JP5208408B2  Relative position estimation system  Google Patents
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 JP5208408B2 JP5208408B2 JP2006338420A JP2006338420A JP5208408B2 JP 5208408 B2 JP5208408 B2 JP 5208408B2 JP 2006338420 A JP2006338420 A JP 2006338420A JP 2006338420 A JP2006338420 A JP 2006338420A JP 5208408 B2 JP5208408 B2 JP 5208408B2
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The present invention relates to a relative position estimation system that estimates a relative position between receiving antennas using radio waves from a reference station whose position is known.
Measuring the displacement and strain of a structure mounted on a shaker and the vibration and vibration of a structure such as a bridge is very useful for studies such as improving earthquake resistance or preventing fatigue failure. In order to correct displacement and distortion due to vibration, it is necessary to precisely measure the positions of a plurality of measurement points distributed over the entire structure. Therefore, a method has been proposed in which a transmitter is installed at a measurement point, a receiving antenna is installed at a known position other than the structure, and the transmitter position is estimated based on the phase difference of the transmitter radio wave received by the receiving antenna. (For example, refer to Patent Document 1).
However, in the method of estimating the transmitter position using the phase difference, it is necessary to separately estimate the integer bias when the distance between the transmitter and the receiving antenna exceeds the wavelength.
In the conventional method as described above, the initial integer bias is processed as known based on information such as the initial position. Therefore, in the conventional method, it is necessary to measure the distance between the transmitter and the receiving antenna with the accuracy of the wavelength order, and when the information such as the initial position cannot be obtained, the position of the measurement point can be measured. could not.
The present invention has been made to solve the abovedescribed problems, and an object thereof is to obtain a relative position estimation system that makes it possible to estimate an initial integer value bias without using information on an initial position. is there.
The inventions includes N (N ≧ 4, N is an integer) number of reference stations which emit radio waves of different frequencies from each other are provided at known positions different to each other except for the structure, each other at different positions of the structure The M reception antennas installed and one of the M reception antennas as a reference antenna, and the reference antenna at time t _{k} (1 ≦ k ≦ K, K ≧ 4, K is an integer) A reference antenna positioning unit that measures a position, a local signal transmitter that transmits a local signal of a predetermined frequency, and a local signal from the local signal oscillator that is provided for each receiving antenna and that receives signals from each receiving antenna. A down converter for multiplying and converting to a frequency band corresponding to a sampling frequency for A / D conversion, and each via the down converter An A / D converter for converting a received signal into a digital signal, the performs FFT conversion process digitized signal by the A / D converter, the phase discriminating the received signal from each base station to the criteria Tsubonegoto a FFT transformer of calculating the tracking of the phase of each reference station which is output from the FFT converter, as well as integrating the position phase, wherein for each put that criteria station at time t _{ k } received by the reference antenna phase, and the phase difference detecting means for calculating a phase difference between the phase of the put that criteria station every time t _{k} received by the receiving antenna other than the reference antenna for each reference station, output from the phase difference detecting means relative vector and integer reference antenna and the receiving antenna m (2 ≦ m ≦ M) based on the position and the position of the reference stations have been said phase difference for each reference station to definitive time t _{ k } and the reference antenna It is a relative position estimation system provided with the position calculation part which calculates the initial value of the difference of value bias.
According to the present invention, since it is possible to estimate the difference in the initial integer bias together with the relative position between the receiving antennas without using the information on the initial position, the measurement point can be obtained even in the case where the information on the initial position cannot be obtained. It is possible to determine the relative position between the two, and there is an effect that the information on the initial position becomes unnecessary.
Embodiment 1 FIG.
1 is a block diagram showing a configuration of a relative position estimation system according to Embodiment 1 of the present invention. The relative position estimation system according to Embodiment 1 shown in FIG. 1 has different known positions q _{n} (threedimensional vectors, 1 ≦ n ≦ N, N ≧ 4, n and N are integers) other than the structure. N reference stations 1 1 _{to} 1 _{N} which are provided and radiate radio waves of different frequencies, M receiving antennas 2 _{1 to} 2 _{M} installed at different positions of the structure, and M receiving antennas One of the reference antennas is used as a reference, and the position p _{r} (t _{k} ) (threedimensional vector) of the reference antenna at time t _{k} (1 ≦ k ≦ K, K ≧ 4, K is an integer) is measured. a reference antenna positioning unit 9, respectively provided for each receiving antenna, varying the frequency of the signals received by the respective receiving antennas in the frequency band corresponding to the sampling frequency of the laterdescribed a / D converter 5 _{1} to 5 _{M} Local having a frequency converter and the down converter _{3} 1 to 3 _{M,} the signal received by the receiving antenna _{2.} 1 to _{2 M,} the frequency band corresponding to the sampling frequency of the laterdescribed A / D converter _{5} 1 to 5 _{M} for A local signal transmitter 4 for transmitting a signal and A / D converters 5 _{1 to} 5 _{M} for converting an analog signal received by each receiving antenna into a digital signal are provided.
The relative position estimation system according to Embodiment 1 shown in FIG. 1 performs FFT (Fast Fourier Transformation) conversion processing on the signals digitized by the A / D converters 5 _{1 to} 5 _{M} , and converts the received signals to The FFT converters 6 _{1 to} 6 _{M} that discriminate each signal radiated by the reference station and calculate the phase thereof, track the phase of the signal output from the FFT converter, and integrate the phase of the received signal from each reference station The phase of the received signal of each reference station at time t _{k} (1 ≦ k ≦ K, K ≧ 4) received by the reference antenna and the phase of the received signal of each reference station at time t _{k} received by a receiving antenna other than the reference antenna reference a in which the phase difference detecting means 7 _{1} to _{7N,} the phase difference and the reference antenna positioning unit 9 of each reference station at time _{t k (1 ≦ k ≦ K} ) is output to calculate the difference between the Position of Tena _{p} r _{(t} k), the position _{q} and reception reference antenna _{n} based on the antenna m of the base station (2 ≦ m ≦ M, provided that, m = 1 reference antenna to) the relative vector of _{d} m (t _{k} ) (a threedimensional vector, 1 ≦ k ≦ K) and an initial integer value bias difference ΔW _{n} (t _{1} ) (1 ≦ n ≦ N, W _{n} (t _{1} ) is an integer); It has.
Next, the operation of the relative position estimation system according to the first embodiment will be described with reference to the drawings. In the first embodiment, one of M reception antennas is used as a reference, and the relative position (relative vector) between the reference antenna and the other reception antenna is estimated. In the following description, a reference antenna that is the reference antenna # 1 (m = 1) among the M receiving antennas is used as a reference antenna. Then, the relative vector at the observation time t _{k} of the receiving antenna #m (2 ≦ m ≦ M) with reference to the reference antenna is d _{m} (t _{k} ), and the relative vector represented by the following expression (1) by the following processing: Estimate d _{m} (t _{k} ). [] ^{T} represents transposition of a matrix or a vector.
d _{m} (t _{k} ) = [x _{m} (t _{k} ) y _{m} (t _{k} ) z _{m} (t _{k} )] ^{T} (1)
First, it is assumed that N (N ≧ 4) reference stations are installed. The positions of the reference stations are known, and the reference station position of the reference station number #n (n ≦ N) is q _{n} (= [X _{n} Y _{n} Z _{n} ] ^{T} , threedimensional vector).
Now, radio waves of frequency (f _{1} + f _{c} ) from the reference station # 1, ... radio waves of frequency (f _{n} + f _{c} ) from _{#n} , ..., #N to frequency (f _{N} + f _{c} ) radio waves emitted, and received by the reference antenna and the receiving antenna #m at the observation start time t _{k} it. In this case, first, the reference antenna, the down converter _{3 1,} is multiplied by a local signal and a reception signal of a frequency _{f c} output by the local signal oscillator 4, respectively _{f 1, f 2, ···,} f N Is converted to a signal having a frequency of. They received signal is converted into a digital signal by the A / D converter 5 _{1.} Then, the FFT processing is performed by FFT transformer _{61,} the reference station from the received signal the phases of radiation signals is calculated.
Similarly, but the reception antenna #m (2 ≦ m ≦ M) , the down converter _{3 m,} is multiplied by a local signal and a reception signal of a frequency _{f c} output by the local signal oscillator 4, respectively _{f} 1, _{f 2} ,..., F _{N} is converted into a signal having a frequency. These received signals are converted into digital signals by the A / D converter 5 _{m} . Thereafter, an FFT conversion process is performed on the digital signal by the FFT converter 6 _{m} , and the phase of the signal radiated from each reference station is calculated from the received signal.
The above contents will be described using equations. Now, it is assumed that the radio wave s _{n} (t) radiated by the reference station #n is as follows. However, a _{n} (t) is the power of the radio wave radiated from the reference station #n.
s _{n} (t) = a _{n} (t) exp [j2π (f _{c} + f _{n} ) t] (2)
The received signals r _{n, 1} (t _{k} ) received by the reference antenna at the observation time t _{k} and the received signals r _{n, m} (t _{k} ) received by the receiving antenna #m are given by the following equations. However _{, an, 1} (t _{k} ) is the power of the received signal at the reference antenna, and an _{, m} (t _{k} ) is the power of the received signal at the receiving antenna #m.
r _{n, 1} (t _{k} ) = a _{n, 1} (t _{k} ) exp [jφ ′ _{n, 1} (t _{k} )] (3)
r _{n, m} (t _{k} ) = a _{n, m} (t _{k} ) exp [jφ ′ _{n, m} (t _{k} )] (4)
Here, φ ′ _{n, 1} (t _{k} ) is the phase of the received signal at the reference antenna, and φ ′ _{n, m} (t _{k} ) is the phase of the received signal at the receiving antenna #m. Can be expressed as
φ ′ _{n, 1} (t _{k} ) = 2π (f _{c} + f _{n} ) t _{k} −2π · W ′ _{n, 1} (t _{k} )
+ 2π / λ _{n} ( p _{r} (t _{k} ) −q _{n} ) (5)
φ ′ _{n, m} (t _{k} ) = 2π (f _{c} + f _{n} ) t _{k} −2π · W ′ _{n, m} (t _{k} )
+ 2π / λ _{n} ( p _{r} (t _{k} ) + d _{m} (t _{k} ) −q _{n} ) (6)
_{However,} p r _{(t k)} at the position of the reference _{antenna,  p r (t k)} q n  is the distance from the reference station #n to the reference _{element,  p r (t k)} + d m ( t _{k} ) −q _{n}  is the distance from the reference station #n to the receiving antenna #m. Also, λ _{n} represents the wavelength of a radio wave having a frequency (f _{c} + f _{n} ) (radio wave emitted from the reference station #n), and c represents the speed of the radio wave (the speed of light). Further, W ′ _{n, 1} (t _{k} ), W ′ _{n, m} (t _{k} ) are integers satisfying the following conditions, and hereinafter, these integers are referred to as integer value biases. In particular, the integer value biases W ′ _{n, 1} (t _{1} ), W ′ _{n, m} (t _{1} ) at the observation start time t _{1} are referred to as initial integer value biases.
0 ≦ 2π (f _{c} + f _{n} ) t _{k} −2π · W ′ _{n, 1} (t _{k} )
+ 2π / λ _{n} ( p _{r} (t _{k} ) −q _{n} ) <2π (7)
0 ≦ 2π (f _{c} + f _{n} ) t _{k} −2π · W ′ _{n, m} (t _{k} )
_{+ 2π / λ n ( p} r (t k) + d m (t k) q n ) <2π (8)
A / D converter 5 _{1} received signal r _{'1} output from the _{(received} signal of the reference antenna), since the radio wave reference station # 1 to N is radiated are mixed, _{1} frequency f by the following equation ~f _{N} signals are mixed. Here, i is a sample number and Δt is a sampling interval of the A / D converter.
Similarly, the reception signal r ′ _{m} (the reception signal of the reception antenna #m) output from the A / D converter 5 _{m} (2 ≦ m ≦ M) is also mixed with radio waves emitted from the reference stations # 1 to N. Therefore, the following equation is obtained.
It should be noted that the relationship between the sample number i and the observation time t _{k} is expressed by the following equation. However, I _{FFT} is a score of FFT conversion in FFT converters 6 _{1 to} 6 _{M} , which will be described later, and Ceil (*) is a function that rounds the element of * to the nearest integer greater than *.
(Ceil (i / I _{FFT} )) · I _{FFT} · Δt = t _{k} (11)
The FFT converter _{61} performs the FFT using the received signal r of the reference antenna _{'1 ((k1)} I FFT +1) ~r' 1 (kI FFT). Signal reference station #n is emitted because the frequency is converted to f _{n,} frequency bin f _{n} corresponds to the signal of the reference station #n. Then, the phase φ ′ _{n, 1} (t _{k} ) of the signal radiated from the reference station #n is calculated from the FFT calculated value with the frequency bin of f _{n} and output.
Similarly, the FFT converter 6 _{m} performs the FFT using the received signals r ′ _{m} ((k−1) I _{FFT} +1) to r ′ _{m} (kI _{FFT} ) of the receiving antenna #m, and the reference station #n The phase φ ′ _{n, m} (t _{k} ) of the radiated signal is calculated and output.
The phase difference detection means 7 _{1 to} 7 _{N} track the phase output from the FFT converters 6 _{1 to} 6 _{M} , calculate the difference between the phase of the reference antenna and the phase of the reception antenna #m, and are the result. The phase difference is output to the position calculation means 8. First, the phase _{φ '1,1 (t k) ~φ} ' signal reference station # 1 output from the FFT transformer _{6} 1 to 6 _{M} is emitted to the phase difference detecting means _{7 1 1, M (t k} ) but the phase _{φ '2,1 (t k) ~φ} ' of the phase difference detecting means _{7} to _{2} signal reference station # 2 output from the FFT transformer _{6} 1 to 6 _{M} is radiated 2, M _{(t} k) but, ..., the phase difference detecting means _{7} signal reference station #N outputted from the FFT transformer _{6} 1 to 6 _{M} is emitted to the _{N} phase _{φ 'N, 1 (t k} ) ~φ' N, M (T _{k} ) is input. Then, the phase difference detecting unit _{7 n,} and the signal received by the reference antenna output from the FFT converter _{61} phase _{φ 'n, 1 (t k} ) of the (reference station #n radiation), FFT transformer _{6 m} The phase φ ′ _{n, m} (t _{k} ) of the signal (reference station #n radiated) received by the receiving antenna #m output from (2 ≦ m ≦ M) is tracked and corrected, and the corrected phase The difference is calculated and output to the position calculation unit 8.
Here, the operation of the phase difference detecting means 7 _{n} will be described separately for the case where the observation time is t _{1} (observation start time) and the case where t _{k} (k ≧ 2). First, when the observation time is _{t 1,} the phase difference detecting unit _{7 n,} the phase phi _{'n,} 1 of the signal received by the reference antenna output from the FFT converter _{61} (reference station #n radiation) _{(t 1} ) As a corrected phase value φ _{n, 1} (t _{1} ). Further, the phase value obtained by correcting the phase φ ′ _{n, m} (t _{1} ) itself of the signal (reference station #n radiated) received by the receiving antenna #m output from the FFT converter 6 _{m} (2 ≦ m ≦ M). _{Let} φ _{n, m} (t _{1} ). Finally, a corrected phase value difference Δφ _{n} (t _{1} ) is calculated and output to the position calculation unit 8.
Δφ _{n} (t _{1} ) = φ _{n, m} (t _{1} ) −φ _{n, 1} (t _{1} ) (12)
If Expressions (5) and (6) are substituted into Expression (12), the phase value difference Δφ _{n} (t _{1} ) can be expressed as the following expression.
_{Δφ n (t 1) = 2π} / λ n ( p r (t 1) + d m (t 1) q n )
−2π / λ _{n} ( p _{r} (t _{1} ) −q _{n} ) −2π · ΔW _{n} (t _{1} )
(13)
Here, ΔW _{n} (t _{1} ) is an initial integer value bias difference expressed by the following equation.
ΔW _{n} (t _{1} ) = W ′ _{n, m} (t _{1} ) −W ′ _{n, 1} (t _{1} ) (14)
Next, when the observation time is t _{k} (k ≧ 2), the phase difference detection unit 7 _{n} firstly outputs the phase values φ ′ _{n, 1} (t _{k} ) output from the FFT converters 6 _{1 to} 6 _{M} , Tracking is performed for φ ′ _{n, m} (t _{k} ). This is because the information being observed is the phase, and when the phase value exceeds 2π, the phase value observed by the FFT converter 6 _{m} is a value obtained by subtracting an integer multiple of 2π, and the phase value is less than 0. This is because an integer multiple of 2π is added. Number Therefore, during the observation start time _{t 1} of the observation time _{t k,} the phase phi _{'n,} 1 _{to (t k), φ' n} , m (t k) becomes count and below 0 beyond 2π And the observed phase is corrected using the difference in the number of times (count value difference).
Now, the signal received by the reference antenna output from the FFT converter _{61} with the phase (reference station #n radiation) is phi _{'n,} 1 _{(t k),} from the observation start time _{t 1} to the observation time _{t k} If the difference in the count value between them is V _{n, 1} (t _{k} ), the corrected phase values φ _{n, 1} (t _{k} ) are as follows:
φ _{n, 1} (t _{k} ) = φ ′ _{n, 1} (t _{k} ) + 2πV _{n, 1} (t _{k} ) (15)
The difference between the count values V _{n, 1} (t _{k} ), the initial integer value bias W ′ _{n, 1} (t _{1} ), and the integer value bias W ′ _{n, 1} (t _{k} ) Since there is a relationship, the corrected phase values φ _{n, 1} (t _{k} ) can be expressed as in equation (17).
W ′ _{n, 1} (t _{1} ) + V _{n, 1} (t _{k} ) = W ′ _{n, 1} (t _{k} ) (16)
φ _{n, 1} (t _{k} ) = 2π (f _{c} + f _{n} ) t _{k} −2π · W ′ _{n, 1} (t _{1} )
+ 2π / λ _{n} ( p _{r} (t _{k} ) −q _{n} ) (17)
Further, the phase of the signal received by the receiving antenna #m output from the FFT converter 6 _{m} (radiation from the reference station #n) is φ ′ _{n, m} (t _{k} ), and the observation time t _{k} from the observation start time t _{1.} If the difference between the count values up to Vn _{, m} (t _{k} ) is corrected, the corrected phase value φ _{n, m} (t _{k} ) is expressed by the following equation.
φ _{n, m} (t _{k} ) = φ ′ _{n, m} (t _{k} ) + 2πV _{n, m} (t _{k} ) (18)
The difference between the count values V _{n, m} (t _{k} ), the initial integer value bias W ′ _{n, m} (t _{1} ), and the integer value bias W ′ _{n, m} (t _{k} ) Since there is a relationship, the corrected phase value φ _{n, m} (t _{k} ) can be expressed as in Expression (20).
W ′ _{n, m} (t _{1} ) + V _{n, m} (t _{k} ) = W ′ _{n, m} (t _{k} ) (19)
φ _{n, m} (t _{k} ) = 2π (f _{c} + f _{n} ) t _{k} −2π · W ′ _{n, m} (t _{1} )
_{+ 2π / λ n ( p} r (t k) + d m (t k) q n ) (20)
Finally, using the corrected phase values φ _{n, 1} (t _{k} ), φ _{n, m} (t _{k} ), the phase φ _{n, 1} (t _{k} ) received by the reference antenna and the reception by the receiving antenna #m the phase φ _{n,} m _{(t k)} the difference Δφ _{n} _{(t k)} to calculate output.
Δφ _{n} (t _{k} ) = φ _{n, m} (t _{k} ) −φ _{n, 1} (t _{k} ) (21)
If equations (17) and (20) are substituted into equation (21), Δφ _{n} (t _{k} ) can be expressed as equation (22).
Δφ _{n} (t _{k} ) = 2π / λ _{n} ( p _{r} (t _{k} ) + d _{m} (t _{k} ) −q _{n} )
−2π / λ _{n} ( p _{r} (t _{k} ) −q _{n} ) −2π · ΔW _{n} (t _{1} ) (22)
In the above description, the phase value φ ′ _{n, m} (t _{k} ) itself output from the FFT converter 6 _{m} is tracked and corrected, but the phase difference Δφ _{n} (t _{k} ) is tracked and corrected. Things can be used.
The reference antenna positioning unit 9 measures the position of the reference antenna at the observation time t _{k} , and its value p _{r} (t _{k} ) (= [x _{r} (t _{k} ) y _{r} (t _{k} ) z _{r} (t _{k} )] ^{T} ) is output to the position calculation unit 8. When measuring the response of a structure mounted on a shaker, a reference antenna is installed on the shaker, and p _{r} (from the position of the reference antenna and the motion of the vibration set by the shaker itself. t _{k} ) may be calculated. Further, the position of the reference antenna may be measured using GPS (Grobal Positioning System) or the like.
The position calculator 8 is based on the phase difference Δφ _{n} (t _{k} ) output from the phase difference detectors 7 _{1 to} 7 _{N} and the reference antenna position p _{r} (t _{k} ) output from the reference antenna positioning unit 9. estimates the relative vector between the reference antenna and the receiving antenna #m d _{m (t} _{k),} the difference between the initial integer ambiguity. As shown in the equation (22), the value obtained by subtracting the difference of the initial integer bias from the difference between the “distance from the reference station # 1 to the receiving antenna #m” and the “distance from the reference station # 1 to the reference antenna” is 2 Since it is equal to the value obtained by multiplying the phase difference of the signals received by the two antennas by the wavelength, the following equation is established using the phase difference value Δφ _{n} (t _{1} ) at the observation time t _{1} .
Assuming that the reference station number N is 4 (n = 1,..., 4), the equations become the following equations (24) to (27).
The unknowns in the equations (24) to (27) are related to relative vectors (x _{m} (t _{1} ), y _{m} (t _{1} ), z _{m} (t _{1} )) are 3, and are related to the difference in the initial integer bias. (ΔW _{1} (t _{1} ), ΔW _{2} (t _{1} ), ΔW _{3} (t _{1} ), ΔW _{4} (t _{1} )) is 4. For this reason, the total number of unknowns is 7 and the number of equations exceeds 4 and the unknowns cannot be determined.
Therefore, an equation using the phase differences Δφ _{1} (t _{2} ) to Δφ _{4} (t _{2} ) at the observation time t _{2} is considered. Then equation kick in the observation time _{t 2} is the formula (28)  (31).
Here, the phase differences Δφ _{1} (t _{2} ) to Δφ _{4} (t _{2} ) at the observation time t _{2} are corrected by counting and correcting the number of times the phase value exceeds 2π from the time t _{1.} ) right to (31), the difference [Delta] W _{1} of the initial integer ambiguity at time _{t 1 (t 1) ~ΔW} can be expressed by _{4} _{(t 1).} As a result, in Equations (24) to (31), the unknown related to the relative vector increases by 3 to 6, but the unknown related to the difference in the initial integer bias remains 4 and does not increase. However, in this case as well, the number of unknowns is 10 and exceeds the number 8 of equations, so the unknowns cannot be determined.
Further, the phase difference Δφ _{1} _{(t} 3) at the observation time _{t 3 ~Δφ 4 (t 3)} , and the phase difference Δφ _{1} _{(t} 4) at the observation time _{t 4 ~Δφ 4} Consider equations with _{(t 4)} . Then equation takes the observation time _{t 3} is the formula (32)  (35), the equation at the observation time _{t 4} becomes Equation (36)  (39).
The unknowns in the equations (24) to (39) are 12 for the relative vector, 4 for the difference in the initial integer value bias, and the total number of unknowns is 16. On the other hand, since the number of equations is 16, in this case, the number of unknowns is equal to the number of equations, and the unknowns can be determined.
If generalized and the number of observation times is K and the number of reference stations is N, the condition that the number of equations exceeds the number of unknowns and can be determined as unknowns is Equation (40).
NK ≧ 3K + N (40)
However, it is assumed that the reference antenna positions p _{r} (t _{1} ),..., P _{r} (t _{K} ) at each observation time are different from each other. When the number of equations is larger than the number of unknowns, the unknowns are determined by obtaining a least square solution.
In this way, the distance between the receiving antennas is measured in advance, and the initial integer bias difference is estimated together with the relative vector between the receiving antennas without separately calculating the initial value of the integer bias difference between them. Is possible. In the above description, the method using the observation values at the continuous observation times of the times t _{1 to} t _{4} has been described. However, since the phase is tracked, it is not necessary to use the continuous observation values, and the condition of the expression (40) is satisfied. Can be estimated using observation values at discontinuous times.
In the above embodiment, the case where the relative position between the measurement points of the structure placed on the shaker is measured has been described as an example. The present invention can also be applied based on the same principle as described above when measuring the relative position between each measurement point.
Embodiment 2. FIG.
In the first embodiment described above, the position of the reference station is fixed. However, even if the position of the reference station moves, if the position is known, the unknowns in the equations (23) and (24) to (39) do not increase. Therefore, if the reference station has a reference station moving means and a reference station positioning means, and the position q _{w} (t _{k} ) of the reference station at the observation time t _{k} is observed and the result is transmitted to the position calculation unit 8, the unknown number does not increase. The unknown can be determined under the same conditions as in equation (40).
In the case of the second embodiment, it is effective when the structure hardly moves, and the relative position of the reference station and the receiving antenna is changed by moving the reference station, whereby the equations (24) to (39) Since the equation changes, the difference in the initial integer bias can be determined. Once once to determine the integer ambiguity, because it tracks the phase in the phase difference detecting unit _{71} can determine the relative position between the receiving antennas in the same manner as the conventional method.
Embodiment 3 FIG.
In the first embodiment described above, the amount of calculation increases because the equation for calculation in the position calculation unit 8 includes the square or square root of the unknown. Therefore, instead of the position calculating unit 8, as the interval reference station and the receiving antennas are sufficiently separated, it may be provided with the recent position calculating unit _{81} for determining the relative position vector by approximation.
That is, an approximate position calculation unit is provided instead of the position calculation unit 8, and the approximate position calculation unit is based on the phase difference for each reference station, the position of the reference antenna, and the position of the reference station at time t _{k} (1 ≦ k ≦ K). By combining a plurality of equations that the length of the relative vector of the reference antenna and the receiving antenna m projected in the direction of the reference station is equal to the radio wave propagation distance difference, the relative vector of the reference antenna and the receiving antenna m and the initial integer bias Estimate the difference.
If the reference station #n and the receiving antenna #m are sufficiently separated from each other, the radio wave from the reference station #n received by the receiving antenna can be approximated by a plane wave. As a result, the difference between the “distance between the reference station #n and the reference antenna” and the “distance between the reference station #n and the reception antenna #m” indicates that the estimated relative vector d _{m} (t _{k} ) is the reference vector as shown in FIG. It can be regarded as the length h _{m} (t _{k} ) projected in the direction of. As a result, the equation becomes:
In Expression (41), since there is no unknown square or square root element, it is possible to reduce the amount of calculation compared to the conventional method. It should be noted that the condition of the number of reference stations N and the number of observations K for which this method is established is expressed by equation (40) because the relationship between the number of unknowns and the number of equations is the same as in the first embodiment.
Further, in the equation (41), the reference station is fixed. Naturally, even when the reference station is moving, if the position is known, the unknown number can be estimated as in the second embodiment. it can.
1 1 _{to} 1 _{N} reference station, 2 _{1 to} 2 _{M} receiving antenna, 3 _{1 to} 3 _{M} down converter, 4 local signal transmitter, 5 _{1 to} 5 _{M} A / D converter, 6 _{1 to} 6 _{M} FFT converter, 7 _{1 to} 7 _{N} phase difference detecting means, 8 position calculating section, 9 reference antenna positioning section.
Claims (3)
 N (N ≧ 4, N is an integer) reference stations that are provided at different known positions other than the structure and radiate radio waves of different frequencies;
M receiving antennas installed at different positions of the structure;
A reference antenna positioning unit that measures the position of the reference antenna at time t _{k} (1 ≦ k ≦ K, K ≧ 4, K is an integer), with one of the M receiving antennas serving as a reference antenna;
A local signal transmitter for transmitting a local signal of a predetermined frequency;
A down converter that is provided for each receiving antenna and converts a signal received by each receiving antenna with a local signal from the local signal oscillator to a frequency band corresponding to a sampling frequency for A / D conversion;
An A / D converter for converting each received signal through the down converter into a digital signal;
A FFT transformer wherein performs FFT conversion process digitized signal by the A / D converter, to calculate the phase of the received signal from each base station by discrimination based on quasi Tsubonegoto,
The tracking the phase of each reference station which is output from the FFT converter, as well as integrating the position phase, and the phase of the put that criteria station every time t _{ k } received by the reference antenna, receiving nonreference antenna phase difference detection means for calculating for each reference station a phase difference between the phase of each put that criteria station at time t _{k} received by the antenna,
Relative vector and integer of reference and receiving antennas m (2 ≦ m ≦ M) based on the position and the position of the reference station of the phase difference and the reference antenna of each base station which definitive time t _{ k } which is output from the phase difference detecting means A relative position estimation system comprising: a position calculation unit that calculates an initial value of a numerical bias difference.  The relative position estimation system according to claim 1,
The reference station has a reference station moving means and a reference station positioning means, and transmits the result of positioning the position of each moving reference station at each observation time to the position calculation unit,
Wherein the position calculation unit calculates the initial value of the difference between the relative vector and the integer value bias of the reference antenna and the receiving antenna m on the basis of the position and the position of the reference station of the phase difference and the reference antenna of each base station which definitive time t _{ k } A relative position estimation system characterized by that.  N (N ≧ 4, N is an integer) reference stations that are provided at different known positions other than the structure and radiate radio waves of different frequencies;
M receiving antennas installed at different positions of the structure;
A reference antenna positioning unit that measures the position of the reference antenna at time t _{ k } (1 ≦ k ≦ K, K ≧ 4, K is an integer), with one of the M receiving antennas serving as a reference antenna;
A local signal transmitter for transmitting a local signal of a predetermined frequency;
A down converter that is provided for each receiving antenna and converts a signal received by each receiving antenna with a local signal from the local signal oscillator to a frequency band corresponding to a sampling frequency for A / D conversion;
An A / D converter for converting each received signal through the down converter into a digital signal;
An FFT converter that performs an FFT conversion process on the signal digitized by the A / D converter, discriminates a received signal from each reference station for each reference station, and calculates its phase;
Time tracking the phase of each reference station which is output from the FFT converter, as well as integrating the phase, and the phase of each reference station at time t _{ k } received by the reference antenna, and received by the receiving antenna other than the reference antenna phase difference detection means for calculating, for each reference station, a phase difference between said phase for each reference station at t _{ k } ;
Based on the position and the position of the reference station of the phase difference and the reference antenna of each base station which definitive time t _{ k } which is output from the phase difference detecting means, a relative vector of the reference antenna and the receiving antenna m (2 ≦ m ≦ M) An approximate position calculating unit that estimates an initial value of a difference between a relative vector of the reference antenna and the receiving antenna m and an integer bias by regarding that the length projected in the direction of the reference station is equal to the radio wave propagation distance difference ;
The relative position estimation system comprising the.
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