阅读说明：本技术 基于干涉仪测向的lfmcw雷达多目标检测方法 (LFMCW radar multi-target detection method based on interferometer direction finding ) 是由 张仁李 黄垒 盛卫星 马晓峰 韩玉兵 于 2019-11-13 设计创作，主要内容包括：本发明公开了一种干涉仪测向的LFMCW雷达多目标检测方法,包括以下步骤：确定干涉仪三个实基线以及一个虚基线的长度；三通道雷达回波信号的采集与处理；经快速傅里叶变换后,对三个通道的上下扫频差拍信号频谱进行周期图积累,再对积累后的频谱进行恒虚警检测；将上扫频段和下扫频段谱峰两两配对,得到谱峰配对矩阵,并计算矩阵内每对谱峰的角度差、多普勒频率和归一化幅度差；利用角度差、多普勒频率和归一化幅度差对矩阵进行筛选；对于配对完成的谱峰,计算得到目标的距离、速度。本发明能够减少三角调制LFMCW雷达上下扫频配对时出现的虚假目标,提高多目标检测的可靠性,且能够测量多目标的距离、速度和角度信息。(The invention discloses an LFMCW radar multi-target detection method for direction finding of an interferometer, which comprises the following steps: determining the lengths of three real baselines and one virtual baseline of the interferometer; collecting and processing three-channel radar echo signals; after fast Fourier transform, carrying out periodogram accumulation on the up-down frequency sweep beat signal frequency spectrums of the three channels, and then carrying out constant false alarm detection on the accumulated frequency spectrums; pairing the spectral peaks of the upper sweep frequency section and the lower sweep frequency section pairwise to obtain a spectral peak pairing matrix, and calculating the angle difference, Doppler frequency and normalized amplitude difference of each pair of spectral peaks in the matrix; screening the matrix by using the angle difference, the Doppler frequency and the normalized amplitude difference; and calculating the distance and the speed of the target for the matched spectral peaks. The invention can reduce false targets generated during up-down sweep frequency matching of the triangular modulation LFMCW radar, improve the reliability of multi-target detection, and can measure the distance, speed and angle information of multiple targets.)

1. An LFMCW radar multi-target detection method based on interferometer direction finding is characterized by comprising the following steps:

step 1, selecting the length of each base line of an interferometer array element according to the wavelength of a radar working wave band, direction finding precision, phase difference measurement error between channels and a direction finding angle range;

step 2, the radar transmits symmetric triangular LFMCW signals to the space, and the three array element antennas receive echo signals of a target; mixing the received target echo signal with the transmitting end symmetric triangle LFMCW signal to obtain beat echo signals of three antenna receiving channels, including an upper sweep frequency beat signal

step 3, carrying out up-down frequency sweep digital beat message on three channelsFast Fourier transform is carried out on the signals to obtain frequency spectrums of up-down frequency sweep digital beat signals, periodogram accumulation is carried out on the frequency spectrums of three channels, constant false alarm detection is carried out on the accumulated frequency spectrums, and the obtained spectrum peak of an up-down frequency sweep threshold is P_i ⁺Frequency value of f_i ⁺Corresponding to a magnitude of

Step 4, for the frequency f_i ⁺，Spectral peaks of different channels

Step 5, for the accumulated beat signal frequency spectrum, the upper sweep spectrum peak P_i ⁺With lower swept spectral peak

Step 6, carrying out first round screening on the matrix by utilizing the angle difference, reserving the spectrum peak pair with the angle difference meeting the requirement, deleting the spectrum peak pair which does not meet the requirement, and regarding the spectrum peak pair as an effective pair if the line and the column of the spectrum peak pair are the only remained spectrum peak pair in the rest spectrum peak pairs in the matrix, and deleting the line and the column of the matrix; performing a second round of screening on the matrix by using the Doppler frequency range, solving a Doppler frequency range corresponding to a system speed measurement range, simultaneously solving the Doppler frequency of each remaining spectral peak pair, reserving the spectral peak pairs in the system Doppler frequency measurement range, deleting the spectral peak pairs which are not in the system Doppler frequency measurement range, regarding the spectral peak pairs as an effective pair if the spectral peak pairs are in the remaining spectral peak pairs in the matrix, and deleting the rows and the columns of the matrix; finally, screening the matrix by using the normalized amplitude difference, recording the number of the total targets as MAX [ M, N ], and calculating the number of the targets which are not detected; arranging the remaining spectrum peak pairs in ascending order according to the normalized amplitude difference, and taking out the spectrum peak pairs with undetected target number in the arrangement according to the sequence of the normalized amplitude difference from small to large, and taking the spectrum peak pairs as effective pairings;

and 7, calculating the distance value and the speed value of the target according to the upper and lower sweep frequency beat frequency values of each pair of spectral peaks after the effective pairing is completed.

2. The LFMCW radar multi-target detection method based on interferometer direction finding according to claim 1, wherein the lengths of the respective baseline of the selected interferometer completed in step 1 are specifically:

step 1-1, determining the length of a long base line; the basic formula for measuring the angle of the interferometer is as follows (1):

wherein

get

the longest base line d can be obtained by the formula (2)_maxThe method comprises the following steps:

wherein λ_maxFor maximum wavelength of the transmitted signal, theta_maxAt the maximum detection angle, d_maxThe longest baseline length required for the system;

step 1-2, determining the length of a short base line; the phase difference measurement range of the practical system is (-pi, pi)]When D is more than lambda/2, the phase difference measured by the system is smaller than the phase difference of the actual incoming wave, namely the measured phase difference is fuzzy, so that the angle measurement result is incorrect; considering the error of the measured phase difference between the channels

wherein λ_minIs the minimum wavelength of the transmitted signal;

step 1-3, determining the length of each base line; taking the shortest base line as a virtual base line, wherein the length of the virtual base line meets the length setting condition of the short base line in the step 1-2, and the measured phase difference psi obtained by frequency domain phase discrimination between the channels₁No blurring, a blurring multiple N₁Is zero, i.e. is substantially out of phase with the channelEqual, then there are:

wherein d is₁Is the length of the shortest virtual baseline; if the phase difference measurement error between channels is not considered, the fuzzy short base line without ambiguity can directly solve the ambiguity of any long base line, and the ambiguity solving formula is as follows (6):

wherein k is 2,3,4, k is a base line serial number; d_kIs the kth baseline length; n is a radical of_kIs the kth baseline phase difference blur multiple; psi_kIs the kth baseline phase difference measurement;

the formula for deblurring is as follows (7):

wherein N'_kIn order to consider the k-th baseline phase difference fuzzy multiple when the phase difference measurement error between the channels is considered, the simplified formula (7) is obtained:

to ensure the ambiguity resolution result is correct, the following relationship is required:

setting the maximum value of phase difference measurement error between any two antennas

(1) real baseline solution real baseline fuzzy multiple K₁The requirements are as follows:

(2) Real baseline solution and virtual baseline fuzzy multiple K₂The requirements are as follows:

(3) Fuzzy multiple K of real baseline in solution of virtual baseline₃The requirements are as follows:

(4) Virtual base line solution virtual base line fuzzy multiple K₄The requirements are as follows:

Determining a baseline configuration from the phase difference measurement error; selection of 3 antenna elements, D₁，D₂The distances between the array elements 1 and 2 and the array elements 2 and 3 are respectively, the three real base lines are d₂＝D₁，d₃＝D₂，d₄＝D₂+D₁(ii) a The virtual base line is d₁＝D₂-D₁(ii) a The shortest virtual base line needs to satisfy d₁＝D₂-D₁≤d_min(ii) a The longest real base line needs to satisfy d₄＝D₂+D₁≥d_max(ii) a Let D₁＝d₂＝md₁Then d is₃＝(m+1)d₁，d₄＝(2m+1)d₁Calculating the value of m according to the above requirements; if m has no solution, the number of antenna elements needs to be increased, so that more length combinations of real baselines and virtual baselines are generated to meet the solution ambiguity condition.

3. The LFMCW radar multi-target detection method based on interferometer direction finding as claimed in claim 1, wherein step 4 is implemented for a frequency f_i ⁺，Spectral peaks of different channels

i, Q paths of signals after FFT of the two paths are respectively I₁(f)、Q₁(f)、I₂(f)、Q₂(f) At a peak frequency f_bThe solving formula of the measured phase difference is shown as an expression (10), and if the measured phase difference result is not in (-pi, pi)]Within the range, it is required to change it to (- π, π) by. + -. 2k π]Internal;

ψ＝arctan[Q₁(f_b)/I₁(f_b)]-arctan[Q₂(f_b)/I₂(f_b)](10)

for spectral peaks with the same frequency value of different channels, the measured phase difference of the real base line is the measured phase difference of the spectral peak on the two channels, and the measured phase difference of the virtual base line is the difference value of the measured phase differences of the two real base lines; measured phase difference psi from each baseline_kThe angle value of the spectrum peak is obtained by using the iterative calculation of the formula (11),

wherein psi_kMeasured phase difference for the kth baseline, N_kFor the kth baseline phase difference blur factor,

4. The LFMCW radar multi-target detection method based on interferometer direction finding as claimed in claim 1, wherein the step 5 of calculating each spectral peak pair

whereinFor the frequency value f of the upper sweep_i ⁺The angle values corresponding to the spectral peaks,

wherein

5. The method for detecting the multiple targets of the LFMCW radar based on the interferometer direction finding according to claim 1, wherein the step 6 is to perform a first round of screening by using the angle difference, and the specific screening formula is as follows:

wherein

6. The LFMCW radar multi-target detection method based on interferometer direction finding according to claim 1, wherein the distance and the speed of the spectral peaks which are effectively paired in step 7 are calculated by the following specific formula:

where c is the propagation velocity of electromagnetic waves in vacuum,

Technical Field

The invention belongs to the technical field of millimeter wave radar target detection, and particularly relates to an LFMCW radar multi-target detection method based on interferometer direction finding.

Background

Chirped continuous wave radar refers to a continuous wave radar in which the frequency of the transmitted signal increases or decreases linearly with time. The chirp continuous wave radar obtains range information and velocity information of a target by comparing the difference between the frequency of an echo signal and the frequency of a transmitted signal. The chirp continuous wave radar has a relatively large time-bandwidth product, has the characteristics of small volume, light weight, simple structure, lower transmitting power, high resolution, no blind area and the like compared with a pulse radar, and is more and more widely applied to short-distance and high-resolution detection occasions.

At present, the target detection methods of the chirped continuous wave radar mainly include a target detection method based on frequency shift keying continuous wave modulation, a target detection method based on symmetric triangular wave modulation, a target detection method based on sawtooth wave modulation, and a target detection method based on trapezoidal wave modulation. In the methods, a target detection method based on frequency shift keying continuous wave modulation obtains a moving target parameter by detecting target Doppler frequency shift and intermediate frequency signal phase difference. For a static target, because the Doppler frequency shift of the static target is zero, target information of the static target cannot be obtained by using a frequency shift keying continuous wave; the target detection method based on the symmetrical triangular wave modulation can overcome the problem to a certain extent by using the symmetrical triangular wave, but the problem that the frequency spectrum of the up-down scanning frequency band is difficult to pair under the condition of multiple targets exists, so that the method is difficult to distinguish the multiple targets; the target detection method based on sawtooth wave modulation can better solve the problems of speed distance coupling and multi-target resolution by performing two-dimensional fast Fourier transform processing on a plurality of frequency modulation period difference frequency signals, however, generally, due to the limitation of hardware frequency modulation slope and the requirement of distance measurement precision, the frequency modulation period is too long, and speed ambiguity is easily caused; the traditional target detection method based on trapezoidal wave modulation can solve a series of problems of static target detection, up-down frequency sweep pairing, speed blurring and the like in the target detection method by carrying out quantitative analysis on beat signal frequency spectrums of an up-down frequency sweep and a constant frequency sweep, but false targets are easily generated in practical application of the target detection method.

Disclosure of Invention

The invention aims to provide an LFMCW radar multi-target detection method based on interferometer direction finding, which solves the problem of difficult frequency spectrum matching of an upper sweep frequency band and a lower sweep frequency band under the multi-target condition by adding an interferometer direction finding technology on the basis of sending symmetrical triangular linear frequency modulation continuous waves and improves the reliability of multi-target detection.

The technical solution for realizing the purpose of the invention is as follows: an LFMCW radar multi-target detection method based on interferometer direction finding comprises the following steps:

step 1, selecting the length of each base line of an interferometer array element according to the wavelength of a radar working wave band, direction finding precision, phase difference measurement error between channels and a direction finding angle range;

step 2, the radar transmits symmetric triangular LFMCW signals to the space, and the three array element antennas receive echo signals of a target; mixing the received target echo signal with the transmitting end symmetric triangle LFMCW signal to obtain beat echo signals of three antenna receiving channels, including an upper sweep frequency beat signal

And down sweep segment difference beat signalWherein n is the serial number of the antenna unit channel, and n is 1,2 and 3; obtaining digital beat signals of three channels through A/D conversion;

step 3, performing fast Fourier transform on the up-down frequency sweep digital beat signals of the three channels to obtain frequency spectrums of the up-down frequency sweep digital beat signals, performing periodogram accumulation on the frequency spectrums of the three channels, and performing constant false alarm detection on the accumulated frequency spectrums to obtain a spectrum peak P of an upper frequency sweep threshold_i ⁺Frequency value of f_i ⁺Corresponding to amplitude A_i ⁺I is 1,2 … M, wherein M represents the number of over-threshold spectrum peaks in the frequency spectrum of the up-sweep frequency-segment beat signal; the spectrum peak of the lower sweep frequency over the threshold isFrequency value of

Corresponding to a magnitude of

j is 1,2 … N, N represents the number of over-threshold spectrum peaks in the frequency spectrum of the lower sweep frequency section beat signal; in the beat signal frequency spectrum of three channels, the frequency value of the sweep frequency on the nth channel is recorded as f_i ⁺Has a spectral peak ofThe lower sweep frequency value is

Spectral peak marker

Step 4, for the frequency f_i ⁺，f_j ^-Spectral peaks of different channels

Calculating the phase difference between different antenna receiving channels corresponding to each frequency by using a frequency domain phase discrimination method; the phase difference of the long baseline ambiguity is deblurred by the phase difference of the short baseline ambiguity to obtain the phase difference of the long baseline ambiguity, and the angle value theta of the corresponding spectral peak of the frequency value is obtained by the phase difference of the long baseline_i ⁺，

Step 5, for the accumulated beat signal frequency spectrum, the upper sweep spectrum peak P_i ⁺With lower swept spectral peak

Pairwise pairing to obtain M × N pairing results (P)_i ⁺,P_j ^-) Forming a spectral peak pairing matrix, and calculating the azimuth angle difference delta theta of each pair of spectral peaks in the matrix_ijAnd normalized amplitude difference

Step 6, carrying out first round screening on the matrix by utilizing the angle difference, reserving the spectrum peak pair with the angle difference meeting the requirement, deleting the spectrum peak pair which does not meet the requirement, and regarding the spectrum peak pair as an effective pair if the line and the column of the spectrum peak pair are the only remained spectrum peak pair in the rest spectrum peak pairs in the matrix, and deleting the line and the column of the matrix; performing a second round of screening on the matrix by using the Doppler frequency range, solving a Doppler frequency range corresponding to a system speed measurement range, simultaneously solving the Doppler frequency of each remaining spectral peak pair, reserving the spectral peak pairs in the system Doppler frequency measurement range, deleting the spectral peak pairs which are not in the system Doppler frequency measurement range, regarding the spectral peak pairs as an effective pair if the spectral peak pairs are in the remaining spectral peak pairs in the matrix, and deleting the rows and the columns of the matrix; finally, screening the matrix by using the normalized amplitude difference, recording the number of the total targets as MAX [ M, N ], and calculating the number of the targets which are not detected; arranging the remaining spectrum peak pairs in ascending order according to the normalized amplitude difference, and taking out the spectrum peak pairs with undetected target number in the arrangement according to the sequence of the normalized amplitude difference from small to large, and taking the spectrum peak pairs as effective pairings;

and 7, calculating the distance value and the speed value of the target according to the upper and lower sweep frequency beat frequency values of each pair of spectral peaks after the effective pairing is completed.

Further, the length of each baseline of the selected interferometer completed in step 1 is specifically:

step 1-1, determining the length of a long base line; the basic formula for measuring the angle of the interferometer is as follows (1):

wherein

Receiving the phase difference of incoming waves for two array elements, wherein D is the length of a base line, lambda is the wavelength of a transmitted signal, and theta is an incident angle; and (2) differentiating two sides of the formula (1) by considering the wave angle as a function of the phase difference:

get

Measuring the error of the phase difference between channels, wherein delta theta is the angle measurement error caused by the phase difference error;

the longest base line d can be obtained by the formula (2)_maxThe method comprises the following steps:

wherein λ_maxFor maximum wavelength of the transmitted signal, theta_maxAt the maximum detection angle, d_maxThe longest baseline length required for the system;

step 1-2, determining the length of a short base line; the phase difference measurement range of the practical system is (-pi, pi)]When D is more than lambda/2, the phase difference measured by the system is smaller than the phase difference of the actual incoming wave, namely the measured phase difference is fuzzy, so that the angle measurement result is incorrect; considering the error of the measured phase difference between the channels

The shortest base length d_minThe method comprises the following steps:

wherein λ_minIs the minimum wavelength of the transmitted signal;

step 1-3, determining the length of each base line; taking the shortest base line as a virtual base line, wherein the length of the virtual base line meets the length setting condition of the short base line in the step 1-2, and the measured phase difference psi obtained by frequency domain phase discrimination between the channels₁No blurring, a blurring multiple N₁Is zero, i.e. is substantially out of phase with the channelEqual, then there are:

wherein d is₁Is the length of the shortest virtual baseline; if the phase difference measurement error between channels is not considered, the fuzzy short base line without ambiguity can directly solve the ambiguity of any long base line, and the ambiguity solving formula is as follows (6):

wherein k is 2,3,4, k is a base line serial number; d_kIs the kth baseline length; n is a radical of_kIs the kth baseline phase difference blur multiple; psi_kIs the kth baseline phase difference measurement;

taking into account the phase difference measurement error between the channels

In the case of (2), the short baseline can only solve the long baseline under a certain length condition, i.e. the ambiguity resolution must be performed step by step, and the formula of the ambiguity resolution is as follows:

wherein N'_kIn order to consider the k-th baseline phase difference fuzzy multiple when the phase difference measurement error between the channels is considered, the simplified formula (7) is obtained:

to ensure the ambiguity resolution result is correct, the following relationship is required:

setting the maximum value of phase difference measurement error between any two antennas

The phase difference measurement errors between each pair of receiving channels are independent, and the maximum value of the phase difference measurement errors of the real base line is

The maximum value of the phase difference measurement error of the virtual base line is

Several situations can arise:

(1) real baseline solution real baseline fuzzy multiple K₁The requirements are as follows:by

Can obtain the product

(2) Real baseline solution and virtual baseline fuzzy multiple K₂The requirements are as follows:

by

Can obtain the product

(3) Fuzzy multiple K of real baseline in solution of virtual baseline₃The requirements are as follows:by

Can obtain the product

(4) Virtual base line solution virtual base line fuzzy multiple K₄The requirements are as follows:

by

Can obtain the product

Determining a baseline configuration from the phase difference measurement error; selection of 3 antenna elements, D₁，D₂The distances between the array elements 1 and 2 and the array elements 2 and 3 are respectively, the three real base lines are d₂＝D₁，d₃＝D₂，d₄＝D₂+D₁(ii) a The virtual base line is d₁＝D₂-D₁(ii) a The shortest virtual base line needs to satisfy d₁＝D₂-D₁≤d_min(ii) a The longest real base line needs to satisfy d₄＝D₂+D₁≥d_max(ii) a Let D₁＝d₂＝md₁Then d is₃＝(m+1)d₁，d₄＝(2m+1)d₁Calculating the value of m according to the above requirements; if m has no solution, the number of antenna elements needs to be increased, so that more length combinations of real baselines and virtual baselines are generated to meet the solution ambiguity condition.

Further, step 4 is for a frequency f_i ⁺，f_j ^-Spectral peaks of different channels

n is 1,2, 3; calculating the phase difference between different antenna receiving channels corresponding to each frequency by using a frequency domain phase discrimination method; the phase difference of the long baseline is deblurred by the phase difference of the short baseline without ambiguity to obtain the phase difference value of the long baseline without ambiguity, and the angle value of the corresponding spectral peak of the frequency value is obtained by the phase difference value of the long baseline

The method specifically comprises the following steps:

i, Q paths of signals after FFT of the two paths are respectively I₁(f)、Q₁(f)、I₂(f)、Q₂(f) At a peak frequency f_bThe solving formula of the measured phase difference is shown as an expression (10), and if the measured phase difference result is not in (-pi, pi)]Within the range, it is required to change it to (- π, π) by. + -. 2k π]Internal;

ψ＝arctan[Q₁(f_b)/I₁(f_b)]-arctan[Q₂(f_b)/I₂(f_b)](10)

for spectral peaks with the same frequency value of different channels, the measured phase difference of the real base line is the measured phase difference of the spectral peak on the two channels, and the measured phase difference of the virtual base line is the difference value of the measured phase differences of the two real base lines; measured phase difference psi from each baseline_kThe angle value of the spectrum peak is obtained by using the iterative calculation of the formula (11),

wherein psi_kMeasured phase difference for the kth baseline, N_kFor the kth baseline phase difference blur factor,is the actual phase difference of the kth baseline, θ_kThe measured angle value of the kth base line;

further, calculating each spectral peak pair (P) as described in step 5_i ⁺,P_j ^-) Angle difference and normalized amplitude difference of (d), spectral peak pair (P)_i ⁺,

) Angle difference of (delta theta)_ijThe calculation formula is as follows:

wherein theta is_i ⁺For the frequency value f of the upper sweep_i ⁺The angle values corresponding to the spectral peaks,

for lower swept frequency value f_j ^-Corresponding to the angular value of the spectral peak. Spectral peak pair (P)_i ⁺,

) Normalized amplitude difference ofThe calculation formula is as follows:

wherein A is_i ⁺For the frequency value f of the upper sweep_i ⁺Corresponding to the magnitude value of the spectral peak,

for lower swept frequency value f_j ^-An amplitude value corresponding to a spectral peak; a. the_maxRepresenting the amplitude maxima of all the upper and lower sweep spectral peaks.

Further, in step 6, the angular difference is used for the first round of screening, and a specific screening formula is as follows:

wherein theta is_i ⁺，Are frequency values f respectively_i ⁺，f_j ^-Angle values corresponding to spectral peaks; and delta theta is an angle measurement error caused by the system measurement phase difference error, namely angle measurement precision.

Further, in step 7, for the spectrum peak that completes the effective pairing, the distance and velocity are calculated, and the specific formula is as follows:

where c is the propagation velocity of electromagnetic waves in vacuum, f_b ⁺For the frequency value of the up-swept beat signal, f_b ^-For the frequency value of the lower sweep beat signal, μ is the sweep slope of the LFMCW signal, f₀Is the center frequency of the transmitted signal.

Compared with the prior art, the invention has the following remarkable advantages: (1) the invention has simple modulation of the transmitted waveform, less equipment amount and simple calculation, and can obtain the information of distance, speed, azimuth angle and the like of multiple targets; (2) the azimuth angle of the target is measured by using a virtual baseline method, the measured angle is not fuzzy and has high precision, and the method has higher applicability in occasions using high-frequency signals for direction finding; (3) when matching the upper and lower sweep frequency spectrum peaks, the angular value is used for primary screening, the Doppler frequency and the normalized amplitude difference are used for secondary screening, the spectrum peaks belonging to the same target can be correctly matched, the generation probability of false targets is reduced, and accurate target speed and distance information can be acquired. Has higher reliability.

The present invention is described in further detail below with reference to the attached drawing figures.

Drawings

Fig. 1 is a schematic flow chart of the LFMCW radar multi-target detection method based on interferometer direction finding.

Fig. 2 is a schematic diagram of the direction-finding principle of a general interferometer.

Fig. 3 is a schematic diagram of the principle of virtual baseline method interference direction finding.

Fig. 4 is a working waveform diagram of a symmetric triangular LFMCW signal transmitted to the space by a radar, wherein (a) is a transmitting waveform and a receiving waveform diagram of the LFMCW radar, and (b) is a corresponding beat signal diagram.

FIG. 5 is a diagram of a multi-objective distribution model.

Fig. 6 is a spectrogram of periodogram-accumulated spectra of beat signals of three receiving channels.

Detailed Description

As shown in fig. 1, the present invention provides a Linear Frequency Modulation Continuous Wave (LFMCW) radar multi-target detection method based on interferometer direction finding, which includes the following steps:

step 1, selecting the length of each baseline of an interferometer array element according to the requirements of the wavelength of a radar working wave band, direction finding precision, phase difference measurement error between channels, direction finding angle range and the like;

the interferometer direction finding schematic is shown in figure 2. There is a far field wave in the theta direction of A, B two-element antenna, and the electric wave arriving at the antenna is approximately plane wave. The distance between the two antennas is the base length D, the wavelength of the signal is lambda, and when the signal reaches the antennas A and B, the phase difference of the incoming waves is

Then there are:

because the phase difference measuring range is (-pi, pi), when the length of the direction-finding base line formed by two antennas is greater than half wavelength, the measured phase difference is less than the actual incoming wave phase difference, i.e. the measured phase difference is fuzzy, and further the angle-measuring result is incorrect, the angle value is regarded as a function of the phase difference, and the differential equation (2) on two sides of equation (1) is obtained:

get

Measuring error of phase difference between channels, wherein delta theta is angle measurement error caused by the phase difference error; according to the formula (2), under the condition that the phase difference error between the channels is not changed, the longer the base length is, the smaller the angle measurement error is, and the higher the angle measurement precision is. The angle measurement error is large and the angle measurement precision is insufficient due to the fact that the base length is too small. In engineering, a long-base line and a short-base line direction finding method are generally adopted, the short base line ensures that phase difference measurement is not fuzzy, and the long base line ensures direction finding accuracy. The phase difference of the long baseline ambiguity is deblurred by the phase difference of the short baseline ambiguity, and a direction finding result with high accuracy is obtained. When the working signal frequency is very high, if the problem of actual antenna size placement is considered, the short baseline can not be realized frequently, so the virtual baseline is selected as the short baseline. The virtual baseline is an actual non-existent baseline obtained by subtracting the lengths of two real baselines. The direction measurement by the virtual baseline method is shown in FIG. 3, and the distances between the antennas A and B and between the antennas B and C are D₁，D₂. The two are subtracted to obtain the distance D₂-D₁The virtual short base line only needs to consider that the length of the virtual short base line meets the requirement of no ambiguity in direction finding.

Step 1-1, determining the length of the long baseline. In order to satisfy sufficient angle measurement accuracy, the longest baseline obtainable from equation (2) may be set as:

wherein λ_maxFor maximum wavelength of the transmitted signal, theta_maxAt the maximum detection angle, d_maxThe longest baseline length required for the system.

And 1-2, determining the length of the short baseline. In order to prevent the measured phase difference from being blurred, the existence of a measurement error of the phase difference between the channels is considered by the formula (1)

The shortest base length d_minCan be set as follows:

wherein λ_minIs the minimum wavelength of the transmitted signal.

And 1-3, determining the length of each base line. The shortest base line is a virtual base line, and if the length of the virtual base line meets the length of the short base line in the step 1-2, the measured phase difference phi is₁No blurring, a blurring multiple N₁Is zero, i.e. out of phase with the actual incoming wave

Equal, then there are:

wherein d is₁Is the length of the shortest virtual baseline. If the inter-channel phase difference measurement error is not considered, the fuzzy short base line without the fuzzy can directly solve the fuzzy of any long base line, and the solution fuzzy formula is as shown in formula (6):

wherein k is 2,3,4, k is a base line serial number; d_kIs the kth baseline length; n is a radical of_kIs the kth baseline phase difference blur factor. Psi_kIs the kth baseline phase difference measurement.

Taking into account inter-channel phase difference measurement errors

In the case of (2), the short baseline can only solve the long baseline under certain conditions, and the ambiguity resolution must be performed step by step, wherein the ambiguity resolution formula is as follows:

wherein N'_kIn order to consider the k-th baseline phase difference fuzzy multiple when the inter-channel phase difference measurement error is taken into consideration, the simplified formula (7) is obtained:

to ensure the ambiguity resolution result is correct, the following relationship is required:

setting the maximum value of phase difference measurement error between any two antennas

The phase difference measurement errors of each pair of receiving channels are independent, and the maximum value of the phase difference measurement errors of the real base line is

The maximum value of the phase difference measurement error of the virtual base line is

Then the following situations may arise:

(1) real baseline solution real baseline fuzzy multiple K₁The requirements are as follows:

by

Can obtain the product

(2) Real baseline solution and virtual baseline fuzzy multiple K₂The requirements are as follows:

by

Can obtain the product

(3) Fuzzy multiple K of real baseline in solution of virtual baseline₃The requirements are as follows:

byCan obtain the product

(4) Virtual base line solution virtual base line fuzzy multiple K₄The requirements are as follows:

by

Can obtain the product

A baseline configuration is determined from the phase difference measurement error. The design selects 3 antenna elements, D₁，D₂The distances between the array elements 1 and 2 and the array elements 2 and 3 are respectively, the three real base lines are d₂＝D₁，d₃＝D₂，d₄＝D₂+D₁(ii) a The virtual base line is d₁＝D₂-D₁. The shortest virtual base line needs to satisfy d₁＝D₂-D₁≤d_min. The longest real base line needs to satisfy d₄＝D₂+D₁≥d_max. Let D₁＝d₂＝md₁Then d is₃＝(m+1)d₁，d₄＝(2m+1)d₁The appropriate m value is calculated according to the above requirements. If m has no solution, the number of antenna elements needs to be increased, so that more length combinations of real baselines and virtual baselines are generated to meet the solution ambiguity condition. And finally determining the design of the interferometer baseline.

And 2, transmitting a symmetrical triangular LFMCW signal to the space by the radar, wherein the working waveform of the signal is shown in figure 4. Transmitted waveThe center frequency of the shape is f₀Modulating a bandwidth B with a period T at the operating frequency_CPIIs used to generate a chirped continuous wave. T is_CPIReferred to as Coherent Processing Interval (Coherent Processing Interval). The transmitted up-swept chirp signal can be expressed as:

wherein A is₀Which represents the magnitude of the amplitude of the transmitted signal,

indicating the initial phase of the transmitted signal. Fm slope mu-2B/T_CPI. Assuming that the initial distance of a target is R and the initial radial velocity relative to the radar is V, after a transmission signal is reflected by the target, an array element antenna receives a delayed echo signal, and the expression is as follows:

wherein K_rAttenuation factor, τ, representing the amplitude of the transmitted waveform after propagating reflection_maxThe target time delay corresponding to the maximum detection distance is usually taken as the sampling starting moment, and the starting echo time delay is tau₀2R/c, instantaneous echo time delay τ (t) ═ τ₀-kt，k＝2V/c＝f_d/f₀< 1. The method comprises the following steps of mixing a transmitting signal with an echo signal to obtain a beat signal, and obtaining a simulated beat signal, wherein the expression is as follows:

wherein f is_d＝kf₀＝2V₀Where/λ denotes the Doppler frequency, λ c/f₀Which is indicative of the wavelength of the emitted signal,representing the phase of the constant term. And similarly, a beat signal of the lower frequency sweep can be obtained.As can be seen from equation (12), the beat signal of the chirped continuous wave can be approximated to a dot frequency signal, and then a/D conversion is performed to obtain a digital beat signal; the frequency of the spectrum peak of the up-sweep beat signal of the digital beat signal is f_b ⁺The frequency of the spectrum peak of the lower sweep frequency beat signal is f_b ^-Respectively expressed as:

the up-sweep beat signals of the three antenna receiving channels can be obtained by the analysis

And down sweep segment difference beat signal

Where n is the serial number of the antenna receiving channel, and n is 1,2, and 3. And obtaining digital beat signals of three channels through A/D conversion.

And 3, performing fast Fourier transform on the up-down frequency sweep digital beat signals of the three channels to obtain frequency spectrums of the up-down frequency sweep digital beat signals, performing periodogram accumulation on the frequency spectrums of the three channels firstly to prevent deviation of the positions of the spectrum peaks detected by constant false alarms of the three channels, and then performing constant false alarm detection on the accumulated frequency spectrums to obtain the frequency spectrum peak with the upper frequency sweep threshold as P_i ⁺Frequency value of f_i ⁺Corresponding to amplitude A_i ⁺I is 1,2 … M, wherein M represents the number of over-threshold spectrum peaks in the frequency spectrum of the up-sweep frequency-segment beat signal; the spectrum peak of the lower sweep frequency over the threshold is

Frequency value of

Corresponding to a magnitude ofj is 1,2 … N, N represents the down sweep segment beat signalThe number of over-threshold spectral peaks in the frequency spectrum; in the beat signal frequency spectrum of three channels, the frequency value of the sweep frequency on the nth channel is recorded as f_i ⁺Has a spectral peak of

The lower sweep frequency value is f_j ^-Spectral peak marker

Step 4, for the frequency f_i ⁺，

Spectral peaks of different channels

n is 1,2, 3. And calculating the phase difference between different antenna receiving channels corresponding to each frequency value by using a frequency domain phase discrimination method. The phase difference of the long baseline ambiguity is deblurred by the phase difference of the short baseline ambiguity to obtain the phase difference of the long baseline ambiguity, and the angle value theta of the corresponding spectral peak of the frequency value is obtained by the phase difference of the long baseline_i ⁺，

The method specifically comprises the following steps:

i, Q paths of signals after FFT of the two paths are respectively I₁(f)、Q₁(f)、I₂(f)、Q₂(f) At a peak frequency f_bThe equation for solving the measured phase difference is shown as the formula (14), and if the measured phase difference result is not in (-pi, pi)]Within the range, it is required to change it to (- π, π) by. + -. 2k π]And (4) the following steps.

ψ＝arctan[Q₁(f_b)/I₁(f_b)]-arctan[Q₂(f_b)/I₂(f_b)](14)

For spectral peaks with the same frequency value of different channels, the measured phase difference of the real base line is the measured phase difference of the spectral peak on the two channels, and the measured phase difference of the virtual base line is the measured phase difference of the two real base linesThe difference in the head difference. Measured phase difference psi from each baseline_kThe angle value of the spectrum peak is obtained by using the iterative calculation of the formula (15),

wherein psi_kMeasured phase difference for the kth baseline, N_kFor the kth baseline phase difference blur factor,

is the actual phase difference of the kth baseline, θ_kIs the value of the angle measured with the kth baseline.

Step 5, for the accumulated beat signal frequency spectrum, the upper sweep spectrum peak P_i ⁺With lower swept spectral peak P_j ^-Pairwise pairing to obtain M × N pairing results (P)_i ⁺,

) Forming a spectral peak pairing matrix, wherein i is 1,2, …, M, j is 1,2, …, N.

Can be expressed as:

calculating each spectral peak pair (P)_i ⁺,P_j ^-) The angular difference and the normalized amplitude difference. Spectral peak pair (P)_i ⁺,P_j ^-) Angle difference of (delta theta)_ijThe calculation formula is as follows:

wherein theta is_i ⁺For the frequency value f of the upper sweep_i ⁺The angle values corresponding to the spectral peaks,

for lower swept frequency value f_j ^-Corresponding to the angular value of the spectral peak. Spectral peak pair (P)_i ⁺,P_j ^-) Normalized amplitude difference of

The calculation formula is as follows:

wherein A is_i ⁺For the frequency value f of the upper sweep_i ⁺Corresponding to the magnitude value of the spectral peak,

for lower swept frequency value f_j ^-Corresponding to the magnitude value of the spectral peak. A. the_maxRepresenting the amplitude maxima of all the upper and lower sweep spectral peaks.

And 6, performing a first round of screening on the matrix by using the angle difference, reserving the spectral peak pairs with the angle difference meeting the requirements, and deleting the spectral peak pairs which do not meet the requirements. The specific angle requirement formula is as follows:

where Δ θ is the angular accuracy. Among the remaining pairs of spectral peaks in the matrix, if there is one that is the only one left in the row and column, then the pair is considered as a valid pair, and the row and column of the matrix are deleted. Then solving a Doppler frequency range corresponding to a system speed measurement range, wherein a calculation formula is as follows (19):

f_d＝2Vf₀/c (19)

and (3) solving the Doppler frequency of each residual spectrum peak pair by using the formula (13), deleting the spectrum peak pairs which are not in the measurement range of the system Doppler frequency, and regarding the spectrum peak pairs as an effective pair if the spectrum peak pairs are only left in the row and the column of the matrix, and deleting the row and the column of the matrix. The total number of the targets to be detected is recorded as MAX [ M, N ], and the number of the targets which are not detected yet is calculated. And (4) arranging the residual spectrum peak pairs in an ascending order according to the normalized amplitude difference, and taking out the spectrum peak pairs with undetected target number in the arrangement according to the sequence of the normalized amplitude difference from small to large, wherein the spectrum peak pairs are used as effective pairs.

And 7, calculating the distance value and the speed value of the target according to the upper and lower sweep frequency beat frequency values of each pair of spectral peaks after the effective pairing is completed. The concrete formula is as follows:

where c is the propagation velocity of electromagnetic waves in vacuum, f_b ⁺For the frequency value of the peak of the up-swept beat signal, f_b ^-Is the frequency value of the spectrum peak of the lower sweep beat signal, mu is the sweep slope of the LFMCW signal, f₀Is the center frequency of the transmitted signal.

The above effects of the present invention are further verified and explained by the simulation experiment.