JP2006030022A - Distance measurement apparatus and distance measurement method using radio waves - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a distance measurement apparatus using radio waves which can measure a distance to an object to be measured at a short distance with high precision. <P>SOLUTION: The distance measurement apparatus using radio waves which can measure a distance from an antenna to an object to be measured at a short distance with high precision can be achieved by detecting a beat signal by quadrature detection, correcting an error concerning the quadrature relationship between the in-phase component of the beat signal and the quadrature component of the beat signal, and performing discrete Fourier transformation on a complex data series which includes a data series of the in-phase component of the beat signal as the real part and a data series of the quadrature component of the beat signal as the imaginary part. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a distance measuring device and a distance measuring method for measuring a distance to an object to be measured using radio waves.

  As a distance measuring device that measures the distance to the object to be measured in a non-contact manner, a distance measuring device that uses FMCW radio waves is known. The FMCW system transmits a frequency-modulated continuous wave signal as a transmission wave to the device under test, and generates a beat signal by mixing the received wave reflected by the device under test and the transmission wave. In this method, the distance from the frequency of the beat signal to the object to be measured is measured (Patent Document 1).

  The beat signal obtained by mixing is an analog signal. Therefore, in order to obtain the value of the frequency of the beat signal, the beat signal is A / D converted, the data series generated thereby is subjected to discrete Fourier transform, and the amplitude value of the frequencies obtained by the discrete Fourier transform is It is necessary to detect the maximum frequency value.

JP 2003-240842 A

  In order to perform highly accurate distance measurement with a distance measuring device using radio waves, it is necessary to detect the frequency of the beat signal with high accuracy. However, a conventional distance measuring device using radio waves cannot obtain a sufficient accuracy for measuring a distance to an object to be measured at a short distance. This will be described in detail below.

となる。ここで、δ（ｋ−ω）及びδ（ｋ＋ω）はディラックのデルタ関数である。ディラックのデルタ関数δ（ｘ）は、ｘ≠０のときにδ（ｘ）＝０となり、

となる条件を満たす関数である。すなわち、関数δ（ｋ−ω）は、ｋ≠ωとなるときに０となる関数であり、関数δ（ｋ＋ω）は、ｋ≠−ωとなるときに０となる関数である。従って、角周波数ωのビート信号をフーリエ変換すると、角周波数“＋ω”のスペクトラム（これを「実像」と呼ぶ）と、角周波数“−ω”のスペクトラム（これを「鏡像」と呼ぶ）と、が現れる。 If the beat signal (A · cos (ωt + φ)) having the angular frequency ω is obtained by the above-described mixing, the beat signal is
A · cos (ωt + φ) = A · (e φ e jωt + e -φ e -jωt) / 2 ··· (1)
It can be expressed as Here, A indicates the amplitude of the beat signal, and φ indicates the phase of the beat signal. When the beat signal represented by Equation (1) is Fourier transformed,

It becomes. Here, δ (k−ω) and δ (k + ω) are Dirac delta functions. Dirac's delta function δ (x) becomes δ (x) = 0 when x ≠ 0,

Is a function that satisfies the following condition. That is, the function δ (k−ω) is a function that becomes 0 when k ≠ ω, and the function δ (k + ω) is a function that becomes 0 when k ≠ −ω. Therefore, when the beat signal of the angular frequency ω is Fourier transformed, the spectrum of the angular frequency “+ ω” (referred to as “real image”) and the spectrum of the angular frequency “−ω” (referred to as “mirror image”), Appears.

  As described above, in a distance measuring device using radio waves, in order to detect the frequency of a beat signal, A / D conversion is performed on the beat signal obtained by mixing, and the data sequence generated thereby is subjected to discrete Fourier transform. is doing. For this reason, when the data series of the beat signal having each frequency ω is subjected to discrete Fourier transform, as shown in FIG. 7A, the real image of the beat signal pointed by a square centered on the angular frequency “+ ω” and the angular frequency “ A spectrum having two sinc function characteristics of a mirror image of a beat signal pointed by a triangle centered at −ω ″ appears. In the arithmetic unit mounted on the distance measuring device using radio waves, a spectrum obtained by adding these two spectra is calculated, and the value of the frequency at which the amplitude value of the added spectrum is maximized is calculated. The frequency is calculated.

  In such a distance measuring apparatus using radio waves, when the frequency of the beat signal is high (when the distance from the antenna to the object to be measured is long), as shown in FIG. Each spectrum of the mirror image “−ω” is separated from each other. For this reason, there is no (or small) error between the frequency value at which the amplitude value of the spectrum of the real image (and mirror image) becomes maximum and the frequency value at which the amplitude value of the added spectrum becomes maximum. Therefore, when the frequency of the beat signal is high (when the distance from the antenna to the object to be measured is long), there is no (or small) error in the frequency of the beat signal detected by the distance measuring device using radio waves.

  On the other hand, when the frequency of the beat signal is low (when the distance from the antenna to the object to be measured is short), the spectrum of each of the real image “+ ω” and the mirror image “−ω” of the beat signal is as shown in FIG. Approach each other. For this reason, an error occurs between the frequency value at which the amplitude value of the spectrum of the real image (and mirror image) is maximum and the frequency value at which the amplitude value of the added spectrum is maximum. Therefore, in the conventional distance measuring device using radio waves, when the frequency of the beat signal is low (when the distance from the antenna to the object to be measured is short), an error occurs in the frequency of the detected beat signal, and the short distance However, it was not possible to obtain sufficient accuracy to measure the distance to the object to be measured.

  The present invention has been made with respect to the above-described problems, and an object of the present invention is to provide a distance measuring device and a distance measuring method using radio waves that can accurately measure the distance to an object to be measured at a short distance. Is to realize.

  The configuration of the present invention includes a transmission system that transmits radio waves whose frequency changes with time in a certain range from an antenna to a device under test, and a reception system that receives radio waves reflected by the device under test via an antenna. And the same frequency of the difference frequency component having the same phase as that of the transmitted radio wave by performing quadrature detection of the radio wave received by the transmitted radio wave. A frequency detection unit that detects a component, a frequency component of a difference between the frequency of the transmitted radio wave and a frequency of the received radio wave, and an orthogonal component of the difference frequency component having a phase that is π / 2 different from that of the transmitted radio wave; The A / D converter that A / D converts the in-phase component and the quadrature component of the difference frequency component to generate a data sequence, and calculates the data sequence of the in-phase component and the quadrature component of the generated difference frequency component. And a calculation unit that measures the distance from the antenna to the object to be measured, and the calculation unit calculates an error related to the orthogonal relationship between the in-phase component of the difference frequency component and the orthogonal component of the difference frequency component. Based on the calculated error, an error correction circuit that corrects an error related to the orthogonal relationship between the in-phase component of the difference frequency component and the orthogonal component of the difference frequency component, and the difference frequency component of which the error is corrected The complex data series with the error corrected with the in-phase component data series as the real part and the error frequency-corrected quadrature component data series as the imaginary part is subjected to the discrete Fourier transform to obtain the difference from the antenna. And a circuit for measuring the distance to the object to be measured.

  In addition, the error correction circuit performs a discrete Fourier transform on a complex data sequence in which the data sequence of the in-phase component of the difference frequency component is a real part and the data sequence of the quadrature component of the difference frequency component is an imaginary part, and a spectrum obtained by this And a first complex number including the amplitude and phase of the frequency component of the difference corresponding to the frequency at which the spectrum amplitude is maximized, and a frequency of the spectrum. A circuit for extracting a second complex number including an amplitude and a phase of a frequency component of a difference corresponding to a frequency having a maximum amplitude and a frequency symmetric with respect to the DC axis, a first complex number, and a second complex number, , Subtracting the first complex number and the second complex number by using one of them as a conjugate complex number, the in-phase component of the difference frequency component, and the difference frequency component Corrects the amplitude and phase errors of the quadrature component, the amplitude and phase errors of the quadrature component, and the in-phase component of the difference frequency component and the quadrature component of the difference frequency component based on the calculated error It is desirable to provide the circuit which performs.

  In addition, the error correction circuit, when the frequency at which the amplitude of the extracted spectrum is maximum is zero, calculates the first complex number including the amplitude and phase of the frequency component of the difference corresponding to the non-zero frequency of the calculated spectrum. A complex number including a complex number including the amplitude and phase of a difference frequency component corresponding to a frequency that is symmetric with respect to a frequency other than zero and a DC axis is defined as a second complex number, and the in-phase component of the difference frequency component and the difference frequency component It is desirable to calculate the amplitude and phase error of the orthogonal component.

  Further, the error correction circuit calculates a Lissajous figure from the data series of the in-phase component of the difference frequency component and the data series of the orthogonal component of the difference frequency component, and calculates the difference frequency component from the calculated Lissajous figure. You may correct | amend the error of the amplitude and phase of an in-phase component and the orthogonal component of a frequency component of a difference.

  Another configuration of the present invention includes a step of transmitting a radio wave whose frequency varies with time in a certain range from an antenna to a device to be measured, and a step of receiving a radio wave reflected by the device to be measured through the antenna. And the same frequency of the difference frequency component having the same phase as that of the transmitted radio wave by performing quadrature detection of the radio wave received by the transmitted radio wave. Detecting a component, a frequency component of a difference between a frequency of a transmitted radio wave and a frequency of a received radio wave, and a quadrature component of a difference frequency component having a phase different from that of the transmitted radio wave by π / 2, and a difference An A / D conversion is performed on the in-phase component and the quadrature component of the frequency component, and a data sequence is generated, and an in-phase component and a quadrature component data sequence of the generated frequency component of the difference are calculated. Measuring the distance from the antenna to the object to be measured, and measuring the distance from the antenna to the object to be measured includes an in-phase component of the difference frequency component and an orthogonal component of the difference frequency component. Calculating an error related to the orthogonal relationship, and correcting the error related to the orthogonal relationship between the in-phase component of the difference frequency component and the orthogonal component of the difference frequency component based on the calculated error; Discrete Fourier transform of a complex data series with corrected errors, with the in-phase component data series of the difference frequency component as the real part and the error frequency corrected quadrature component data series as the imaginary part And measuring the distance from the antenna to the object to be measured.

  In addition, the step of correcting the error related to the orthogonal relationship includes a discrete Fourier transform on a complex data sequence in which the in-phase component data sequence of the difference frequency component is a real part and the complex data sequence of the difference frequency component orthogonal component is an imaginary part. The first step including the step of calculating the spectrum obtained thereby, the frequency at which the calculated spectrum has the maximum amplitude, and the amplitude and phase of the frequency component of the difference corresponding to the frequency at which the spectrum has the maximum amplitude Extracting the complex number and the second complex number including the amplitude and phase of the frequency component of the difference corresponding to the frequency at which the amplitude of the spectrum is maximum and the frequency symmetric with respect to the DC axis, and the first complex number, By subtracting the first complex number and the second complex number from either one of the second complex numbers as a conjugate complex number, And a step of calculating an amplitude and phase error of the orthogonal component of the difference frequency component, and an in-phase component of the difference frequency component and an orthogonal component of the difference frequency component based on the calculated error It is desirable to have a step of correcting an error in amplitude and phase.

  The step of correcting the error related to the orthogonal relationship includes the amplitude and phase of the frequency component of the difference corresponding to the non-zero frequency of the calculated spectrum when the frequency at which the amplitude of the extracted spectrum is maximum is zero. The complex number is the first complex number, the complex number including the amplitude and phase of the difference frequency component corresponding to the non-zero frequency and the frequency symmetric with respect to the DC axis is the second complex number, the in-phase component of the difference frequency component, It is desirable to calculate the amplitude and phase error of the orthogonal component of the difference frequency component.

  Further, the step of correcting the error related to the orthogonal relationship calculates a Lissajous figure from the data series of the in-phase component of the difference frequency component and the data series of the orthogonal component of the difference frequency component, and from the calculated Lissajous figure, You may correct | amend the error of the amplitude and phase of the in-phase component of a difference frequency component, and the orthogonal component of a difference frequency component.

  According to the present invention, an error relating to the orthogonal relationship between the in-phase component of the difference frequency component and the orthogonal component of the difference frequency component is calculated, and based on the calculated error, the in-phase component of the difference frequency component; The error from the orthogonal component of the frequency component of the difference is corrected, and the complex data sequence of the beat signal with the corrected error is subjected to discrete Fourier transform, so that the distance from the antenna to the object to be measured is reduced. A distance measuring device and a distance measuring method using radio waves that can be measured with high accuracy can be realized.

  Hereinafter, a distance measuring device using radio waves according to an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a distance measuring device using radio waves according to the present embodiment. FIG. 2 is a graph showing a frequency shift with respect to time of a transmission wave transmitted from a distance measurement device using radio waves according to the present embodiment and a reception wave received. First, the configuration of a distance measuring device using radio waves according to the first embodiment will be described.

“First Embodiment”
In FIG. 1, a distance measuring device 1 using radio waves is connected to a device under test from a transmitting antenna 21 via a receiving system 23 and a transmitting system that transmits radio waves that change with time in a certain range. And a receiving system for receiving radio waves reflected by the measurement object. Here, the transmission system includes an oscillation unit 11, a frequency modulation unit 12, a mixer 13, an IF oscillation unit 14, a filter 15, a coupler 16, a mixer 17, a filter 18, and a transmission antenna 21. The reception system includes a reception antenna 23, a mixer 40, a filter 41, a quadrature detection unit 42, capacitors 46-1, 46-2, A / D conversion units 47-1, 47-2, and a calculation unit 50, and includes quadrature detection. The unit 42 includes mixers 43-1 and 43-2, a π / 2 phase shifter 44, and filters 45-1 and 45-2. The distance measuring device 1 using radio waves includes an RF oscillation unit 30 for performing up-conversion of the transmission wave to the RF frequency band and down-conversion of the reception wave to the IF frequency band.

  In addition, the calculation unit 50 calculates an error (amplitude error and phase error) related to the orthogonal relationship of the quadrature component with the in-phase component of the beat signal, and based on the calculated error, the quadrature of the in-phase component and the quadrature component of the beat signal. An error correction circuit that corrects an error related to the relationship and a circuit that measures the distance from the antenna to the object to be measured by performing a discrete Fourier transform on the complex data series of the beat signal in which the error is corrected are provided. This will be described later.

  The antenna is installed so as to face the object to be measured so that the transmitting antenna 21 can transmit the electric wave to the object to be measured, and the receiving antenna 23 can receive the reflected wave. The transmitting antenna 21 and the receiving antenna 23 may have a structure in which the antenna is shared for transmission and reception, and the transmission wave and the reception wave are separated by a circulator, as described in Patent Document 1. It is desirable to arrange them separately. If the antenna is shared for transmission and reception as in the distance measuring device described in Patent Document 1, the transmitted wave is reflected inside the antenna (without being radiated), and this reflected wave is received as a received wave via the circulator. End up. The reflected wave reflected inside the antenna is received at a frequency that is almost the same as the transmitted wave because the transmission distance is extremely close to zero and very short. Therefore, if the antenna is shared for transmission and reception, a low-frequency beat signal is always detected by mixing the transmission wave and the reception wave. Such a low-frequency beat signal causes an error in detection of the frequency of the beat signal when the distance from the antenna to the object to be measured is short (in some cases, not close). Therefore, it is desirable to arrange the antennas separately for transmission and reception with sufficient isolation (for example, 50 dB or more). Hereinafter, the operation of the distance measuring apparatus using the radio wave of the first embodiment will be described in detail.

In FIG. 1, an oscillating unit 11 generates a transmission wave (radio wave) having a fundamental frequency f ₀ and outputs it. The frequency modulation unit 12 receives the transmission wave described above, modulates the frequency of the transmission wave, and changes the transmission wave linearly with respect to the time T [sec] in the frequency f _{0 to} f ₀ + B [Hz] range. Output. The frequency-modulated transmission wave is input to the mixer 13 and mixed with the IF signal output from the IF oscillation unit 14. The transmission wave mixed by the mixer 13 is filtered by the filter 15 so that only high-frequency components pass, and is up-converted to the IF frequency band (f _{IF to} f _IF + B [Hz]).

The transmission wave up-converted to the IF frequency band is input to the coupler 16. The transmission wave input to the coupler 16 is input to the mixer 17 and the quadrature detection unit 42. The transmission wave input to the mixer 17 is mixed with the RF signal output from the RF oscillation unit 30. The transmission wave mixed by the mixer 17 is filtered by the filter 18 so that only high-frequency components pass, and is up-converted to an RF frequency band (f _{RF to} f _RF + B [Hz]). The transmission wave up-converted to the RF frequency band is radiated from the transmission antenna 21 to the object to be measured.

A transmission wave radiated from the transmission antenna 21 to the object to be measured is reflected by the object to be measured and received by the reception antenna 23 as a reception wave. This received wave is delayed with respect to the transmitted wave by a time δt [sec] that propagates back and forth the distance R [m] to the object to be measured. The received wave is input to the mixer 40. The received wave input to the mixer 40 is mixed with the RF signal output from the RF oscillation unit 30. The transmission wave mixed by the mixer 40 is filtered by the filter 41 so that only low-frequency components pass, and is down-converted to the IF frequency band (f _{IF to} f _IF + B [Hz]). The received wave down-converted to the IF frequency band is input to the quadrature detection unit 42.

  The received wave input to the quadrature detection unit 42 is input to the mixers 43-1 and 43-2. The reception wave input to the mixer 43-1 is mixed with the transmission wave output from the coupler 16. The received wave mixed by the mixer 43-1 is filtered by the filter 45-1 so that only the low frequency component passes, and has a frequency δf [Hz] which is a difference between the frequency of the transmitted wave and the frequency of the received wave, which will be described later. A cosine wave component that is an in-phase component of the beat signal is output. The received wave input to the mixer 43-2 is mixed with the transmitted wave output from the coupler 16 and shifted by π / 2 phase by the π / 2 phase shifter 44 (as will be described later). Strictly speaking, the phase shift is not π / 2 but includes an error). The received wave mixed by the mixer 43-2 is filtered by the filter 45-2 so that only a high-frequency component passes, and a beat having a frequency δf [Hz] which is a difference between the frequency of the transmission wave and the frequency of the reception wave, which will be described later. A sine wave component which is an orthogonal component of the signal is output.

FIG. 2 shows a state of frequency shift between the transmission wave and the reception wave input to the quadrature detection unit 42. FIG. 2 is a graph showing the frequency transition of the transmission wave and the reception wave, with the horizontal axis representing time and the vertical axis representing frequency. The transmission wave output from the coupler 16 is linearly shifted with respect to time T [sec] in the frequency f _{IF to} f _IF + B [Hz] range. Further, the received wave input to the quadrature detection unit 42 is also input after being linearly shifted with respect to the time T [sec] in the frequency range from f _{IF to} f _IF + B [Hz]. Here, the reception wave input to the quadrature detection unit 42 is delayed by a time δt [sec] corresponding to the transmission wave that travels back and forth the distance R [m] to the object to be measured as described above. Is input. On the other hand, the transmission wave input to the quadrature detection unit 42 is shifted by the frequency δf [Hz] (by the time δt [sec]) with respect to the reception wave. Accordingly, the quadrature detection unit 42 outputs a cosine wave component and a sine wave component of a beat signal having a frequency δf [Hz] which is a difference between the frequency of the transmission wave and the frequency of the reception wave.

Here, when the frequency fluctuation width of the transmission wave is B [Hz] and the fluctuation time is T [sec], the time for which the radio wave is reflected by the measured object and reciprocates is:
δt = Tδf / B (4)
It is represented by Therefore, if the propagation speed of the radio wave is c [m / sec], the distance R [m] to the object to be measured is
R = cTδf / 2B (5)
Is obtained by calculating.

  As described above, the beat signals output from the mixers 45-1 and 45-2 are analog signals. Therefore, in order for the calculation unit 50 to calculate the distance R [m] from the frequency δf [Hz] of the beat signal, it is necessary to convert the beat signal into a digital signal (data series) and calculate it. However, if this beat signal is subjected to discrete Fourier transform using real number data, the influence of the mirror image of the spectrum of the beat signal as described above cannot be eliminated. Therefore, in the distance measurement device using the radio wave according to the first embodiment, the cosine wave component that is the in-phase component of the beat signal output from the quadrature detection unit 42 described above is a real part, and the sine wave component that is a quadrature component. The influence of the mirror image is eliminated by performing a discrete Fourier transform on the complex data series with imaginary part as. This will be described in detail below.

  The in-phase component of the beat signal output from the filter 45-1 of the quadrature detection unit 42 is input to the A / D conversion unit 47-1 after the low frequency component including the DC component is removed by the capacitor 46-1. . The in-phase component of the beat signal input to the A / D conversion unit 47-1 is A / D converted with a predetermined number of samples. As an example, the predetermined number of samples is 256. Therefore, the A / D conversion unit 47-1 outputs a data series (in-phase component) composed of 256 pieces of data. On the other hand, the quadrature component of the beat signal output from the filter 45-2 of the quadrature detection unit 42 is input to the A / D conversion unit 47-2 after the low frequency component including the DC component is removed by the capacitor 46-2. Is done. The quadrature component of the beat signal input to the A / D conversion unit 47-2 is A / D converted with the same number of samples (256) as the predetermined number of samples described above. Therefore, the A / D conversion unit 47-2 outputs a data sequence (of orthogonal components) composed of 256 pieces of data. Here, the data series generated by the A / D conversion units 47-1 and 47-2 is input to the calculation unit 50, the frequency δf [Hz] of the beat signal described above is calculated, and the transmission antenna 21 (or 23) is calculated. ) To the object to be measured. Hereinafter, the process of the calculating part 50 is demonstrated in detail.

  As described above, the beat signal output from the A / D conversion unit 47-1 and input to the calculation unit 50 is a cosine wave component (A · cos (ωt + θ)) that is an in-phase component of the beat signal. On the other hand, the beat signal output from the A / D converter 47-2 and input to the arithmetic unit 50 is a sine wave component (A · γ · sin (ωt + θ + φ)) that is an orthogonal component of the beat signal. Here, γ is the amplitude ratio (amplitude error) of the in-phase component and the quadrature component of the beat signal. Φ is the degree of phase shift (phase error) between the in-phase component and the quadrature component. Therefore, if the cosine wave component, which is the in-phase component of the beat signal, and the sine wave component, which is the quadrature component of the beat signal, have an ideal quadrature relationship, γ = 1 and φ = 0.

  However, as described above, the frequency of the transmission wave input to the π / 2 phase shifter 44 via the coupler 16 is shifted. Along with this, the wavelength of the transmission wave also changes. For this reason, the phase of the transmission wave input to the mixer 43-2 is not necessarily π / 2 with respect to the transmission wave input to the mixer 43-1. Therefore, it is difficult to always maintain an ideal quadrature relationship between the in-phase component and the quadrature component of the beat signal output from the quadrature detection unit 42. Therefore, in the distance measuring apparatus 1 using radio waves according to the first embodiment, an error in the orthogonal relationship included in the beat signal generated by mixing is detected by a discrete Fourier transform, and the error of the beat signal is determined by the detected error. Correction is performed, and the error-corrected beat signal is again subjected to discrete Fourier transform to calculate the frequency of the beat signal. This will be described in detail below.

As described above, the in-phase component I (t) of the beat signal and the quadrature component Q (t) of the beat signal are
I (t) = A · cos (ωt + θ) (6a)
Q (t) = A · γ · sin (ωt + θ + φ) (6b)
It can be expressed as Here, when the in-phase component of the beat signal represented by Expression (6a) is a real part and the quadrature component of the beat signal represented by Expression (6b) is an imaginary part, the beat signal is
f (t) = A · cos (ωt + θ) + jA · γ · sin (ωt + θ + φ)
= (A / 2) [(1 + γe ^jφ ) e ^{j (ωt + θ)} + (1−γe ^−jφ ) e ^{−j (ωt + θ)} ]
(7)
It can be expressed as a complex number.

となる。ここで、δ（ｋ−ω）及びδ（ｋ＋ω）は、前述したディラックのデルタ関数である。すなわち、デルタ関数δ（ｋ−ｘ）は、ｋ≠ｘのときにδ（ｋ−ｘ）＝０となり、デルタ関数δ（ｋ＋ｘ）は、ｋ≠−ｘのときにδ（ｋ＋ｘ）＝０となる関数である。従って、誤差を含む角周波数ωのビート信号の複素数をフーリエ変換すると、角周波数“＋ω”のスペクトラムと、角周波数“−ω”のスペクトラムと、が現れる。 When the complex number of the beat signal represented by Equation (7) is Fourier transformed,

It becomes. Here, δ (k−ω) and δ (k + ω) are the Dirac delta functions described above. That is, the delta function δ (k−x) is δ (k−x) = 0 when k ≠ x, and the delta function δ (k + x) is δ (k + x) = 0 when k ≠ −x. It is a function. Accordingly, when the complex number of the beat signal having an angular frequency ω including an error is Fourier-transformed, a spectrum with an angular frequency “+ ω” and a spectrum with an angular frequency “−ω” appear.

  As described above, in the distance measuring apparatus 1 using radio waves, the beat signal obtained by mixing is A / D converted in order to detect the frequency of the beat signal, and the complex data sequence generated thereby is discretely generated. Fourier transform. Accordingly, when the complex data series of the beat signal of the angular frequency ω including the error in the orthogonal relationship is subjected to the discrete Fourier transform, as shown in FIG. 3A, the beat signal pointed by the square centered on the angular frequency “+ ω” is shown. A spectrum having two sinc function characteristics of a real image and a mirror image of a beat signal pointed by a triangle centered on an angular frequency “−ω” appears.

  As shown in FIG. 3a, when the distance from the antenna to the object to be measured is short, the frequency of the beat signal decreases, so that the spectrum of each of the real image “+ ω” and the mirror image “−ω” approaches each other. An error occurs between the frequency value at which the amplitude value of the spectrum of (and the mirror image) becomes maximum and the frequency value at which the amplitude value of the added spectrum becomes maximum. Such an error causes a decrease in the accuracy of distance measurement, and thus needs to be removed in order to perform a distance measurement with higher accuracy. Hereinafter, error correction will be described.

The computing unit 50 performs discrete Fourier transform on the complex data series of the input beat signal in a finite interval N. The spectrum of the beat signal subjected to discrete Fourier transform in the finite section N has a periodicity in which the spectrum (real image and mirror image) repeats for each finite section N, as shown in FIG. First, the calculation unit 50 searches for data corresponding to the frequency having the highest amplitude from the spectrum calculated in the finite interval N. The data corresponding to the searched frequency having the highest amplitude is defined as F (k _max ).

とすることができる。後述するが、第１の実施形態では、このＦ（ｋ_ｍａｘ）及びＦ（Ｎ−ｋ_ｍａｘ）に基づいて、ビート信号の同相成分と直交成分の振幅誤差γ及び位相誤差φを補正する。 _Then, the _{k max} to explore the _{-k max,} sign-inverted. Here, as described above, since the computing unit 50 performs discrete Fourier transform in the finite interval N, computation can be performed only in the 0 to N−1 region. Further, as described above, a spectrum obtained by performing discrete Fourier transform on a complex data series of input beat signals in a finite interval N has a periodicity in which the spectrum (real image and mirror image) repeats every N times. . Therefore, F the _{(N-k max),} and data corresponding to _{-k max} is a sign inversion of _{k max.} Thereby, the data F (k _max ) and the data F (N−k _max ) are

It can be. As will be described later, in the first embodiment, the amplitude error γ and the phase error φ of the in-phase component and the quadrature component of the beat signal are corrected based on the F (k _max ) and F (N−k _max ).

Here, when k _max = 0, it becomes impossible to extract the two expressions shown in Expression 9 (a) and Expression (9b). Therefore, when k _max = 0, F (1) and F (N−1) are compared, and F (k _max ) and F (N−k) are obtained as in equations (10) and (10b). _max ).

を得ることができる。すなわち、式（１１ｂ）に示すようにビート信号の振幅誤差γと、ビート信号の位相誤差φと、が検出される。 Here, when calculating the sum and difference of the complex number shown in Expression (9a) and the complex number of the complex number shown in Expression (9b),

Can be obtained. That is, as shown in Expression (11b), the beat signal amplitude error γ and the beat signal phase error φ are detected.

を得ることができる。 Furthermore, by expanding the formulas represented in formulas (11a) and (11b),

Can be obtained.

Here, when the in-phase component I (t) of the beat signal shown in Expression (6a) and the quadrature component Q (t) of the beat signal shown in Expression (6b) are expanded,
I (t) = A · cos (ωt + θ) = A · cos (ωt) · cos (θ) −A · sin (ωt) · sin (θ) (13a)
Q (t) = A · γ · sin (ωt + θ + φ) = A · γ · sin (ωt) · cos (θ + φ) + A · γ · cos (ωt) · sin (θ + φ) (13b)
Can guide you. Further, if the in-phase component of the beat signal after correction is set as I ′ (t) ≡A · cos (ωt) and the orthogonal component of the beat signal after correction is set as Q ′ (t) ≡A · sin (ωt). Equation (13a) and Equation (13b) are
I (t) = I ′ (t) · cos (θ) −Q ′ (t) · sin (θ)
(14a)
Q (t) = I ′ (t) · γ · sin (θ + φ) + Q ′ (t) · γ · cos (θ + φ)
(14b)
And can be put. By solving the simultaneous equations of the equations (14a) and (14b) and substituting the equations (12a) to (12d), I ′ (t) shown in the equations (15a) and (15b) and Q ′ (t) can be derived. That is,
I ′ (t) = f _I (I (t), Q (t)) (15a)
Q ′ (t) = f _Q (I (t), Q (t)) (15b)
As described above, the in-phase component I ′ (t) of the beat signal after correction and the quadrature component Q ′ (t) of the beat signal after correction are in-phase component I (t) of the beat signal input to the arithmetic unit 50. And a function of the orthogonal component Q (t).

If the in-phase component I ′ (t) of the corrected beat signal shown in equation (15a) is the real part and the orthogonal component Q ′ (t) of the corrected beat signal shown in equation (15b) is the imaginary part, the correction is performed. The complex data series f ′ (t) of the later beat signal is
f ′ (t) = I ′ (t) + jQ ′ (t) (16)
It can be. By performing a discrete Fourier transform on the complex data sequence f ′ (t) of the beat signal (of the angular frequency ω) having the ideal orthogonal relationship after correction, the angular frequency “+ ω” is centered as shown in FIG. Only the spectrum of the real image of the beat signal having the sinc function characteristic pointed by the quadrangle is calculated.

  Therefore, in the distance measuring device using the radio wave shown in the first embodiment, the spectrum of the mirror image is not calculated unlike the distance measuring device using the conventional radio wave. Thereby, in the distance measuring device using the radio wave shown in the first embodiment, when measuring the distance to the object to be measured at a short distance as in the conventional distance measuring device using the radio wave (beat signal) The error due to the influence of the mirror image of the spectrum can be eliminated from the frequency at which the amplitude value of the detected beat signal becomes maximum.

Therefore, in the distance measuring apparatus 1 using the radio wave shown in the first embodiment, the beat signal is not affected by the mirror image from the spectrum of the real image of the beat signal calculated by the calculation unit 50 shown in FIG. can be calculated when the frequency of the signal is low peak amplitude of the spectrum of the beat signal (when the distance from the antenna to the object to be measured is close) is the maximum frequency f _{p [Hz].} From the calculated peak frequency f _p [Hz], the distance R [m] from the transmitting antenna 21 (or receiving antenna 23) of the distance measuring apparatus 1 to the device under test is
R = cf _p T / 2B (17)
It can be expressed as

In addition, when the distance measuring device 1 using radio waves is applied to a water level measuring device, if the distance measuring device 1 using radio waves is installed at the water depth L ₀ , the water level L [m]
L = L ₀ −cf _p T / 2B (18)
It can be expressed as

As described above, when k _max = 0, F (1) and F (N−1) are compared, and F (k _max ) and F (F) are obtained as in equations (10a) and (10b). Since (N−k _max ) is detected, a value including an error as shown in FIG. 5 is calculated for the distance from the antenna to be measured to the object to be measured. Therefore, a distance measuring apparatus using radio waves has a table showing the relationship between the distance to the object to be measured and the calculated distance as shown in FIG. It is desirable to measure the distance to the measurement object.

“Second Embodiment”
As described above, the distance measuring apparatus using the radio wave described in the first embodiment detects a beat signal by quadrature detection, uses the in-phase component data series of the beat signal as a real part, and calculates the quadrature component of the beat signal. Discrete Fourier transform of the complex data series with the data series as an imaginary part to calculate the first complex number and the second complex number, and based on this, the in-phase component of the beat signal and the quadrature component of the beat signal Amplitude and phase errors were calculated. However, as described above, when k _max = 0, a table showing the relationship between the distance to the object to be measured and the calculated distance is prepared, and the object to be measured is referred to this table. Unless the distance was measured, the distance to the object to be measured could not be calculated accurately. Therefore, in the second embodiment, a distance measuring device using radio waves that can correct an error between the in-phase component and the quadrature component of the beat signal will be described more simply.

FIG. 6A shows the Lissajous figure calculated when the in-phase component I (t) of the beat signal is x and the quadrature component Q (t) of the beat signal is y (t). here,
x = A · cos (ωt + θ) (19a)
y = A · γ · sin (ωt + θ + φ) (19b)
It is. If the in-phase component and the quadrature component of the beat signal are in an ideal quadrature relationship (γ = 1, φ = 0), the Lissajous figure is an ideal circle. However, if an error is included in the orthogonal relationship between the in-phase component and the quadrature component of the beat signal, an ellipse as shown in FIG. In the distance measuring device using radio waves shown in the second embodiment, a Lissajous figure is calculated from a beat signal including an error in an orthogonal relationship, and is orthogonal to the in-phase component of the beat signal by the calculated Lissajous figure (degree of ellipse thereof). An error is detected in the orthogonal relationship between the components, and the error of the beat signal is corrected based on the detected error. Details will be described below.

The in-phase component and the quadrature component of the beat signal shown in Equation (19a) and Equation (19b)
x / A = cos (ωt + θ) (20a)
y / (A · γ) = sin (ωt + θ + φ)
= Sin (ωt + θ) cos (φ) + cos (ωt + θ) sin (φ)
(20b)
Replace with When formula (20b) is expanded,
sin (ωt + θ) = {y / (A · γ) − (x / A) · sin (φ)} / cos (φ)
(21)
It becomes.

となる。ここで、式（２２）で描かれる軌跡がリサージュ図形である。 When the equations (20a) and (21) are squared and added,

It becomes. Here, the locus drawn by Expression (22) is a Lissajous figure.

と置くことができる。 Here, when Expression (22) is set as αx ² + βy ² + σxy = 1,

And can be put.

となる。 Here, the data sequence y _n of the quadrature component of the data sequence x _n and the beat signal of the in-phase component of the input beat signal to the arithmetic unit 50, calculating the ellipse equation,
αx _n ² + βy _n ² + σx _n y _n = 1 + ε _n (24)
Meet. Where epsilon _n is the error when calculating the ellipse equation from x _n and y _n. Here, when the sum V of the square error is calculated,

It becomes.

となる。 That is, in _order to obtain the parameters α, β, and σ of the ellipse from the data series x _n of the in-phase component of the beat signal and the data series yn of the quadrature component of the beat signal, a condition that minimizes the sum V of the square errors is calculated. You can find it. In order to calculate the condition that the sum V of the square errors is minimized, a condition that the result of partial differentiation of the sum V of the square errors with the parameters α, β, and σ of the ellipse may be obtained. When partial differentiation is performed on the sum of squared errors V,

It becomes.

が得られる。すなわち、式（２７ａ）〜式（２７ｃ）を解法することにより、
α ＝ ｆ_α（ｘ_ｎ，ｙ_ｎ） ・・・ （２８ａ）
β ＝ ｆ_β（ｘ_ｎ，ｙ_ｎ） ・・・ （２８ｂ）
σ ＝ ｆ_σ（ｘ_ｎ，ｙ_ｎ） ・・・ （２８ｃ）
のようにα、β、σを算出することができる。 When the equations are expanded so that these equations (26a) to (26c) become zero,

Is obtained. That is, by solving the equations (27a) to (27c),
α = f _α (x _n , y _n ) (28a)
β = _fβ (x _n , y _n ) (28b)
σ = f _σ (x _n , y _n ) (28c)
Α, β, and σ can be calculated as follows.

のように、ビート信号の振幅誤差γ及び位相誤差φを検出することができる。従って、検出された振幅誤差γ及び位相誤差φに基づいてビート信号の振幅と位相を補正することが可能となる。振幅と位相が補正されたビート信号の同相成分と直交成分のリサージュ図形を図６ｂに示す。なお、誤差が補正されたビート信号は、第１の実施形態と同様に、ビート信号の同相成分のデータ系列を実部とし、ビート信号の直交成分のデータ系列を虚部とした複素データ系列を、離散フーリエ変換することにより、アンテナから近距離の被測定物までの距離を精度良く測定することが可能となる。 By substituting α, β, and σ calculated in Expression (28a) to Expression (28b) into Expression (23a) to Expression (23b),

As described above, the amplitude error γ and the phase error φ of the beat signal can be detected. Therefore, it is possible to correct the amplitude and phase of the beat signal based on the detected amplitude error γ and phase error φ. FIG. 6B shows a Lissajous figure of the in-phase component and the quadrature component of the beat signal whose amplitude and phase are corrected. As in the first embodiment, the beat signal whose error is corrected is a complex data sequence in which the in-phase component data series of the beat signal is a real part and the quadrature component data series of the beat signal is an imaginary part. By performing the discrete Fourier transform, the distance from the antenna to the object to be measured at a short distance can be measured with high accuracy.

  As described above, the distance measuring device using the radio wave according to the first and second embodiments detects the beat signal by quadrature detection, corrects the error of the beat signal, and then corrects the in-phase component of the beat signal. It is possible to accurately measure the distance from the antenna to the object to be measured by performing a discrete Fourier transform on the complex data series with the real part of the data series and the data series of the orthogonal component of the beat signal as the imaginary part. It is possible to realize a distance measuring device that can be used.

  In addition, as described above, the distance measuring device using the radio wave according to the present embodiment radiates the radio wave to the water surface and measures the water level from the beat signal of the received wave and the transmitted wave reflected. Needless to say, the present invention does not depart from the spirit of the present invention. It can be diverted to a measuring device or a landslide sensor that detects a landslide by calculating a distance to a rock that may cause a landslide and detecting a landslide by changing the distance to the rock. When the distance measuring device using the radio wave shown in the present embodiment is applied to a water level measuring device or a landslide sensor as described above, it may be applied as a telemeter system. The measured distance (water level) is transmitted to a central control center or the like through a wired or wireless line. The telemeter system on the opposite side can save distance data, create forms, determine water increase, detect disasters early, etc., and contribute to disaster prevention work.

It is a block diagram of the distance measuring device using the electric wave concerning this embodiment. It is a graph of the change of the frequency to the time of the electric wave transmitted from the distance measuring device using the electric wave concerning this embodiment, and the received electric wave. It is a graph which shows the relationship between the frequency and amplitude value after performing discrete Fourier transform on the complex data series of the beat signal including the error in the distance measuring device using the radio wave according to the first embodiment. It is a graph which shows the relationship between the frequency and amplitude value after performing discrete Fourier transform on the complex data series of the beat signal including the error in the distance measuring device using the radio wave according to the first embodiment. It is a graph which shows the relationship between the frequency and amplitude value after carrying out the discrete Fourier transform of the complex data series of the beat signal which correct | amended the error with the distance measuring device using the electromagnetic wave which concerns on 1st Embodiment. In the distance measuring device using the radio wave according to the first embodiment, the relationship between the distance to the object to be measured after the discrete Fourier transform of the complex data sequence of the beat signal whose error is corrected and the calculated distance is shown. It is a graph. It is a Lissajous figure calculated when the in-phase component of the beat signal including the error according to the second embodiment is the x axis and the quadrature component of the beat signal including the error is the y axis. It is a Lissajous figure calculated when the in-phase component of the beat signal in which the error is corrected according to the second embodiment is the x axis and the quadrature component of the beat signal in which the error is corrected is the y axis. It is a graph which shows the relationship between the frequency and amplitude value after carrying out the discrete Fourier transform of the real number data series which concerns on the conventional embodiment. It is a graph which shows the relationship between the frequency and amplitude value after carrying out the discrete Fourier transform of the real number data series which concerns on the conventional embodiment.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 Distance measuring device using radio waves, 11 Oscillator, 12 Frequency modulator, 13, 17, 40, 43-1, 43-2 Mixer, 14 IF oscillator, 15 Filter, 16 Coupler, 18, 41, 45- 1,45-2 filter, 21 transmitting antenna, 23 receiving antenna, 30 RF oscillator, 42 quadrature detector, 44 π / 2 phase shifter, 46-1, 46-2 capacitor, 47-1, 47-2 A / D conversion unit, 50 calculation unit.

Claims (8)

A transmission system for transmitting radio waves whose frequency changes with time in a certain range from the antenna to the device under test;
A receiving system for receiving the radio wave reflected by the object to be measured via the antenna;
By performing quadrature detection of the received radio wave with the transmitted radio wave, the in-phase component of the difference frequency component having the frequency component of the difference between the frequency of the transmitted radio wave and the frequency of the received radio wave and the same phase as the transmitted radio wave A frequency detection unit for detecting a frequency component of a difference between a frequency of a transmitted radio wave and a frequency of a received radio wave and an orthogonal component of a difference frequency component having a phase different from that of the transmitted radio wave by π / 2;
An A / D converter that performs A / D conversion on the in-phase component and the quadrature component of the difference frequency component, and generates a data series;
An arithmetic unit that measures the distance from the antenna to the object to be measured by calculating a data sequence of the in-phase component and the quadrature component of the generated frequency component of the difference,
With
The calculation unit
Calculate an error related to the orthogonal relationship between the in-phase component of the difference frequency component and the quadrature component of the difference frequency component, and based on the calculated error, the in-phase component of the difference frequency component and the orthogonality of the difference frequency component An error correction circuit for correcting an error related to the orthogonal relationship between the component and
A complex data sequence in which the error is corrected with the data series of the in-phase component of the frequency component of the difference whose error is corrected as a real part and the data sequence of the orthogonal component of the frequency component of the difference whose error is corrected as an imaginary part, A circuit for measuring the distance from the antenna to the object to be measured by performing a discrete Fourier transform;
A distance measuring device using radio waves, characterized by comprising: A distance measuring device using radio waves according to claim 1,
The error correction circuit
A circuit that calculates a spectrum obtained by performing a discrete Fourier transform on a complex data sequence in which the data sequence of the in-phase component of the difference frequency component is a real part and the data sequence of the quadrature component of the difference frequency component is an imaginary part;
Search for the frequency that maximizes the calculated spectrum amplitude, the first complex number including the amplitude and phase of the difference frequency component corresponding to the frequency that maximizes the spectrum amplitude, and the frequency that maximizes the spectrum amplitude And a second complex number including the amplitude and phase of the frequency component of the difference corresponding to the frequency symmetric with respect to the DC axis, and
By subtracting the first complex number and the second complex number from either the first complex number or the second complex number as a conjugate complex number, the in-phase component of the difference frequency component and the difference A circuit for calculating an orthogonal component of the frequency component and an amplitude and phase error of
Based on the calculated error, a circuit for correcting the amplitude and phase errors of the in-phase component of the difference frequency component and the quadrature component of the difference frequency component;
A distance measuring device using radio waves, characterized by comprising: A distance measuring device using radio waves according to claim 2,
The error correction circuit
When the frequency at which the amplitude of the extracted spectrum is maximum is zero, the complex number including the amplitude and phase of the difference frequency component corresponding to the non-zero frequency of the calculated spectrum is the first complex number, and the non-zero frequency And the complex number including the amplitude and phase of the difference frequency component corresponding to the frequency symmetric with respect to the DC axis as the second complex number, and the amplitude of the in-phase component of the difference frequency component and the orthogonal component of the difference frequency component A distance measuring device using radio waves characterized by calculating a phase error. A distance measuring device using radio waves according to claim 1,
The error correction circuit
A Lissajous figure is calculated from the data sequence of the in-phase component of the difference frequency component and the data series of the quadrature component of the difference frequency component, and the in-phase component of the difference frequency component and the difference are calculated based on the calculated Lissajous figure. A distance measuring device using radio waves, wherein an error in amplitude and phase of the orthogonal component of the frequency component is corrected. A step of transmitting a radio wave whose frequency changes with time in a certain range from an antenna to a device under test;
Receiving the radio wave reflected by the object to be measured via the antenna;
By performing quadrature detection of the received radio wave with the transmitted radio wave, the in-phase component of the difference frequency component having the frequency component of the difference between the frequency of the transmitted radio wave and the frequency of the received radio wave and the same phase as the transmitted radio wave Detecting a frequency component of the difference between the frequency of the transmitted radio wave and the frequency of the received radio wave and an orthogonal component of the frequency component of the difference having a phase different from that of the transmitted radio wave by π / 2;
A / D conversion of the in-phase component and the quadrature component of the difference frequency component to generate a data series;
A step of measuring a distance from the antenna to the object to be measured by calculating a data sequence of the in-phase component and the quadrature component of the generated frequency component of the difference;
Have
The process of measuring the distance from the antenna to the object to be measured
Calculate an error related to the orthogonal relationship between the in-phase component of the difference frequency component and the quadrature component of the difference frequency component, and based on the calculated error, the in-phase component of the difference frequency component and the orthogonality of the difference frequency component Correcting an error related to the orthogonal relationship between the components;
A complex data sequence in which the error is corrected with the data series of the in-phase component of the frequency component of the difference whose error is corrected as a real part and the data sequence of the orthogonal component of the frequency component of the difference whose error is corrected as an imaginary part, A step of measuring a distance from the antenna to the object to be measured by performing a discrete Fourier transform;
A distance measuring method using radio waves, characterized by comprising: A distance measuring method using radio waves according to claim 5,
The step of correcting the error related to the orthogonal relationship is as follows.
A step of performing a discrete Fourier transform on a complex data sequence in which a data sequence of an in-phase component of a difference frequency component is a real part and a data sequence of a quadrature component of a difference frequency component is an imaginary part, and calculating a spectrum obtained thereby;
Search for the frequency that maximizes the calculated spectrum amplitude, the first complex number including the amplitude and phase of the difference frequency component corresponding to the frequency that maximizes the spectrum amplitude, and the frequency that maximizes the spectrum amplitude And a second complex number including the amplitude and phase of the frequency component of the difference corresponding to the frequency symmetric with respect to the DC axis, and
By subtracting the first complex number and the second complex number from either the first complex number or the second complex number as a conjugate complex number, the in-phase component of the difference frequency component and the difference Calculating the orthogonal component of the frequency component and the amplitude and phase error of
Correcting the amplitude and phase errors of the in-phase component of the difference frequency component and the quadrature component of the difference frequency component based on the calculated error;
A distance measuring method using radio waves, characterized by comprising: A distance measuring method using radio waves according to claim 6,
The step of correcting the error related to the orthogonal relationship is as follows.
When the frequency at which the amplitude of the extracted spectrum is maximum is zero, the complex number including the amplitude and phase of the difference frequency component corresponding to the non-zero frequency of the calculated spectrum is the first complex number, and the non-zero frequency And the complex number including the amplitude and phase of the difference frequency component corresponding to the frequency symmetric with respect to the DC axis as the second complex number, and the amplitude of the in-phase component of the difference frequency component and the orthogonal component of the difference frequency component A distance measurement method using radio waves, characterized by calculating a phase error. A distance measuring method using radio waves according to claim 5,
The step of correcting the error related to the orthogonal relationship is as follows.
A Lissajous figure is calculated from the data sequence of the in-phase component of the difference frequency component and the data series of the quadrature component of the difference frequency component, and the in-phase component of the difference frequency component and the difference are calculated based on the calculated Lissajous figure. A distance measurement method using radio waves, characterized by correcting an error in amplitude and phase of the orthogonal component of the frequency component.

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