JP2019174206A - Signal processing device, signal processing method and signal processing program - Google Patents

Abstract

To provide a signal processing device, a signal processing method, and a signal processing program, which can enhance a distance resolution.SOLUTION: A signal processing device includes: a reception section configured to receive a reflection wave obtained by reflecting a detection wave of which frequency is discretely changed by an object; a phase detection section configured to detect a phase of the reflection wave; an extension processing section configured to vectorize a correlation matrix of a phase vector obtained by output from the phase detection section by using the Khatri-Rao product and generate an extended phase vector; and a distance calculation section configured to calculate a distance to the object on the basis of a peak of a distance spectrum obtained by performing an inverse discrete Fourier transformation of the extended phase vector.SELECTED DRAWING: Figure 1

Description

  The present disclosure relates to a signal processing device, a signal processing method, and a signal processing program.

  A radar sensor is known as an example of an apparatus that detects the position of a target. The radar sensor includes a transmission unit that transmits radio waves toward a target, a reception unit that receives a reflected wave reflected from the target, and a processing unit that processes the received signal to calculate the position of the target. . According to the radar sensor, since the radio wave is used, there is an advantage that the position of the target can be detected without being influenced by the weather. In addition, when the target is a person, the radar sensor has an advantage that the position of the person can be detected while protecting the privacy of the person.

  On the other hand, the radar sensor may be inferior in accuracy (spatial resolution and distance resolution) to other sensors such as an image sensor. Therefore, various attempts have been made to increase the accuracy of the radar sensor. For example, Patent Documents 1 and 2 and Non-Patent Document 1 indicate that by performing an extended array process using the Khatri-Rao product, the number of antenna elements can be virtually expanded to increase the spatial resolution of the radar sensor. Disclosure.

JP 2017-090229 A JP 2017-227487 A

WK Ma, TH Hsieh and CY Chi, “DOA estimation ofquasi-stationary signals with less sensors than sources and unknown spatialnoise covariance: A Khatri-Rao subspace approach,” IEEE Trans. Signal Process, vol.58, no.4, pp. 2168-2180, April 2010

  In recent years, advanced technologies such as IoT technology and automatic driving technology have been actively developed, and higher accuracy of the radar sensor is expected. However, an effective technique for increasing the distance resolution has not been proposed yet.

  Thus, the present disclosure describes a signal processing device, a signal processing method, and a signal processing program that can increase the distance resolution.

  A signal processing device according to an aspect of the present disclosure includes a receiving unit configured to receive a reflected wave in which a detection wave whose frequency is discretely changed is reflected by an object, and a phase detection of the reflected wave The phase detection unit configured in the above and the extended processing unit configured to vectorize the correlation matrix of the phase vector obtained from the output from the phase detection unit using the Khatri-Rao product to generate the extended phase vector And a distance calculation unit configured to calculate a distance to the object based on a peak of a distance spectrum obtained by performing inverse discrete Fourier transform on the extended phase vector.

  A signal processing method according to another aspect of the present disclosure includes a phase vector obtained from a phase detection of a reflected wave reflected by an object and a detection signal whose frequency is discretely changed, and an output obtained by phase detection of the reflected wave The correlation matrix is vectorized using the Khatri-Rao product to generate an extended phase vector, and the distance to the object is calculated based on the peak of the distance spectrum obtained by inverse discrete Fourier transform of the extended phase vector. Calculating.

  A signal processing program according to another aspect of the present disclosure causes a computer to execute the above method.

  According to the signal processing device, the signal processing method, and the signal processing program according to the present disclosure, it is possible to increase the distance resolution.

FIG. 1 is a block diagram illustrating an example of a radar sensor. FIG. 2 is a diagram illustrating an example of the output of the local transmission frequency. 3A shows an example of a continuous detection wave, FIG. 3B shows an example of a pulse detection wave, and FIG. 3C shows an example of a reflected wave. FIG. 4 is a flowchart for explaining a processing procedure for estimating the distance from the radar sensor to the target. FIG. 5A shows the power spectrum density for each frequency in the pulse detection wave, FIG. 5B shows the phase amplitude with respect to the number of steps in the phase detection output before the expansion processing, and FIG. Indicates the amplitude of the phase with respect to the number of steps in the extended phase vector, and FIG. 5D shows the power spectral density for each frequency in the extended phase vector of FIG. FIG. 6 is a diagram showing a distance spectrum. FIG. 7 is a diagram illustrating the root mean square error of one of the two targets. FIG. 8A is a graph showing the peak-to-range side lobe ratio with respect to SHR in the first side lobe, and FIG. 8B is a graph showing the peak-to-range side lobe ratio with respect to SHR in the average side lobe. FIG. 9A is a graph showing the standard deviation with respect to SHR in the first side lobe, and FIG. 9B is a graph showing the standard deviation with respect to SHR in the average side lobe.

  Hereinafter, an example of an embodiment according to the present disclosure will be described in more detail with reference to the drawings. In the following description, the same reference numerals are used for the same elements or elements having the same function, and redundant description is omitted.

[Radar sensor]
First, the configuration of the radar sensor 1 (signal processing device) will be described with reference to FIG. The radar sensor 1 is configured to transmit, for example, a broadband radio wave. The frequency bandwidth of the radio wave transmitted by the radar sensor 1 may be, for example, 100 MHz or more, 300 MHz or more, 500 MHz or more, or 1 GHz or more. . In particular, the radar sensor 1 may be an ultra wide band (UWB) wireless sensor having a frequency bandwidth of 500 MHz or more.

  As shown in FIG. 1, the radar sensor 1 includes a coherent oscillator 10, a local oscillator 12, a step signal generator 14, a mixer 16, a pulse modulator 18, a transmission antenna 20, and a reception antenna 22 ( Receiver), mixer 24, phase detector 26 (phase detector), Fourier transformer 28 (phase detector), expansion processor 30, and inverse discrete Fourier transformer 32 (distance calculator) including.

  In the radar sensor 1, the coherent oscillator 10, the local oscillator 12, the step signal generator 14, the mixer 16, the pulse modulator 18, and the transmission antenna 20 function as a radio wave transmitter 34. In the radar sensor 1, a coherent oscillator 10, a local oscillator 12, a step signal generator 14, a receiving antenna 22, a mixer 24, a phase detector 26, a Fourier transformer 28, an extension processing unit 30, and an inverse discrete Fourier transformer 32 are included. It functions as a radio wave receiver 36 (signal processing device).

The coherent oscillator 10 is configured to output an IF signal s ₁ (t), which is a continuous wave signal having an intermediate frequency f _COHO , to the mixer 16 and the phase detector 26. The IF signal s ₁ (t) is expressed by Equation 1 as a function of time t.

The local oscillator 12 is configured to output an RF signal s ₂ (t), which is a continuous wave signal having a local oscillation frequency f _STALO , to the mixers 16 and 24. The RF signal s ₂ (t) is expressed by Equation 2 as a function of time t.

The step signal generator 14 is configured to output a frequency control voltage V _T for controlling the local oscillation frequency f _STALO of the local oscillator 12 to the local oscillator 12 based on a predetermined output pattern α. Specifically, any one of the N frequencies discretized by equally dividing the frequency band of the radar sensor 1 into N at a constant frequency interval Δf is transmitted locally based on the output pattern α. Assigned to the frequency f _STALO (where N is a natural number).

That is, assuming that the minimum value of the frequency band of the radar sensor 1 is f _min = f ₁ , the maximum value f _max = f _N of the frequency band is f _min + (N−1) Δf, and the local transmission frequency f _STALO is f ₁ = f _min , f ₂ = f _min + Δf, f ₃ = f _min + 2Δf,..., F _N = f _min + (N−1) Δf. Therefore, if the frequency corresponding to the output pattern α _k is f _αk , the local transmission frequency f _STALO is expressed by Equation 3 (where k is a natural number from 1 to N).
f _STALO = f _αk (3)

For example, when the output pattern α is (α ₁ , α ₂ , α ₃ , α ₄ , α ₅ , α ₆ ) = ( ₁ , ₂ , ₃ , ₄ , ₅ , ₆ ), the output order of the local transmission frequency f _STALO becomes _{(f 1, f 2, f} 3, f 4, f 5, f 6) = (f min, f min + Δf, f min + 2Δf, f min + 3Δf, f min + 4Δf, f min + 5Δf). In this case, as shown in FIG. _2A , the local oscillation frequency f _STALO is incremented by Δf and changes stepwise. In other words, the local transmission frequency f _{STALO at} this time is expressed by Expression 4 using a floor function (a function that returns a maximum integer equal to or less than x with respect to a real number x and expressed as floor (x)). be able to.

On the other hand, for example, when the output pattern α is (α ₁ , α ₂ , α ₃ , α ₄ ) = ( ₃ , ₂ , ₄ , ₁ ), the output order of the local transmission frequency f _STALO is (f ₃ , f ₂ , f ₄ , f ₁ ) = (f _min + 2Δf, f _min + Δf, f _min + 3Δf, f _min ). In this case, as shown in FIG. _2B , the local oscillation frequency f _STALO changes stepwise and in random order at intervals of Δf.

The mixer 16 mixes the IF signal s ₁ (t) output from the coherent oscillator 10 and the RF signal s ₂ (t) output from the local oscillator 12, and pulses the continuous detection wave s ₃ (t). It is configured to output to the modulator 18. The continuous detection wave s ₃ (t) is expressed by Equation 5 as a function of time t.

Here, FIG. 3A shows a waveform of the continuous detection wave s ₃ (t) as an example. As shown in FIG. 3 (a), the continuous detection wave _s 3 (t), the frequency change of the local oscillation frequency _{f STALO (f α1, f α2} , f α3, ···, f αn) with the, The frequency changes stepwise with a constant pulse period τ _PRF .

The pulse modulator 18 outputs a pulse detection wave s ₄ (t) obtained by pulse-modulating the continuous detection wave s ₃ (t) to the transmission antenna 20. The pulse detection wave s ₄ (t) is expressed by Equation 6 as a function of time t. In Equation 6, τ _P is a pulse width, and a relationship of τ _P <τ _PRF is established. In Expression 6, rect (x) is a rectangular function represented by Expression 7.

Here, FIG. 3B shows, as an example, the waveform of a pulse detection wave s ₄ (t) obtained by pulse-modulating the continuous detection wave s ₃ (t) of FIG. As shown in FIG. 3B, the pulse detection wave s ₄ (t) has a frequency f _{STALO by} a constant pulse width τ _P starting from each time when the frequency of the continuous detection wave s ₃ (t) changes. It becomes a cosine wave of + f _COHO , and changes so as to be 0 in other periods.

The transmission antenna 20 is configured to transmit the pulse detection wave s ₄ (t) output from the pulse modulator 18 toward the detection space. As shown in FIG. 1, when the target TR is present in the detection space, the pulse detection wave s ₄ (t) is reflected by the target TR.

The receiving antenna 22 is configured to receive a reflected wave s ₅ (t) from the target TR, a radio wave transmitted from another device, and the like. When the time from when the pulse detection wave s ₄ (t) is transmitted from the transmission antenna 20 until the reception antenna 22 receives the reflected wave s ₅ (t) is denoted by _tr , the pulse of the reflected wave s ₅ (t) It is delayed by more time than pulse _{t r} of the pulse detection wave _s 4 (t). Therefore, the reflected wave _s 5 (t), the pulse detection wave _s 4 (t), phase delay occurs corresponding to the time _{t r.} In addition, when the target TR is moving at a relative speed v _r relative to the radar sensor 1, the reflected wave s ₅ (t) includes Doppler with respect to the pulse detection wave s ₄ (t). frequency shift _{f d} due to the effect occurs. Therefore, the reflected wave s ₅ (t) is expressed by Equation 8 as a function of time t.

Here, the time _tr and the frequency shift f _d are obtained by using the light velocity c, the linear distance d from the radar sensor 1 to the target TR, and the fundamental frequency f _c (= f _min + f _COHO ), respectively, using Equation 9 , 10.

The mixer 24 mixes the RF signal s ₂ (t) output from the local oscillator 12 with the reflected wave s ₅ (t) received by the receiving antenna 22, and low-passes the upper sideband component of the mixed wave. A process of removing by the filter and a process of outputting the lower sideband component of the mixed wave after the filter process to the phase detector 26 as the down-converted signal s ₆ (t) are executed. The down-convert signal s ₆ (t) is expressed by Equation 11 as a function of time t.

The phase detector 26 mixes the in-phase component s _1I (t) of the IF signal s ₁ (t) output from the coherent oscillator 10 and the down-converted signal s ₆ (t) and outputs the same from the coherent oscillator 10. Two I / Q signals s _7I (t) and s _7Q (t) generated by mixing the orthogonal component s _1Q (t) of the IF signal s ₁ (t) and the down-converted signal s ₆ (t) Is output to the Fourier transformer 28. The I / Q signals s _7I (t) and s _7Q (t) are expressed by equations 12 and 13, respectively, as a function of time t. In Expressions 12 and 13, C is a constant.

The Fourier transformer 28 performs A / D conversion on the I / Q signals s _7I (t) and s _7Q (t) output from the phase detector 26, and performs s _7I (t ) -Js _7Q (t) is performed, and a discrete spectrum s ₇ (f) is generated. The discrete spectrum S ₇ (f) is expressed by Equation 14 using the delta function δ (x). In Expression 14, A is a constant.

From Equation 14, the phase detection output R _n of the _nth received pulse (center frequency f _n ) is expressed by Equation 15 using the phase φ _n .

Assuming that f _d << f _c + (n−1) Δf holds, the center frequency f _n = f _c + (n−1) Δf, so that when f _n × 2d / c is θ _n , the phase φ _n is expressed by Equation 16.

Here, when the number of arrival waves of the nth received pulse is L, the phase detection output r (n) uses the amplitude s _l of the l-th arrival wave and the phase θ _l (n) of the _l- th arrival wave. by replacing the a and phi _n of formula 15 respectively Te, formula 17 (where, L is a natural number, l is an integer of 0 to L.). The Fourier transformer 28 is configured to output the phase detection output r (n) to the extension processing unit 30.

ただし、式１９において、｛ｓ｝は、Ｌ個の要素からなる到来波ごとの振幅ベクトルである。式１９において、｛ｖ｝は、Ｎ個の要素からなる雑音ベクトルである。式１９において、［Ａ］はＮ×Ｌの行列であり式２０で表される。なお、本明細書の本文中では、記号「［」及び「］」で囲まれた値が行列であることを意味する。

The extension processing unit 30 is configured to generate a phase vector using the phase detection output r (n) output from the Fourier transformer 28. When a steering vector {a} representing a phase component of N phase detection outputs is defined by Expression 18, a phase vector {r} composed of N elements obtained by summing up the phase detection outputs at each step of Expression 17 is expressed by Expression 19 can be represented. However, in Expression 18, white Gaussian noise v (n) due to heat in the device is also taken into consideration. In the text of this specification, the value enclosed by the symbols “{” and “}” means a vector quantity.

However, in Equation 19, {s} is an amplitude vector for each incoming wave composed of L elements. In Equation 19, {v} is a noise vector composed of N elements. In Equation 19, [A] is an N × L matrix and is represented by Equation 20. In the text of this specification, the value enclosed by the symbols “[” and “]” means a matrix.

式２１において、Ｈは複素共役転置を表しており、［Ｉ_Ｎ］はＮ×Ｎの単位行列である。ただし、振幅と雑音とはそれぞれ無相関であり、

としている。 The extended processing unit 30 is configured to generate a correlation matrix [R _rr ] of the phase vector {r}. The correlation matrix [R _rr ] is an N × N matrix and is expressed by Equation 21.

In Equation 21, H represents a complex conjugate transpose, and [I _N ] is an N × N unit matrix. However, amplitude and noise are uncorrelated with each other,

It is said.

ここで、ｐ_ｌ＝｜ｓ_ｌ｜^２である。式２１及び式２２より、相関行列［Ｒ_ｒｒ］は式２３に変形できる。

When arriving waves from multiple targets are uncorrelated with each other, [D] can be expressed by Equation 22 using a diagonal matrix diag [•].

Here, p _l = | s _l | ² . From Equation 21 and Equation 22, the correlation matrix [R _rr ] can be transformed into Equation 23.

The extended processing unit 30 generates an extended phase vector {y} by vectorizing the correlation matrix [R _rr ] using the Khatri-Rao product, and outputs the extended phase vector {y} to the inverse discrete Fourier transformer 32. Is configured to do. The extended phase vector {y} is expressed by Expression 24.

（以下、「ＫＲ行列」と称する。）は式１９の行列［Ａ］と対応しており、式２４の｛ｐ｝は式１９の振幅ベクトル｛ｓ_ｌ｝と対応しており、式２４の

は式１９の雑音ベクトル｛ｖ｝と対応している。ＫＲ行列はＮ×Ｎの行列であり、その要素数が拡張位相ベクトル｛ｙ｝の要素数となる。従って、拡張処理部３０の拡張処理を経ることで、ステップ周波数の自由度がＮからＮ^２に仮想的に拡張される。 Comparing Equation 19 and Equation 24, the matrix of Equation 24

(Hereinafter referred to as “KR matrix”) corresponds to the matrix [A] in Equation 19, {p} in Equation 24 corresponds to the amplitude vector {s _l } in Equation 19, and

Corresponds to the noise vector {v} of Equation 19. The KR matrix is an N × N matrix, and the number of elements is the number of elements of the extended phase vector {y}. Therefore, the degree of freedom of the step frequency is virtually expanded from N to N ² through the expansion process of the expansion processing unit 30.

The elements of the KR matrix in the extended phase vector {y} can be expressed by Equation 25.

式２６は、ｎ_Ａ，ｎ_Ｂの組み合わせ次第で、同じ値を有する複数の要素がＫＲ行列に存在しうることを示している。周波数間隔Δｆが各ステップで等しい場合には、ＫＲ行列は２Ｎ−１個の異なる要素を持つ。 Assuming that the column is n _A and the row is n _B , the n _A column n _B row of the matrix of Equation 25 can be expressed as Equation 26 (where n _A and n _B are natural numbers of 1 to N, respectively). is there.).

Equation 26 shows that a plurality of elements having the same value can exist in the KR matrix depending on the combination of n _A and n _B. If the frequency interval Δf is equal at each step, the KR matrix has 2N−1 different elements.

At this time, if n _A −n _B = m, one element y (m) of the extended phase vector {y} can be expressed by Expression 27 using Expression 24 and Expression 26. Since n _A and n _B are natural numbers of 1 to N, m is an integer of −N + 1,..., 0,.

The inverse discrete Fourier transformer 32 is configured to apply an inverse discrete Fourier transform to the extended phase vector {y} output from the extension processing unit 30 to generate a distance spectrum R _KR (φ). Specifically, the distance spectrum R _KR (φ) is expressed by Expression 28 by applying an inverse discrete Fourier transform to the element y (m).

From Equation 28, when φ = (2N−1) Δf × 2d / c, the distance spectrum R _KR (φ) shows a sharp peak. Therefore, the inverse discrete Fourier transformer 32 calculates the linear distance d to the target TR using Equation 29 using the phase φ _peak where the distance spectrum R _KR (φ) has a peak.

  The function of each element of the radar sensor 1 may be realized by operating one or a plurality of controllers (control units) included in the radar sensor 1. Alternatively, each function may be realized by executing a program (signal processing program) recorded in a computer, a dedicated electric circuit (for example, a logic circuit), or an integrated circuit (ASIC: Application Specific) in which the circuit is integrated. Integrated Circuit) may be realized.

[Distance estimation method]
Next, a method for estimating the distance from itself to the target TR by the radar sensor 1 will be described with reference to FIG.

First, the coherent oscillator 10 outputs the IF signal s ₁ (t) to the mixer 16, and the local oscillator 12 outputs the RF signal s ₂ (t) to the mixer 16 (see step S1 in FIG. 4). The local oscillation frequency f _STALO of the local oscillator 12 takes one of the values obtained by discretizing the frequency band of the radar sensor 1 into N by the step signal generator 14 at the frequency interval Δf.

Next, the mixer 16 mixes the IF signal s ₁ (t) and the RF signal s ₂ (t) to generate a continuous detection wave s ₃ (t) (see step S2 in FIG. 4). The mixer 16 outputs the generated continuous detection wave s ₃ (t) to the pulse modulator 18.

Next, the pulse modulator 18 performs pulse modulation on the continuous detection wave s ₃ (t) to generate the pulse detection wave s ₄ (t) (see step S3 in FIG. 4). The pulse modulator 18 outputs the generated pulse detection wave s ₄ (t) to the transmission antenna 20.

Next, the transmission antenna 20 transmits the pulse detection wave s ₄ (t) toward the detection space (see step S4 in FIG. 4). The pulse detection wave s ₄ (t) transmitted to the detection space is reflected by the target TR existing in the detection space. The receiving antenna 22 receives the reflected wave s ₅ (t) from the target TR (see step S5 in FIG. 4).

Next, the local oscillator 12 outputs the RF signal s ₂ (t) to the mixer 24, and the transmission antenna 20 outputs the reflected wave s ₅ (t) to the mixer 24 (see step S6 in FIG. 4). The mixer 24 mixes the IF signal s ₁ (t) and the reflected wave s ₅ (t) and performs filtering to generate a down-converted signal s ₆ (t) (see step S7 in FIG. 4). .

Next, the coherent oscillator 10 outputs the IF signal s ₁ (t) to the phase detector 26, and the mixer 24 outputs the down-converted signal s ₆ (t) to the phase detector 26 (step S8 in FIG. 4). reference). The phase detector 26 mixes the in-phase component s _1I (t) of the IF signal s ₁ (t) and the down-converted signal s ₆ (t), and the quadrature component s _1Q (t of the IF signal s ₁ (t). ) And the down-convert signal s ₆ (t) are mixed to generate two I / Q signals s _7I (t) and s _7Q (t) (see step S9 in FIG. 4). The phase detector 26 outputs the generated two I / Q signals s _7I (t) and s _7Q (t) to the Fourier transformer 28.

Next, the Fourier transformer 28 performs a fast Fourier transform based on the I / Q signals s _7I (t) and s _7Q (t) to generate a phase detection output r (n) (see step S10 in FIG. 4). ). The Fourier transformer 28 outputs the generated phase detection output r (n) to the extension processing unit 30.

  Next, the expansion processing unit 30 generates a phase vector using the phase detection output r (n), and vectorizes the correlation matrix of the phase vector using the Khatri-Rao product, thereby expanding the phase vector {y}. Is generated (see step S11 in FIG. 4). The extension processing unit 30 outputs the generated extended phase vector {y} to the inverse discrete Fourier transformer 32.

Next, the inverse discrete Fourier transformer 32 applies an inverse discrete Fourier transform to the extended phase vector {y} to generate a distance spectrum R _KR (φ) (see step S12 in FIG. 4). The inverse discrete Fourier transformer 32 calculates the linear distance d to the target TR using the phase φ _{peak in} which the obtained distance spectrum R _KR (φ) shows a sharp peak (see step S13 in FIG. 4). Thus, the linear distance d from the radar sensor 1 to the target TR is estimated. That is, the method for estimating the straight line distance d is also a signal processing method for processing the received reflected wave s ₅ (t).

[Action]
In the above embodiment, the frequency of the reflected wave s ₅ (t) received by the receiving antenna 22 is also discretized similarly to the pulse detection wave s ₄ (t). Therefore, when the reflected wave s ₅ (t) is phase-detected by the phase detector 26 and the Fourier transformer 28, a phase detection output r (n) including a discretized phase difference is output from the Fourier transformer 28. . Based on the correlation matrix [R _rr ] of the phase vector {r} obtained from the phase detection output r (n), the extended processing unit 30 generates the extended phase vector {y} using the Khatri-Rao product. The number of elements of the extended phase vector {y} is virtually expanded with respect to the number of elements of the phase vector {r}. In other words, the frequency bandwidth is virtually expanded. Since the distance resolution is inversely proportional to the frequency bandwidth, the distance resolution can be increased by virtual extension of the frequency bandwidth.

In the above embodiment, the pulse detection wave s ₄ (t) has a plurality of frequencies each having a predetermined frequency band equally divided at a constant frequency interval Δf between a minimum value and a maximum value as a center frequency. This is a pulse signal in which the pulse is changed stepwise. Therefore, when the number of elements of the phase vector {r} is N, the number of effective elements of the extended phase vector {y} is 2N−1. Therefore, the distance resolution can be increased 2N-1 times compared to the case where the expansion process using the Khatri-Rao product is not performed.

Here, _let us consider a case where the phase detection output R _n is directly subjected to inverse discrete Fourier transform without being expanded by the expansion processing unit 30. Applying an inverse discrete Fourier transform on the phase detection output R _n, the distance spectrum R represented by the formula 30 (phi) is generated.

式２９と式３１とを対比すると、拡張処理部３０による拡張処理を経た後の式２９のほうが、距離分解能が２Ｎ−１倍高まっていることが確認された。 From Equation 30, when φ = NΔf × 2d / c, the distance spectrum R (φ) shows a sharp peak. Therefore, when the phase φ _{peak in} which the distance spectrum R (φ) shows a _peak is used, the linear distance d to the target TR is calculated by Equation 31.

Comparing Expression 29 and Expression 31, it was confirmed that the distance resolution was increased by 2N-1 times in Expression 29 after the expansion processing by the expansion processing unit 30.

In the above embodiment, the pulse detection wave s ₄ (t) has a plurality of frequencies each having a predetermined frequency band equally divided at a constant frequency interval Δf between a minimum value and a maximum value as a center frequency. The pulse signal may be a pulse signal that changes stepwise while being arranged in an arbitrary order. In this case, the plurality of pulses constituting the pulse detection wave s ₄ (t) are arranged in such a way that the center frequency changes at random instead of being arranged in order so that the center frequency follows a certain rule such as ascending order or descending order. . Therefore, the probability that the pulse detection wave s ₄ (t) and the interference wave interfere with each other is reduced. Therefore, even if there is a radio wave transmitted from another device, the object can be detected with high accuracy.

[Modification]
As mentioned above, although embodiment concerning this indication was described in detail, you may add various deformation | transformation to said embodiment in the range which does not deviate from a claim and the summary.

(1) For example, in the above embodiment, the pulse detection wave s ₄ (t) is centered on each frequency in which a predetermined frequency band is equally divided between the minimum value and the maximum value at a constant frequency interval Δf. Any pulse signal may be used as long as a plurality of pulses having a frequency change stepwise. That is, the plurality of pulses may be arranged in order according to a certain rule such as the ascending order or descending order of the center frequency.

(2) In the step signal generator 14, at least from the N frequencies discretized by equally dividing the frequency band of the radar sensor 1 into N at a constant frequency interval Δf between the minimum value and the maximum value. Any value of the remaining used frequencies from which one unused frequency is removed may be assigned to the local transmission frequency f _STALO based on the output pattern α. In other words, the pulse detection wave s ₄ (t) may be a pulse signal in which a plurality of pulses each having the plurality of use frequencies as the center frequency are changed in a step shape.

In this case, a frequency that can be influenced by the interference wave is excluded from the detection wave as an unused frequency. That is, a spectrum hole is set in the pulse detection wave s ₄ (t). FIG. 5A shows an example of the power spectral density for each frequency in the pulse detection wave s ₄ (t) in which the spectrum hole is set. Therefore, the receiving antenna 22 can receive the reflected wave s ₅ (t) that has not been interfered by the interference wave. Therefore, the target TR can be detected with high accuracy even when radio waves transmitted from other devices exist. At this time, each element of the phase detection output generated based on the reflected wave s ₅ (t) is a step number corresponding to the frequency of FIG. 5A as illustrated in FIG. Yes. In the number of steps corresponding to the spectrum hole, the amplitude is substantially zero.

Thereafter, an extended phase vector {y} in which a phase difference corresponding to an unused frequency is interpolated is obtained by performing an extension process using a Khatri-Rao product. FIG. 5C shows an example of the phase amplitude with respect to the number of steps in the obtained extended phase vector {y}. As shown in FIG. 5C, through the expansion process, not only the number of steps is virtually expanded, but also the amplitude at the number of steps corresponding to the spectrum hole is complemented. Therefore, even when the pulse detection wave s ₄ (t) in which the spectrum hole is set is used, the distance resolution can be increased. FIG. 5D shows an example of the power spectral density for each frequency corresponding to the step number of the extended phase vector {y} in FIG. FIG. 5D is not a real signal but a virtual signal corresponding to the extended phase vector {y}.

When a spectrum hole is set in the pulse detection wave s ₄ (t), surrounding radio waves are measured in advance by the receiving antenna 22 to detect a frequency that interferes with the pulse detection wave s ₄ (t). The frequency may be set as an unused frequency. Alternatively, when interference is detected when the pulse detection wave s ₄ (t) is transmitted from the transmission antenna 20, the frequency is set as an unused frequency from the pulse detection wave s ₄ (t) to be transmitted next. You may do it.

(3) As described above, even if the spectrum detection hole is not set in the pulse detection wave s ₄ (t) and the reflected wave s ₅ (t) causing interference with the external radio wave is expanded as it is. Good. In this case, the extended phase vector {y} is generated assuming that the frequency at which interference occurs is as if there is no interference or the interference is reduced through the extension process. Therefore, even if a spectrum hole is not set, the influence due to interference can be greatly reduced.

(4) The radar sensor 1 may be used in a multipath environment. For example, when there are two correlated targets, the correlation matrix [R _rr ] of Expression 21 can be expressed by Expression 32.

In Expression 32, θ ₁ (n _A ) −θ ₁ (n _B ) and θ ₂ (n _A ) −θ ₂ (n _B ) are target signals when each target is uncorrelated. On the other hand, θ ₁ (n _A ) −θ ₂ (n _B ) and θ ₂ (n _A ) −θ ₁ (n _B ) are surplus components obtained when the correlation of signals obtained from each target is large. The surplus component causes distortion in the extended phase vector {y} in the extension process.

式３３に含まれるｎ_Ａｄ_１−ｎ_Ｂｄ_２より、余剰成分θ_１（ｎ_Ａ）−θ_２（ｎ_Ｂ）はステップごとに変化していることが分かる。式２１の相関行列［Ｒ_ｒｒ］は、無相関時に、対角成分が全て同じ値となるテプリッツ行列となることから、式３２の相関行列［Ｒ_ｒｒ］もテプリッツ行列となるよう式３２の相関行列［Ｒ_ｒｒ］の対角方向に平均を取ることで、余剰成分を限りなく０に近づけることができる。これにより、相関信号による歪みを軽減することが可能となる。 By the way, the surplus component θ ₁ (n _A ) −θ ₂ (n _B ) can be expressed by Expression 33.

From n _A d ₁ −n _B d ₂ included in Expression 33, it is understood that the surplus component θ ₁ (n _A ) −θ ₂ (n _B ) changes for each step. Since the correlation matrix [R _rr ] in Expression 21 is a Toeplitz matrix in which all diagonal components have the same value when there is no correlation, the correlation in Expression 32 is set so that the correlation matrix [R _rr ] in Expression 32 also becomes a Toeplitz matrix. By taking the average in the diagonal direction of the matrix [R _rr ], the surplus component can be made as close to zero as possible. As a result, it is possible to reduce distortion caused by the correlation signal.

  (5) The radar sensor 1 may include a plurality of transmission antennas 20 and reception antennas 22 each. That is, an array antenna type radar sensor 1 may be used. In this case, the reflected wave of the detection wave transmitted from each transmitting antenna is received by the corresponding receiving antenna 22, the correlation matrix based on the signal for each receiving antenna 22 is generated, and the correlation matrix is expressed by Khatri. Vectorization using the -Rao product to generate an extended space vector and calculation of the arrival direction of the reflected wave from the object using the MUSIC method or the like may be performed based on the extended space vector . In this case, since the number of array elements is virtually increased by the expansion process, the spatial resolution can be increased.

  (6) In the above embodiment, the transmitting antenna 20 that transmits radio waves and the receiving antenna 22 that receives radio waves are different elements, but radio waves may be transmitted and received using the same single antenna. In this case, the transmitted radio wave and the received radio wave may be separated by a circulator, for example.

  (7) Although the radar sensor 1 has been described in the above embodiment, the claims and the gist thereof may be applied to sensors other than the radar sensor 1. That is, various sensors (for example, an ultrasonic sensor) configured to be able to receive a reflected wave of a transmitted wave are also included in the claims and the gist thereof.

[Example 1]
Here, it was confirmed by simulation that the distance resolution can be enhanced through the expansion process. The specifications of the radar sensor 1 were set as follows.
f _min = 76.68 GHz
Δf = 10 MHz
N = 64
Two targets TR _A and TR _B are arranged in the detection space. Target TR _A is the distance from the radar sensor 1 is fixed to a position where the 7m. The target TR _B is arranged so that the distance from the radar sensor 1 is within a range of 7 m to 7.5 m and the distance to the target TR _A can be changed. In order to verify only the distance resolution, the reflection intensity from the targets TR _A and TR _B was made constant. The signal-to-noise ratio with respect to the amplitude of the narrow-band pulse was 5 dB, and the noise was not correlated with the signal.

First, the target TR _B was placed at 7.31 m. The two targets TR _A and TR _B at this time are detected by the radar sensor 1, and the distance spectrum is calculated for each of the cases without the extension process and the case with the extension process. The distance spectrum at this time is shown in FIG.

Next, the target object TR _B was placed at 7.285 m, and similarly, the distance spectrum was calculated according to the presence or absence of the expansion process. The distance spectrum at this time is shown in FIG.

Next, the target TR _B was placed at 7.18 m, and similarly, the distance spectrum was calculated according to the presence or absence of the expansion process. The distance spectrum at this time is shown in FIG.

From FIG. 6, when there is no expansion processing, the radar sensor 1 recognizes the two targets TR _A and TR _B separately when the distance between the two targets TR _A and TR _B is 0.285 m or less. It was confirmed that it was not possible. On the other hand, in the case where there is an extension process, the radar sensor 1 has two targets TR _A regardless of whether the distance between the two targets TR _A and TR _B is 0.31 m, 0.285 m, or 0.18 m. , TR _B can be recognized separately. Further, it was confirmed that the width of the main lobe was improved and the range side lobe was improved in the case where there was an extension process, compared to the case where there was no extension process.

式３４において、Ｋはモンテカルロシミュレーションの試行回数を示す。ここでは、Ｋ＝２００に設定した。また、ｘ_ｌ（ｋ）は目標物ＴＲ_Ａまでの距離の真値を示し、

は目標物ＴＲ_Ａに最も近い信号の推定点までの距離を示す。推定点は、−３ｄＢ以上の極大値と定義した。 Next, the interval d _AB between the two targets TR _A and TR _B is variously changed, and the root mean square error (RMSE) of the target TR _A is expressed by the equation with and without the extension process. 34, respectively.

In Expression 34, K represents the number of trials of the Monte Carlo simulation. Here, K = 200 was set. _{Further, x} l (k) denotes the true value of the distance to the target TR _A,

Denotes the distance to the estimated point of the closest signal to the target TR _A. The estimation point was defined as a maximum value of −3 dB or more.

The calculation result of RMSE is shown in FIG. As shown in FIG. 7, the RMSE increased when the distance d _AB was less than 0.31 m without the extension process. Therefore, it was confirmed that when the distance between the two targets TR _A and TR _B is less than 0.31 m, the radar sensor 1 cannot recognize the two targets TR _A and TR _B separately. On the other hand, in the case of the extension process, the RMSE increased when the distance d _AB was less than 0.18 m. Therefore, it was confirmed that when the distance between the two targets TR _A and TR _B is less than 0.18 m, the radar sensor 1 cannot recognize the two targets TR _A and TR _B separately. Therefore, it was confirmed that the distance resolution was increased about twice when the extended processing was performed compared to the case without the extended processing.

[Example 2]
The second embodiment is different from the first embodiment in that only the target TR _A is used without using the target TR _B and in that a spectrum hole is randomly set in the pulse detection wave s ₄ (t). Specifically, in the second embodiment, while changing the ratio SHR (Spectrum hole rate) of the spectrum hole N _SH with respect to the total number N of narrow-band pulse trains, the peak-to-range side lobe in each of the first side lobe and the average side lobe is changed. The ratio was calculated for each case without the extension process and with the extension process. Further, the standard deviation in each of the first side lobe and the average side lobe was calculated while changing the SHR, when there was no extension process and when there was an extension process. In these calculations, a Monte Carlo simulation was performed with 1000 trials. SHR is defined by Equation 35.
SHR = N _SH / N × 100 (35)

  FIG. 8 shows the peak-to-range sidelobe ratio results for SHR. As shown in FIG. 8, in the case of no extension processing, the range side lobe deteriorated as SHR increased. On the other hand, in the case of the extended processing, even when SHR increases, the degradation of the range side lobe is extremely small, and the peak-to-range side lobe ratio is the same as that in the case where no spectrum hole is set. In addition, in the case of the extension process, the average range side lobe was improved by about 5 dB compared to the case where the spectrum hole was not set. This is due to the phase expansion by the expansion process.

  FIG. 9 shows the result of standard deviation with respect to SHR. As shown in FIG. 9, the standard deviation increased as SHR increased in the case of no expansion processing. On the other hand, in the case of the extension processing, the standard deviation hardly increased even when SHR increased, and was equivalent to the case where no spectrum hole was set.

  From the above, it was confirmed that both the peak-to-range sidelobe ratio and the standard deviation are improved by interpolating the spectrum hole when the extended processing is performed compared to the case without the extended processing.

[Example]
Example 1. A signal processing apparatus according to an example of the present disclosure includes a receiving unit configured to receive a reflected wave in which a detection wave whose frequency is discretely changed is reflected by an object, and phase-detecting the reflected wave The phase detection unit configured in the above and the extended processing unit configured to vectorize the correlation matrix of the phase vector obtained from the output from the phase detection unit using the Khatri-Rao product to generate the extended phase vector And a distance calculation unit configured to calculate a distance to the object based on a peak of a distance spectrum obtained by performing inverse discrete Fourier transform on the extended phase vector. In this case, the frequency of the reflected wave received by the receiving unit is also discretized in the same manner as the detection wave. For this reason, when the reflected wave is phase-detected by the phase detection unit, a phase detection output including a discretized phase difference is output from the phase detection unit. When the extended processing unit generates an extended phase vector using the Khatri-Rao product based on the phase vector correlation matrix obtained from the phase detection output, the number of elements of the extended phase vector is the number of elements of the phase vector. Is virtually expanded. In other words, the frequency bandwidth is virtually expanded. Since the distance resolution is inversely proportional to the frequency bandwidth, the distance resolution can be increased by virtual extension of the frequency bandwidth.

  Example 2. In the apparatus of Example 1, a plurality of pulses each having a center frequency at each frequency obtained by equally dividing a predetermined frequency band between a minimum value and a maximum value at a constant frequency interval in a predetermined frequency band changed in a step shape. It may be a pulse signal. In this case, if the number of elements of the phase vector is N, the number of effective elements of the extended phase vector is 2N-1. Therefore, the distance resolution can be increased 2N-1 times compared to the case where the expansion process using the Khatri-Rao product is not performed.

  Example 3 In the apparatus of Example 1 or Example 2, the detection wave is a residual obtained by removing at least one unused frequency from each frequency in which a predetermined frequency band is equally divided between the minimum value and the maximum value at a constant frequency interval. The pulse signal may be a pulse signal in which a plurality of pulses each having a plurality of operating frequencies as a center frequency are changed stepwise. In this case, by removing the frequency that can be affected by the interference wave from the detection wave as an unused frequency, that is, by setting a spectrum hole in the detection wave, the receiving unit has received interference due to the interference wave. Receive no reflected waves. Therefore, it is possible to detect an object with high accuracy even when radio waves transmitted from other devices exist. In addition, an extended phase vector in which the phase difference corresponding to the unused frequency is interpolated can be obtained by performing the extended process using the Khatri-Rao product. Therefore, even when a detection wave in which a spectrum hole is set is used, the distance resolution can be increased.

  Example 4 In any of the devices of Examples 1 to 3, the detection wave includes a plurality of pulses each having a predetermined frequency band equally divided at a constant frequency interval between a minimum value and a maximum value as center frequencies. However, it may be a pulse signal that changes stepwise while being arranged in an arbitrary order. In this case, the plurality of pulses constituting the detection wave are not arranged in order so that the center frequency follows a certain rule such as ascending order or descending order, but are arranged so that the center frequency changes randomly. Therefore, the probability that the detection wave and the interference wave interfere with each other is reduced. Therefore, even if there is a radio wave transmitted from another device, the object can be detected with high accuracy.

  Example 5. A signal processing method according to another example of the present disclosure includes: a phase vector obtained from a phase detection of a reflected wave of a detection wave whose frequency is discretely changed and reflected from an object; and an output obtained by phase detection of the reflected wave The correlation matrix is vectorized using the Khatri-Rao product to generate an extended phase vector, and the distance to the object is calculated based on the peak of the distance spectrum obtained by inverse discrete Fourier transform of the extended phase vector. Calculating. In this case, the same effects as the apparatus of Example 1 are obtained.

  Example 6 In the method of Example 5, in the detection wave, a plurality of pulses each having a predetermined frequency band equally divided at a constant frequency interval between a minimum value and a maximum value as center frequencies are changed in a step shape. It may be a pulse signal. In this case, the same effects as the apparatus of Example 2 are obtained.

  Example 7. In the method of Example 5 or Example 6, the detection wave is a residual obtained by removing at least one unused frequency from each frequency obtained by equally dividing a predetermined frequency band at a certain frequency interval between a minimum value and a maximum value. The pulse signal may be a pulse signal in which a plurality of pulses each having a plurality of operating frequencies as a center frequency are changed stepwise. In this case, the same effects as the apparatus of Example 3 are obtained.

  Example 8 In any of the methods of Example 5 to Example 7, the detection wave is a plurality of pulses each having a predetermined frequency band equally divided at a constant frequency interval between a minimum value and a maximum value as center frequencies. However, it may be a pulse signal that changes stepwise while being arranged in an arbitrary order. In this case, the same function and effect as the apparatus of Example 4 can be obtained.

  Example 9 A signal processing program according to another example of the present disclosure causes a computer to execute any of the methods of Example 5 to Example 8. In this case, the same effects as those of any of the methods of Examples 5 to 8 are achieved.

  DESCRIPTION OF SYMBOLS 1 ... Radar sensor (signal processing device), 10 ... Coherent oscillator, 12 ... Local oscillator, 14 ... Step signal generator, 16 ... Mixer, 18 ... Pulse modulator, 20 ... Transmitting antenna, 22 ... Receiving antenna (receiving unit) ), 24... Mixer, 26... Phase detector (phase detection unit), 28... Fourier transformer (phase detection unit), 30.

Claims (9)

A receiving unit configured to receive a reflected wave in which a detection wave whose frequency is discretely changed is reflected by an object;
A phase detector configured to phase detect the reflected wave;
An extended processing unit configured to vectorize a correlation matrix of a phase vector obtained from an output from the phase detection unit using a Khatri-Rao product to generate an extended phase vector;
A signal processing apparatus comprising: a distance calculation unit configured to calculate a distance to the object based on a peak of a distance spectrum obtained by performing inverse discrete Fourier transform on the extended phase vector.   The detection wave is a pulse signal in which a plurality of pulses each having a center frequency corresponding to each frequency obtained by equally dividing a predetermined frequency band between a minimum value and a maximum value at a constant frequency interval are stepped. The apparatus of claim 1.   The detection wave is centered on each of a plurality of remaining used frequencies obtained by removing at least one unused frequency from each frequency obtained by equally dividing a predetermined frequency band between a minimum value and a maximum value at a constant frequency interval. The apparatus according to claim 1, wherein the plurality of pulses having a frequency is a pulse signal that changes in a step shape.   In the detection wave, a plurality of pulses each having a predetermined frequency band equally divided between a minimum value and a maximum value at a constant frequency interval and each having a center frequency as a center frequency are arranged in steps. The apparatus according to claim 1, wherein the apparatus is a changed pulse signal. Phase detection of a reflected wave reflected by an object with a detection wave whose frequency is discretely changed;
Generating an extended phase vector by vectorizing a correlation matrix of a phase vector obtained from an output obtained by phase detection of the reflected wave using Khatri-Rao;
Calculating a distance to the object based on a peak of a distance spectrum obtained by performing inverse discrete Fourier transform on the extended phase vector.   The detection wave is a pulse signal in which a plurality of pulses each having a center frequency corresponding to each frequency obtained by equally dividing a predetermined frequency band between a minimum value and a maximum value at a constant frequency interval are stepped. The method of claim 5.   The detection wave is centered on a plurality of remaining used frequencies obtained by dividing at least one unused frequency from each frequency obtained by equally dividing a predetermined frequency band between a minimum value and a maximum value at a constant frequency interval. The method according to claim 5 or 6, wherein the plurality of pulses having a frequency is a pulse signal changed in a stepped manner.   In the detection wave, a plurality of pulses each having a predetermined frequency band equally divided between a minimum value and a maximum value at a constant frequency interval and each having a center frequency as a center frequency are arranged in steps. The method according to claim 5, wherein the method is a changed pulse signal.   The signal processing program which makes a computer perform the method as described in any one of Claims 5-8.

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