CN111505618A - Decoupling correction ranging method based on frequency estimation and suitable for field of vehicle-mounted millimeter wave radar - Google Patents

Decoupling correction ranging method based on frequency estimation and suitable for field of vehicle-mounted millimeter wave radar Download PDF

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CN111505618A
CN111505618A CN202010289645.7A CN202010289645A CN111505618A CN 111505618 A CN111505618 A CN 111505618A CN 202010289645 A CN202010289645 A CN 202010289645A CN 111505618 A CN111505618 A CN 111505618A
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frequency
time dimension
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distance
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CN111505618B (en
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黄永明
李杨
宋依欣
杨哲
倪天恒
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Southeast 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
    • 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
    • G01S13/08—Systems for measuring distance only
    • G01S13/32—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
    • G01S13/34—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal
    • 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
    • G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
    • G01S13/583—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves and based upon the Doppler effect resulting from movement of targets
    • G01S13/584—Velocity or trajectory determination systems; Sense-of-movement determination systems using transmission of continuous unmodulated waves, amplitude-, frequency-, or phase-modulated waves and based upon the Doppler effect resulting from movement of targets adapted for simultaneous range and velocity measurements
    • 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
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/93—Radar or analogous systems specially adapted for specific applications for anti-collision purposes
    • G01S13/931—Radar or analogous systems specially adapted for specific applications for anti-collision purposes of land vehicles
    • 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
    • G01S7/35—Details of non-pulse systems
    • G01S7/352—Receivers
    • 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
    • G01S7/35—Details of non-pulse systems
    • G01S7/352—Receivers
    • G01S7/356—Receivers involving particularities of FFT processing

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  • Remote Sensing (AREA)
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  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a decoupling correction distance measurement method based on frequency estimation, which is suitable for the field of vehicle-mounted millimeter wave radar and comprises the following steps that firstly, a complex modulation spectrum analysis technology is adopted to locally amplify a distance range concerned by people in a fast time dimension in combination with an actual application scene; then, aiming at the problem of coupling terms which are often ignored in the existing distance measurement scheme, distance-speed coupling and fast-time-slow-time coupling terms are removed through distance-Doppler two-dimensional combined processing and frequency domain interpolation correction, and the accuracy of distance measurement is further improved; in addition, the Jacobsen algorithm is adopted to carry out discrete spectrum correction, the accuracy is improved, meanwhile, the low calculation complexity and the real-time requirement are guaranteed, and the effectiveness and the performance superiority compared with other traditional schemes are proved by simulation results.

Description

Decoupling correction ranging method based on frequency estimation and suitable for field of vehicle-mounted millimeter wave radar
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a decoupling correction high-precision ranging method based on frequency estimation, which is suitable for the field of parameter estimation of a vehicle-mounted millimeter wave radar system.
Background
Typical advanced driver assistance applications such as Adaptive Cruise Control (ACC), Blind Spot Detection (BSD) and Forward Collision Warning (FCW) require high performance sensor based. Compared with other sensors such as a camera, an ultrasonic radar and a laser radar, the vehicle-mounted millimeter wave radar has an effect and a position which are difficult to replace in the field of unmanned driving due to small volume, low cost and all-weather adaptability, and is a hot point of research in academia and industry. Different transmitting waveforms have different characteristics and applicable scenes, and are main factors for determining the performance of the vehicle-mounted millimeter wave radar system. The linear frequency modulation continuous wave is relatively simple in signal generation and processing, can detect the distance and speed information of a target, does not have the distance blind area problem existing in a continuous wave radar, and is widely applied to vehicle-mounted millimeter wave radar products.
For a vehicle-mounted millimeter wave radar system, it is crucial to estimate the distance information of an object to be detected. In a vehicle-mounted FMCW system, a frequency estimation algorithm of Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) is adopted, the operation speed is high, and the method has the advantages of remarkable signal-to-noise ratio gain, insensitivity of algorithm parameters and the like for sinusoidal signals. However, the ranging algorithm based on FFT peak frequency estimation also has some problems, which can be summarized as (1) the frequency estimation resolution of FFT is limited by the number of sampling points, and finite length FFT has the problems of barrier effect and sector loss. (2) The peak frequency obtained by FFT of the beat signal has problems of fast-slow time coupling and range-speed coupling, that is, even if the frequency estimation is accurate, the range information estimation is inaccurate. On one hand, the problems of the barrier effect, the fan loss and the like are all caused by the inherent characteristics of the FFT, and influence is caused on the frequency estimation and the amplitude estimation of the peak position. Another aspect is the fast time-slow time linear coupling term that the phase of the beat signal of a chirped continuous wave radar system has, and the range-velocity coupling term that the fast time dimension FFT results in the peak frequency, i.e. an accurate frequency estimate does not imply an accurate range estimate.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems in the ranging scheme, the invention provides a high-precision ranging scheme based on ZFT. The frequency spectrum of a beat signal is locally refined by using complex modulation band selection spectrum analysis (ZFT), and a frequency estimation value is further corrected by using three spectral line peak values with the largest frequency spectrum after ZFT through a Jacobsen algorithm, so that the measurement accuracy is improved, the calculation complexity is low, the real-time processing is convenient, and the hardware and time limitation of a vehicle-mounted FMCW radar system is well met. For the influence of the coupling term, on one hand, a distance Doppler two-dimensional processing method is adopted, the unambiguous velocity information is extracted through slow time dimension FFT and ambiguity resolution processing, and the unambiguous velocity is used for distance velocity decoupling. On the other hand, aiming at the coupling of fast time and slow time, the phenomenon that the peak frequency of the fast time dimension shifts along with the slow time is solved by an interpolation correction method. On one hand, the distance information corresponding to frequency estimation is more accurate through correction of the coupling term, and meanwhile, the signal-to-noise ratio gain of two-dimensional FFT is improved, and the method is beneficial to the subsequent steps of arrival angle estimation and the like.
The technical scheme is as follows: a decoupling correction ranging method based on frequency estimation and suitable for the field of vehicle-mounted millimeter wave radars comprises the following steps:
step 1: establishing a mathematical model of echo signals of the millimeter wave vehicle-mounted radar system to obtain expressions of transmitting signals, receiving signals and beat signals;
step 2: the method comprises the steps that an orthogonal double-channel receiving signal is adopted by a system to be considered, discrete sampling is carried out on the orthogonal double-channel receiving signal, and a discrete form y (m, n) of a complex beat signal is obtained under the condition that a coupling term is considered;
and step 3: carrying out fast time dimension complex modulation spectrum analysis (ZFT) on the discrete form complex beat signal obtained in the step (2) to obtain a complex beat signal Y (k, n) after spectrum refinement;
and 4, step 4: correcting the coupling of the fast time dimension and the slow time dimension in the fast time dimension by utilizing a simplified frequency domain correction scheme on the Y (k, n) obtained in the step 3;
and 5: for the complex beat signal obtained in step 4 after removing the coupling term in the fast-slow time dimension
Figure BDA0002449892430000021
The Jacobsen algorithm is adopted, three spectral lines with the largest FFT frequency spectrum are used for correcting the fast time dimension peak frequency corresponding to the target distance to a certain degree, and the corrected fast time dimension peak frequency is obtained
Figure BDA0002449892430000022
Step 6: performing a slow time dimension FFT operation on the echo signal, using the peak frequency of the slow time dimension
Figure BDA0002449892430000023
And (5) correcting the distance-speed coupling to obtain a final distance estimation value.
Further, in step 1, a mathematical model of an echo signal of the millimeter wave vehicle-mounted radar system is established to obtain expressions of a transmitting signal, a receiving signal and a beat signal, and the method comprises the following steps:
the wave form of the transmitting signal of the millimeter wave vehicle-mounted radar system is a group of carrier frequency f0In the transmitting period, a plurality of transmitting antennas transmit linear frequency modulation continuous wave signals with certain frequency sweep bandwidth in a time-sharing mode in sequence, and at the time t, the ith frequency sweep period transmits a signal xt(t, i) the expression is:
Figure BDA0002449892430000024
wherein, i is 1,2Sa，A,f0,
Figure BDA0002449892430000025
Respectively, amplitude of transmitted signal, carrier frequency and initial phase，μ＝B0T is the chirp rate, B0Is the sweep bandwidth, T is the period of a chirp continuous wave, NsaWhen t is 0, the radial distance from the target vehicle in front of the radar is r, the target with the radial speed v is positive in the direction in which the radial speed and the radar distance are decreasing, so that the received signal x isrThe expression of (t, i) can be written as:
Figure BDA0002449892430000031
wherein A is0Is the amplitude of the received signal, τ is 2(r-vt)/c is the time delay caused by the distance between the target and the radar, c is the speed of light, the received signal and the original transmitting signal are mixed, and the intermediate frequency signal, also called beat signal, is obtained by the low-pass filter, at time t, the expression y of the i-th periodic beat signali(t) can be written as:
Figure BDA0002449892430000032
time η -t-iT within a single transmission period is referred to as fast time η, the time between different transmission periods
Figure BDA00024498924300000311
Referred to as slow time, the above equation can be organized as:
Figure BDA0002449892430000033
if in the above formula c is considered-2And
Figure BDA0002449892430000036
if the term is negligible, then the fast time dimension is FFT, resulting in fast time dimension peak frequencies for r and v as:
Figure BDA0002449892430000034
similarly, if the FFT is performed on the slow time dimension, the peak frequency of the slow time dimension with respect to v is obtained as:
Figure BDA0002449892430000035
further, in step 2, the system is considered to adopt the orthogonal dual-channel received signal, and discrete sampling is performed on the orthogonal dual-channel received signal, so as to obtain a discrete form y (m, n) of the complex beat signal under the condition that the coupling term is considered, and the method is as follows:
obtained from step 1
Figure BDA0002449892430000037
The expression of (b) shows that the coupling can be divided into two aspects, namely distance-velocity coupling: distance and velocity coupling term of-2 vf0The other side is fast time slow time coupling: the fast-time and slow-time coupling is mainly formed by
Figure BDA0002449892430000038
In
Figure BDA0002449892430000039
Due to the term, we only consider here
Figure BDA00024498924300000310
While not counting η2Influence of item because of η2The presence of the term mainly has an effect on the fast time FFT itself, independent of coupling.
Considering the number of fast time dimension sampling points as N for a single sawtooth wave frequency sweep periodsTransmitting N within one coherent processing cyclesaNumber of sampling points in sawtooth, i.e. slow time dimension, NsaConsider that the system uses an orthogonal two-channel received signal, which is orthogonally transformed to obtain a discrete form y (m, n) of the complex beat signal under consideration of the coupling term:
Figure BDA0002449892430000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002449892430000042
is a constant independent of time, fs＝T/NsIs the sampling frequency of the fast time dimension, f s11/T is the sampling frequency of the slow time dimension, fc-2 μ v/c is the coefficient of the fast time slow time coupling term.
Further, in step 3, fast time-dimension complex modulation spectrum analysis (ZFFT) is performed on the discrete-form complex beat signal Y (m, n) obtained in step 2 to obtain a complex beat signal Y (k, n) after spectrum refinement, and the method is as follows:
(3.1) Complex modulation Shift frequency
In the millimeter wave vehicle-mounted radar system, the distance between the target and the radar is usually within a specific distance range, or the linear distance range between the target and the vehicle-mounted radar can be judged through other prior information, and the fast time dimension peak frequency corresponding to the distance range is f1～f2If the center frequency of the band to be observed is fm＝(f2-f1) 2, for the complex beat signal y (m, n)
Figure BDA0002449892430000043
Carrying out complex modulation to obtain a frequency shift signal y1(m,n)：
Figure BDA0002449892430000044
Figure BDA0002449892430000045
Wherein Y (k, n) is a frequency domain signal corresponding to Y (m, n),
Figure BDA0002449892430000046
center frequency fmCorresponding line number Lc＝fmA/Δ f, a line spacing Δ f ═ fs/NsTherefore, the discrete Fourier change Y of the signal after complex modulation is determined by the frequency shift property of DFT1(k, n) should satisfy:
Y1(k,n)＝Y(k+Lc,n)
that is to say the centre frequency f after complex modulationmShifted to zero frequency;
(3.2) Low pass Filtering
In order to prevent aliasing of a frequency band component of interest by an unnecessary frequency band caused after a reduction in sampling frequency, anti-aliasing filtering is first required, and a frequency refinement multiple D ═ f is defineds/(f2-f1) The cut-off frequency of the low-pass filter is fe＝fs2D, where the output of the filter is:
Figure BDA0002449892430000051
where h (k) is the frequency response function of an ideal low-pass filter, the time domain signal output by the filter is:
Figure BDA0002449892430000052
(3.3) resampling
To obtain Y2The part of the refined frequency spectrum near the (k, n) zero frequency can be reduced to f by adopting a resampling modesThe original sampling points are sampled once every D (D is a positive integer), and the expression of the re-sampled signal is y3(m,n)＝y2(Dm,n)；
(3.4) Complex FFT processing
N is carried out on the resampled signalsFFT of the points, get y3(m, n) has a frequency spectrum of
Figure BDA0002449892430000053
(3.5) spectral modification
The obtained NsShifting the frequency of the strip spectral line to the actual frequency to obtain a frequency band after ZFFT refinement:
Figure BDA0002449892430000054
from the above formula, it can be seen that the analysis of the complex frequency modulation refining band selection spectrum reflects that the local refining is performed in a certain frequency range, and the reduction of the distance measurement precision caused by the fence effect is compensated under the condition of not increasing the number of sampling points.
Further, in step 4, the Y (k, n) obtained in step 3 is corrected in the fast time dimension by using a simplified frequency domain correction scheme, and the method is as follows:
from the step (3.5), it can be seen that the N is obtained after the complex modulation band selection analysis ZFFT is subjected to spectral line adjustmentsObtaining N after direct pair fast time dimension FFT of root spectral linesThe discrete spectral lines are the same, so the expression of Y (k, n) in step 3 can be calculated as follows:
Figure BDA0002449892430000061
in the above formula, sa (x) represents a sampling function, which is defined as sa (x) sin (x)/x, and it can be seen from the above formula that the FFT is followed by the FFT in the fast time dimension
Figure BDA0002449892430000062
When the peak position of (a) is ω ═ 0, the deviation Δ k (N) of the peak position due to coupling and the fast time are in a linear relationship, and the slope is Nsfc/fsfs1。
The peak position deviation delta k (n) is corrected by replacing Y (k, n) with Y (k + delta k (n), the influence of a coupling term is eliminated by sampling a sinc function interpolation mode, and the interpolated signal is called as
Figure BDA0002449892430000063
The formula for interpolation of the sinc function along the fast time dimension is:
Figure BDA0002449892430000064
in the formula
Figure BDA0002449892430000065
Figure BDA0002449892430000066
And round [. C]Rounding, P is the number of sinc interpolation kernels, if the interpolation result is accurate, then
Figure BDA0002449892430000067
The expression of (a) is approximately written as:
Figure BDA0002449892430000071
further, in step 5, the complex beat signal obtained in step 4 after removing the coupling term in the fast time-slow time dimension is processed
Figure BDA0002449892430000072
The Jacobsen algorithm is adopted, three spectral lines with the largest FFT frequency spectrum are used for correcting the fast time dimension peak frequency corresponding to the target distance to a certain degree, and the corrected fast time dimension peak frequency is obtained
Figure BDA0002449892430000073
The method comprises the following steps:
recording the received signal after the coupling correction
Figure BDA0002449892430000074
Maximum spectral line position number kdRepresenting the relative deviation of the actual peak frequency of the fast time dimension of the received signal from the corresponding frequency of the maximum spectral line, the actual peak frequency f of the fast time dimension of the signalr,vCan be expressed as fr,v＝(kd+)fs/NsThen, according to the Jacobsen algorithm, the relative deviation estimation of the actual peak frequency of the received signal in the fast time dimension and the frequency corresponding to the maximum spectral line
Figure BDA0002449892430000075
Can be calculated using the following formula:
Figure BDA0002449892430000076
in the formula, real (-) is operated to obtain the real peak frequency f of the signalr,vIs estimated value of
Figure BDA0002449892430000077
Can be written as:
Figure BDA0002449892430000078
further, in step 6, a slow time dimension FFT operation is performed on the echo signal, and the peak frequency f of the slow time dimension is utilizedvAnd (3) correcting the distance-velocity coupling to obtain a final distance estimation value, wherein the method comprises the following steps:
(6.1) performing slow time dimension FFT on the received echo signals processed in the step 1-5 to obtain a peak frequency estimation of the slow time dimension
Figure BDA0002449892430000079
(6.2) utilizing the fast time dimension peak frequency estimation value obtained in the step 5
Figure BDA00024498924300000710
And (6.1) Peak frequency estimation in the Slow time dimension
Figure BDA00024498924300000711
Calculating distance without coupling correction
Figure BDA0002449892430000081
And velocity
Figure BDA0002449892430000082
(possibly blurred) estimates:
Figure BDA0002449892430000083
Figure BDA0002449892430000084
(6.3) obtaining the unambiguous speed estimation of the target by using a multi-frequency or multi-carrier equal speed ambiguity resolution method
Figure BDA0002449892430000085
(6.4) utilization of
Figure BDA0002449892430000086
Decoupling correction is carried out on the distance to obtain the final distance estimation
Figure BDA0002449892430000087
Figure BDA0002449892430000088
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention discloses a decoupling correction high-precision distance measurement method technology based on frequency estimation, which is suitable for the field of parameter estimation of vehicle-mounted millimeter wave radar systems. The simulation result proves the effectiveness and the performance superiority compared with other traditional schemes.
Drawings
FIG. 1 shows the variation of the miss-detection rate with distance in the embodiment of the present invention, with a target speed of 10 m/s;
FIG. 2 is a diagram showing the variation of the undetected rate with distance according to the embodiment of the present invention, wherein the target speed is 40 m/s;
FIG. 3 is a diagram illustrating the variation of the average error of distance estimation with distance according to an embodiment of the present invention, wherein the target speed is 10 m/s;
FIG. 4 shows the average error of the distance estimation as a function of the distance according to the embodiment of the present invention, and the target speed is 40 m/s.
Detailed Description
The present invention is further illustrated by the following examples, which are intended to be purely exemplary of the invention and are not intended to limit its scope, as various equivalent modifications of the invention will become apparent to those skilled in the art after reading the present invention and fall within the scope of the appended claims.
The invention provides a decoupling correction ranging method based on frequency estimation, which is suitable for the field of vehicle-mounted millimeter wave radars and comprises the following steps:
step 1: establishing a mathematical model of echo signals of the millimeter wave vehicle-mounted radar system to obtain expressions of transmitting signals, receiving signals and beat signals;
step 2: the method comprises the steps that an orthogonal double-channel receiving signal is adopted by a system to be considered, discrete sampling is carried out on the orthogonal double-channel receiving signal, and a discrete form y (m, n) of a complex beat signal is obtained under the condition that a coupling term is considered;
and step 3: carrying out fast time dimension complex modulation spectrum analysis (ZFT) on the discrete form complex beat signal obtained in the step (2) to obtain a complex beat signal Y (k, n) after spectrum refinement;
and 4, step 4: correcting the coupling of the fast time dimension and the slow time dimension in the fast time dimension by utilizing a simplified frequency domain correction scheme on the Y (k, n) obtained in the step 3;
and 5: for the complex beat signal obtained in step 4 after removing the coupling term in the fast-slow time dimension
Figure BDA0002449892430000091
Adopting a Jacobsen algorithm, and utilizing three spectral lines with maximum FFT frequency spectrum to align the target distanceCorrecting to a certain extent from the corresponding fast time dimension peak frequency to obtain the corrected fast time dimension peak frequency
Figure BDA0002449892430000092
Step 6: performing a slow time dimension FFT operation on the echo signal, using the peak frequency of the slow time dimension
Figure BDA0002449892430000093
And (5) correcting the distance-speed coupling to obtain a final distance estimation value.
Further, in step 1, a mathematical model of an echo signal of the millimeter wave vehicle-mounted radar system is established to obtain expressions of a transmitting signal, a receiving signal and a beat signal, and the method comprises the following steps:
the wave form of the transmitting signal of the millimeter wave vehicle-mounted radar system is a group of carrier frequency f0In the transmitting period, a plurality of transmitting antennas transmit linear frequency modulation continuous wave signals with certain frequency sweep bandwidth in a time-sharing mode in sequence, and at the time t, the ith frequency sweep period transmits a signal xt(t, i) the expression is:
Figure BDA0002449892430000094
wherein, i is 1,2Sa，A,f0,
Figure BDA0002449892430000095
Respectively, amplitude of the transmitted signal, carrier frequency and initial phase, mu ═ B0T is the chirp rate, B0Is the sweep bandwidth, T is the period of a chirp continuous wave, NsaWhen t is 0, the radial distance from the target vehicle in front of the radar is r, the target with the radial speed v is positive in the direction in which the radial speed and the radar distance are decreasing, so that the received signal x isrThe expression of (t, i) can be written as:
Figure BDA0002449892430000096
wherein A is0Is the amplitude of the received signal, τ is 2(r-vt)/c is the time delay caused by the distance between the target and the radar, c is the speed of light, the received signal and the original transmitting signal are mixed, and the intermediate frequency signal, also called beat signal, is obtained by the low-pass filter, at time t, the expression y of the i-th periodic beat signali(t) can be written as:
Figure BDA0002449892430000101
time η -t-iT within a single transmission period is referred to as fast time η, the time between different transmission periods
Figure BDA0002449892430000106
Referred to as slow time, the above equation can be organized as:
Figure BDA0002449892430000102
if in the above formula c is considered-2And
Figure BDA0002449892430000107
if the term is negligible, then the fast time dimension is FFT, resulting in fast time dimension peak frequencies for r and v as:
Figure BDA0002449892430000103
similarly, if the FFT is performed on the slow time dimension, the peak frequency of the slow time dimension with respect to v is obtained as:
Figure BDA0002449892430000104
further, in step 2, the system is considered to adopt the orthogonal dual-channel received signal, and discrete sampling is performed on the orthogonal dual-channel received signal, so as to obtain a discrete form y (m, n) of the complex beat signal under the condition that the coupling term is considered, and the method is as follows:
obtained from step 1
Figure BDA0002449892430000108
The expression of (b) shows that the coupling can be divided into two aspects, namely distance-velocity coupling: distance and velocity coupling term of-2 vf0The other side is fast time slow time coupling: the fast-time and slow-time coupling is mainly formed by
Figure BDA0002449892430000109
In
Figure BDA00024498924300001010
Due to the term, we only consider here
Figure BDA00024498924300001011
While not counting η2Influence of item because of η2The presence of the term mainly has an effect on the fast time FFT itself, independent of coupling.
Considering the number of fast time dimension sampling points as N for a single sawtooth wave frequency sweep periodsTransmitting N within one coherent processing cyclesaNumber of sampling points in sawtooth, i.e. slow time dimension, NsaConsider that the system uses an orthogonal two-channel received signal, which is orthogonally transformed to obtain a discrete form y (m, n) of the complex beat signal under consideration of the coupling term:
Figure BDA0002449892430000105
in the formula (I), the compound is shown in the specification,
Figure BDA0002449892430000111
is a constant independent of time, fs＝T/NsIs the sampling frequency of the fast time dimension, f s11/T is the sampling frequency of the slow time dimension, fc-2 μ v/c is the coefficient of the fast time slow time coupling term.
Further, in step 3, fast time-dimension complex modulation spectrum analysis (ZFFT) is performed on the discrete-form complex beat signal Y (m, n) obtained in step 2 to obtain a complex beat signal Y (k, n) after spectrum refinement, and the method is as follows:
(3.1) Complex modulation Shift frequency
In the millimeter wave vehicle-mounted radar system, the distance between the target and the radar is usually within a specific distance range, or the linear distance range between the target and the vehicle-mounted radar can be judged through other prior information, and the fast time dimension peak frequency corresponding to the distance range is f1～f2If the center frequency of the band to be observed is fm＝(f2-f1) 2, to complex beat signal
Figure BDA0002449892430000112
Carrying out complex modulation to obtain a frequency shift signal y1(m,n)：
Figure BDA0002449892430000113
Figure BDA0002449892430000114
Wherein Y (k, n) is a frequency domain signal corresponding to Y (m, n),
Figure BDA0002449892430000115
center frequency fmCorresponding line number Lc＝fmA/Δ f, a line spacing Δ f ═ fs/NsTherefore, the discrete Fourier change Y of the signal after complex modulation is determined by the frequency shift property of DFT1(k, n) should satisfy:
Y1(k,n)＝Y(k+Lc,n)
that is to say the centre frequency f after complex modulationmShifted to zero frequency;
(3.2) Low pass Filtering
In order to prevent aliasing of a frequency band component of interest by an unnecessary frequency band caused after a reduction in sampling frequency, anti-aliasing filtering is first required, and a frequency refinement multiple D ═ f is defineds/(f2-f1) The cut-off frequency of the low-pass filterIs fe＝fs2D, where the output of the filter is:
Figure BDA0002449892430000116
where h (k) is the frequency response function of an ideal low-pass filter, the time domain signal output by the filter is:
Figure BDA0002449892430000121
(3.3) resampling
To obtain Y2The part of the refined frequency spectrum near the (k, n) zero frequency can be reduced to f by adopting a resampling modesThe original sampling points are sampled once every D (D is a positive integer), and the expression of the re-sampled signal is y3(m,n)＝y2(Dm,n)；
(3.4) Complex FFT processing
N is carried out on the resampled signalsFFT of the points, get y3(m, n) has a frequency spectrum of
Figure BDA0002449892430000122
(3.5) spectral modification
The obtained NsShifting the frequency of the strip spectral line to the actual frequency to obtain a frequency band after ZFFT refinement:
Figure BDA0002449892430000123
from the above formula, it can be seen that the analysis of the complex frequency modulation refining band selection spectrum reflects that the local refining is performed in a certain frequency range, and the reduction of the distance measurement precision caused by the fence effect is compensated under the condition of not increasing the number of sampling points.
Further, in step 4, the Y (k, n) obtained in step 3 is corrected in the fast time dimension by using a simplified frequency domain correction scheme, and the method is as follows:
from the step (3.5), it can be seen that the N is obtained after the complex modulation band selection analysis ZFFT is subjected to spectral line adjustmentsObtaining N after direct pair fast time dimension FFT of root spectral linesThe discrete spectral lines are the same, so the expression of Y (k, n) in step 3 can be calculated as follows:
Figure BDA0002449892430000131
in the above formula, sa (x) represents a sampling function, which is defined as sa (x) sin (x)/x, and it can be seen from the above formula that the FFT is followed by the FFT in the fast time dimension
Figure BDA0002449892430000132
When the peak position of (a) is ω ═ 0, the deviation Δ k (N) of the peak position due to coupling and the fast time are in a linear relationship, and the slope is Nsfc/fsfs1。
The peak position deviation delta k (n) is corrected by replacing Y (k, n) with Y (k + delta k (n), the influence of a coupling term is eliminated by sampling a sinc function interpolation mode, and the interpolated signal is called as
Figure BDA0002449892430000133
The formula for interpolation of the sinc function along the fast time dimension is:
Figure BDA0002449892430000134
in the formula
Figure BDA0002449892430000135
Figure BDA0002449892430000136
And round [. C]Rounding, P is the number of sinc interpolation kernels, if the interpolation result is accurate, then
Figure BDA0002449892430000137
The expression of (a) is approximately written as:
Figure BDA0002449892430000141
further, in step 5, the complex beat signal obtained in step 4 after removing the coupling term in the fast time-slow time dimension is processed
Figure BDA00024498924300001411
The Jacobsen algorithm is adopted, three spectral lines with the largest FFT frequency spectrum are used for correcting the fast time dimension peak frequency corresponding to the target distance to a certain degree, and the corrected fast time dimension peak frequency is obtained
Figure BDA0002449892430000142
The method comprises the following steps:
recording the received signal after the coupling correction
Figure BDA0002449892430000143
Maximum spectral line position number kdRepresenting the relative deviation of the actual peak frequency of the fast time dimension of the received signal from the corresponding frequency of the maximum spectral line, the actual peak frequency f of the fast time dimension of the signalr,vCan be expressed as fr,v＝(kd+)fs/NsThen, according to the Jacobsen algorithm, the relative deviation estimation of the actual peak frequency of the received signal in the fast time dimension and the frequency corresponding to the maximum spectral line
Figure BDA0002449892430000144
Can be calculated using the following formula:
Figure BDA0002449892430000145
in the formula, real (-) is operated to obtain the real peak frequency f of the signalr,vIs estimated value of
Figure BDA0002449892430000146
Can be written as:
Figure BDA0002449892430000147
further, in step 6, a slow time dimension FFT operation is performed on the echo signal, and the peak frequency f of the slow time dimension is utilizedvAnd (3) correcting the distance-velocity coupling to obtain a final distance estimation value, wherein the method comprises the following steps:
(6.1) performing slow time dimension FFT on the received echo signals processed in the step 1-5 to obtain a peak frequency estimation of the slow time dimension
Figure BDA0002449892430000148
(6.2) utilizing the fast time dimension peak frequency estimation value obtained in the step 5
Figure BDA0002449892430000149
And (6.1) Peak frequency estimation in the Slow time dimension
Figure BDA00024498924300001410
Calculating distance without coupling correction
Figure BDA0002449892430000151
And velocity
Figure BDA0002449892430000152
(possibly blurred) estimates:
Figure BDA0002449892430000153
Figure BDA0002449892430000154
(6.3) obtaining the unambiguous speed estimation of the target by using a multi-frequency or multi-carrier equal speed ambiguity resolution method
Figure BDA0002449892430000155
(6.4) utilization of
Figure BDA0002449892430000156
Decoupling correction is carried out on the distance to obtain the final distance estimation
Figure BDA0002449892430000157
Figure BDA0002449892430000158
In the part, a target distance estimation simulation platform is built according to actual vehicle-mounted millimeter wave radar system parameters to verify the effectiveness of the proposed high-precision ranging algorithm. The performance of four different ranging schemes is compared, the first scheme is a decoupling correction high-precision ranging method based on frequency estimation and suitable for the field of parameter estimation of vehicle-mounted millimeter wave radar systems, the second scheme is different from the first scheme in that a Jacobsen algorithm is not adopted to compensate straddle loss, the third scheme is that distance estimation is carried out only by adopting a frequency spectrum peak value after complex modulation band selection analysis, and the fourth scheme is that distance estimation is carried out directly through FFT peak value frequency. Other system parameters of the four schemes are the same, and main simulation parameter settings of the system are shown in table 1. The range of the target is 30-90m, the azimuth angle and the elevation angle are 10 degrees and 0 degree respectively, and the radar scattering sectional area is 30 dBsm. We analyzed and compared the performance of the four solution distance estimation solutions at target speeds of 10m/s and 40m/s, respectively.
Table 1: system parameter setting
Figure BDA0002449892430000159
FIG. 1 and FIG. 2 show the variation of the false drop rate of a target with distance when the target speed is 10m/s and 40m/s, respectively. As can be seen from fig. 1, when the target speed is relatively small, the influence on the distance estimation is relatively small, and the target missed detection rates of the four ranging schemes are all maintained at a relatively low probability. The difference of the missed detection rate between the four ranging schemes is small, and the missed detection rate of the original ranging scheme is slightly higher than that of the other schemes only after the position of the target exceeds 70m (when the amplitude of the received signal is small). Meanwhile, as can be seen from fig. 2, when the target speed is high, due to the coupling of the fast time and the slow time dimension, for different slow time dimension units, the peak frequency after fast time dimension FFT falls on different distance units, and the larger the speed is, the more obvious the distance migration phenomenon is, the level of the accumulated signal-to-noise ratio after two-dimensional FFT deteriorates, and further the constant false alarm detection cannot be passed. The omission factor of the original scheme is greatly increased, and the omission factor reaches 20% when the target is far away. Meanwhile, thanks to the frequency band refinement and decoupling operations, the signal-to-noise ratio degradation phenomena of other distance estimation schemes are relieved and compensated to a certain extent, so that the missed detection rates of the other three distance measurement schemes are generally maintained at a very low probability, and the performance superiority of the high-precision distance measurement scheme provided by the invention is not very obvious from the viewpoint of the missed detection rate.
FIG. 3 and FIG. 4 show the average error of distance estimation as a function of distance for target speeds of 10m/s and 40m/s, respectively. On one hand, as can be seen from the comparison between fig. 3 and fig. 4, when the target speed is relatively small, the average ranging errors of the four ranging schemes are relatively small, and the difference between the ranging errors of the schemes is relatively small. It is explained that the estimation of the target distance parameter in the vehicle-mounted millimeter wave radar system is related to the target speed, and the larger the speed is, the larger the influence on the distance estimation is. On the other hand, as can be seen from fig. 3 or fig. 4, the ranging scheme proposed herein has the smallest ranging average error, and the performance is improved significantly compared to the original scheme of performing the range estimation through the peak frequency. The complex modulation spectrum refinement, the coupling correction and the Jacobsen algorithm play a role in more accurately measuring the distance, and the coupling correction plays a most obvious role in improving the distance measuring performance. This is because both the complex modulation band-select analysis and the Jacobsen algorithm are essentially improvements to the FFT algorithm, solving the problem of the fence effect or the fan-shaped loss, and the space for improvement is limited when the spectral resolution of the system itself is high. The coupling correction technology solves the problems of range migration and main lobe widening for the correction of fast time and slow time coupling and improves the accumulated signal-to-noise ratio, and the correction for the distance speed coupling is a feedback correction for the original distance estimation, the coupling distance is firstly obtained, and then the compensation is carried out through the accurate estimation of the speed parameter. The correction operation of the coupling term can be performed from the simulation result, which is particularly important when the target speed is high. In the vehicle-mounted millimeter wave radar system, the speed of the target is usually the relative speed between the vehicle to be detected and the target, and the speed range can reach-30 m/s to 60m/s, so that it is necessary to adopt the improved ranging scheme proposed herein to perform more accurate ranging in the speed range.

Claims (7)

1. A decoupling correction ranging method based on frequency estimation and suitable for the field of vehicle-mounted millimeter wave radars is characterized by comprising the following steps:
step 1: establishing a mathematical model of echo signals of the millimeter wave vehicle-mounted radar system to obtain expressions of transmitting signals, receiving signals and beat signals;
step 2: the method comprises the steps that an orthogonal double-channel receiving signal is adopted by a system to be considered, discrete sampling is carried out on the orthogonal double-channel receiving signal, and a discrete form y (m, n) of a complex beat signal is obtained under the condition that a coupling term is considered;
and step 3: carrying out fast time-dimensional complex modulation spectrum analysis on the discrete complex beat signal obtained in the step 2 to obtain a complex beat signal Y (k, n) after spectrum refinement;
and 4, step 4: correcting the coupling of the fast time dimension and the slow time dimension in the fast time dimension by utilizing a simplified frequency domain correction scheme on the Y (k, n) obtained in the step 3;
and 5: for the complex beat signal obtained in step 4 after removing the coupling term in the fast-slow time dimension
Figure FDA0002449892420000011
The Jacobsen algorithm is adopted, three spectral lines with the largest FFT frequency spectrum are used for correcting the fast time dimension peak frequency corresponding to the target distance to a certain degree, and the corrected fast time dimension peak frequency is obtained
Figure FDA0002449892420000012
Step 6: performing a slow time dimension FFT operation on the echo signal, using the peak frequency of the slow time dimension
Figure FDA0002449892420000013
And (5) correcting the distance-speed coupling to obtain a final distance estimation value.
2. The decoupling correction ranging method based on frequency estimation applicable to the field of vehicle-mounted millimeter wave radars as claimed in claim 1, wherein in step 1, a mathematical model of echo signals of a millimeter wave vehicle-mounted radar system is established to obtain expressions of transmitting signals, receiving signals and beat signals, and the method comprises the following steps: the wave form of the transmitting signal of the millimeter wave vehicle-mounted radar system is a group of carrier frequency f0In the transmitting period, a plurality of transmitting antennas transmit linear frequency modulation continuous wave signals with certain frequency sweep bandwidth in a time-sharing mode in sequence, and at the time t, the ith frequency sweep period transmits a signal xt(t, i) the expression is:
Figure FDA0002449892420000014
wherein, i is 1,2Sa，A,f0,
Figure FDA0002449892420000015
Respectively, amplitude of the transmitted signal, carrier frequency and initial phase, mu ═ B0T is the chirp rate, B0Is the sweep bandwidth, T is the period of a chirp continuous wave, NsaWhen t is 0, the radial distance from the target vehicle in front of the radar is r, the target with the radial speed v is positive in the direction in which the radial speed and the radar distance are decreasing, so that the received signal x isrThe expression of (t, i) can be written as:
Figure FDA0002449892420000021
wherein A is0Is the amplitude of the received signal, τ is 2(r-vt)/c is the time delay caused by the distance between the target and the radar, c is the speed of light, the received signal and the original transmitting signal are mixed, and the intermediate frequency signal, also called beat signal, is obtained by the low-pass filter, at time t, the expression y of the i-th periodic beat signali(t) can be written as:
Figure FDA0002449892420000022
time η -t-iT within a single transmission period is referred to as fast time η, the time between different transmission periods
Figure FDA0002449892420000026
Referred to as slow time, the above equation can be organized as:
Figure FDA0002449892420000023
if in the above formula c is considered-2And
Figure FDA0002449892420000027
if the term is negligible, then the fast time dimension is FFT, resulting in fast time dimension peak frequencies for r and v as:
Figure FDA0002449892420000024
similarly, if the FFT is performed on the slow time dimension, the peak frequency of the slow time dimension with respect to v is obtained as:
Figure FDA0002449892420000025
3. the decoupling correction ranging method based on frequency estimation in the field of vehicle-mounted millimeter wave radar according to claim 2, wherein in the step 2, the system is considered to adopt orthogonal dual-channel received signals, and discrete sampling is performed on the signals, so as to obtain the discrete form y (m, n) of the complex beat signal under the condition that the coupling term is considered, and the method is as follows:
obtained from step 1
Figure FDA0002449892420000028
The expression of (b) shows that the coupling can be divided into two aspects, namely distance-velocity coupling: distance and velocity coupling term of-2 vf0The other side is fast time slow time coupling: the fast-time and slow-time coupling is mainly formed by
Figure FDA0002449892420000029
In
Figure FDA00024498924200000210
Caused by an item, only consider
Figure FDA00024498924200000211
While not counting η2The influence of the item;
considering the number of fast time dimension sampling points as N for a single sawtooth wave frequency sweep periodsTransmitting N within one coherent processing cyclesaNumber of sampling points in sawtooth, i.e. slow time dimension, NsaConsider that the system uses an orthogonal two-channel received signal, which is orthogonally transformed to obtain a discrete form y (m, n) of the complex beat signal under consideration of the coupling term:
Figure FDA0002449892420000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002449892420000035
is a constant independent of time, fs＝T/NsIs the sampling frequency of the fast time dimension, fs11/T is sampling frequency of slow time dimensionRate, fc-2 μ v/c is the coefficient of the fast time slow time coupling term.
4. The decoupling correction ranging method based on frequency estimation in the field of vehicle-mounted millimeter wave radar as claimed in claim 3, wherein in step 3, fast time-dimension complex modulation spectrum analysis (ZFFT) is performed on the discrete complex beat signal Y (m, n) obtained in step 2 to obtain the complex beat signal Y (k, n) after spectrum refinement, and the method is as follows:
(3.1) Complex modulation Shift frequency
Judging the linear distance range between the target and the vehicle-mounted radar through prior information, wherein the fast time dimension peak frequency corresponding to the distance range is f1～f2If the center frequency of the band to be observed is fm＝(f2-f1) 2, for the complex beat signal y (m, n)
Figure FDA0002449892420000036
Carrying out complex modulation to obtain a frequency shift signal y1(m,n)：
Figure FDA0002449892420000032
Figure FDA0002449892420000037
Wherein Y (k, n) is a frequency domain signal corresponding to Y (m, n),
Figure FDA0002449892420000033
center frequency fmCorresponding line number Lc＝fmA/Δ f, a line spacing Δ f ═ fs/NsTherefore, the discrete Fourier change Y of the signal after complex modulation is determined by the frequency shift property of DFT1(k, n) should satisfy:
Y1(k,n)＝Y(k+Lc,n)
that is to say the centre frequency f after complex modulationmShifted to zero frequency;
(3.2) Low pass Filtering
Firstly, anti-aliasing filtering is needed, and a frequency refinement multiple D ═ f is defineds/(f2-f1) The cut-off frequency of the low-pass filter is fe＝fs2D, where the output of the filter is:
Figure FDA0002449892420000034
where h (k) is the frequency response function of an ideal low-pass filter, the time domain signal output by the filter is:
Figure FDA0002449892420000041
(3.3) resampling
To obtain Y2The part of the refined frequency spectrum near the (k, n) zero frequency can be reduced to f by adopting a resampling modesD, namely resampling the original sampling points every D, wherein D is a positive integer, and obtaining a resampled signal expression y3(m,n)＝y2(Dm,n)；
(3.4) Complex FFT processing
N is carried out on the resampled signalsFFT of the points, get y3The spectrum of (m, n) is:
Figure FDA0002449892420000042
(3.5) spectral modification
The obtained NsShifting the frequency of the strip spectral line to the actual frequency to obtain a frequency band after ZFFT refinement:
Figure FDA0002449892420000043
5. the decoupling calibration method based on frequency estimation applied to the field of vehicle-mounted millimeter wave radar according to claim 4A positive high-precision method, characterized in that in step 4, a simplified frequency domain correction scheme is used for Y (k, n) obtained in step 3, and correction of fast-time-slow-time dimension coupling is performed in the fast-time dimension, the method being as follows: from the step (3.5), it can be seen that the N is obtained after the complex modulation band selection analysis ZFFT is subjected to spectral line adjustmentsObtaining N after direct pair fast time dimension FFT of root spectral linesThe discrete spectral lines are the same, so the expression of Y (k, n) in step 3 can be calculated as follows:
Figure FDA0002449892420000051
in the above formula, sa (x) represents a sampling function, which is defined as sa (x) sin (x)/x, and it can be seen from the above formula that the FFT is performed in the fast time dimension
Figure FDA0002449892420000052
When the peak position of (a) is ω ═ 0, the deviation Δ k (N) of the peak position due to coupling and the fast time are in a linear relationship, and the slope is Nsfc/fsfs1；
The peak value position deviation delta k (n) is corrected by replacing Y (k, n) with Y (k + delta k (n), the influence of a coupling term is eliminated by sampling a sinc function interpolation mode, and the interpolated signal is called as
Figure FDA0002449892420000057
The formula for interpolation of the sinc function along the fast time dimension is:
Figure FDA0002449892420000053
in the formula
Figure FDA0002449892420000054
Figure FDA0002449892420000055
And round [. C]Rounding, P is the number of sinc interpolation kernels, if the interpolation result is accurate, then
Figure FDA0002449892420000056
The expression of (a) is approximately written as:
Figure FDA0002449892420000061
6. the decoupling correction ranging method based on frequency estimation in the field of vehicle-mounted millimeter wave radar as claimed in claim 5, wherein in step 5, the complex beat signal obtained in step 4 after the fast-slow time dimension coupling term is removed is subjected to the step
Figure FDA0002449892420000062
The Jacobsen algorithm is adopted, three spectral lines with the largest FFT frequency spectrum are used for correcting the fast time dimension peak frequency corresponding to the target distance to a certain degree, and the corrected fast time dimension peak frequency is obtained
Figure FDA0002449892420000063
The method comprises the following steps: recording the received signal after the coupling correction
Figure FDA0002449892420000064
Maximum spectral line position number kdRepresenting the relative deviation of the actual peak frequency of the fast time dimension of the received signal from the corresponding frequency of the maximum spectral line, the actual peak frequency f of the fast time dimension of the signalr,vCan be expressed as fr,v＝(kd+)fs/NsThen, according to the Jacobsen algorithm, the relative deviation estimation of the actual peak frequency of the received signal in the fast time dimension and the frequency corresponding to the maximum spectral line
Figure FDA0002449892420000065
Can be calculated using the following formula:
Figure FDA0002449892420000066
in the formula, real (-) is operated to obtain the real peak frequency f of the signalr,vIs estimated value of
Figure FDA0002449892420000067
Can be written as:
Figure FDA0002449892420000068
7. the decoupling correction high-precision ranging method based on frequency estimation in the field of parameter estimation of millimeter wave radar systems on vehicles according to claim 6, wherein in step 6, a slow time dimension FFT operation is performed on the echo signal, and a peak frequency f of the slow time dimension FFT operation is utilizedvAnd (3) correcting the distance-velocity coupling to obtain a final distance estimation value, wherein the method comprises the following steps:
(6.1) performing slow time dimension FFT on the received echo signals processed in the step 1-5 to obtain a peak frequency estimation of the slow time dimension
Figure FDA0002449892420000069
(6.2) utilizing the fast time dimension peak frequency estimation value obtained in the step 5
Figure FDA0002449892420000071
And (6.1) Peak frequency estimation in the Slow time dimension
Figure FDA0002449892420000072
Calculating distance without coupling correction
Figure FDA0002449892420000073
And velocity
Figure FDA0002449892420000074
Estimated value of (a):
Figure FDA0002449892420000075
Figure FDA0002449892420000076
(6.3) obtaining the unambiguous speed estimation of the target by using a multi-frequency or multi-carrier equal speed ambiguity resolution method
Figure FDA0002449892420000077
(6.4) utilization of
Figure FDA0002449892420000078
Decoupling correction is carried out on the distance to obtain the final distance estimation
Figure FDA0002449892420000079
Figure FDA00024498924200000710
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