CN116184349B - Frequency modulation continuous wave radar super-resolution positioning method based on phase regression - Google Patents

Frequency modulation continuous wave radar super-resolution positioning method based on phase regression Download PDF

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CN116184349B
CN116184349B CN202310110081.XA CN202310110081A CN116184349B CN 116184349 B CN116184349 B CN 116184349B CN 202310110081 A CN202310110081 A CN 202310110081A CN 116184349 B CN116184349 B CN 116184349B
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intermediate frequency
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CN116184349A (en
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杨婧
梅子燕
刘鑫
黄欣
覃文智
王孟
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Nantong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/415—Identification of targets based on measurements of movement associated with the target
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/42—Simultaneous measurement of distance and other co-ordinates
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/50—Systems of measurement based on relative movement of target
    • G01S13/52—Discriminating between fixed and moving objects or between objects moving at different speeds
    • G01S13/536—Discriminating between fixed and moving objects or between objects moving at different speeds using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention provides a frequency modulation continuous wave radar super-resolution positioning method based on phase regression, belongs to the technical field of artificial intelligent positioning, and solves the problems of low resolution and high computational complexity of frequency modulation continuous wave radar positioning. The technical proposal is as follows: the method comprises the following steps: step 1: establishing a plane rectangular coordinate system, and determining an intermediate frequency mixed signal expression received by each antenna; step 2: determining an initial position of a target object; step 3: the final position of the target object is determined by establishing a regression optimization model, using a target optimization algorithm to maximize the predicted phases of the antenna arrays to approximate their actual phases. The beneficial effects of the invention are as follows: the invention can improve the distance and angle resolution, reduce the calculation complexity and improve the robustness of the algorithm.

Description

Frequency modulation continuous wave radar super-resolution positioning method based on phase regression
Technical Field
The invention relates to the technical field of artificial intelligence positioning, in particular to a frequency modulation continuous wave radar super-resolution positioning method based on phase regression.
Background
In recent years, humans use global positioning systems for outdoor positioning and navigation. In 2020, china formally builds a global satellite navigation system which belongs to China, namely a Beidou satellite navigation system, and the global satellite navigation system is smoothly put into use. But indoor high-precision positioning cannot use the existing satellite positioning technology. For indoor high-precision positioning, the mainstream positioning technologies include radar, infrared, bluetooth, ultrasonic, wi-Fi, RFID, UWB and the like. As a radar positioning technology, a Frequency Modulated Continuous Wave (FMCW) technology has characteristics of no blind area, high sensitivity, high resolution, simple processing procedure, moderate cost, and the like, so the FMCW technology has received great attention in recent years.
The intermediate frequency signal acquired by FMCW radar is subject to noise, in particular gaussian noise interference. In order to improve the accuracy of the positioning, i.e. to improve the accuracy of the signal spectrum estimation. To solve this problem, the scholars often use methods such as fourier transform, filtering method and life algorithm to explore, and the two-dimensional discrete fourier algorithm is simple and can meet the requirement of signal instantaneity, but has the problem of low frequency estimation accuracy. The laplace operator has linear, displacement invariance to isolated point detection of the spectrum and all filtered images have zero average gray scale, but would have unacceptable sensitivity to noise. The frequency corrected by the Rife algorithm can be improved, but the estimation error is easy to increase after interference, and the estimation value is inaccurate when the frequency spectrum deviation is smaller. The phase expansion aims at the problem that the intermediate frequency signal is folded due to the overlarge angle of the target object, so that the phases are continuous, but the conditions of serious noise, abrupt phase change, discontinuous phase and the like are easy to exist. The least square method can accurately estimate the frequency of a single-frequency signal in the intermediate frequency signal group, but has poor practicability and large calculated amount.
How to solve the technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a frequency modulation continuous wave radar super-resolution positioning method based on phase regression, which solves the problem of lower resolution in positioning a target object, can improve the distance and angle resolution, reduces the computational complexity and improves the robustness of an algorithm.
The invention is characterized in that: the method comprises the steps of determining intermediate frequency mixed signals received by each antenna, obtaining a two-dimensional distance-angle spectrum by using two-dimensional fast Fourier transform to reduce noise, detecting isolated points of the spectrum by using a Laplacian, correcting intermediate frequency by using a Rife algorithm, determining the initial position of an object according to the intermediate frequency, extracting the phase of intermediate frequency signals of echo signals of each antenna from the FFT spectrum, expanding the phases to obtain expanded actual phases, determining a regression optimization model, and finally determining the final position of the object by using a target optimization algorithm.
In order to achieve the aim of the invention, the invention adopts the technical scheme that: a frequency modulation continuous wave radar super-resolution positioning method based on phase regression comprises the following steps:
step 1: determining an intermediate frequency signal obtained by mixing a radar transmitting signal, a receiving signal and two signals in a chirp period, establishing a plane rectangular coordinate system by taking the center of an antenna array as an origin and the antenna array as an x-axis according to the structure of the antenna array and carrier frequency parameters of the radar transmitting signal, and determining an intermediate frequency mixed signal expression received by each antenna;
step 1.1: the expression for determining the frequency f (t) of the radar-transmitted signal in one chirp period is:
f(t)＝f 0 +γt,0≤t≤T
transmitted wave signal s TX (t)：
Where f (t) denotes the frequency of the radar transmission signal, s TX (t) represents a transmitted wave signal, A TX Representing the signal transmission power, f 0 Representing carrier frequency, gamma representing frequency modulation slope, T representing chirp period, j representing imaginary unit;
determining the radar passing distance as R 0 Is reflected by an object RX (t)：
Wherein s is RX (t) represents the radar passing distance R 0 Is reversed by the object of (2)Post-transmission received signal, A RX Which is indicative of the received power of the signal,represents the receiving time delay, c represents the speed of light, R 0 Representing the distance of the object from the radar;
due to the transmitted signal s TX (t) and acceptance signal s RX (t) at [ tau ] 0 ,T]With overlap, the two signals are input into a mixer to obtain an intermediate frequency signal s IF (t)：
Wherein s is IF (t) is an intermediate frequency signal,is s RX Conjugate function of (t), intermediate frequency signal s IF (t) ignore τ 0 2 (τ 0 1) due to the frequency f of the intermediate frequency signal IF ＝γτ 0 Therefore->
Step 1.2: taking the center of an antenna array as an origin, taking the antenna array as an x axis, establishing a plane rectangular coordinate system, and determining the coordinates of the (n+1) th antenna as (x) n ,y n ) Whereiny n ＝0，n＝0,1,…,N a -1, wherein L is the aperture of the equivalent virtual antenna array, N a Is the number of antenna arrays;
step 1.3: determining the kth object O k Distance from the center of the antenna array is R k And an included angle theta with the y axis k The object corresponds to the coordinates (X k ,Y k ) Wherein X is k ＝R k sinθ k ，Y k ＝R k cosθ k K=1, 2, …, K being the number of objects;
step 1.4: determining a receiving delay τ, namely:
wherein the method comprises the steps ofRepresents the distance from the (n+1) th antenna to the (k) th object;
step 1.5: determining the intermediate frequency signal s of the kth object received by the (n+1) th antenna n,k (t), namely:
wherein a is k Is the reflectivity of the object, gamma is the chirp rate, f 0 Is the carrier frequency of the signal,is a phase term;
step 1.6: determining that the radius of the antenna is far smaller than the object distance, and performing step 1.5 on the intermediate frequency signal s n,k Frequency term of (t)R in (a) n,k ≈R k The echo direction angles of all the antennas are approximately equal, so the optical path difference of the object reaching two adjacent antennas is dsin theta k Based on the 1 st antenna (n=0), R in the phase term n,k The writing is as follows:
R n,k ＝R 0,k +nd sinθ k ,n＝0，1，…N a -1
then the intermediate frequency signal s received by the n+1th antenna n Expression of (t):
wherein:the reflected signal intermediate frequency representing the kth object, k=1, 2, K;represents the angle-dependent frequency, +.>Represents the initial phase, R 0,k Representing the distance from the 1 st antenna to the kth object;
step 1.7: determining that the intermediate frequency signal received by the (n+1) th antenna is a mixed signal z of the intermediate frequency signals with noise points of K target objects n (t), namely:
wherein omega n Representing noise, s n,k (t) is an intermediate frequency signal of the kth object received by the (n+1) th antenna;
step 2: denoising the received intermediate frequency signal by using a two-dimensional fast Fourier transform to obtain a two-dimensional distance-angle spectrum, detecting an isolated point peak value of the two-dimensional spectrum by using a Laplacian operator, correcting the intermediate frequency by using a life algorithm, and determining the initial position of a target object;
step 2.1: two-dimensional fourier transform (FFT) removes gaussian noise from the target echo signal:
(1) Sampling the intermediate frequency signal received by the antenna array in a chirp period, wherein the sampling interval is T s And converts the sampled data into two-dimensional intermediate frequency signal group S (n, t s )：
S(n,t s ),n＝0,1,2…N a -1,t s ＝0,1,2…,N t -1
Wherein the method comprises the steps ofINT represents rounding, each row of the two-dimensional intermediate frequency signal group is an intermediate frequency signal received by an antenna array at a certain moment t, and each row of the intermediate frequency signal is an intermediate frequency signal received by the antenna array at all sampling times in the period;
(2) For the intermediate frequency signal group S (n, t s ) Performing one-dimensional FFT (fast Fourier transform) on the row vector in the matrix to obtain FFT spectrum F (n, v):
(3) Performing one-dimensional FFT conversion again on the column vector in the FFT spectrum F (n, v) obtained in the step 2.1 (2) to obtain F (u, v), namely a two-dimensional FFT spectrum F (u, v) of the intermediate frequency signal group:
step 2.2: the process of detecting isolated points by a filtering method comprises the following steps:
(1) Detection is performed using a laplace check two-dimensional FFT spectrum:
wherein the partial derivative is calculated by second-order finite difference, namely:
(2) Determining T H Is a prescribed non-negative threshold, Z is the response of the filter at the center of the Laplacian kernel, if the absolute value of the response of the filter exceeds the threshold T H It is considered that a point is detected at the center position (u, v) of the core, the response of this point at the center of the laplace core is denoted as Z (u, v), and when outputting a signal, such a point is marked as 1, and all the other points are marked as 0, so as to obtain the expression form of the output signal g (u, v), namely:
determining the number K of objects based on the number of isolated points, the position of which is (u) k ,v k ) Wherein u is k Is the peak value of the angular frequency corresponding to the kth object, v k Is the peak value of the intermediate frequency corresponding to the kth object, and the intermediate frequency f of each object is determined IF,k And an angle dependent frequency f d,k Is a function of the estimated value of (a):
wherein the intermediate frequency resolution Δf IF And angular frequency resolution Δf d The method comprises the following steps:
step 2.3: the life algorithm corrects the intermediate frequency process:
(1) Determining frequency resolution
(2) Finding the maximum f of frequencies in the FFT spectrum m And its corresponding index value f k ；
(3) Let the amplitude of the frequencies at k-1 and k+1 be f respectively k-1 、f k+1 ；
(4) The amplitude values at k-1 and k+1 are respectively judged to determine the frequency deviation value delta f The method comprises the following steps:
(5) Calculating intermediate frequency correction value
Correcting all the intermediate frequency by using five steps in the step 2.3 to obtain the corrected intermediate frequency of each object
Step 2.4: preliminary positioning is carried out on the target object according to the corrected frequency, and the distance estimated value of the target object kAnd angle estimate +.>The method comprises the following steps of:
substituting the spectral resolution to obtain the distance resolution R res And angular resolution theta res The method comprises the following steps of:
step 3: extracting the intermediate frequency signal phase of each antenna echo signal from the FFT spectrum, expanding the phase to obtain an expanded actual phase, determining a regression optimization model, using a target optimization algorithm to enable the predicted phase of the antenna array to be maximally approximate to the actual phase of the antenna array, and determining the final position of the target object;
step 3.1: according to the intermediate frequency, from phi n,k Extracting the intermediate frequency signal phase of each antenna from the FFT spectrum F (n, v) in step 2.1 (2):
wherein imag [ F (n, v) k )]Is F (n, v) k ) Is the imaginary part of real [ F (n, v) k )]Is F (n, v) k ) Of (F) (n, v) k ) Is the one-dimensional FFT spectrum of the kth object;
step 3.2: determining the predicted phase of the intermediate frequency signal according to the intermediate frequency signal expression in the step 1.5Is represented by the expression:
when the angle of the object is small (θ k When the angle is less than or equal to 5 DEG, the change of the antenna phase is small, the distribution is a curve, when theta k At > 5 deg., the phase change is large, and the distribution is approximately a straight line.
Step 3.3: phase unwrapping
When the angle of the target object is relatively large, the intermediate frequency signal phase phi obtained in step 3.1 n,k Will be within the interval [ -pi, pi]The inner fold is generated, thus causing discontinuous phase, and the phase expansion is needed, and the steps are as follows:
(1) Based on predicted phaseEstimating the phase difference of adjacent two antennas +.>
(2) Determining phase jump point positions
(i) When (when)If the phase difference of adjacent antennas is +>Then the current antenna phase is considered to have a jump;
(ii) When (when)When the current phase satisfies +.>Then the subsequent antenna n+1 phase is considered to jump, where a is the fitting factor;
(3) Processing jumping points
Periodically processing the jumping points, i.e. ifWhen the phase is backward, 2 pi is subtracted from all phases, otherwise, 2 pi is added to ensure the continuity of the phases;
(4) Repeating the above judgment until the whole phase is continuous to obtain the actual phase after expansion
Step 3.4: phase regression fitting
Establishing an optimization model to carry out regression fitting on the unfolded intermediate frequency signal phase, taking the distance R and the angle theta of each target object as decision variables, and enabling the predicted phase of the antenna to be maximally approximate to the unfolded actual phase through an optimization algorithmFor the kth object, selecting a Mean Square Error (MSE) as a regression evaluation index, and optimizing the object model as follows:
the decision variables R and theta are optimized through an optimization algorithm, only the search is needed in the range of the estimated resolution, the change range is smaller, the solution can be carried out by adopting an exhaustion method, and the solution can also be carried out by adopting a gradient descent method or other optimization methods.
When the angle of the target is largerThe phase difference between the antennas is approximately +.>Thus the phase distribution of the antenna array is a straight line with a slope of +.>The slope is used as an optimization target to be calculated more simply and rapidly, so the optimization target model can be as follows:
wherein the method comprises the steps ofUnwrapping phase for antenna>Is due to noise>Is not a straight line, can be fitted by least squares>Is used to determine the slope of the (c) for the (c),
and the optimized results R and theta are the final estimated positions of the target objects.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the frequency modulation continuous wave radar super-resolution positioning algorithm based on phase regression, super-resolution positioning is carried out on a moving target object, fourier transformation is combined with isolated point detection and a life algorithm, the distance resolution and the angle resolution of the target object are improved, the position judgment of the object is more accurate, the calculation complexity is reduced, and meanwhile the robustness of the algorithm is improved.
(2) According to the invention, an intermediate frequency signal of a target object is obtained through FMCW radar positioning, a two-dimensional fast Fourier transform is used for carrying out noise reduction on the intermediate frequency signal to obtain a two-dimensional distance-angle spectrum, a Laplacian operator is used for carrying out isolated point detection, a Rife algorithm is used for correcting the intermediate frequency, and the corrected frequency is used for calculating the angle and distance of the target object, so that the initial position of the target object is determined. Extracting the intermediate frequency signal phase of each antenna echo signal from the FFT spectrum, utilizing phase expansion to obtain the expanded actual phase, determining a regression optimization model, using a target optimization algorithm to enable the predicted phase of the antenna array to be maximally approximate to the actual phase of the antenna array, and obtaining the final position of the target object.
(3) According to the structure of the antenna array and carrier frequency parameters of radar transmitting signals, determining an expression of an intermediate frequency signal received by each antenna; denoising the intermediate frequency signal by using a two-dimensional Fast Fourier Transform (FFT) to obtain a two-dimensional distance-angle spectrum, performing isolated point peak detection on the two-dimensional spectrum by using a Laplacian operator to obtain estimated values of the frequency and the angle frequency of the intermediate frequency signal, correcting the intermediate frequency by using a Rife algorithm, calculating the distance and the angle of a target object by using the corrected frequency, thereby improving the positioning distance resolution, and determining the initial position of the target object; and then extracting the actual intermediate frequency phase of each antenna echo signal from the FFT spectrum, performing phase expansion to obtain a continuous phase distribution curve, establishing a regression optimization model as a regression objective function according to the relation between the position of the target object and the phase of the antenna array, using the distance and the angle as decision variables, using an optimization algorithm to enable the predicted phase of the antenna array to be maximally approximate to the actual phase of the antenna array, and determining the final position of the target object. Compared with the traditional frequency estimation algorithm, the FMCW radar super-resolution positioning algorithm provided by the invention has the advantages of low calculation complexity, good robustness, improved distance resolution and angle resolution, and higher positioning accuracy.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
FIG. 1 is an overall flow chart of a frequency modulated continuous wave radar super-resolution positioning method based on phase regression;
FIG. 2 is a schematic diagram of radar positioning in the frequency modulated continuous wave radar super-resolution positioning method based on phase regression according to the invention;
FIG. 3 is a graph of a two-dimensional distance-angle spectrum after two-dimensional discrete Fourier transform in the frequency modulated continuous wave radar super-resolution positioning method based on phase regression;
FIG. 4 is a schematic diagram of the object position after the isolated point detection in the frequency modulated continuous wave radar super-resolution positioning method based on phase regression according to the present invention;
FIG. 5 is a schematic diagram of the object position after being corrected by the Rife algorithm in the frequency modulation continuous wave radar super-resolution positioning method based on phase regression;
FIG. 6 is a schematic diagram of initial phases corresponding to a target object in the frequency modulated continuous wave radar super-resolution positioning method based on phase regression according to the present invention;
fig. 7 is a schematic diagram of phase jump of an antenna in the fm continuous wave radar super-resolution positioning method based on phase regression according to the present invention;
FIG. 8 is a schematic diagram of the fitting effect of the predicted phase and the actual phase of an object in the super-resolution positioning method of the frequency modulation continuous wave radar based on phase regression;
fig. 9 is a schematic diagram of a final fitting position of an object in the super-resolution positioning method of the fm continuous wave radar based on phase regression.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. Of course, the specific embodiments described herein are for purposes of illustration only and are not intended to limit the invention.
Example 1
Referring to fig. 1 to 9, the invention provides a frequency modulation continuous wave radar super-resolution positioning algorithm based on phase regression, which specifically comprises the following steps:
step 1: determining an intermediate frequency signal obtained by mixing a radar transmitting signal, a receiving signal and two signals in a chirp period, establishing a plane rectangular coordinate system by taking the center of an antenna array as an origin and the antenna array as an x-axis according to the structure of the antenna array and carrier frequency parameters of the radar transmitting signal, and determining an intermediate frequency mixed signal expression received by each antenna;
step 1.1: the expression for determining the frequency f (t) of the radar-transmitted signal in one chirp period is:
f(t)＝f 0 +γt,0≤t≤T
transmitted wave signal s TX (t)：
Where f (t) denotes the frequency of the radar transmission signal, s TX (t) represents a transmitted wave signal, A TX Representing the signal transmission power, f 0 Representing carrier frequency, gamma representing frequency modulation slope, T representing chirp period, j representing imaginary unit;
determining the radar passing distance as R 0 Is reflected by an object RX (t)：
Wherein s is RX (t) represents the radar passing distance R 0 A is a received signal after being reflected by an object RX Which is indicative of the received power of the signal,represents the receiving time delay, c represents the speed of light, R 0 Representing the distance of the object from the radar;
due to the transmitted signal s TX (t) and acceptance signal s RX (t) at [ tau ] 0 ,T]With overlap, the two signals are input into a mixer to obtain an intermediate frequency signal s IF (t)：
Wherein s is IF (t) is an intermediate frequency signal,is s RX Conjugate function of (t), intermediate frequency signal s IF (t) ignore τ 0 2 (τ 0 1) due to the frequency f of the intermediate frequency signal IF ＝γτ 0 Therefore->Step 1.2: taking the center of an antenna array as an origin, taking the antenna array as an x axis, establishing a plane rectangular coordinate system, and determining the coordinates of the (n+1) th antenna as (x) n ,y n ) Whereiny n ＝0，
n＝0,1,…,N a -1, wherein L is an equivalent virtual dayAperture of line array, N a Is the number of antenna arrays;
step 1.3: determining the kth object O k Distance from the center of the antenna array is R k And an included angle theta with the y axis k The object corresponds to the coordinates (X k ,Y k ) Wherein X is k ＝R k sinθ k ，Y k ＝R k cosθ k K=1, 2, …, K being the number of objects;
step 1.4: determining a receiving delay τ, namely:
wherein the method comprises the steps ofRepresents the distance from the (n+1) th antenna to the (k) th object;
step 1.5: determining the intermediate frequency signal s of the kth object received by the (n+1) th antenna n,k (t), namely:
wherein a is k Is the reflectivity of the object, gamma is the chirp rate, f 0 Is the carrier frequency of the signal,is a phase term;
step 1.6: determining that the radius of the antenna is far smaller than the object distance, and performing step 1.5 on the intermediate frequency signal s n,k Frequency term of (t)R in (a) n,k ≈R k The echo direction angles of all the antennas are approximately equal, so the optical path difference of the object reaching two adjacent antennas is dsin theta k Based on the 1 st antenna (n=0), R in the phase term n,k The writing is as follows:
R n,k ＝R 0,k +nd sinθ k ,n＝0，1，…N a -1
then the intermediate frequency signal s received by the n+1th antenna n Expression of (t):
wherein:the reflected signal intermediate frequency representing the kth object, k=1, 2, K;represents the angle-dependent frequency, +.>Represents the initial phase, R 0,k Representing the distance from the 1 st antenna to the kth object; step 1.7: determining that the intermediate frequency signal received by the (n+1) th antenna is a mixed signal z of the intermediate frequency signals with noise points of K target objects n (t), namely:
wherein omega n Representing noise, s n,k (t) is an intermediate frequency signal of the kth object received by the (n+1) th antenna;
step 2: denoising the received intermediate frequency signal by using a two-dimensional fast Fourier transform to obtain a two-dimensional distance-angle spectrum, detecting an isolated point peak value of the two-dimensional spectrum by using a Laplacian operator, correcting the intermediate frequency by using a life algorithm, and determining the initial position of a target object;
step 2.1: two-dimensional fourier transform (FFT) removes gaussian noise from the target echo signal:
(1) Sampling the intermediate frequency signal received from the antenna array in a chirp periodAt a distance of T s And converts the sampled data into two-dimensional intermediate frequency signal group S (n, t s )：
S(n,t s ),n＝0,1,2…N a -1,t s ＝0,1,2…,N t -1
Wherein the method comprises the steps ofINT represents rounding, each row of the two-dimensional intermediate frequency signal group is an intermediate frequency signal received by an antenna array at a certain moment t, and each row of the intermediate frequency signal is an intermediate frequency signal received by the antenna array at all sampling times in the period;
(2) For the intermediate frequency signal group S (n, t s ) Performing one-dimensional FFT (fast Fourier transform) on the row vector in the matrix to obtain FFT spectrum F (n, v):
(3) Performing one-dimensional FFT conversion again on the column vector in the FFT spectrum F (n, v) obtained in the step 2.1 (2) to obtain F (u, v), namely a two-dimensional FFT spectrum F (u, v) of the intermediate frequency signal group:
step 2.2: the process of detecting isolated points by a filtering method comprises the following steps:
(1) Detection is performed using a laplace check two-dimensional FFT spectrum:
wherein the partial derivative is calculated by second-order finite difference, namely:
(2) Determining T H Is a prescribed non-negative threshold value, Z is the filter in LaplaraResponse of the kernel center, if the absolute value of the response of the filter exceeds the threshold T at this point H It is considered that a point is detected at the center position (u, v) of the core, the response of this point at the center of the laplace core is denoted as Z (u, v), and when outputting a signal, such a point is marked as 1, and all the other points are marked as 0, so as to obtain the expression form of the output signal g (u, v), namely:
determining the number K of objects based on the number of isolated points, the position of which is (u) k ,v k ) Wherein u is k Is the peak value of the angular frequency corresponding to the kth object, v k Is the peak value of the intermediate frequency corresponding to the kth object, and the intermediate frequency f of each object is determined IF,k And an angle dependent frequency f d,k Is a function of the estimated value of (a):
wherein the intermediate frequency resolution Δf IF And angular frequency resolution Δf d The method comprises the following steps:
step 2.3: the life algorithm corrects the intermediate frequency process:
(1) Determining frequency resolution
(2) Finding the maximum f of frequencies in the FFT spectrum m And its corresponding index value f k ；
(3) Let the amplitude of the frequencies at k-1 and k+1 be f respectively k-1 、f k+1 ；
(4) The amplitude values at k-1 and k+1 are respectively judged to determine the frequency deviation value delta f The method comprises the following steps:
(5) Calculating intermediate frequency correction value
Correcting all the intermediate frequency by using five steps in the step 2.3 to obtain the corrected intermediate frequency of each object
Step 2.4: preliminary positioning is carried out on the target object according to the corrected frequency, and the distance estimated value of the target object kAnd angle estimate +.>The method comprises the following steps of:
substituting the spectral resolution to obtain the distance resolution R res And angular resolution theta res The method comprises the following steps of:
step 3: extracting the intermediate frequency signal phase of each antenna echo signal from the FFT spectrum, expanding the phase to obtain an expanded actual phase, determining a regression optimization model, using a target optimization algorithm to enable the predicted phase of the antenna array to be maximally approximate to the actual phase of the antenna array, and determining the final position of the target object;
step 3.1: extracting the intermediate frequency signal phase phi of each antenna from the FFT spectrum F (n, v) in step 2.1 (2) according to the intermediate frequency n,k ：
Wherein imag [ F (n, v) k )]Is F (n, v) k ) Is the imaginary part of real [ F (n, v) k )]Is F (n, v) k ) Of (F) (n, v) k ) Is the one-dimensional FFT spectrum of the kth object;
step 3.2: determining the predicted phase of the intermediate frequency signal according to the intermediate frequency signal expression in the step 1.5Is represented by the expression:
when the angle of the object is small (θ k When the angle is less than or equal to 5 DEG, the change of the antenna phase is small, the distribution is a curve, when theta k At > 5 deg., the phase change is large, and the distribution is approximately a straight line.
Step 3.3: phase unwrapping
When the angle of the target object is relatively large, the intermediate frequency signal phase phi obtained in step 3.1 n,k Will be within the interval [ -pi, pi]The inner fold is generated, thus causing discontinuous phase, and the phase expansion is needed, and the steps are as follows:
(1) Based on predicted phaseEstimating the phase difference of adjacent two antennas +.>
/>
(2) Determining the phase jump point position (i) asIf the phase difference of adjacent antennasThen the current antenna phase is considered to have a jump;
(ii) When (when)When the current phase satisfies +.>Then the subsequent antenna n+1 phase is considered to jump, where a is the fitting factor;
(3) Processing jumping points
Periodically processing the jumping points, i.e. ifWhen the phase is backward, 2 pi is subtracted from all phases, otherwise, 2 pi is added to ensure the continuity of the phases;
(4) Repeating the above judgment until the whole phase is continuous to obtain the actual phase after expansionStep 3.4: phase regression fitting
Establishing an optimization model to carry out regression fitting on the unfolded intermediate frequency signal phase, taking the distance R and the angle theta of each target object as decision variables, and enabling the predicted phase of the antenna to be maximally approximate to the unfolded actual phase through an optimization algorithmFor the kth object, selectThe variance (MSE) is used as a regression evaluation index, and the optimization target model is as follows:
the decision variables R and theta are optimized through an optimization algorithm, only the search is needed in the range of the estimated resolution, the change range is smaller, the solution can be carried out by adopting an exhaustion method, and the solution can also be carried out by adopting a gradient descent method or other optimization methods.
When the angle of the target is largerThe phase difference between the antennas is approximately +.>Thus the phase distribution of the antenna array is a straight line with a slope of +.>The slope is used as an optimization target to be calculated more simply and rapidly, so the optimization target model can be as follows:
wherein the method comprises the steps ofUnwrapping phase for antenna>Is due to noise>Is not a straight line, can be fitted by least squares>Is used to determine the slope of the (c) for the (c),
and the optimized results R and theta are the final estimated positions of the target objects.
To verify the effect of the present embodiment, positioning simulation verification and formation adjustment simulation verification are performed.
Fig. 1 is an overall flowchart of a frequency modulated continuous wave radar super resolution positioning algorithm based on phase regression.
FIG. 2 is a schematic diagram of radar positioning, using the center of an antenna array as the origin, the antenna array as the x-axis, and the perpendicular to the antenna array as the y-axis to establish a planar rectangular coordinate system, N a The equivalent virtual antenna arrays are uniformly arranged on the x axis.
Fig. 3 is a two-dimensional distance-angle spectrogram obtained after the intermediate frequency signal group is primarily denoised through two-dimensional Fast Fourier Transform (FFT), and the number of target objects is primarily determined to be two from fig. 3.
Fig. 4 is a diagram of the object position obtained after performing outlier detection on the intermediate frequency signal group subjected to preliminary noise reduction, wherein the target objects are located at different distances right in front of the radar. At this time, R 0,1 ＝5.990m，R 0,2 =6.011 m, polar coordinates are (5.990,0 °), (6.011,0 °).
FIG. 5 is a diagram of the object position obtained by correcting the intermediate frequency signal frequency by the Rife algorithm for both objects, and R at this time is known after the Rife algorithm correction 0,1 ＝6.011m，R 0,2 Polar coordinates are (6.011, -0.414 °), (6.091, -0.395 °), respectively, = 6.091 m.
Fig. 6 is a schematic diagram of initial phases corresponding to two target objects, and the phases of the two objects do not show bilateral symmetry, so that a certain deviation still exists between the direction angles of the two target objects, and further judgment and correction are needed.
Fig. 7 is a schematic diagram of phases drawn according to an intermediate frequency signal calculation formula, and it can be found from fig. 7 that phases of some antennas generate hops between-pi and pi, that is, there are hopping points, and phase unwrapping is required to ensure continuity of a phase fitting curve.
Fig. 8 is a schematic diagram of the fitting effect of the predicted phase and the actual phase of the target object, after the phase expansion, the predicted phase approaches the actual phase of the object infinitely, and the predicted phase and the actual phase have no error basically, so that the actual position of the object can be calculated according to the predicted phase.
FIG. 9 is a final fitting position diagram of target objects, the distances of the target objects obtained from the predicted phases are R 0,1 ＝6.011m，R 0,2 = 6.091m, polar coordinates (6.011, -0.207 °) (6.091,0.197 °).
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (4)

1. A frequency modulation continuous wave radar super-resolution positioning method based on phase regression is characterized by comprising the following steps:
step 1: determining an intermediate frequency signal obtained by mixing a radar transmitting signal, a receiving signal and two signals in a chirp period, establishing a plane rectangular coordinate system by taking the center of an antenna array as an origin and the antenna array as an x-axis according to the structure of the antenna array and carrier frequency parameters of the radar transmitting signal, and determining an intermediate frequency mixed signal expression received by each antenna;
step 2: denoising the received intermediate frequency signal by using a two-dimensional fast Fourier transform to obtain a two-dimensional distance-angle spectrum, detecting an isolated point peak value of the two-dimensional spectrum by using a Laplacian operator, correcting the intermediate frequency by using a Rife algorithm, and finally determining the initial position of a target object;
step 3: extracting the intermediate frequency signal phase of each antenna echo signal from the one-dimensional FFT spectrum, expanding the phase to obtain the expanded actual phase, establishing a regression optimization model, enabling the predicted phase of the antenna array to maximally approximate to the actual phase by using a target optimization algorithm, and determining the final position of the target object.
2. The method for super-resolution positioning of a fm continuous wave radar based on phase regression according to claim 1, wherein said step 1 comprises the steps of:
step 1.1: the expression for determining the frequency f (t) of the radar-transmitted signal in one chirp period is:
f(t)＝f 0 +γt,0≤t≤T
transmitted wave signal s TX (t)：
Where f (t) denotes the frequency of the radar transmission signal, s TX (t) represents a transmitted wave signal, A TX Representing the signal transmission power, f 0 Representing carrier frequency, gamma representing frequency modulation slope, T representing chirp period, j representing imaginary unit;
determining the radar passing distance as R 0 Is reflected by an object RX (t)：
Wherein s is RX (t) represents the radar passing distance R 0 A is a received signal after being reflected by an object RX Which is indicative of the received power of the signal,represents the receiving time delay, c represents the speed of light, R 0 Representing the distance of the object from the radar;
due to the transmitted signal s TX (t) and received signal s RX (t) at [ tau ] 0 ,T]With overlap, the two signals are input into a mixer to obtain an intermediate frequency signal s IF (t)：
Wherein s is IF (t) is an intermediate frequency signal,is s RX Conjugate function of (t), intermediate frequency signal s IF (t) ignore τ 0 2 Term, since the frequency of the intermediate frequency signal is f IF ＝γτ 0 Therefore->
Step 1.2: taking the center of an antenna array as an origin, taking the antenna array as an x axis, establishing a plane rectangular coordinate system, and determining the coordinates of the (n+1) th antenna as (x) n ,y n ) WhereinWhere L is the aperture of the equivalent virtual antenna array, N a Is the number of antenna arrays;
step 1.3: determining the kth object O k Distance from the center of the antenna array is R k And an included angle theta with the y axis k The object corresponds to the coordinates (X k ,Y k ) Wherein X is k ＝R k sinθ k ，Y k ＝R k cosθ k K=1, 2, …, K being the number of objects;
step 1.4: determining a receiving delay τ, namely:
wherein the method comprises the steps ofRepresents the distance from the (n+1) th antenna to the (k) th object;
step 1.5: determining the intermediate frequency signal s of the kth object received by the (n+1) th antenna n,k (t), namely:
wherein a is k Is the reflectivity of the object, gamma is the chirp rate, f 0 Is the carrier frequency of the signal,is a phase term;
step 1.6: determining that the radius of the antenna is far smaller than the object distance, and performing step 1.5 on the intermediate frequency signal s n,k Frequency term of (t)R in (a) n,k ≈R k The echo direction angles of all the antennas are approximately equal, so the optical path difference of the object reaching two adjacent antennas is dsin theta k Based on the 1 st antenna (n=0), R in the phase term n,k The writing is as follows:
R n,k ＝R 0,k +nd sinθ k ,n＝0,1,…,N a -1
then the intermediate frequency signal s received by the n+1th antenna n Expression of (t):
wherein:the reflected signal intermediate frequency representing the kth object, k=1, 2, …, K;represents the angle-dependent frequency, +.>f 0 Represents the initial phase, R 0,k Representing the distance from the 1 st antenna to the kth object;
step 1.7: determining that the intermediate frequency signal received by the (n+1) th antenna is a mixed signal z of the intermediate frequency signals with noise points of K target objects n (t), namely:
wherein omega n Representing noise, s n,k And (t) is an intermediate frequency signal of the kth object received by the (n+1) th antenna.
3. The method for super-resolution positioning of a fm continuous wave radar according to claim 2, wherein said step 2 comprises the steps of:
step 2.1: the two-dimensional Fourier transform removes Gaussian noise in the target echo signal:
(1) Sampling the intermediate frequency signal received by the antenna array in a chirp period, wherein the sampling interval is T s And converts the sampled data into two-dimensional intermediate frequency signal group S (n, t s )：
S(n,t s ),n＝0,1,2…N a -1,t s ＝0,1,2…,N t -1
Wherein the method comprises the steps ofINT stands for rounding, two-dimensional intermediate frequency signal set S (n, t s ) Each of which is an antenna within the periodAll the intermediate frequency signals received by the sampling time, wherein each column is the intermediate frequency signal received by the antenna array at a certain time t;
(2) For the intermediate frequency signal group S (n, t s ) Performing one-dimensional FFT (fast Fourier transform) on the row vector in the matrix to obtain FFT spectrum F (n, v):
(3) Performing one-dimensional FFT conversion again on the column vector in the FFT spectrum F (n, v) obtained in the step 2.1 (2) to obtain F (u, v), namely a two-dimensional FFT spectrum F (u, v) of the intermediate frequency signal group:
step 2.2: the process of detecting isolated points by a filtering method comprises the following steps:
(1) Detection is performed using a laplace check two-dimensional FFT spectrum:
wherein the partial derivative is calculated by second-order finite difference, namely:
(2) Determining T H Is a prescribed non-negative threshold, Z is the response of the filter at the center of the Laplacian kernel, if the absolute value of the response of the filter exceeds the threshold T H It is considered that a point is detected at the center position Z (u, v) of the kernel, the response of this point at the center of the laplace kernel is denoted as Z (u, v), and when outputting a signal, such a point is marked as 1, and all the other points are marked as 0, resulting in a representation of the output signal g (u, v), namely:
determining the number K of objects based on the number of isolated points, the position of which is (u) k ,v k ) Wherein u is k Is the peak value of the angular frequency corresponding to the kth object, v k Is the peak value of the intermediate frequency corresponding to the kth object, and the intermediate frequency f of each object is determined IF,k And an angle dependent frequency f d,k Is a function of the estimated value of (a):
wherein the intermediate frequency resolution Δf IF And angular frequency resolution Δf d The method comprises the following steps:
step 2.3: the life algorithm corrects the intermediate frequency process:
(1) Determining frequency resolution
(2) Finding the maximum f of frequencies in the FFT spectrum m And its corresponding index value f k ；
(3) Let the amplitude of the frequencies at k-1 and k+1 be f respectively k-1 、f k+1 ；
(4) The amplitude values at k-1 and k+1 are respectively judged to determine the frequency deviation value delta f The method comprises the following steps:
(5) Calculating intermediate frequency correction value
Correcting all the intermediate frequency by using five steps in the step 2.3 to obtain the corrected intermediate frequency of each object
Step 2.4: preliminary positioning is carried out on the target object according to the corrected frequency, and the distance estimated value of the target object kAnd angle estimate +.>The method comprises the following steps of:
substituting the spectral resolution to obtain the distance resolution R res And angular resolution theta res The method comprises the following steps of:
4. the method for super-resolution positioning of a fm continuous wave radar according to claim 3, wherein said step 3 comprises the steps of:
step 3.1: extracting the intermediate frequency signal phase Φ of each antenna from the one-dimensional FFT spectrum F (n, v) in step (2) of step 2.1 according to the intermediate frequency n,k ：
Wherein imag [ F (n, v) k )]Is F (n, v) k ) Is the imaginary part of real [ F (n, v) k )]Is F (n, v) k ) Of (F) (n, v) k ) Is the one-dimensional FFT spectrum of the kth object;
step 3.2: determining the predicted phase of the intermediate frequency signal according to the intermediate frequency signal expression in the step 1.5Is represented by the expression:
when the angle theta of the target object k When the angle is less than or equal to 5 DEG, the phase change of the antenna is small, the distribution is a curve, when theta k At > 5 deg., the phase change is large, and the distribution is approximately a straight line;
step 3.3: phase unwrapping
When the angle of the target object is relatively large, the intermediate frequency signal phase phi obtained in step 3.1 n,k Will be within the interval [ -pi, pi]The inner fold is generated, thus causing discontinuous phase, and the phase expansion is needed, and the steps are as follows:
(1) Based on predicted phaseEstimating the phase difference of adjacent two antennas +.>
(2) Determining phase jump point positions
(i) When (when)If the phase difference of adjacent antennas is +>Then the current antenna phase is considered to have a jump;
(ii) When (when)When the current phase satisfies +.>Then the subsequent antenna n+1 phase is considered to jump, where a is the fitting factor;
(3) Processing jumping points
Periodically processing the jumping points, i.e. ifWhen the phase is backward, 2 pi is subtracted from all phases, otherwise, 2 pi is added to ensure the continuity of the phases;
(4) Repeating the above judgment until the whole phase is continuous to obtain the actual phase after expansion
Step 3.4: phase regression fitting
Establishing an optimization model to carry out regression fitting on the unfolded intermediate frequency signal phase, taking the distance R and the angle theta of each target object as decision variables, and enabling the predicted phase of the antenna to be maximally approximate to the unfolded actual phase through an optimization algorithmFor the kth object, selecting the mean square error as a regression evaluation index, and optimizing the object model as follows:
min:
the distance variable R and the angle variable theta are optimized through an optimization algorithm, only the range of the estimated resolution is required to be searched, the variation range is smaller, the solution is carried out by adopting an exhaustion method, and the solution is also carried out by adopting a gradient descent method or other optimization methods;
when the angle of the target is largerThe phase difference between the antennas is approximately +.>Thus the phase distribution of the antenna array is a straight line with a slope of +.>The slope is used as an optimization target to be calculated more simply and rapidly, so that the optimization target model is as follows:
min:
wherein the method comprises the steps ofUnwrapping phase for antenna>Is due to noise>Is not a straight line, fitting by least square>And optimizing the obtained results R and theta to obtain the final estimated position of the target object.
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