CN110208760B - Radar echo simulation method based on time domain upsampling - Google Patents

Radar echo simulation method based on time domain upsampling Download PDF

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CN110208760B
CN110208760B CN201910446786.2A CN201910446786A CN110208760B CN 110208760 B CN110208760 B CN 110208760B CN 201910446786 A CN201910446786 A CN 201910446786A CN 110208760 B CN110208760 B CN 110208760B
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radar
echo
time domain
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frequency
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CN110208760A (en
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郑适
刘瑞冬
张爱军
孙嘉
李拴劳
党红杏
谭小敏
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Xian Institute of Space Radio Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes

Abstract

A radar echo simulation method based on time domain up-sampling relates to the microwave remote sensing field; the method comprises the following steps: step one, setting a maximum quantization error delta Rmax(ii) a Up-sampling the frequency
Figure DDA0002073889300000011
Step two, calculating an upsampling multiple L; step three, discretizing the radar emission signal x (t) to obtain x [ n ]](ii) a Step four, to x [ n ]]Carrying out N-point discrete Fourier transform to obtain an emission signal frequency spectrum X (f); step five, calculating the echo time delay tau of the ith scattering point of the radar irradiated targetiAnd echo intensity ai(ii) a Step six, calculating the impulse response h of the discrete time domaini[m]And a discrete time domain impulse response h [ m ]](ii) a Step seven, calculating target frequency domain response H (f); step eight, calculating the echo signal spectrum Y (f); ninthly, performing N-point discrete inverse Fourier transform on the echo signal frequency spectrum Y (f) to obtain a time domain echo signal; the invention has high precision, simple realization and high reliability, greatly reduces the operation amount, improves the simulation efficiency and is suitable for the echo simulation of the range radar.

Description

Radar echo simulation method based on time domain upsampling
Technical Field
The invention relates to the field of microwave remote sensing, in particular to a radar echo simulation method based on time domain upsampling.
Background
The radar echo semi-physical simulation is an effective means for verifying a data processing algorithm, and provides an important reference for designing and optimizing a radar system. The high-precision simulation echo method can carry out vivid simulation on a specific physical scene, generate echo data which is more consistent with an actually measured signal, and replace an external field test to a certain extent. The accuracy of the simulated echo and the actually measured echo directly influences the test of the processing algorithm and the evaluation of the system performance.
For a specific physical scene, the scattering condition is complex, a radar emission signal can generate certain distortion, an echo signal has no analytic solution, all scattering points of the whole scene are required to be used as targets, and a numerical method is adopted to simulate the echo. Common radar echo simulation methods can be classified into three categories: time domain algorithm, two-dimensional frequency domain algorithm and inverse imaging echo algorithm. The time-domain algorithm calculates the time delay and the scattering intensity of the simulation target, namely the time-domain impulse response of the target, can truly reflect the generation process of the echo from the time domain, has clear physical concept, high algorithm precision, accurate introduction of motion error and the like, and has the defect of huge operation amount. The two-dimensional frequency domain algorithm starts from the scattering coefficient distribution of a target, deduces a two-dimensional frequency spectrum of a system transfer function, replaces time domain convolution with two-dimensional FFT, and greatly reduces the operation amount. The inverse imaging algorithm utilizes the complex data images after imaging and generates echo signals before imaging through inverse processing of imaging processing, the method is high in operation speed, various errors in the imaging process are brought, the accuracy is low, and other actual errors are difficult to introduce. By combining the three methods, with the development of high-performance computing technology, the operand bottleneck of the time domain algorithm is being broken through, and the time domain algorithm is favored again.
In a time domain method for simulating radar echoes, time delay and echo intensity of each scattering point need to be calculated for a complex scene, and finally radar receiving signals are generated through superposition. In the echo calculation of each scattering point, the distance and the scattering intensity of the scattering point are calculated firstly to obtain the time domain impulse response of the scattering point, and then the time domain impulse response is convoluted with a radar emission signal. In the analog signal, the position of the echo signal is continuous, that is, the time delay of the echo signal can be arbitrarily taken, and in the actual digital calculation process, the echo signal is discretized to a certain range gate, and the time delay is also discretized to a nearby range gate. In a traditional radar time domain echo simulation method, the size of a range gate is limited by sampling frequency, time domain impulse response of a scattering point and radar emission signals are limited by the sampling frequency, and time delay of echo signals is quantized by the sampling frequency. This discrete quantization process produces quantization errors, resulting in large errors in the phase of the echo processing. When the requirement of the distance measurement precision is high, the large quantization error of the simulation signal is difficult to meet the test requirement.
When the microwave speed and distance measuring sensor is applied to a landing system, the distance measuring precision is required to reach the decimeter level when the sensor approaches the ground surface, and the simulation quantization error caused by hundred-million sampling frequency is also the decimeter level, so that the simulation signal can not test the real error of a radar system and a processing algorithm. For a radar system with high ranging accuracy requirement, the quantization error must be eliminated or reduced, and a high-accuracy radar echo simulation method is required.
In order to compensate for quantization errors, the distance left off in the time domain discretization process needs to be compensated. There are documents that propose frequency domain compensation methods: based on the nature of the fourier transform, a shift in the position of the time domain signal is equivalent to a phase shift of the frequency domain signal. The small time delay dt, which is left out during the time domain quantization, is compensated by the phase shift dt · ω in the frequency domain. However, when the scene is complex, the slant distance of each scattering point is different, the time delay required for compensation of each scattering point may be different, and the frequency domain compensation method consumes a huge amount of computation. There is also a method of time domain up-sampling proposed in the literature, which adopts a higher simulation sampling rate in the simulation process, reduces the quantization error, generates an echo signal, and then extracts the echo signal to obtain a time domain signal that matches the system sampling rate. The method has large computation amount and large storage amount in the whole simulation process.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a radar echo simulation method based on time domain up-sampling, and the method has the advantages of high precision, simple implementation and high reliability, greatly reduces the operation amount, improves the simulation efficiency, and is suitable for ranging radar echo simulation.
The above purpose of the invention is realized by the following technical scheme:
a radar echo simulation method based on time domain up-sampling comprises the following steps:
step one, setting a maximum quantization error delta R according to the ranging precision of the radarmax(ii) a According to Δ RmaxUp-sampling the frequency
Figure GDA0002960573500000031
Step two, according to the frequency after the up-sampling
Figure GDA0002960573500000032
And radar system sampling frequency fsCalculating an upsampling multiple L;
step three, setting a radar emission signal x (T), wherein T belongs to [0, T); wherein T is the time length of a transmitted signal; sampling frequency f by radar systemsDiscretizing the radar emission signal x (t) to obtain x [ n ]](ii) a N-0, 1, 2, … …, N-1; n is a positive integer greater than or equal to 1;
step four, sampling frequency f according to the radar systemsFor x [ n ]]Carrying out N-point discrete Fourier transform to obtain a transmitted signal frequency spectrum X (f);
step five, calculating that the target irradiated by the radar is uniformly divided into q scattering points; q is a positive integer; calculating the echo time delay tau of the ith scattering pointiAnd echo intensity ai；
Step six, adopting the sampling frequency Lf of the up-sampling L timessTime delay tau for each scattering pointiCarrying out quantization; obtaining the time delay quantization value m of each scattering pointτiCalculating the discrete time domain impulse response h of each scattering pointi[m](ii) a The discrete time domain impulse responses of all scattering points are superposed to obtain the discrete time domain impulse response h [ m ] of the target scene]；
Step seven, pair h [ m]LN point discrete Fourier transform is carried out to obtain the frequency range corresponding to the frequency spectrum, which is f e [0, Lfs) Taking f as [0, f ∈ ins) As a target frequency domain response h (f);
step eight, multiplying the emission signal spectrum X (f) obtained in the step four with the target frequency domain response H (f) obtained in the step seven, and calculating an echo signal spectrum Y (f);
performing N-point discrete inverse Fourier transform on the echo signal frequency spectrum Y (f) to obtain a time domain echo signal Y' (f); and outputting the result as a radar echo simulation result.
In the above radar echo simulation method based on time domain up-sampling, in the first step, the frequency after up-sampling
Figure GDA0002960573500000033
The calculation method comprises the following steps:
Figure GDA0002960573500000041
wherein c is the speed of light.
In the above radar echo simulation method based on time domain upsampling, in the second step, the calculation method of the upsampling multiple L is as follows:
Figure GDA0002960573500000042
in the formula (I), the compound is shown in the specification,
Figure GDA0002960573500000043
represents a ceiling operation;
l is a positive integer of 1 or more.
In the above radar echo simulation method based on time domain upsampling, in the fifth step, the echo time delay τ isiThe calculation method comprises the following steps:
Figure GDA0002960573500000044
in the formula, RiIs the slope distance of the ith scattering point;
and c is the speed of light.
In the above radar echo simulation method based on time domain up-sampling, the echo intensity aiThe calculation method comprises the following steps:
Figure GDA0002960573500000045
in the formula, PtIs the transmit power;
Grgain for the transmit antenna;
Gtgain for the receive antenna;
λ is the wavelength;
σiis the radar scattering cross section.
In the above radar echo simulation method based on time domain upsampling, in the sixth step, the time delay quantization value m of each scattering pointτiThe calculation method comprises the following steps:
Figure GDA0002960573500000051
in the formula (I), the compound is shown in the specification,
Figure GDA0002960573500000052
rounding is performed.
In the above method for simulating radar echo based on time domain up-sampling, the discrete time domain impulse response hi[m]The calculation method comprises the following steps:
hi[m]＝δ[m-mτi]
wherein m is 0, 1, 2, …, N, …, LN-1;
δ [ ] is a discrete impulse function.
In the above radar echo simulation method based on time domain upsampling, the method for calculating the discrete time domain impulse response h [ m ] of the target scene is as follows:
Figure GDA0002960573500000053
in the above method for simulating radar echo based on time domain upsampling, in the step eight, the method for calculating the echo signal spectrum y (f) is as follows:
Y(f)＝X(f)×H(f)。
compared with the prior art, the invention has the following advantages:
(1) the invention adopts the time domain up-sampling technology, reduces the quantization error brought by the sampling rate of the radar system, improves the precision of radar simulation signals, and realizes the high coincidence degree of the semi-physical simulation and the actual scene of radar echo signals;
(2) the invention adopts the frequency domain down-sampling technology, reduces the operation amount of echo simulation, improves the simulation operation efficiency and realizes the high goodness of fit between the radar signal semi-physical simulation and the radar system.
Drawings
Fig. 1 is a schematic diagram of a simulation process of radar echo according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
the traditional radar sampling technology has certain quantization error of a radar echo simulation signal limited by sampling frequency, and the quantization error is in urgent need of elimination or reduction under the requirement of high ranging precision. The high-precision radar echo simulation method based on time domain up-sampling provided by the invention greatly reduces quantization error, and then generates echo signals adaptive to the sampling rate of a system through frequency domain down-sampling. The existing high-precision simulation method adopts a method of sampling time domain after time domain up sampling, and a large amount of convolution operation before time domain extraction generates a large amount of operation. Compared with the prior art, the method has the advantages that the high precision is guaranteed, the calculation amount is greatly reduced, and the simulation efficiency is improved.
As shown in fig. 1, which is a schematic diagram of a radar echo simulation process, it can be known that a radar echo simulation method based on time domain upsampling includes the following steps:
step one, setting a maximum quantization error delta R according to the ranging precision of the radarmax(ii) a According to Δ RmaxUp-sampling the frequency
Figure GDA0002960573500000061
Frequency after up-sampling
Figure GDA0002960573500000062
The calculation method comprises the following steps:
Figure GDA0002960573500000063
wherein c is the speed of light.
Step two, according to the frequency after the up-sampling
Figure GDA0002960573500000064
And radar system sampling frequency fsCalculating an upsampling multiple L;
the calculation method of the upsampling multiple L comprises the following steps:
Figure GDA0002960573500000065
in the formula (I), the compound is shown in the specification,
Figure GDA0002960573500000066
represents a ceiling operation;
l is a positive integer of 1 or more.
At this time, the quantization error is reduced by L times. The selection of the up-sampling multiple L is determined according to the actual distance measurement precision requirement, so that the sampling quantization error is far smaller than the distance measurement precision requirement. The actual sampling rate of the radar system is fsAnd the next step is to perform down-sampling processing on the up-sampled signal and reduce the sampling rate to fsThe latter signal can be used by the actual system, here using frequency domain down-sampling.
Step three, setting a radar emission signal x (T), wherein T belongs to [0, T); wherein T is the time length of a transmitted signal; sampling frequency f by radar systemsDiscretizing the radar emission signal x (t) to obtain x [ n ]](ii) a N-0, 1, 2, … …, N-1; n is a positive integer greater than or equal to 1;
step four, sampling frequency f according to the radar systemsFor x [ n ]]Performing N-point discrete Fourier transform to obtain a transmission signal frequency spectrumX(f)；
Step five, calculating that the target irradiated by the radar is uniformly divided into q scattering points; q is a positive integer; calculating the echo time delay tau of the ith scattering pointiAnd echo intensity ai；
Echo time delay tauiThe calculation method comprises the following steps:
Figure GDA0002960573500000071
in the formula, RiIs the slope distance of the ith scattering point;
and c is the speed of light.
Echo intensity aiThe calculation method comprises the following steps:
Figure GDA0002960573500000072
in the formula, PtIs the transmit power;
Grgain for the transmit antenna;
Gtgain for the receive antenna;
λ is the wavelength;
σiis the radar scattering cross section.
Step six, adopting the sampling frequency Lf of the up-sampling L timessTime delay tau for each scattering pointiCarrying out quantization; obtaining the time delay quantization value m of each scattering pointτi；
Time delay quantization value m of each scattering pointτiThe calculation method comprises the following steps:
Figure GDA0002960573500000073
in the formula (I), the compound is shown in the specification,
Figure GDA0002960573500000074
rounding is performed.
Calculating discrete time domain impulse response h of each scattering pointi[m]；
Discrete time domain impulse response hi[m]The calculation method comprises the following steps:
hi[m]＝δ[m-mτi]
wherein m is 0, 1, 2, …, N, …, LN-1;
δ [ ] is a discrete impulse function.
Superposing the discrete time domain impulse responses of all scattering points to obtain a discrete time domain impulse response hm of the target scene;
the method for calculating the discrete time domain impulse response h [ m ] of the target scene comprises the following steps:
Figure GDA0002960573500000081
step seven, pair h [ m]LN point discrete Fourier transform is carried out to obtain the frequency range corresponding to the frequency spectrum, which is f e [0, Lfs) Taking f as [0, f ∈ ins) As a target frequency domain response h (f); this process completes the frequency domain down-sampling. H (f) time-domain impulse response with retained upsampling
Figure GDA0002960573500000082
While limiting the frequency range to the original sampling frequency fsIn the embodiment, if IFFT is performed on H (f), the sampling rate of the corresponding time domain signal is reduced to fs。
Step eight, multiplying the emission signal spectrum X (f) obtained in the step four with the target frequency domain response H (f) obtained in the step seven, and calculating an echo signal spectrum Y (f);
performing N-point discrete inverse Fourier transform on the echo signal frequency spectrum Y (f) to obtain a time domain echo signal Y' (f); the calculation method of the echo signal spectrum Y (f) comprises the following steps:
y (f) ═ x (f) × h (f). And outputting the result as a radar echo simulation result.
By the sampling method, not only time domain up-sampling is realized and the quantization error is reduced, but also the echo signal consistent with the sampling rate of the system is obtained by frequency domain down-sampling. The method is applied to the microwave speed and distance measuring radar of the lander, has lower quantization error in a short distance section, can simulate an actual scene more truly, and can generate the echo signal which can be better applied to system performance test, thereby effectively verifying the effectiveness and efficiency of the method.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (9)

1. A radar echo simulation method based on time domain up-sampling is characterized in that: the method comprises the following steps:
step one, setting a maximum quantization error delta R according to the ranging precision of the radarmax(ii) a According to Δ RmaxUp-sampling the frequency
Figure FDA0002960573490000011
Step two, according to the frequency after the up-sampling
Figure FDA0002960573490000012
And radar system sampling frequency fsCalculating an upsampling multiple L;
step three, setting a radar emission signal x (T), wherein T belongs to [0, T); wherein T is the time length of a transmitted signal; sampling frequency f by radar systemsDiscretizing the radar emission signal x (t) to obtain x [ n ]](ii) a N-0, 1, 2, … …, N-1; n is a positive integer greater than or equal to 1;
step four, sampling frequency f according to the radar systemsFor x [ n ]]Carrying out N-point discrete Fourier transform to obtain a transmitted signal frequency spectrum X (f);
step five, calculating that the target irradiated by the radar is uniformly divided into q scattering points; q is a positive integer; calculating the echo time delay tau of the ith scattering pointiAnd echo intensity ai；
Step six, adopting the sampling frequency Lf of the up-sampling L timessTime delay tau for each scattering pointiCarrying out quantization; obtaining the time delay quantization value m of each scattering pointτiCalculating the discrete time domain impulse response h of each scattering pointi[m](ii) a Dispersing all scattering pointsThe time domain impulse responses are superposed to obtain the discrete time domain impulse response h [ m ] of the target scene]；
Step seven, pair h [ m]LN point discrete Fourier transform is carried out to obtain the frequency range corresponding to the frequency spectrum, which is f e [0, Lfs) Taking f as [0, f ∈ ins) As a target frequency domain response h (f);
step eight, multiplying the emission signal spectrum X (f) obtained in the step four with the target frequency domain response H (f) obtained in the step seven, and calculating an echo signal spectrum Y (f);
performing N-point discrete inverse Fourier transform on the echo signal frequency spectrum Y (f) to obtain a time domain echo signal Y' (f); and outputting the result as a radar echo simulation result.
2. The radar echo simulation method based on time domain up-sampling according to claim 1, wherein: in the step one, the frequency after up-sampling
Figure FDA0002960573490000021
The calculation method comprises the following steps:
Figure FDA0002960573490000022
wherein c is the speed of light.
3. The radar echo simulation method based on time domain up-sampling according to claim 2, wherein: in the second step, the calculation method of the upsampling multiple L comprises the following steps:
Figure FDA0002960573490000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002960573490000024
represents a ceiling operation;
l is a positive integer of 1 or more.
4. The radar echo simulation method based on time domain up-sampling according to claim 3, wherein: in the fifth step, the echo time delay tauiThe calculation method comprises the following steps:
Figure FDA0002960573490000025
in the formula, RiIs the slope distance of the ith scattering point;
and c is the speed of light.
5. The time-domain upsampling-based radar echo simulation method according to claim 4, wherein: echo intensity aiThe calculation method comprises the following steps:
Figure FDA0002960573490000026
in the formula, PtIs the transmit power;
Grgain for the transmit antenna;
Gtgain for the receive antenna;
λ is the wavelength;
σiis the radar scattering cross section.
6. The radar echo simulation method based on time domain up-sampling according to claim 5, wherein: in the sixth step, the time delay quantization value m of each scattering pointτiThe calculation method comprises the following steps:
Figure FDA0002960573490000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002960573490000032
rounding is performed.
7. The time-domain upsampling-based radar echo simulation method according to claim 6, wherein: the discrete time domain impulse response hi[m]The calculation method comprises the following steps:
hi[m]＝δ[m-mτi]
wherein m is 0, 1, 2, …, N, …, LN-1;
δ [ ] is a discrete impulse function.
8. The radar echo simulation method based on time domain up-sampling according to claim 7, wherein: the method for calculating the discrete time domain impulse response h [ m ] of the target scene comprises the following steps:
Figure FDA0002960573490000033
9. the time-domain upsampling-based radar echo simulation method according to claim 8, wherein: in the eighth step, the method for calculating the echo signal spectrum y (f) includes:
Y(f)＝X(f)×H(f)。
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