satellite 1-2 and transmits the second received signal to the signal processing device 3. Antenna 2-3 receives a third received signal transmitted from the third satellite 1-3 and transmits the third received signal to the signal processing device 3.

[0013] The signal processing device 3 comprises a signal acquisition unit 11, a position calculation unit 12, and a speed calculation unit 13. The signal acquisition unit 11 is implemented, for example, by the signal acquisition circuit 21 shown in Figure 2. The signal acquisition unit 11 acquires a first received signal, which is the received signal of each electromagnetic wave, from the first satellite 1-1 via antenna 2-1. The signal acquisition unit 11 acquires a second received signal, which is the received signal of each electromagnetic wave, from the second satellite 1-2 via antenna 2-2. The signal acquisition unit 11 acquires a third received signal, which is the received signal of each electromagnetic wave, from the third satellite 1-3 via antenna 2-3. The signal acquisition unit 11 outputs the first received signal, the second received signal, and the third received signal to the position calculation unit 12 and the speed calculation unit 13, respectively.

[0014] The position calculation unit 12 is implemented, for example, by the position calculation circuit 22 shown in Figure 2. The position calculation unit 12 acquires a first received signal, a second received signal, and a third received signal from the signal acquisition unit 11. The position calculation unit 12 calculates the position of the target using an equation relating to the time difference between the reception time of the first received signal and the reception time of the second received signal, an equation relating to the time difference between either the reception time of the first received signal or the reception time of the second received signal and the reception time of the third received signal, and the constraint condition that the target is on the surface of the Earth. The position calculation unit 12 outputs position information indicating the position of the target to the velocity calculation unit 13.

[0015] The signal processing device 3 shown in Figure 1 includes a position calculation unit 12, which outputs position information indicating the target's position to the speed calculation unit 13. However, this is merely one example, and the position information indicating the target's position may also be output to the speed calculation unit 13 from an external device to the signal processing device 3 shown in Figure 1.

[0016] The speed calculation unit 13 is implemented, for example, by the speed calculation circuit 23 shown in Figure 2. The speed calculation unit 13 includes an equation creation unit 13a and a speed calculation processing unit 13b. The speed calculation unit 13 acquires a first received signal, a second received signal, and a third received signal from the signal acquisition unit 11. The speed calculation unit 13 acquires position information from the position calculation unit 12. The speed calculation unit 13 calculates the speed of the target using the first equation, the second equation, and the position information. The first equation is an equation relating to the frequency difference between the Doppler frequency included in the first received signal and the Doppler frequency included in the second received signal, and includes terms relating to the speed difference between the first satellite 1-1 and the target, and terms relating to the speed difference between the second satellite 1-2 and the target. The second equation is an equation relating to the frequency difference between the Doppler frequency contained in either the first or second received signal and the Doppler frequency contained in the third received signal, and includes a term relating to the speed difference between either the first satellite 1-1 or the second satellite 1-2 and the target, and a term relating to the speed difference between the third satellite 1-3 and the target. The speed calculation unit 13 displays the speed of the target on, for example, a display device (not shown).

[0017] The equation generation unit 13a acquires the first received signal, the second received signal, and the third received signal from the signal acquisition unit 11. The equation generation unit 13a creates a system of equations including the first equation, the second equation, and an equation indicating the constraint that the target is moving in a direction perpendicular to the Earth's radial direction. The velocity calculation processing unit 13b acquires position information from the position calculation unit 12. Using the position information, the velocity calculation processing unit 13b finds the solution to the system of equations created by the equation generation unit 13a as the velocity of the target.

[0018] In Figure 1, it is assumed that the signal acquisition unit 11, position calculation unit 12, and speed calculation unit 13, which are components of the signal processing device 3, are each implemented by dedicated hardware as shown in Figure 2. That is, it is assumed that the signal processing device 3 is implemented by a signal acquisition circuit 21, a position calculation circuit 22, and a speed calculation circuit 23. The signal acquisition circuit 21, position calculation circuit 22, and speed calculation circuit 23 can be, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC (Application Specific Integrated Circuit), an FPGA (Field-Programmable Gate Array), or a combination thereof.

[0019] The components of the signal processing device 3 are not limited to those implemented by dedicated hardware; the signal processing device 3 may also be implemented by software, firmware, or a combination of software and firmware. The software or firmware is stored as a program in the computer's memory. The computer refers to the hardware that executes the program, and includes, for example, a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a central processing unit, a processing unit, an arithmetic unit, a microprocessor, a microcomputer, a processor, or a DSP (Digital Signal Processor).

[0020] Figure 3 is a hardware configuration diagram of a computer when the signal processing device 3 is implemented by software or firmware. When the signal processing device 3 is implemented by software or firmware, programs that cause the computer to execute the respective processing procedures in the signal acquisition unit 11, the position calculation unit 12, and the speed calculation unit 13 are stored in the memory 31. The computer's processor 32 then executes the programs stored in the memory 31.

[0021] In addition, FIG. 2 shows an example in which each component of the signal processing device 3 is realized by dedicated hardware, and FIG. 3 shows an example in which the signal processing device 3 is realized by software, firmware, or the like. However, this is only an example, and some components in the signal processing device 3 may be realized by dedicated hardware, and the remaining components may be realized by software, firmware, or the like.

[0022] Next, the operation of the positioning system shown in FIG. 1 will be described. FIG. 4 is a flowchart showing a signal processing method that is a processing procedure of the signal processing device 3. A target that is a radio wave source may repeatedly emit electromagnetic waves. When electromagnetic waves are repeatedly emitted from the target, the first satellite 1-1 receives each electromagnetic wave. The first satellite 1-1 transmits a first reception signal p １ (t ａ ) to the antenna 2-1. The first reception signal p １ (t ａ ) is a reception signal when the reception time of the electromagnetic wave by the first satellite 1-1 is t ａ . The first reception signal p １ (t ａ ) contains information on the reception time t ａ .

[0023] When electromagnetic waves are repeatedly emitted from the target, the second satellite 1-2 receives each electromagnetic wave. The second satellite 1-2 transmits a second reception signal p ２ (t ｂ ) to the antenna 2-2. The second reception signal p ２ (t ｂ ) is a reception signal when the reception time of the electromagnetic wave by the second satellite 1-2 is t ｂ . The second reception signal p ２ (t ｂ ) contains information on the reception time t ｂ .

[0024] When electromagnetic waves are repeatedly emitted from the target, the third satellite 1-3 receives each electromagnetic wave. The third satellite 1-3 transmits a third reception signal p３ (t ｃ ) is transmitted to antenna 2-3. Third received signal p ３ (t ｃ ) is when the reception time of electromagnetic waves from the third satellite 1-3 is t ｃ This is the received signal. The third received signal p ３ (t ｃ ) is the reception time t ｃ It contains information about this.

[0025] Antenna 2-1 receives the first received signal p transmitted from the first satellite 1-1. １ (t ａ ) receives the first received signal p １ (t ａ The signal is transmitted to the signal processing device 3. Antenna 2-2 receives the second received signal p transmitted from the second satellite 1-2. ２ (t ｂ ) receives the second received signal p ２ (t ｂ The signal is transmitted to the signal processing device 3. Antenna 2-3 receives the third received signal p transmitted from the third satellite 1-3. ３ (t ｃ ) receives the third received signal p ３ (t ｃ The signal is transmitted to the signal processing device 3.

[0026] The signal acquisition unit 11 receives the first received signal p from the first satellite 1-1 via the antenna 2-1. １ (t ａ The signal acquisition unit 11 receives the second received signal p from the second satellite 1-2 via antenna 2-2. ２ (t ｂ The signal acquisition unit 11 also receives the third received signal p from the third satellite 1-3 via antenna 2-3. ３ (t ｃ The signal acquisition unit 11 acquires the first received signal p １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ) are output to the position calculation unit 12 and the speed calculation unit 13, respectively.

[0027] The position calculation unit 12 receives the first received signal p from the signal acquisition unit 11. １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ ) and are obtained. Since the orbit of the first satellite 1-1 is known, the reception time t ａ The position p of the first satellite 1-1 in ｓ１ (t ａ ) is known. The orbit of the second satellite 1-2 is known, therefore the reception time t ｂ The position of the second satellite 1-2 in p ｓ２ (t ｂ ) is known. The orbit of the third satellite 1-3 is known, therefore the reception time t ｃ The position p of the third satellite 1-3 in ｓ３ (t ｃ The position p of the first satellite 1-1 is known. ｓ１ (t ａ ), the position p of the second satellite 1-2 ｓ２ (t ｂ ) and the position p of the third satellite 1-3 ｓ３ (t ｃ Each of these may, for example, be stored in the internal memory of the position calculation unit 12, or it may be provided from outside the signal processing device 3.

[0028] The position calculation unit 12 calculates the target position as p, as shown in the following equation (1). ｔａｒ Assuming this is the case, the reception time t of each electromagnetic wave by the first satellite 1-1 ａ The reception time t of the electromagnetic waves from the second satellite 1-2 ｂ Time difference τ １２ We create equation (1) relating to the time difference τ. １２ For example, the first received signal p １ (t ａ ) and the second received signal p ２ (t ｂ The time difference τ is calculated by correlation processing between ). １２The process of calculating it is a known technique, so detailed description is omitted. Also, as shown in the following equation (2), the position calculation unit 12 calculates the reception time t of each electromagnetic wave by the second satellite 1-2 ｂ and the reception time t of each electromagnetic wave by the third satellite 1-3 ｃ to create an equation (2) regarding the time difference τ ２３ between them. The time difference τ ２３ is calculated, for example, by correlation processing between the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ ).

[0029] Here, the position calculation unit 12 creates an equation (2) regarding the time difference τ ｂ between the reception time t of each electromagnetic wave by the second satellite 1-2 ｃ and the reception time t of each electromagnetic wave by the third satellite 1-3 ２３ . However, this is just an example, and the position calculation unit 12 may create an equation (2) regarding the time difference τ ａ between the reception time t of each electromagnetic wave by the first satellite 1-1 ｃ and the reception time t of each electromagnetic wave by the third satellite 1-3 １３ as shown in the following equation (3).

[0030] In equations (1) to (3), c is the propagation speed of electromagnetic waves.

[0031] Figure 5 is an explanatory diagram showing the relationship between the position p ｔａｒ of the target and the positions of the first satellite 1-1, the second satellite 1-2, and the third satellite 1-3, respectively. In the example of Figure 5, it is assumed that the target exists on the surface of the earth. In Figure 5, v ｓ１ is the speed of the first satellite 1-1 at the reception time t ａ , v ｓ２ is the speed of the second satellite 1-2 at the reception time t ｂ , and v ｓ３ is the speed of the third satellite 1-3 at the reception time t ｃ . r １ is at the reception time tａ The distance between the first satellite 1-1 and the target, r ２ The reception time t ｂ The distance between the second satellite 1-2 and the target, r ３ The reception time t ｃ This is the distance between the third satellite 1-3 and the target.

[0032] The position calculation unit 12 solves a system of equations consisting of the first equation shown in equation (1), the second equation shown in equation (2) (or the second equation shown in equation (3)), and the following equation (4) which shows the constraint conditions, thereby determining the target position p ｔａｒ The following is calculated (Step ST4 in Figure 4). The constraint condition shown in equation (4) is that the target is located on the Earth's surface. The position p of the target, which is an unknown radio source. ｔａｒ The element is p ｔａｒ = (x, y, z) Ｔ If this is the case, then the first equation, the second equation, and the equation representing the constraint conditions are all nonlinear systems of equations in x, y, and z. These nonlinear systems of equations in x, y, and z can be solved, for example, by optimization using the Gauss-Newton method.

[0033] In equation (4), R Ｅ p is the radius of the Earth. The position calculation unit 12 calculates the target position p ｔａｒ Position information indicating this is output to the speed calculation unit 13.

[0034] The equation creation unit 13a of the speed calculation unit 13 receives the first received signal p from the signal acquisition unit 11. １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ The equation creation unit 13a creates a system of equations including the first equation, the second equation, and an equation showing the constraint conditions (step ST5 in Figure 4).

[0035] The first equation is as shown in equation (5) below, where p is the first received signal. １ (t ａ The Doppler frequency and the second received signal p included in )２ (t ｂ ) The frequency difference ν from the Doppler frequency included in ) １２ This is an equation relating to the frequency difference ν. １２ For example, the first received signal p １ (t ａ ) and the second received signal p ２ (t ｂ The frequency difference ν is calculated by correlation processing between ). １２ The process by which this is calculated is based on publicly known technology, so a detailed explanation will be omitted. Furthermore, the first equation is given by the velocity v of the first satellite 1-1. ｓ１ (t ａ ) and target speed v ｔａｒ Speed ​​difference (v ｓ１ (t ａ )-v ｔａｒ The section concerning ) and the speed v of the second satellite 1-2 ｓ２ (t ｂ ) and target speed v ｔａｒ Speed ​​difference (v ｓ２ (t ｂ )-v ｔａｒ The second equation includes terms relating to the second received signal p, as shown in equation (6) below. ２ (t ｂ ) The Doppler frequency and the third received signal p ３ (t ｃ ) The frequency difference ν from the Doppler frequency included in ) ２３ This is an equation relating to the frequency difference ν. ２３ For example, the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ It is calculated by correlation processing between ). The second equation is the velocity v of the second satellite 1-2. ｓ２ (t ｂ ) and target speed v ｔａｒ Speed ​​difference (v ｓ２ (t ｂ )-v ｔａｒ The section concerning ) and the speed v of the third satellite 1-3 ｓ３ (t ｃ ) and target speed v ｔａｒ Speed ​​difference (v ｓ３ (tｃ )-v ｔａｒ It includes sections relating to )

[0036] In equations (5) and (6), λ is the wavelength of the electromagnetic wave. １ n is a unit vector from the target to the first satellite 1-1. ２ n is a unit vector from the target to the second satellite 1-2. ３ This is a unit vector from the target to the third satellite 1-3.

[0037] Here, the equation generation unit 13a generates the equation shown in equation (6) as the second equation. However, this is just one example, and the equation generation unit 13a may also generate the equation shown in equation (10) as the second equation. The second equation shown in equation (10) is given by the first received signal p １ (t ａ ) The Doppler frequency and the third received signal p ３ (t ｃ The velocity difference v corresponds to the frequency difference with the Doppler frequency contained in ). １３ This is an equation relating to the velocity difference v. １３ The velocity v of the first satellite 1-1 is ｓ１ (t ａ ) and the speed v of the third satellite 1-3 ｓ３ (t ｃ This is the difference from ). The second equation is the velocity v of the first satellite 1-1. ｓ１ (t ａ ) and target speed v ｔａｒ Speed ​​difference (v ｓ１ (t ａ )-v ｔａｒ The section concerning ) and the speed v of the third satellite 1-3 ｓ３ (t ｃ ) and target speed v ｔａｒ Speed ​​difference (v ｓ３ (t ｃ )-v ｔａｒ It includes sections relating to )

[0038]

[0039] The equation generation unit 13a sets a constraint condition that the target moves in a direction perpendicular to the Earth's radial direction, as shown in equation (11) below. Figure 6 is an explanatory diagram showing that the target is moving in a direction perpendicular to the Earth's radial direction.

[0040]

[0041] The speed calculation processing unit 13b acquires position information from the position calculation unit 12. The speed calculation processing unit 13b calculates the position p of the target indicated by the position information. ｔａｒ By using this, we can solve the system of equations consisting of the first equation shown in equation (5), the second equation shown in equation (6) (or the second equation shown in equation (10)), and the constraint condition shown in equation (11), thereby obtaining the target velocity v ｔａｒ The following equation (12) is obtained by transforming the system of equations: the first equation shown in equation (5), the second equation shown in equation (6), and the equation showing the constraint conditions shown in equation (11). In equation (12), "≡" is a mathematical symbol that means the left side and the right side are equivalent. The following equation (13) is obtained by transforming equation (12).

[0042]

[0043] The target position p calculated by the position calculation unit 12 ｔａｒ And the target speed v calculated by the speed calculation unit 13 ｔａｒ This is displayed, for example, on a display device not shown. This allows the target position p to be determined. ｔａｒ and target speed v ｔａｒ This makes it possible to confirm the target position p calculated by the position calculation unit 12. ｔａｒ And the target speed v calculated by the speed calculation unit 13 ｔａｒ This signal is output to, for example, a tracking device (not shown). This enables the tracking device to track the target.

[0044] In the above embodiment 1, the signal processing device 3 is configured to include: a signal acquisition unit 11 that acquires electromagnetic wave reception signals from three or more satellites that receive electromagnetic waves when electromagnetic waves are emitted from a target; a first equation relating to the frequency difference between the Doppler frequency included in the reception signal from the first satellite among the three or more satellites and the Doppler frequency included in the reception signal from the second satellite among the three or more satellites, each including a term relating to the speed difference between the first satellite 1-1 and the target and a term relating to the speed difference between the second satellite 1-2 and the target; a second equation relating to the frequency difference between the Doppler frequency included in either the reception signal from the first satellite 1-1 or the reception signal from the second satellite 1-2 and the Doppler frequency included in the reception signal from the third satellite 1-3 among the three or more satellites, each including a term relating to the speed difference between either the first satellite 1-1 or the second satellite 1-2 and the target and a term relating to the speed difference between the third satellite 1-3 and the target; and position information indicating the position of the target. Therefore, the signal processing device 3 can calculate the target speed using the passive sensor.

[0045] Embodiment 2. Embodiment 2 describes a signal processing device 3 in which the speed calculation unit 15 uses position information to find the solution to a system of equations including the first equation, the second equation, and the third equation as the target speed.

[0046] Figure 7 is a configuration diagram showing a positioning system including a signal processing device 3 according to Embodiment 2. In Figure 7, the same reference numerals as in Figure 1 indicate the same or corresponding parts, so a detailed explanation is omitted. Figure 8 is a hardware configuration diagram showing the hardware of the signal processing device 3 according to Embodiment 2. In Figure 8, the same reference numerals as in Figure 2 indicate the same or corresponding parts, so a detailed explanation is omitted. The positioning system shown in Figure 7 comprises a first satellite 1-1, a second satellite 1-2, a third satellite 1-3, a fourth satellite 1-4, antennas 2-1, 2-2, 2-3, 2-4, and a signal processing device 3.

[0047] The fourth satellite 1-4 receives each electromagnetic wave as it is repeatedly emitted from the target. The fourth satellite 1-4 transmits a fourth received signal, which is the received signal for each electromagnetic wave, to antenna 2-4.

[0048] Antennas 2-1, 2-2, 2-3, and 2-4 each function as passive sensors. Antenna 2-4 receives a fourth received signal transmitted from the fourth satellite 1-4 and transmits the fourth received signal to the signal processing device 3.

[0049] The signal processing device 3 includes a signal acquisition unit 14, a position calculation unit 12, and a speed calculation unit 15. The signal acquisition unit 14 is implemented, for example, by the signal acquisition circuit 24 shown in Figure 8. The signal acquisition unit 14 acquires a first received signal, which is the received signal of each electromagnetic wave, from the first satellite 1-1 via antenna 2-1. The signal acquisition unit 14 acquires a second received signal, which is the received signal of each electromagnetic wave, from the second satellite 1-2 via antenna 2-2. The signal acquisition unit 14 acquires a third received signal, which is the received signal of each electromagnetic wave, from the third satellite 1-3 via antenna 2-3. The signal acquisition unit 14 acquires a fourth received signal, which is the received signal of each electromagnetic wave, from the fourth satellite 1-4 via antenna 2-4. The signal acquisition unit 14 outputs the first received signal, the second received signal, and the third received signal to the position calculation unit 12, and outputs the first received signal, the second received signal, the third received signal, and the fourth received signal to the speed calculation unit 15.

[0050] The speed calculation unit 15 is implemented, for example, by the speed calculation circuit 25 shown in Figure 8. The speed calculation unit 15 includes an equation creation unit 15a and a speed calculation processing unit 15b. The speed calculation unit 15 acquires a first received signal, a second received signal, a third received signal, and a fourth received signal from the signal acquisition unit 14. The speed calculation unit 15 acquires position information from the position calculation unit 12. The speed calculation unit 15 calculates the speed of the target using the first equation, the second equation, the third equation, and the position information. The third equation is an equation relating to the frequency difference between the Doppler frequency contained in any of the first, second, or third received signals and the Doppler frequency contained in the fourth received signal, and includes a term relating to the speed difference between any of the first satellite 1-1, the second satellite 1-2, or the third satellite 1-3 and the target, and a term relating to the speed difference between the fourth satellite 1-4 and the target. The speed calculation unit 15 displays the target speed on, for example, a display device (not shown).

[0051] The equation creation unit 15a acquires the first, second, third, and fourth received signals from the signal acquisition unit 11. The equation creation unit 15a creates a system of equations including the first, second, and third equations. The speed calculation processing unit 15b acquires position information from the position calculation unit 12. Using the position information, the speed calculation processing unit 15b finds the solution to the system of equations created by the equation creation unit 15a as the target speed.

[0052] In Figure 7, it is assumed that the signal acquisition unit 14, position calculation unit 12, and speed calculation unit 15, which are components of the signal processing device 3, are each implemented by dedicated hardware as shown in Figure 8. That is, it is assumed that the signal processing device 3 is implemented by a signal acquisition circuit 24, a position calculation circuit 22, and a speed calculation circuit 25. The signal acquisition circuit 24, position calculation circuit 22, and speed calculation circuit 25 can each be, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0053] The components of the signal processing device 3 are not limited to those implemented by dedicated hardware; the signal processing device 3 may also be implemented by software, firmware, or a combination of software and firmware. When the signal processing device 3 is implemented by software or firmware, a program that causes the computer to execute the respective processing procedures in the signal acquisition unit 14, the position calculation unit 12, and the speed calculation unit 15 is stored in the memory 31 shown in Figure 3. Then, the processor 32 shown in Figure 3 executes the program stored in the memory 31.

[0054] Furthermore, Figure 8 shows an example in which each component of the signal processing device 3 is implemented by dedicated hardware, while Figure 3 shows an example in which the signal processing device 3 is implemented by software or firmware, etc. However, this is merely one example, and some components of the signal processing device 3 may be implemented by dedicated hardware, while the remaining components may be implemented by software or firmware, etc.

[0055] Next, the operation of the positioning system shown in Figure 7 will be explained. The target, which is a radio wave source, may repeatedly emit electromagnetic waves. The first satellite 1-1 receives each electromagnetic wave when it is repeatedly emitted from the target. The first satellite 1-1 receives a first received signal p, which is the received signal of each electromagnetic wave. １ (t ａ The second satellite 1-2 receives the electromagnetic waves when they are repeatedly emitted from the target. The second satellite 1-2 receives the second received signal p, which is the received signal of each electromagnetic wave. ２ (t ｂ ) is transmitted to antenna 2-2.

[0056] The third satellite 1-3 receives each electromagnetic wave when it is repeatedly emitted from the target. The third satellite 1-3 receives a third received signal p, which is the received signal of each electromagnetic wave. ３ (t ｂThe fourth satellite 1-4 receives each electromagnetic wave as it is repeatedly emitted from the target. The fourth satellite 1-4 receives the fourth received signal p, which is the received signal of each electromagnetic wave. ４ (t ｄ ) is transmitted to antenna 2-4. The fourth received signal p ４ (t ｄ ) is when the reception time of electromagnetic waves from the fourth satellite 1-4 is t ｄ This is the received signal. The fourth received signal p ４ (t ｄ ) is the reception time t ｄ It contains information about this.

[0057] Antenna 2-1 receives the first received signal p transmitted from the first satellite 1-1. １ (t ａ ) receives the first received signal p １ (t ａ The signal is transmitted to the signal processing device 3. Antenna 2-2 receives the second received signal p transmitted from the second satellite 1-2. ２ (t ｂ ) receives the second received signal p ２ (t ｂ The signal is transmitted to the signal processing device 3. Antenna 2-3 receives the third received signal p transmitted from the third satellite 1-3. ３ (t ｃ ) receives the third received signal p ３ (t ｃ The signal is transmitted to the signal processing device 3. Antenna 2-4 receives the fourth received signal p transmitted from the fourth satellite 1-4. ４ (t ｄ ) receives the fourth received signal p ４ (t ｄ The signal is transmitted to the signal processing device 3.

[0058] The signal acquisition unit 14 receives the first received signal p from the first satellite 1-1 via the antenna 2-1. １ (t ａ The signal acquisition unit 14 receives the second received signal p from the second satellite 1-2 via antenna 2-2. ２ (t ｂThe signal acquisition unit 14 receives the third received signal p from the third satellite 1-3 via antenna 2-3. ３ (t ｃ The signal acquisition unit 14 also receives the fourth received signal p from the fourth satellite 1-4 via antenna 2-4. ４ (t ｄ The signal acquisition unit 14 acquires the first received signal p １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ ) outputs to the position calculation unit 12. The signal acquisition unit 14 receives the first received signal p １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ ) and the fourth received signal p ４ (t ｄ ) and are output to the speed calculation unit 15.

[0059] The position calculation unit 12 calculates the target position p, similar to the first embodiment. ｔａｒ The position calculation unit 12 calculates the target position p. ｔａｒ Position information indicating this is output to the speed calculation unit 15.

[0060] The equation creation unit 15a of the speed calculation unit 15 receives the first received signal p from the signal acquisition unit 14. １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ ) and the fourth received signal p ４ (t ｄ The equation creation unit 15a creates a system of equations including the first equation shown in equation (5), the second equation shown in equation (6), and the third equation shown in equation (14).

[0061] The third equation is as shown in equation (14) below, where the first received signal p １ (t ａThe Doppler frequency and the fourth received signal p included in ) ４ (t ｄ ) The frequency difference ν from the Doppler frequency included in ) １４ This is an equation relating to the frequency difference ν. １４ For example, the first received signal p １ (t ａ ) and the fourth received signal p ４ (t ｄ It is calculated by correlation processing between ). The third equation is the velocity v of the first satellite 1-1. ｓ１ (t ａ ) and target speed v ｔａｒ Speed ​​difference (v ｓ１ (t ａ )-v ｔａｒ The section concerning ) and the velocity v of the fourth satellite 1-4 ｓ４ (t ｄ ) and target speed v ｔａｒ Speed ​​difference (v ｓ４ (t ｄ )-v ｔａｒ It includes sections relating to )

[0062] In equations (14) to (15), n ４ This is the unit vector from the target to the fourth satellite 1-4.

[0063] The speed calculation processing unit 15b acquires position information from the position calculation unit 12. The speed calculation processing unit 15b calculates the position p of the target indicated by the position information. ｔａｒ By using this, we can solve the system of equations consisting of the first equation shown in equation (5), the second equation shown in equation (6) (or the second equation shown in equation (10)), and the third equation shown in equation (14), thereby obtaining the target velocity v ｔａｒ The following equation (16) is a transformed version of the system of equations consisting of the first equation shown in equation (5), the second equation shown in equation (10), and the third equation shown in equation (14). The following equation (17) is a transformed version of equation (16).

[0064]

[0065] The target position p calculated by the position calculation unit 12 ｔａｒAnd the target speed v calculated by the speed calculation unit 15 ｔａｒ This is, for example, displayed on a display device (not shown). Also, the target position p calculated by the position calculation unit 12. ｔａｒ And the target speed v calculated by the speed calculation unit 15 ｔａｒ This is, for example, output to a tracking device (not shown in the diagram).

[0066] In the signal processing device 3 shown in Figure 7, the equation generation unit 15a generates the equation shown in equation (14) as the third equation. However, this is only one example, and the equation generation unit 15a may also generate the equation shown in equation (18) or equation (19) below as the third equation.

[0067]

[0068] In the above embodiment 2, the signal processing device 3 is configured such that the speed calculation unit 15 calculates the speed of the target using a first equation, a second equation, a third equation relating to the frequency difference between the Doppler frequency contained in any of the signals received by the first satellite 1-1, the second satellite 1-2, or the third satellite 1-3 and the Doppler frequency contained in the signal received by the fourth satellite 1-4 among the three or more satellites, each including a term relating to the speed difference between any of the first satellite 1-1, the second satellite 1-2, or the third satellite 1-3 and the target, and a term relating to the speed difference between the fourth satellite 1-4 and the target, and position information. Therefore, the signal processing device 3 can calculate the speed of the target using a passive sensor.

[0069] Embodiment 3. Embodiment 3 describes a signal processing device 3 that includes a differential calculation unit 16 for differentiating the second equation with respect to time.

[0070] Figure 9 is a configuration diagram showing a positioning system including a signal processing device 3 according to Embodiment 3. In Figure 9, the same reference numerals as in Figure 1 indicate the same or corresponding parts, so a detailed explanation is omitted. Figure 10 is a hardware configuration diagram showing the hardware of the signal processing device 3 according to Embodiment 3. In Figure 10, the same reference numerals as in Figure 2 indicate the same or corresponding parts, so a detailed explanation is omitted. The positioning system shown in Figure 9 comprises a first satellite 1-1, a second satellite 1-2, a third satellite 1-3, antennas 2-1, 2-2, 2-3, and a signal processing device 3.

[0071] The signal processing device 3 includes a signal acquisition unit 11, a position calculation unit 12, a differential calculation unit 16, and a speed calculation unit 17. The differential calculation unit 16 is implemented, for example, by the differential calculation circuit 26 shown in Figure 10. The differential calculation unit 16 obtains a second equation from the speed calculation unit 17. The differential calculation unit 16 differentiates the second equation with respect to time and outputs the second equation after time differentiation to the speed calculation unit 17.

[0072] The speed calculation unit 17 is implemented, for example, by the speed calculation circuit 27 shown in Figure 10. The speed calculation unit 17 includes an equation creation unit 17a and a speed calculation processing unit 17b. The speed calculation unit 17 acquires a first received signal, a second received signal, and a third received signal from the signal acquisition unit 11. The speed calculation unit 17 acquires position information from the position calculation unit 12. The speed calculation unit 17 calculates the target speed using the first equation, the second equation, the second equation after time differentiation by the differential calculation unit 16, and the position information. The speed calculation unit 17 displays the target speed on, for example, a display device (not shown).

[0073] The equation creation unit 17a acquires the first received signal, the second received signal, and the third received signal from the signal acquisition unit 11. The equation creation unit 17a creates the first equation and the second equation. The equation creation unit 17a outputs the second equation to the differential calculation unit 16 and outputs the first equation and the second equation to the speed calculation processing unit 17b. The speed calculation processing unit 17b acquires position information from the position calculation unit 12. The speed calculation processing unit 17b acquires the first equation and the second equation from the equation creation unit 17a and acquires the second equation after time differentiation from the differential calculation unit 16. Using the position information, the speed calculation processing unit 17b finds the solution to a system of equations including the first equation, the second equation, and the second equation after time differentiation by the differential calculation unit 16 as the target speed.

[0074] In Figure 9, the signal acquisition unit 11, position calculation unit 12, differential calculation unit 16, and speed calculation unit 17, which are components of the signal processing device 3, are assumed to be implemented by dedicated hardware as shown in Figure 10. That is, the signal processing device 3 is assumed to be implemented by a signal acquisition circuit 21, a position calculation circuit 22, a differential calculation circuit 26, and a speed calculation circuit 27. The signal acquisition circuit 21, position calculation circuit 22, differential calculation circuit 26, and speed calculation circuit 27 can be, for example, a single circuit, a composite circuit, a programmed processor, a parallel programmed processor, an ASIC, an FPGA, or a combination thereof.

[0075] The components of the signal processing device 3 are not limited to those implemented by dedicated hardware; the signal processing device 3 may also be implemented by software, firmware, or a combination of software and firmware. When the signal processing device 3 is implemented by software or firmware, a program for causing a computer to execute the respective processing procedures in the signal acquisition unit 11, position calculation unit 12, differential calculation unit 16, and speed calculation unit 17 is stored in the memory 31 shown in Figure 3. Then, the processor 32 shown in Figure 3 executes the program stored in the memory 31.

[0076] Furthermore, Figure 10 shows an example in which each component of the signal processing device 3 is implemented by dedicated hardware, while Figure 3 shows an example in which the signal processing device 3 is implemented by software or firmware, etc. However, this is merely one example, and some components of the signal processing device 3 may be implemented by dedicated hardware, while the remaining components may be implemented by software or firmware, etc.

[0077] Next, the operation of the positioning system shown in Figure 9 will be explained. However, it is the same as the positioning system shown in Figure 1, except for the differential calculation unit 16 and the speed calculation unit 17. Therefore, only the operation of the differential calculation unit 16 and the speed calculation unit 17 will be explained here.

[0078] The equation creation unit 17a of the speed calculation unit 17 receives the first received signal p from the signal acquisition unit 11. １ (t ａ ) and the second received signal p ２ (t ｂ ) and the third received signal p ３ (t ｃ The equation creation unit 17a creates the first equation and the second equation, similar to the equation creation unit 13a shown in Figure 1. The equation creation unit 17a outputs the second equation to the differential calculation unit 16 and outputs the first equation and the second equation to the velocity calculation processing unit 17b.

[0079] The differential calculation unit 16 obtains the second equation from the equation creation unit 17a. The differential calculation unit 16 differentiates the second equation with respect to time, as shown in equation (20) below. In equation (20), a_s1 = d / dt(v ｓ１ ) is the acceleration of the first satellite 1-1, a_s3 = d / dt(v ｓ３ ) is the acceleration of the third satellite 1-3. Here, the differential calculation unit 16 is differentiating the second equation shown in equation (10) with respect to time. However, this is just one example, and the differential calculation unit 16 may also differentiate the second equation shown in equation (6) with respect to time. The differential calculation unit 16 outputs the second equation after differentiation with respect to the velocity calculation processing unit 17b of the velocity calculation unit 17.

[0080]

[0081] The velocity calculation processing unit 17b acquires position information from the position calculation unit 12. The velocity calculation processing unit 17b acquires the first equation and the second equation from the equation creation unit 17a, and acquires the second equation after time differentiation from the differential calculation unit 16. The velocity calculation processing unit 17b calculates the target position p indicated by the position information. ｔａｒ By using this, we can solve the system of equations consisting of the first equation shown in equation (5), the second equation shown in equation (6) (or the second equation shown in equation (10)), and the second equation after time differentiation shown in equation (20), thereby obtaining the target velocity v ｔａｒ We calculate this. Equation (21) shown below is a transformed system of equations consisting of the first equation shown in equation (5), the second equation shown in equation (6), and the second equation after time differentiation shown in equation (20). Since the acceleration of the satellite is sufficiently small, if we ignore the acceleration of the satellite, equation (20) can be transformed into equation (21) below.

[0082]

[0083] In the signal processing device 3 shown in Figure 1, the velocity calculation processing unit 13b uses the constraint that the target is moving in a direction perpendicular to the Earth's radial direction to calculate the target's velocity v ｔａｒ This calculates the target speed v. ｔａｒ If the velocity has a component in the Earth's radial direction, that is, if the target is moving in a direction not perpendicular to the Earth's radial direction, the velocity v calculated by the velocity calculation processing unit 13b ｔａｒ Errors may be present in the calculation results. In the signal processing device 3 shown in Figure 9, the velocity calculation processing device 17b uses the second equation after time differentiation instead of the above constraint conditions to calculate the target velocity v ｔａｒ This calculates the target speed v. ｔａｒ Even if the component has a radial component of the Earth, the velocity v calculated by the velocity calculation processing unit 17b ｔａｒ The possibility of errors being included in the calculation results is reduced.

[0084] Figure 11 shows the target velocity v ｔａｒ The velocity v when it does not have a radial component of the Earth ｔａｒThis is an explanatory diagram showing the calculation results. Figure 11 shows the target speed v ｔａｒ If the Earth does not have a radial component, the velocity v calculated by the velocity calculation processing unit 13b shown in Figure 1 ｔａｒ The calculation result and the speed v calculated by the speed calculation processing unit 17b shown in Figure 9 ｔａｒ This shows that both the calculated result and the result are accurate. Figure 12 shows the target speed v ｔａｒ The velocity v when it has a component in the Earth's radial direction ｔａｒ This is an explanatory diagram showing the calculation results. Figure 12 shows the target speed v ｔａｒ If the vector has a radial component of the Earth, the velocity v calculated by the velocity calculation processing unit 13b shown in Figure 1 ｔａｒ The calculation result is not precise, but the speed v calculated by the speed calculation processing unit 17b shown in Figure 9 ｔａｒ The calculation results are accurate. In Figures 11 and 12, the solid arrows indicate the speed v calculated by the speed calculation processing unit 17b. ｔａｒ The dashed arrow indicates the speed v calculated by the speed calculation processing unit 13b. ｔａｒ The dashed arrows indicate the true velocity.

[0085] In the above embodiment 3, the signal processing device 3 shown in Figure 9 is configured to include a differential calculation unit 16 that performs time differentiation of the second equation, and a velocity calculation unit 17 that calculates the target velocity using the first equation, the second equation, the second equation after time differentiation by the differential calculation unit 16, and position information. Therefore, the signal processing device 3 shown in Figure 9 can calculate the target velocity using a passive sensor, similar to the signal processing device 3 shown in Figure 1, and can also prevent a decrease in the accuracy of velocity calculation even when the target velocity has a component in the radial direction of the Earth.

[0086] Furthermore, this disclosure allows for free combination of each embodiment, modification of any component in each embodiment, or omission of any component in each embodiment.

[0087] The signal processing device and signal processing method according to this invention comprises: a signal acquisition unit that acquires received signals of electromagnetic waves from three or more satellites that receive electromagnetic waves when electromagnetic waves are emitted from a target; a first equation relating to the frequency difference between the Doppler frequency contained in the received signal from a first satellite among the three or more satellites and the Doppler frequency contained in the received signal from a second satellite among the three or more satellites, each including a term relating to the velocity difference between the first satellite and the target and a term relating to the velocity difference between the second satellite and the target; a second equation relating to the frequency difference between the Doppler frequency contained in either the received signal from the first satellite or the received signal from the second satellite and the Doppler frequency contained in the received signal from a third satellite among the three or more satellites, each including a term relating to the velocity difference between either the first satellite or the second satellite and the target and a term relating to the velocity difference between the third satellite and the target; and position information indicating the position of the target, and calculates the velocity of the target. The signal processing device and signal processing method can calculate the velocity of the target using a passive sensor and are suitable for use as a signal processing device and signal processing method.

[0088] 1-1 First satellite, 1-2 Second satellite, 1-3 Third satellite, 1-4 Fourth satellite, 2-1 Antenna, 2-2 Antenna, 2-3 Antenna, 2-4 Antenna, 3 Signal processing unit, 11 Signal acquisition unit, 12 Position calculation unit, 13 Velocity calculation unit, 13a Equation creation unit, 13b Velocity calculation processing unit, 14 Signal acquisition unit, 15 Velocity calculation unit, 15a Equation creation unit, 15b Velocity calculation processing unit, 16 Differential calculation unit, 17 Velocity calculation unit, 17a Equation creation unit, 17b Velocity calculation processing unit, 21 Signal acquisition circuit, 22 Position calculation circuit, 23 Velocity calculation circuit, 24 Signal acquisition circuit, 25 Velocity calculation circuit, 26 Differential calculation circuit, 27 Velocity calculation circuit, 31 Memory, 32 Processor.

Claims

1. A signal processing device comprising: a signal acquisition unit that acquires received signals of electromagnetic waves from three or more satellites that receive electromagnetic waves when electromagnetic waves are emitted from a target; a first equation relating to the frequency difference between the Doppler frequency contained in the received signal from a first satellite among the three or more satellites and the Doppler frequency contained in the received signal from a second satellite among the three or more satellites, each including a term relating to the velocity difference between the first satellite and the target and a term relating to the velocity difference between the second satellite and the target; a second equation relating to the frequency difference between the Doppler frequency contained in either the received signal from the first satellite or the received signal from the second satellite and the Doppler frequency contained in the received signal from a third satellite among the three or more satellites, each including a term relating to the velocity difference between either the first satellite or the second satellite and the target and a term relating to the velocity difference between the third satellite and the target; and position information indicating the position of the target, for calculating the velocity of the target.

2. The signal processing device according to claim 1, characterized in that the velocity calculation unit calculates the velocity of the target using the first equation, the second equation, the constraint that the target moves in a direction perpendicular to the radial direction of the Earth, and the position information.

3. The signal processing apparatus according to claim 2, characterized in that the speed calculation unit comprises an equation creation unit that creates a system of linear equations including the first equation, the second equation, and an equation indicating the constraint condition, and a speed calculation processing unit that uses the position information to find the solution to the system of linear equations created by the equation creation unit as the target speed.

4. The signal processing device according to claim 1, wherein the speed calculation unit calculates the speed of the target using the first equation, the second equation, a third equation relating to the frequency difference between the Doppler frequency contained in any of the signals received by the first satellite, the second satellite, or the third satellite and the Doppler frequency contained in the signal received by the fourth satellite among the three or more satellites, the third equation including a term relating to the speed difference between any of the first satellite, the second satellite, or the third satellite and the target, and a term relating to the speed difference between the fourth satellite and the target, and the position information.

5. The signal processing apparatus according to claim 4, characterized in that the speed calculation unit comprises an equation creation unit that creates a system of linear equations including the first equation, the second equation, and the third equation, and a speed calculation processing unit that uses the position information to find the solution to the system of linear equations created by the equation creation unit as the target speed.

6. The signal processing device according to claim 1, further comprising a differential calculation unit for differentiating the second equation with respect to time, wherein the velocity calculation unit calculates the velocity of the target using the first equation, the second equation, the second equation obtained by the differential calculation unit with respect to time, and the position information.

7. The signal processing apparatus according to claim 6, wherein the speed calculation unit comprises an equation creation unit that creates a system of linear equations including the first equation, the second equation, and the second equation obtained by the differential calculation unit after time differentiation, and a speed calculation processing unit that uses the position information to find the solution to the system of linear equations created by the equation creation unit as the target speed.

8. A signal processing device according to any one of claims 1 to 7, comprising a position calculation unit that calculates the position of a target using an equation relating to the time difference between the time of reception of electromagnetic waves by the first satellite and the time of reception of electromagnetic waves by the second satellite, an equation relating to the time difference between either the time of reception of electromagnetic waves by the first satellite or the time of reception of electromagnetic waves by the second satellite and the time of reception of electromagnetic waves by the third satellite, and a constraint condition that the target is located on the surface of the Earth, and outputs position information indicating the position of the target to the velocity calculation unit.

9. The signal processing device according to any one of claims 1 to 8, characterized in that the signal acquisition unit acquires the electromagnetic wave reception signal from a passive sensor that receives the electromagnetic wave reception signal transmitted from each of the three or more satellites.

10. A signal processing method comprising: a signal acquisition unit acquiring received signals of electromagnetic waves from three or more satellites that have received the electromagnetic waves when electromagnetic waves are emitted from a target; a speed calculation unit calculating the speed of a target using a first equation relating to the frequency difference between the Doppler frequency contained in the received signal from a first satellite among the three or more satellites and the Doppler frequency contained in the received signal from a second satellite among the three or more satellites, each including a term relating to the speed difference between the first satellite and the target and a term relating to the speed difference between the second satellite and the target; a second equation relating to the frequency difference between the Doppler frequency contained in either the received signal from the first satellite or the received signal from the second satellite and the Doppler frequency contained in the received signal from a third satellite among the three or more satellites, each including a term relating to the speed difference between either the first satellite or the second satellite and the target and a term relating to the speed difference between the third satellite and the target; and position information indicating the position of the target.

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