CN109814073B - Method for resolving fuzzy speed measurement by MTD radar - Google Patents

Method for resolving fuzzy speed measurement by MTD radar Download PDF

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CN109814073B
CN109814073B CN201910053062.1A CN201910053062A CN109814073B CN 109814073 B CN109814073 B CN 109814073B CN 201910053062 A CN201910053062 A CN 201910053062A CN 109814073 B CN109814073 B CN 109814073B
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CN109814073A (en
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赵永波
剡熠琛
何学辉
刘宏伟
苏洪涛
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Xidian University
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Abstract

The invention belongs to the technical field of radars and discloses a method for resolving fuzzy speed measurement by an MTD radar. The method comprises the following steps: in a CPI, an MTD radar sequentially transmits pulse group signals with different pulse repetition periods, receives echo signals corresponding to the pulse group signals to obtain an echo data matrix corresponding to each pulse group signal, respectively performs moving target detection on all the pulse-compressed echo data matrices in a DFT channel and an FIR channel to respectively obtain a first Doppler frequency and a second Doppler frequency, judges whether the echo signal of a target is in a clutter area or a noise area, selects the Doppler frequency obtained by one channel as a target Doppler frequency according to a judgment result, and further determines the target speed. The method provided by the invention can improve the robustness of the system and improve the resource utilization rate of the radar, thereby improving the signal-to-noise ratio of the target signal to improve the detection probability of the target signal and the success rate of resolving the speed ambiguity.

Description

Method for resolving fuzzy speed measurement by MTD radar
Technical Field
The invention relates to the technical field of radars, in particular to a Moving Target Detection (Moving Target Detection, MTD) radar ambiguity resolution speed measurement method.
Background
The MTD radar generally operates with a low Pulse Repetition Frequency (PRF), and when the moving speed of a target exceeds the maximum unambiguous velocity of the radar, the moving speed of the target is caused to overlap in a doppler domain, which is called velocity ambiguity, so that the velocity ambiguity needs to be resolved to obtain the moving speed of the target.
Most of the traditional speed ambiguity resolution algorithms utilize Chinese Remainder Theorem (English abbreviation: CRT) or similar algorithms to achieve ambiguity resolution on the basis of varying pulse repetition periods, and because of the varying pulse repetition periods, radar pulse resources need to be split during detection, that is, only signals of each pulse group can be detected respectively to obtain target Doppler channel information corresponding to each pulse group, and then a table is prepared according to the Remainder Theorem, and the real Doppler frequency of a target is resolved by looking up the table, so that the speed of the target is obtained.
The existing method needs to judge whether an echo signal of a target is in a noise area or a clutter area, and then switches to a Discrete Fourier Transform (DFT) channel or a Finite Impulse Response (FIR) channel according to a judgment result to perform moving target detection on the echo signal of the target. In addition, the existing method needs to perform target signal detection on a DFT channel or an FIR channel, speed ambiguity resolution is performed only after the target signal is detected, and when the target signal is detected on the DFT channel or the FIR channel, radar pulse resources need to be split, that is, only pulse groups with different pulse repetition frequencies can be subjected to coherent accumulation respectively, the number of pulses for coherent accumulation is reduced, the utilization rate of the radar resources is low, and when the signal-to-noise ratio of the target is low, the target cannot be detected, and ambiguity resolution speed measurement cannot be performed in the subsequent process.
Disclosure of Invention
The embodiment of the invention provides a method for solving fuzzy speed measurement of an MTD radar, which is characterized in that target detection is carried out on echo signals of a target by using a DFT channel and an FIR channel at the same time, the echo signals of the target are judged to be in a clutter area or a noise area after the target is detected, the Doppler frequency obtained by one channel is selected as a target Doppler frequency according to the judgment result, channel switching is not required frequently, the robustness of the system can be improved, when the DFT channel or the FIR channel is used for detecting the target, pulse group signals with different pulse repetition frequencies are firstly expanded in a Doppler dimension, then all pulse group signals with different pulse repetition frequencies are accumulated, the resource utilization rate of the radar can be improved, and the signal-to-noise ratio of the target signals is improved so as to improve the detection probability of the target signals and the success rate of solving the speed ambiguity.
In order to achieve the above purpose, the embodiment of the invention adopts the following technical scheme:
step 1, in a coherent processing interval CPI, the MTD radar sequentially transmits N pulse group signals with different pulse repetition periods, receives echo signals corresponding to the pulse group signals, and further obtains corresponding echo data matrixes according to the echo signals, thereby obtaining N echo data matrixes.
Wherein the nth echo data matrix of the N echo data matrices is X n N is an integer from 1 to N, N represents the number of pulse group signals transmitted by an MTD radar in a coherent processing interval CPI, and N is more than or equal to 2; x n Is MxQ n Dimension matrix, M represents the number of pulses contained in a pulse group signal, M is not less than 2,Q n Representing the total number of range cells, Q, of the echo signal corresponding to the nth pulse group n ≥2。
Step 2, the nth echo data matrix X in the N echo data matrices n Performing pulse compression processing to obtain corresponding pulse compression data matrix X n ′,X n Is' at M × Q n And (5) dimension matrix.
Step 3, compressing all N pulses into a data matrix X 1 ′,X 2 ′,...,X n ′,...X N ' simultaneously feeding DFT channel and FIR channel, where the DFT channel is according to X 1 ′,X 2 ′,...,X n ′,...X N ' moving target detection is carried out to obtain a first Doppler frequency according to X in an FIR channel 1 ′,X 2 ′,...,X n ′,...X N ' moving target detection is carried out to obtain a second Doppler frequency.
And 4, judging whether the echo signal of the target is in a clutter area or a noise area, if the echo signal of the target is in the noise area, taking the first Doppler frequency as the Doppler frequency of the target, if the echo signal of the target is in the clutter area, taking the second Doppler frequency as the Doppler frequency of the target, and determining the speed of the target according to the Doppler frequency of the target.
The embodiment of the invention provides a method for solving fuzzy speed measurement of an MTD radar, wherein in a CPI, the MTD radar sequentially transmits pulse group signals with different pulse repetition periods, receives echo signals corresponding to the pulse group signals, further obtains corresponding echo data matrixes according to the echo signals, performs pulse compression on all the echo data matrixes, performs moving target detection on all the pulse compressed data matrixes in a DFT channel and an FIR channel respectively to obtain a first Doppler frequency and a second Doppler frequency respectively, further judges whether the echo signal of a target is in a clutter area or a noise area, takes the first Doppler frequency as the Doppler frequency of the target if the echo signal of the target is in the noise area, takes the second Doppler frequency as the Doppler frequency of the target if the echo signal of the target is in the clutter area, and determines the target speed according to the Doppler frequency of the target. The method provided by the invention simultaneously performs target detection on the echo signal of the target by using the DFT channel and the FIR channel, judges whether the echo signal of the target is in a clutter area or a noise area after the target is detected, selects one optimal channel to output a result according to the judgment result, does not need to frequently switch the channels, can improve the robustness of the system, expands the signals of each pulse group in the Doppler dimension when the DFT channel or the FIR channel performs target detection, then accumulates all pulses of a plurality of staggered heavy frequency pulse groups, and can improve the resource utilization rate of the radar, thereby improving the detection probability of the target signal and the success rate of resolving the speed ambiguity.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for resolving fuzzy speed measurement of an MTD radar according to an embodiment of the present invention;
FIG. 2 is a diagram of coherent accumulation results obtained by performing deblurring processing on echo signals of an actually measured target 1 by using a DFT channel processing flow of the method of the present invention;
FIG. 3 is a coherent accumulation result diagram obtained by performing deblurring processing on the echo signal of the actually measured target 1 by using the FIR channel processing flow of the method of the present invention;
FIG. 4 is a distance image contrast diagram of a Doppler channel where a target is located, obtained by performing ambiguity resolution on an echo signal of an actually measured target 1 by using a DFT channel processing flow of the method of the present invention and the prior art;
FIG. 5 is a distance image contrast diagram of a Doppler channel where a target is located, obtained by performing deblurring processing on an echo signal of an actually measured target 1 by using an FIR channel processing flow of the method of the present invention and the prior art;
FIG. 6 is a diagram of coherent accumulation results obtained by performing deblurring processing on the echo signal of the actual measurement target 2 by using the DFT channel processing flow of the method of the present invention;
FIG. 7 is a coherent accumulation result diagram obtained by performing deblurring processing on the echo signal of the actually measured target 2 by using the FIR channel processing flow of the method of the present invention;
FIG. 8 is a distance image contrast diagram of a Doppler channel where a target is located, obtained by performing deblurring processing on an echo signal of an actually measured target 2 by using a DFT channel processing flow of the method of the present invention and the prior art;
fig. 9 is a distance image contrast diagram of a doppler channel where a target is located, which is obtained by performing deblurring processing on an echo signal of an actually measured target 2 by using an FIR channel processing flow of the method of the present invention and the prior art.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flow diagram of a method for resolving a fuzzy velocity measurement by an MTD radar according to an embodiment of the present invention.
Referring to fig. 1, the method for resolving fuzzy speed measurement by using an MTD radar provided by the embodiment of the present invention includes the following steps:
step 1, in a coherent processing interval CPI, the MTD radar sequentially transmits N pulse group signals with different pulse repetition periods, receives echo signals corresponding to the pulse group signals, and further obtains corresponding echo data matrixes according to the echo signals, so that N echo data matrixes are obtained.
Wherein the nth echo data matrix of the N echo data matrices is X n The method comprises the steps that the echo signals corresponding to the nth pulse group signals are obtained, N is an integer from 1 to N, N represents the number of the pulse group signals transmitted by the MTD radar in a coherent processing interval CPI, and N is larger than or equal to 2; x n Is MxQ n Dimension matrix, M represents the number of pulses contained in a pulse group signal, M is not less than 2,Q n Representing the total number of range cells, Q, of the echo signal corresponding to the nth pulse group n ≥2。
Step 2, the nth echo data matrix X in the N echo data matrices n Performing pulse compression processing to obtain corresponding pulse compression data matrix X n ′,X n Is' at M × Q n And (5) dimension matrix.
Step 3, compressing all N pulse compression data matrixes X 1 ′,X 2 ′,...,X n ′,...X N ' simultaneously feeding into DFT channel and FIR channel where the DFT channel is based on X 1 ′,X 2 ′,...,X n ′,...X N ' moving target detection is carried out to obtain a first Doppler frequency according to X in an FIR channel 1 ′,X 2 ′,...,X n ′,...X N ' moving target detection is carried out to obtain a second Doppler frequency.
Further, in step 3, the DFT channel is determined according to X 1 ′,X 2 ′,...,X n ′,...X N ' performing moving target detection, and obtaining the first doppler frequency specifically includes:
(3.1 a) compressing X of the data matrices for all N pulses in the DFT channel n ' Doppler filtering is carried out to obtain Doppler filteredData matrix
Figure BDA0001951480190000061
W n Weight matrix, W, representing the nth DFT filter bank n =[W n,1 ,w n,2 ,...,W n,k ,...,W n,K ],w n,k The weight vector representing the kth filter in the nth DFT filter bank is an mx 1-dimensional column vector,
Figure BDA0001951480190000062
Figure BDA0001951480190000063
representing the mth weight of the kth filter in the n filter banks,
Figure BDA0001951480190000064
where N =1,2, …, N, K =1,2.. K, K = gxm, K representing the number of filters in each filter bank, G representing the encryption multiple of the number of filters in each filter bank, M =1,2.. M, j being the imaginary unit, Y, K being the number of filters in each filter bank n Is KxQ n Dimension matrix, W n Is a matrix of dimension M x K [ ·] H Represents a conjugate transpose operation [ ·] T Indicating a fetch transpose operation.
(3.2 a) the Doppler filtered data matrix Y n Extending F times in the positive direction and the negative direction of the Doppler domain by taking K as a period simultaneously to obtain an extended data matrix
Figure BDA0001951480190000065
Extending the number to a data matrix Z n ' from column Q +1 to column Q n All column elements are removed, so as to obtain extended data matrix Z n
Wherein Z is n ' is P × Q n Dimension matrix, P denotes the number of Doppler channels, P = K × (2F + 1), F denotes the maximum number of ambiguities at velocity, which is a non-negative integer, Z n Is a P × Q dimensional matrix, Q = min { Q } 1 ,Q 2 ,…,Q N And min {. Cndot } represents the minification operation.
(3.3 a) for all extended data matrix Z 1 ,Z 2 ,...,Z n ,...Z N Performing coherent accumulation between pulse groups to obtain a data matrix Z' after coherent accumulation;
further, step (3.3 a) specifically comprises the following sub-steps:
(3.3.1a) determine the total extended data matrix Z 1 Z 2 ,...,Z N The center frequency of the corresponding Doppler channel of each row of (1), wherein the data matrix Z is extended n The center frequency of the Doppler channel corresponding to the p-th row of (1) is
Figure BDA0001951480190000071
Wherein P =1,2, …, P represents the number of doppler channels, P = K × (2f + 1), F represents the maximum blurring time, which is a non-negative integer, PRF n Indicating the pulse repetition frequency of the nth pulse group signal.
(3.3.2a) initializing q N =1。
(3.3.3a) determination of Z N Q (b) to N Center frequency of Doppler channel corresponding to row
Figure BDA0001951480190000072
At Z n ' find the center frequency and
Figure BDA0001951480190000073
nearest center frequency
Figure BDA0001951480190000074
Will be provided with
Figure BDA0001951480190000075
At Z n The corresponding rows in' are denoted as
Figure BDA0001951480190000076
Wherein N' =1,2, …, N-1.
(3.3.4a) Z N Middle q N The line elements are
Figure BDA0001951480190000077
Will all be
Figure BDA0001951480190000078
And
Figure BDA0001951480190000079
carrying out coherent accumulation to obtain the qth data matrix Z' after the coherent accumulation N Line element
Figure BDA00019514801900000710
Figure BDA00019514801900000711
(3.3.5a) q N Adding 1, judging q N And if the value is less than or equal to P, returning to the step (3.3.3a), and if not, turning to the step (3.3.6a).
(3.3.6a) obtaining a data matrix Z' after the phase coherent accumulation; wherein Z' is a P multiplied by Q dimensional matrix.
(3.4 a) detecting the data matrix Z' after the phase coherent accumulation to obtain a detected data matrix Z;
(3.5 a) performing constant false alarm detection on the detected data matrix Z to obtain coordinates of rows of all elements passing through the threshold in the detected data matrix Z, and utilizing the serial numbers of the rows corresponding to all elements passing through the threshold in the detected data matrix Z and the extended data matrix Z n And obtaining a first Doppler frequency.
Preferably, step (3.5 a) comprises the steps of:
(3.5.1a) setting a threshold, initializing l =1;
(3.5.2a) performing constant false alarm detection on the l column element in the detected data matrix Z, judging whether the l column element of the detected data matrix Z has an element which passes the threshold,
(3.5.3a) if not, add 1 to l, go toStep (3.5.2a), if yes, obtaining I l If the threshold value element is passed, the step (3.5.4 a) is carried out;
(3.5.4a) initialization i l =1;
(3.5.5 a) determining the ith column of the detected data matrix Z l The sequence number of the row corresponding to each threshold passing element is
Figure BDA0001951480190000081
Further determination of Z N To (1)
Figure BDA0001951480190000082
Center frequency of Doppler access corresponding to a line
Figure BDA0001951480190000083
At Z n ' finding the center frequency and the center frequency of Doppler corresponding to the P line
Figure BDA0001951480190000084
Closest center frequency, noted
Figure BDA0001951480190000085
Will be provided with
Figure BDA0001951480190000086
At Z n The corresponding line sequence number in
Figure BDA0001951480190000087
Wherein N' =1,2, …, N-1;
(3.5.6a) determination of Z N The first column of
Figure BDA0001951480190000088
Element corresponding to row
Figure BDA0001951480190000089
Determining extended data matrix Z separately 1 ,Z 2 ,...,Z N-1 The first column of
Figure BDA00019514801900000810
Element corresponding to row
Figure BDA00019514801900000811
And is recorded as a column vector
Figure BDA00019514801900000812
(3.5.7a) calculating the ith l Ratio vector corresponding to threshold passing element
Figure BDA0001951480190000091
(3.5.8a) judgment ratio vector
Figure BDA0001951480190000092
Whether all elements are in a preset range, wherein the preset range is [ 1-delta, 1+ delta ]]And delta is the error of the ratio, and if so, the vector is determined to be in the matrix Z N Further determining the center frequency of the Doppler channel corresponding to the row of the element, and recording as the first Doppler frequency T dft (ii) a If not, let i l Adding 1, and repeatedly executing the steps (3.5.4a) to (3.5.8a) until i l =I l Adding 1 to l, and proceeding to step (3.5.2a) until obtaining the first Doppler frequency T dft Wherein l is more than or equal to 1.
Further, in step 3, the FIR channels are according to X 1 ′,X 2 ′,...,X n ′,...X N ' performing moving target detection to obtain the second doppler frequency specifically includes:
(3.1 b) compress X of the data matrix for all N pulses in the FIR channel n Performing Doppler filtering to obtain Doppler filtered data matrix
Figure BDA0001951480190000093
V n Weight matrix, V, representing the nth FIR filter bank n =[v n,1 ,v n,2 ,…,v n,k ,…,v n,K ],V n,k The weight vector representing the kth filter in the nth FIR filter bank is an mx 1-dimensional column vector,
Figure BDA0001951480190000094
R n m × M dimension clutter-plus-noise covariance matrix corresponding to the nth pulse group, a (f) n,k ) Pilot frequency vector at the central frequency of the kth filter in the nth FIR filter group is M multiplied by 1 dimension column vector;
where N =1,2, …, N, K =1,2.. K, K = gxm, K representing the number of filters in each filter bank, G representing the encryption multiple of the number of filters in each filter bank, M =1,2.. M, U n Is KxQ n Dimension matrix, V n Is an M multiplied by K dimensional matrix;
(3.2 b) the Doppler filtered data matrix U n Extending F times in the Doppler domain along the positive direction and the negative direction with K as a period to obtain an extended data matrix
Figure BDA0001951480190000101
Data matrix A after extension of number n ' from the Q +1 th column to the Q th column n All column elements are removed, so as to obtain continuation data matrix A n
Wherein, A n Is' P x Q n Dimension matrix, P denotes the number of Doppler channels, P = K × (2F + 1), F denotes the maximum number of ambiguities in velocity, which is a non-negative integer, A n Is a P × Q dimensional matrix, Q = min { Q } 1 ,Q 2 ,…,Q N The min {. Is } represents the minification operation;
(3.3 b) for all extended data matrix A 1 A 2 ,...,A N And performing coherent accumulation between pulse groups to obtain a data matrix A' after coherent accumulation.
Further, the step (3.3 b) is specifically:
(3.3.1b) determining the center frequency of the kth filter in the nth FIR filter bank
Figure BDA0001951480190000102
Wherein,
Figure BDA0001951480190000103
cw n is shown in PRF n Inner Doppler blind zone width, PRF n Representing the pulse repetition frequency of the nth pulse group,
Figure BDA0001951480190000104
Figure BDA0001951480190000105
(3.3.2b) center frequency f according to the k-th filter in the n-th FIR filter group n,k Determining a data matrix A n P rows of the extended data matrix a, the center frequencies of the doppler channels corresponding to the P rows of the extended data matrix b n The center frequency of the Doppler channel corresponding to the p-th row of (1) is
Figure BDA0001951480190000106
Where N =1,2, …, N, P =1,2, …, P, mod (P, K) represents the remainder of dividing P by K,
Figure BDA0001951480190000111
represents rounding down;
(3.3.3b) determining the Doppler blind zone range of the nth FIR filter group to be B n A 1 to B n PRF in both positive and negative Doppler directions n Is extended for F times periodically to obtain A n Range of Doppler dead zone
Figure BDA0001951480190000112
Wherein,
Figure BDA0001951480190000113
Figure BDA0001951480190000114
u represents and operates;
(3.3.4b) initialization of r N =1;
(3.3.5b) extraction of the matrix A N Middle r N Line elements, as
Figure BDA0001951480190000115
Determination of A N R of N Center frequency of Doppler channel corresponding to row
Figure BDA0001951480190000116
In a set of matrices A 1 A 2 ,...,A N-1 Does not contain the blind area in the middle
Figure BDA0001951480190000117
Is marked as
Figure BDA0001951480190000118
In that
Figure BDA0001951480190000119
Find the center frequency of the corresponding Doppler channel of the P line
Figure BDA00019514801900001110
Closest center frequency, is noted
Figure BDA00019514801900001111
Will matrix
Figure BDA00019514801900001112
Center frequency of
Figure BDA00019514801900001113
The corresponding row is marked as
Figure BDA00019514801900001114
Will matrix
Figure BDA00019514801900001115
The corresponding pulse repetition period is noted as PRT d
Wherein,
Figure BDA00019514801900001116
Figure BDA00019514801900001117
representation matrix A n ' the blind zone does not contain frequencies
Figure BDA00019514801900001118
N' =1,2, …, N-1;
(3.3.6b) will be all
Figure BDA00019514801900001119
And
Figure BDA00019514801900001120
performing coherent accumulation to obtain the r-th matrix of the matrix A N Line element
Figure BDA00019514801900001121
Figure BDA00019514801900001122
(3.3.7b) order r N Adding 1, judging r N If the value is less than or equal to P, returning to the step (3.3.5b) if the value is less than or equal to P, and if the value is not more than P, returning to the step (3.3.8b);
(3.3.8b) obtaining a data matrix A' after coherent integration; wherein A' is a P × Q dimensional matrix.
And (3.4 b) detecting the data matrix A' after the phase coherent accumulation to obtain the data matrix A after the detection of the FIR channel.
(3.5 b) performing constant false alarm detection on the detected data matrix A to obtain the serial numbers of rows corresponding to all the elements of the threshold crossing in the detected data matrix A, and utilizing all the elements of the threshold crossing in the detected data matrix ARow coordinates of elements and extended data matrix A n And obtaining a second Doppler frequency.
Preferably, step (3.5 b) comprises the steps of:
(3.5.1b) setting a threshold, initializing s =1;
(3.5.2b) carrying out constant false alarm detection on the S-th column element in the detected data matrix A, judging whether the S-th column element in the detected data matrix A has a threshold passing element or not,
(3.5.3 b) if not, adding 1 to S, and turning to the step (3.5.2b), if yes, obtaining H s Elements which pass the threshold value go to step (3.5.4 b);
(3.5.4b) initialization h s =1;
(3.5.5 b) determining the h-th element in the S-th column element of the detected data matrix A s The sequence number of the row corresponding to each threshold passing element is
Figure BDA0001951480190000121
Further determination of A N To middle
Figure BDA0001951480190000122
Center frequency of Doppler channel corresponding to row
Figure BDA0001951480190000123
And judge A n′ Doppler blind area B n′ Whether or not to include
Figure BDA0001951480190000124
If all A are n′ (N' =1,2, …, N-1) all contain blind areas
Figure BDA0001951480190000125
Then directly will
Figure BDA0001951480190000126
Second Doppler frequency T as target fir If not, go to step (3.5.6b);
(3.5.6b) in matrix A n′ Zhongzi (Chinese character of' ZhongziDoes not include a fixed Doppler blind zone
Figure BDA0001951480190000127
Is denoted as
Figure BDA0001951480190000128
At the same time
Figure BDA0001951480190000129
Find the center frequency of the corresponding Doppler channel of the P line
Figure BDA00019514801900001210
Closest center frequency, is noted
Figure BDA00019514801900001211
Will be provided with
Figure BDA00019514801900001212
In that
Figure BDA00019514801900001213
The serial number of the corresponding row in (1) is recorded as
Figure BDA0001951480190000131
Wherein,
Figure BDA0001951480190000132
C s representation matrix A n′ Does not contain frequencies
Figure BDA0001951480190000133
The total number of matrices;
(3.5.7a) determination of A N Middle S column to
Figure BDA0001951480190000134
Element corresponding to row
Figure BDA0001951480190000135
Respectively determine
Figure BDA0001951480190000136
Middle S column to
Figure BDA0001951480190000137
Element corresponding to row
Figure BDA0001951480190000138
And is recorded as a column vector
Figure BDA0001951480190000139
(3.5.8a) calculation of h s Ratio vector corresponding to threshold passing element
Figure BDA00019514801900001310
(3.5.9 b) judging the ratio vector
Figure BDA00019514801900001311
Whether all elements are in a preset range, wherein the preset range is [ 1-delta, 1+ delta ]]And delta is the error of the ratio, if yes, the vector is determined to be in the matrix A N Further determining the center frequency of the Doppler channel corresponding to the row of the element, and recording as the second Doppler frequency T fir (ii) a If not, let h s Adding 1, and repeatedly executing the steps from (3.5.4b) to (3.5.9b) until h s =H s Adding 1 to S, and going to step (3.5.2b) until obtaining the second Doppler frequency T fir Wherein s is more than or equal to 1.
It should be noted that, when there are multiple targets, the radar receives echo signals of N pulse groups corresponding to each target, and further obtains a first doppler frequency and a second doppler frequency of each target respectively.
And 4, judging whether the echo signal of the target is in a clutter area or a noise area, if the echo signal of the target is in the noise area, taking the first Doppler frequency as the Doppler frequency of the target, and if the echo signal of the target is in the clutter area, taking the second Doppler frequency as the Doppler frequency of the target, and determining the target speed according to the Doppler frequency of the target.
According to the Doppler frequency of the target, using a predetermined formula
Figure BDA00019514801900001312
Calculating to obtain the speed v of the target;
where T denotes the doppler frequency of the target and λ denotes the operating wavelength of the radar.
The embodiment of the invention provides a method for resolving fuzzy speed measurement of an MTD radar, wherein in a CPI, the MTD radar sequentially transmits pulse group signals with different pulse repetition periods, receives echo signals corresponding to the pulse group signals, further obtains corresponding echo data matrixes according to the echo signals, performs pulse compression on all the echo data matrixes, performs moving target detection on all the pulse compressed data matrixes in a DFT channel and an FIR channel respectively to obtain a first Doppler frequency and a second Doppler frequency respectively, further judges whether the echo signal of a target is in a clutter area or a noise area, takes the first Doppler frequency as the Doppler frequency of the target if the echo signal of the target is in the noise area, takes the second Doppler frequency as the Doppler frequency of the target if the echo signal of the target is in the clutter area, and determines the target speed according to the Doppler frequency of the target. The method provided by the invention simultaneously performs target detection on the echo signal of the target by using the DFT channel and the FIR channel, judges whether the echo signal of the target is in a clutter area or a noise area after the target is detected, selects one optimal output result according to the judgment result, does not need to frequently switch channels, can improve the robustness of the system, and expands the signals of each pulse group in the Doppler dimension when the DFT channel or the FIR channel performs target detection, then accumulates all pulses of a plurality of staggered repetition frequency pulse groups, can improve the resource utilization rate of the radar, thereby improving the detection probability of the target signal and the success rate of resolving the speed ambiguity.
Further, the beneficial effects of the method provided by the embodiment of the invention are further verified through simulation experiments as follows:
the method provided by the invention and the existing method are adopted to carry out moving target detection on the echo signals of the target 1 and the target 2. Processing the echo signal of the target 1 by adopting the method provided by the invention, wherein in a DFT channel, the coherent accumulation result in the step (3.3 a) is shown in figure 2, the x-axis coordinate of the DFT channel represents a distance unit, the y-axis coordinate of the DFT channel represents a Doppler channel, and the z-axis coordinate of the DFT channel represents coherent accumulation amplitude; the coherent accumulation result in step (3.3 b) in the FIR channel is shown in fig. 3, wherein the x-axis coordinate represents the distance unit, the y-axis coordinate represents the doppler channel, and the z-axis coordinate represents the coherent accumulation amplitude; the DFT channel of the invention and the range image contrast map at the target doppler channel obtained by processing the echo signal of the target 1 in the prior art are shown in fig. 4, wherein the abscissa represents the range unit and the ordinate represents the amplitude; the FIR channel of the present invention and the range image contrast map at the target doppler channel obtained by processing the echo data of the target 1 in the prior art are shown in fig. 5, in which the abscissa represents the range unit and the ordinate represents the amplitude.
The echo signal of the target 2 is processed by the method provided by the invention, in the DFT channel, the coherent accumulation result in the step (3.3 a) is shown in figure 6, the x-axis coordinate thereof represents a distance unit, the y-axis coordinate thereof represents a Doppler channel, the z-axis coordinate thereof represents a coherent accumulation amplitude, in the FIR channel, the coherent accumulation result in the step (3.3 b) is shown in figure 7, the x-axis coordinate thereof represents a distance unit, the y-axis coordinate thereof represents a Doppler channel, and the z-axis coordinate thereof represents a coherent accumulation amplitude. The DFT channel of the invention and a range image contrast map at the target doppler channel obtained by processing the echo signal of the target 2 in the prior art are shown in fig. 8, wherein the abscissa represents the range unit and the ordinate represents the amplitude; the FIR channel of the present invention and the range image contrast map at the target doppler channel obtained by the echo data processing of the target 2 of the prior art are shown in fig. 9, in which the abscissa represents the range unit and the ordinate represents the amplitude.
Judging whether the echo signal of the target 1 is in a clutter area or a noise area to obtain that the echo signal of the target 1 is in the clutter area, and as can be seen from fig. 2 and 3, for clutter area data, coherent accumulation amplitude of an FIR channel is really higher than that of a DFT channel, and the DFT channel does not have a clutter suppression effect, so that a real position of the target cannot be detected, and a second doppler frequency of the FIR channel is output as a doppler frequency of the target. As can be seen from fig. 2, the doppler channel of the target is-114 according to the position of the coherent accumulation peak point, and the doppler frequency corresponding to the doppler channel is further negative, that is, the target flies far away from the radar, and the calculated speed of the target is 80.9m/s, which is substantially the same as the calculated speed of the range cell walking obtained by actually measuring two frames of data, so the method is effective for the target in the clutter region.
It is determined whether the echo signal of the target 2 is in the clutter region or the noise region, and if the echo signal of the target 2 is in the noise region, since the FIR channel has a certain performance loss when processing the data in the noise region, and the DFT channel does not have such a loss, as can be seen from fig. 6 and 7, for the data in the noise region, the coherent accumulation amplitude of the DFT channel is actually higher than that of the FIR channel, so the first doppler frequency of the DFT channel is output as the doppler frequency of the target. As can be seen from fig. 7, the doppler channel of the target obtained from the position of the coherent accumulation peak point is-284, and the doppler frequency corresponding to the doppler channel is further negative, that is, the target flies far away from the radar, the calculated velocity of the target is 217.1m/s, which is substantially the same as the velocity calculated by the distance unit walking obtained by actually measuring two frames of data, so the present invention is also effective for the target in the noise area.
The invention and the traditional method both use the range-to-range of the target to carry out constant false alarm detection, further realize the moving target detection, the range-to-range image range of the target can be equivalent to the range of the target signal, and the range of the target range image of the invention is marked as S n Let the range of the target range profile of the prior art be S o As can be seen from fig. 4 and 9, the present invention can increase the target range image amplitude by about two times, i.e., the present invention can increase the target range image amplitude by two times, compared with the prior art
Figure BDA0001951480190000161
The target signal-to-noise ratio obtained by the method is recorded as
Figure BDA0001951480190000162
Remember the prior artThe technique yields a target signal-to-noise ratio of
Figure BDA0001951480190000163
Then, after normalization processing, there are:
Figure BDA0001951480190000164
thus, it can be concluded that: compared with the prior art, the method provided by the invention can improve the signal-to-noise ratio of the target by 3dB, thereby improving the detection probability, and further completing the deblurring speed measurement on the target signal with small signal-to-noise ratio.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (8)

1. A method for resolving fuzzy speed measurement by an MTD radar is characterized by comprising the following steps:
step 1, in a coherent processing interval CPI, sequentially transmitting N pulse group signals with different pulse repetition periods by an MTD (maximum transmission delay) radar, receiving echo signals corresponding to the pulse group signals, and further obtaining corresponding echo data matrixes according to the echo signals so as to obtain N echo data matrixes;
wherein the nth echo data matrix of the N echo data matrices is X n Therein is disclosedObtaining an echo signal corresponding to the nth pulse group signal, wherein N is an integer from 1 to N, N represents the number of pulse group signals transmitted by the MTD radar in one coherent processing interval CPI, and N is more than or equal to 2; x n Is MxQ n Dimension matrix, M represents the number of pulses contained in a pulse group signal, M is not less than 2,Q n Representing the total number of range cells, Q, of the echo signal corresponding to the nth pulse group n ≥2;
Step 2, the nth echo data matrix X in the N echo data matrices n Performing pulse compression processing to obtain corresponding pulse compression data matrix X n ′,X n ' is M × Q n A dimension matrix;
step 3, compressing all N pulse compression data matrixes X 1 ′,X 2 ′,...,X n ′,...X N ' simultaneously feeding into DFT channel and FIR channel where the DFT channel is based on X 1 ′,X 2 ′,...,X n ′,...X N ' moving target detection is carried out to obtain a first Doppler frequency according to X in an FIR channel 1 ′,X 2 ′,...,X n ′,...X N Detecting a moving target to obtain a second Doppler frequency;
and 4, judging whether the echo signal of the target is in a clutter area or a noise area, if the echo signal of the target is in the noise area, taking the first Doppler frequency as the Doppler frequency of the target, if the echo signal of the target is in the clutter area, taking the second Doppler frequency as the Doppler frequency of the target, and determining the speed of the target according to the Doppler frequency of the target.
2. The method of claim 1, wherein in step 3, the DFT channel is according to X 1 ′,X 2 ′,...,X n ′,...X N ' performing moving target detection, and obtaining the first doppler frequency specifically includes:
(3.1 a) compressing X of the data matrices for all N pulses in the DFT channel n ' Doppler filtering is carried out to obtain a Doppler filtered data matrix
Figure FDA0001951480180000021
W n Weight matrix, W, representing the nth DFT filter bank n =[w n,1 ,w n,2 ,...,w n,k ,...,w n,K ],w n,k The weight vector representing the kth filter in the nth DFT filter bank is an mx 1-dimensional column vector,
Figure FDA0001951480180000022
Figure FDA0001951480180000023
representing the mth weight of the kth filter in the n filter banks,
Figure FDA0001951480180000024
where N =1,2, …, N, K =1,2.. K, K = gxm, K representing the number of filters in each filter bank, G representing the encryption multiple of the number of filters in each filter bank, M =1,2.. M, j is the unit of an imaginary number, Y n Is KxQ n Dimension matrix, W n Is a matrix of dimension M x K [ ·] H Represents a conjugate transpose operation [ ·] T Representing a transposition operation;
(3.2 a) the Doppler filtered data matrix Y n Extending F times in the positive direction and the negative direction of the Doppler domain by taking K as a period simultaneously to obtain an extended data matrix
Figure FDA0001951480180000025
Extending the number to a data matrix Z n ' from column Q +1 to column Q n All column elements are removed, so as to obtain extended data matrix Z n
Wherein Z is n Is' P x Q n Dimension matrix, P denotes the number of Doppler channels, P = K × (2F + 1), F denotes the maximum number of ambiguities in velocity, which is a non-negative integer, Z n Is a P × Q dimensional matrix, Q = min { Q } 1 ,Q 2 ,…,Q N The min {. Is } represents the minification operation;
(3.3 a) for all extended data matrix Z 1 ,Z 2 ,...,Z n ,...Z N Performing coherent accumulation between pulse groups to obtain a data matrix Z' after coherent accumulation;
(3.4 a) detecting the data matrix Z' after the phase coherent accumulation to obtain a detected data matrix Z;
(3.5 a) performing constant false alarm detection on the detected data matrix Z to obtain coordinates of rows of all elements passing through the threshold in the detected data matrix Z, and utilizing the serial numbers of the rows corresponding to all elements passing through the threshold in the detected data matrix Z and the extended data matrix Z n And obtaining a first Doppler frequency.
3. Method according to claim 2, characterized in that said step (3.3 a) comprises in particular the sub-steps of:
(3.3.1a) determine the total extended data matrix Z 1 Z 2 ,...,Z N The center frequency of the corresponding Doppler channel of each row of (1), wherein the data matrix Z is extended n The center frequency of the Doppler channel corresponding to the p-th row of (1) is
Figure FDA0001951480180000031
Wherein P =1,2, …, P represents the number of doppler channels, P = K × (2f + 1), F represents the maximum blurring time, which is a non-negative integer, PRF n A pulse repetition frequency representing the nth pulse group signal;
(3.3.2a) initializing q N =1;
(3.3.3a) determination of Z N Q (a) to (b) N Center frequency of Doppler channel corresponding to row
Figure FDA0001951480180000032
At Z n′ Find the center frequency and
Figure FDA0001951480180000033
nearest center frequency
Figure FDA0001951480180000034
Will be provided with
Figure FDA0001951480180000035
At Z n′ Is marked as
Figure FDA0001951480180000036
Wherein N' =1,2, …, N-1;
(3.3.4a) Z N Middle q N The line elements are
Figure FDA0001951480180000037
Will all be
Figure FDA0001951480180000038
And
Figure FDA0001951480180000039
carrying out coherent accumulation to obtain the qth data matrix Z' after the coherent accumulation N Line element
Figure FDA00019514801800000310
Figure FDA00019514801800000311
(3.3.5a) q N Adding 1, judging q N If the value is less than or equal to P, returning to the step (3.3.3a) if the value is less than or equal to P, and if the value is not less than P, turning to the step (3.3.6a);
(3.3.6a) obtaining the data matrix Z' after the phase-coherent accumulation; wherein Z' is a P multiplied by Q dimensional matrix.
4. Method according to claim 2, characterized in that said step (3.5 a) comprises in particular the sub-steps of:
(3.5.1a) setting a threshold, initializing l =1;
(3.5.2a) performing constant false alarm detection on the l column element in the detected data matrix Z, judging whether the l column element of the detected data matrix Z has an element which passes the threshold,
(3.5.3 a) if not, add 1 to l, go to step (3.5.2a), if yes, get I l If the threshold value element is passed, the step (3.5.4 a) is carried out;
(3.5.4a) initialization of i l =1;
(3.5.5 a) determining the ith column of the detected data matrix Z l The sequence number of the row corresponding to each threshold passing element is
Figure FDA0001951480180000041
Further determination of Z N To (1) a
Figure FDA0001951480180000042
Center frequency of Doppler access corresponding to a line
Figure FDA0001951480180000043
At Z n′ Find the center frequency and
Figure FDA0001951480180000044
closest center frequency, noted
Figure FDA0001951480180000045
Will be provided with
Figure FDA0001951480180000046
At Z n′ The corresponding line sequence number in (1) is marked as
Figure FDA0001951480180000047
Wherein N' =1,2, …, N-1;
(3.5.6a) determination of Z N The first column of
Figure FDA0001951480180000048
Element corresponding to row
Figure FDA0001951480180000049
Determining extended data matrix Z separately 1 ,Z 2 ,...,Z N_1 The first column of
Figure FDA00019514801800000410
Element corresponding to row
Figure FDA00019514801800000411
And is recorded as a column vector
Figure FDA00019514801800000412
(3.5.7a) calculating the i th l Ratio vector corresponding to threshold passing element
Figure FDA0001951480180000051
(3.5.8a) judgment ratio vector
Figure FDA0001951480180000052
Whether all elements are in a preset range, wherein the preset range is [ 1-delta, 1+ delta ]]And delta is the error of the ratio, and if so, the vector is determined to be in the matrix Z N Further determining the center frequency of the Doppler channel corresponding to the row of the element, and recording as the first Doppler frequency T dft (ii) a If not, let i l Adding 1, and repeatedly executing the steps (3.5.4a) to (3.5.8a) until i l =I l Adding 1 to l, go to step (3.5.2a) until the first Doppler frequency T is obtained dft Wherein l is more than or equal to 1.
5. Method according to claim 1, characterized in that said step 3In FIR channel according to X 1 ′,X 2 ′,...,X n ′,...X N ' performing moving target detection to obtain the second doppler frequency specifically includes:
(3.1 b) compress X in the data matrix for all N pulses in the FIR channel n ' Doppler filtering is carried out to obtain a Doppler filtered data matrix
Figure FDA0001951480180000053
V n Weight matrix, V, representing the nth FIR filter bank n =[v n,1 ,v n,2 ,…,v n,k ,…,V n,K ],V n,k The weight vector representing the kth filter in the nth FIR filter bank is an mx 1-dimensional column vector,
Figure FDA0001951480180000054
R n m × M dimension clutter-plus-noise covariance matrix corresponding to the nth pulse group, a (f) n,k ) Pilot frequency vector at the central frequency of the kth filter in the nth FIR filter group is M multiplied by 1 dimension column vector;
where N =1,2, …, N, K =1,2.. K, K = gxm, K representing the number of filters in each filter bank, G representing the encryption multiple of the number of filters in each filter bank, M =1,2.. M, U n Is KxQ n Dimension matrix, V n Is an M multiplied by K dimensional matrix;
(3.2 b) the Doppler filtered data matrix U n Extending F times in the positive direction and the negative direction of the Doppler domain by taking K as a period simultaneously to obtain an extended data matrix
Figure FDA0001951480180000061
Data matrix A after extension of number n ' from the Q +1 th column to the Q th column n All column elements are removed, so as to obtain continuation data matrix A n
Wherein A is n Is' P x Q n Dimension matrix, P denotes the number of Doppler channels, P = K × (2F + 1), FRepresenting the maximum number of ambiguities in velocity, being a non-negative integer, A n Is a P × Q dimensional matrix, Q = min { Q } 1 ,Q 2 ,…,Q N The min {. Is } represents the minification operation;
(3.3 b) for all extended data matrix A 1 A 2 ,...,A N Performing coherent accumulation between pulse groups to obtain a data matrix A' after coherent accumulation;
(3.4 b) detecting the data matrix A' after the phase coherent accumulation to obtain a data matrix A after detection in an FIR channel;
(3.5 b) performing constant false alarm detection on the detected data matrix A to obtain the serial numbers of rows corresponding to the elements of all the thresholds in the detected data matrix A, and utilizing the row coordinates of the elements of all the thresholds in the detected data matrix A and the extended data matrix A n And obtaining a second Doppler frequency.
6. The method according to claim 5, characterized in that said step (3.3 b) is in particular:
(3.3.1b) determining the center frequency of the kth filter in the nth FIR filter group
Figure FDA0001951480180000062
Wherein,
Figure FDA0001951480180000063
cw n is shown in PRF n Inner Doppler blind zone width, PRF n Representing the pulse repetition frequency of the nth pulse group,
Figure FDA0001951480180000064
Figure FDA0001951480180000071
(3.3.2b) center frequency f according to the k-th filter in the n-th FIR filter group n,k Determining a data matrix A n P lines of (1) corresponding to the popsCenter frequency of the Lee channel, the continuation data matrix A n The center frequency of the Doppler channel corresponding to the p-th row of (1) is
Figure FDA0001951480180000072
Where N =1,2, …, N, P =1,2, …, P, mod (P, K) represents the remainder of dividing P by K,
Figure FDA0001951480180000073
represents rounding down;
(3.3.3b) determining the Doppler blind area range of the nth FIR filter group as B n A 1 to B n PRF in both positive and negative Doppler directions n Is extended for F times periodically to obtain A n Range of Doppler dead zone
Figure FDA0001951480180000074
Wherein,
Figure FDA0001951480180000075
t=[-F,-(F-1),...,0,1,...F],
Figure FDA0001951480180000076
u represents and is operated;
(3.3.4b) initialization of r N =1;
(3.3.5b) extraction of the matrix A N Middle r N Line elements, denoted as
Figure FDA0001951480180000077
Determination of A N R of N Center frequency of Doppler channel corresponding to row
Figure FDA0001951480180000078
In a set of matrices A 1 A 2 ,...,A N-1 Does not contain the blind area in the middle
Figure FDA0001951480180000079
Is marked as
Figure FDA00019514801800000710
In that
Figure FDA00019514801800000711
Find the center frequency of the corresponding Doppler channel of the P line
Figure FDA00019514801800000712
Closest center frequency, is noted
Figure FDA00019514801800000713
Will matrix
Figure FDA00019514801800000714
Center frequency of
Figure FDA00019514801800000715
The corresponding row is marked as
Figure FDA00019514801800000716
Will matrix
Figure FDA00019514801800000717
The corresponding pulse repetition period is noted as PRT d
Wherein,
Figure FDA00019514801800000718
Figure FDA00019514801800000719
Figure FDA00019514801800000720
representation matrix A n′ Does not contain frequencies
Figure FDA00019514801800000721
N' =1,2, …, N-1;
(3.3.6b) will be all
Figure FDA00019514801800000722
And
Figure FDA00019514801800000723
performing coherent accumulation to obtain the r-th matrix of the matrix A N Line element
Figure FDA0001951480180000081
Figure FDA0001951480180000082
(3.3.7b) order r N Adding 1, judging r N If the value is less than or equal to P, returning to the step (3.3.5b) if the value is less than or equal to P, and if the value is not more than P, returning to the step (3.3.8b);
(3.3.8b) obtaining a data matrix A' after coherent integration; wherein A' is a P × Q dimensional matrix.
7. The method according to claim 5, characterized in that said step (3.5 b) is in particular:
(3.5.1b) setting a threshold, and initializing S =1;
(3.5.2b) carrying out constant false alarm detection on the S-th column element in the detected data matrix A, judging whether the S-th column element in the detected data matrix A has a threshold passing element or not,
(3.5.3 b) if not, adding 1 to S, and turning to the step (3.5.2b), if yes, obtaining H s Elements which pass the threshold value go to step (3.5.4 b);
(3.5.4b) initialization h s =1;
(3.5.5 b) determining the S th column element of the detected data matrix Ah s The sequence number of the row corresponding to each threshold passing element is
Figure FDA0001951480180000083
Further determination of A N To middle
Figure FDA0001951480180000084
Center frequency of Doppler channel corresponding to row
Figure FDA0001951480180000085
And judge A n′ Doppler blind area B n′ Whether or not to include
Figure FDA0001951480180000086
If all A are n′ (N' =1,2, …, N-1) all contain blind areas
Figure FDA0001951480180000087
Then directly will
Figure FDA0001951480180000088
Second Doppler frequency T as target fir If not, go to step (3.5.6b);
(3.5.6b) in matrix A n′ Does not include a Doppler blind zone
Figure FDA0001951480180000089
Is denoted as
Figure FDA00019514801800000810
At the same time
Figure FDA00019514801800000811
Find the center frequency of the corresponding Doppler channel of the P line
Figure FDA0001951480180000091
The closest center frequency, noteIs composed of
Figure FDA0001951480180000092
Will be provided with
Figure FDA0001951480180000093
In that
Figure FDA0001951480180000094
The serial number of the corresponding row in (1) is recorded as
Figure FDA0001951480180000095
Wherein,
Figure FDA0001951480180000096
n′=1,2,…,N-1,c=1,2,...,C s ,C s representation matrix A n′ Does not contain frequencies
Figure FDA0001951480180000097
The total number of matrices;
(3.5.7a) determination of A N Middle S column to
Figure FDA0001951480180000098
Element corresponding to row
Figure FDA0001951480180000099
Respectively determine
Figure FDA00019514801800000910
Middle S column to
Figure FDA00019514801800000916
Element corresponding to row
Figure FDA00019514801800000911
And is recorded as a column vector
Figure FDA00019514801800000912
(3.5.8a) calculation of h s Ratio vector corresponding to threshold passing element
Figure FDA00019514801800000913
(3.5.9 b) judging the ratio vector
Figure FDA00019514801800000914
Whether all elements are in a preset range, wherein the preset range is [ 1-delta, 1+ delta ]]And delta is the error of the ratio, if yes, the vector is determined to be in the matrix A N Further determining the center frequency of the Doppler channel corresponding to the row of the element, and recording as the second Doppler frequency T fir (ii) a If not, let h s Adding 1, and repeatedly executing the steps from (3.5.4b) to (3.5.9b) until h s =H s Adding 1 to S, and going to step (3.5.2b) until obtaining the second Doppler frequency T fir Wherein s is more than or equal to 1.
8. The method according to claim 1, wherein step 4 is specifically:
according to the Doppler frequency of the target, using a predetermined formula
Figure FDA00019514801800000915
Calculating to obtain the speed v of the target;
where T denotes the doppler frequency of the target and λ denotes the operating wavelength of the radar.
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