CN109471095B - FMCW radar distance estimation method based on fast iterative interpolation - Google Patents

FMCW radar distance estimation method based on fast iterative interpolation Download PDF

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CN109471095B
CN109471095B CN201811310159.8A CN201811310159A CN109471095B CN 109471095 B CN109471095 B CN 109471095B CN 201811310159 A CN201811310159 A CN 201811310159A CN 109471095 B CN109471095 B CN 109471095B
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CN109471095A (en
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王伟
段永昌
黄平
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Harbin Engineering University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S13/00Systems 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
    • G01S13/02Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06Systems determining position data of a target
    • G01S13/08Systems for measuring distance only
    • G01S13/32Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated

Abstract

The invention relates to an FMCW radar distance estimation algorithm based on fast iterative interpolation, which aims at the problem that the ranging precision of an on-vehicle anti-collision radar in a multi-target environment is easily interfered by frequency spectrums. The algorithm provided by the simulation verification has higher estimation accuracy in a multi-target environment and under the condition of low signal to noise ratio. And finally, the algorithm is realized by DSP, and the algorithm is proved to meet the requirement of real-time property and is easy to realize in engineering.

Description

FMCW radar distance estimation method based on fast iterative interpolation
Technical Field
The invention relates to an FMCW radar distance estimation algorithm, in particular to an FMCW radar distance estimation algorithm based on fast iterative interpolation, belongs to the technical field of millimeter wave radars and the field of signal processing, and particularly relates to interference among multiple targets.
Background
Frequency Modulated Continuous Wave (FMCW) radar has good speed and distance measuring performance, and thus is widely applied to the aspects of unmanned driving, medical monitoring, channel estimation and the like. However, the conventional FMCW radar has the problems of fence effect and spectrum leakage, which causes large estimation deviation of the distance. For more accurate estimation of the target distance, the current common methods are: a sampling sequence direct zero padding method, a Zoom Fast Fourier Transform (ZFFT) method based on complex modulation, a Fourier Transform-Discrete-time Fourier Transform (FFT-DTFT) combined correction method, a Chirp-Z Transform, and the like. However, the above four methods have the disadvantages of large calculation amount, large estimation error and the like.
In recent years, some frequency estimation methods based on maximum likelihood estimation have been proposed, which can also be used for distance estimation. The document (an improved ZFT algorithm for improving the LFMCW radar ranging accuracy, 2015, (2): 1-4.) provides an iterative interpolation algorithm under a single target signal, and the deviation is gradually corrected in the iterative process by using an interpolation result; the literature (Accurate Frequency Estimators,2007,24 (1): 123-125.) proposes a Frequency deviation correction method based on Discrete Fourier Transform (DFT) samples, which does not need iteration and directly estimates the deviation by using the adjacent spectral peak with the target; on the basis, a deviation correction factor is added in a document (A Method For Fine Resolution timing From Three DFT Samples, IEEE Signal Processing Letters,2011,18 (6): 351-354), so that the precision is improved, but the problem of non-uniform Estimation error exists; the document (frequency iterative interpolation estimation algorithm based on the refined frequency spectrum, electronic and informatics newspaper, 2017,39 (9): 2141-2147.) proposes a method for interpolating signals by using the refined frequency spectrum, thereby solving the problem of non-uniform estimation errors. The method proposed by the above document has a good effect on the deviation estimation of the single-frequency signal, but when the method is applied to a multi-target environment, the deviation of the distance estimation is increased due to inter-spectrum interference. In order to solve the problem, the literature (DFT Interpolation Algorithm for Kaiser-Bessel and Dolph-Chebyshev Windows, IEEE Transactions on Instrumentation & Measurement,2011,60 (3): 784-790) proposes a method for compensating estimation deviation based on high-order polynomial Interpolation, and the method uses high-order polynomial to fit the frequency spectrum of the signal to obtain the accurate frequency value of each target, but the Algorithm has large calculation amount and is not beneficial to hardware implementation. The document (Fine resolution frequency estimation from the same DFT samples: case of windowed data, signal Processing,2015,114 (1): 245-250.) proposes a method for suppressing spectral interference by windowing, and a window function is used for suppressing interference of sidelobes, but the method proposed by the document has the problem that spectral broadening influences estimation performance. In the field of DOA estimation, the literature (Fast iterative polarized beamforming for acquisition single-snapshot DOA estimation, IEEE Geoscience and Remote Sensing Letters,2017,14 (4): 574-578) proposes a method for iteratively and gradually correcting angular deviation, which can avoid the problem of spectrum broadening and solve the interference between multiple target angles, but the method applied to an FMCW radar system has the following problems: in the course of rough estimation, the number of targets is used as prior information, and the original data is required to be corrected when each target spectral peak is estimated, thereby increasing the complexity of the algorithm.
The invention provides an improved FMCW radar distance estimation algorithm based on fast iterative interpolation, which is inspired by solving the spectrum interference under the condition of multiple targets by the iterative correction idea, roughly estimates the position of the target by a constant false alarm detection method to solve the problem that the number of the targets is used as prior information, and replaces the process of repeatedly correcting the original data by using a correction deviation factor in the iterative process. The invention is used for solving the problem of inter-spectrum interference in a multi-target environment, in particular to a method which can eliminate the inter-spectrum interference of multiple targets and obtain more accurate target reflection signal frequency and target distance. The processing process is simplified, and the hardware implementation is facilitated. Theoretical simulation and actual measurement data verify the feasibility of the algorithm.
Disclosure of Invention
In view of the above prior art, the technical problem to be solved by the present invention is to provide an FMCW radar distance estimation algorithm based on fast iterative interpolation, which can overcome the influence of interference between frequency spectrums in a multi-target environment on frequency estimation, so as to estimate the frequency deviation of a target by using the reflected signal of the target itself.
In order to solve the technical problem, the FMCW radar distance estimation algorithm based on fast iterative interpolation comprises the following steps:
step 1: carrying out Fourier transformation on the intermediate frequency signals after AD sampling, and then carrying out constant false alarm detection to estimate the number P of targets and the frequency spectrum unit m where the targets are located i ,i=1,2...P;
Step 2: calculating the spectral unit m of the ith target i Corresponding spectral cell deviation
Figure BDA0001854722580000021
i =1,2 \ 8230p, step 2 comprising the steps of:
step 2.1: setting a target iteration number Q, and enabling the current iteration number Q =0; deviation estimate for ith target after single iteration
Figure BDA0001854722580000022
And amplitude estimator
Figure BDA0001854722580000023
Carry out initialization to
Figure BDA0001854722580000024
i=1,2…P;
Step 2.2: estimating the reflected signal strength of the p-th target
Figure BDA0001854722580000025
p=1,2...P;
Step 2.3: by using
Figure BDA0001854722580000026
Calculating the frequency spectrum interference generated by the p target to the i target
Figure BDA0001854722580000027
Step 2.4: after calculating and removing interference
Figure BDA0001854722580000028
Spectral peaks of spectral units
Figure BDA0001854722580000029
Step 2.5: using spectral peaks
Figure BDA00018547225800000210
Calculating a deviation correction factor
Figure BDA00018547225800000211
Deviation from the spectral unit
Figure BDA00018547225800000212
Step 2.6: q ← Q +1, judging whether Q is smaller than Q, if Q is smaller than or equal to Q, repeating the steps 2.2-2.5; if Q is greater than Q, executing step 3;
and step 3: using spectral units m i And spectral unit deviation
Figure BDA0001854722580000031
Calculate the ithFrequency f of target reflected signal i And the distance value R of the target i
The invention also includes:
1. in step 1, the intermediate frequency signal after AD sampling is subjected to fourier transform expression as follows:
Figure BDA0001854722580000032
wherein s is b (N) represents an intermediate frequency signal after AD sampling, N represents the number of points of Fourier transform, S b (k) And expressing the amplitude of the kth unit in the frequency domain, and estimating that the expression of the target number P satisfies the following conditions:
P=Count{S b (k)>CFAR(S b (k))}
wherein CFAR (S) b (k) Represents a pair S b (k) The result of the constant false alarm detection, count represents the S pair b (k) Greater than CFAR (S) b (k) The number of the amplitude values is counted, and the counted result is the number of the targets;
the spectral unit m where the p-th target is located p The expression is as follows:
Figure BDA0001854722580000033
2. the number of iterations Q in step 2.1 is set to 2.
3. Intensity of reflected signal of p-th target in step 2.2
Figure BDA0001854722580000034
The estimated value expression of (c) satisfies:
Figure BDA0001854722580000035
wherein
Figure BDA0001854722580000036
Is the estimated value of the intensity of the reflected signal of the first target, and the initial value is 0,Δm pl Indicating the frequency spectrum unit m corresponding to the p-th target p Spectral unit m corresponding to the l-th target l At a distance in the frequency domain, the expression satisfies:
Δm pl =Δm p -Δm l
Δδ pl indicating the deviation of the spectrum unit corresponding to the p-th target
Figure BDA0001854722580000037
Deviation of spectral unit corresponding to the l-th target
Figure BDA0001854722580000038
The distance in the frequency domain is expressed as follows:
Δδ pl =Δδ p -Δδ l
4. step 2.3, the p-th target generates spectrum interference to the i-th target
Figure BDA0001854722580000039
The expression satisfies:
Figure BDA0001854722580000041
wherein Δ m ip Indicating the frequency spectrum unit m corresponding to the ith target i M of the spectrum unit corresponding to the p-th target p At a distance in the frequency domain, the expression satisfies:
Δm ip =Δm i -Δm p
Δδ ip indicating the deviation of the spectrum unit corresponding to the ith target
Figure BDA0001854722580000042
Deviation of spectral unit corresponding to p-th target
Figure BDA0001854722580000043
At a distance in the frequency domain, the expression satisfies:
Δδ ip =Δδ i -Δδ p
5. after the interference is removed in step 2.4
Figure BDA0001854722580000044
Spectral peaks of spectral units
Figure BDA0001854722580000045
The expression satisfies:
Figure BDA0001854722580000046
wherein S i,±0.5 Representing direct Fourier transform of an intermediate frequency signal
Figure BDA0001854722580000047
Spectral peak of spectral unit, S i,±0.5 The device consists of two parts: the ith target reflected signal is
Figure BDA0001854722580000048
The spectrum peak and the p target obtained by the Fourier transform of the spectrum unit generate spectrum interference on the i target, and the expression satisfies the following conditions:
Figure BDA0001854722580000049
6. deviation correction factor in step 2.5
Figure BDA00018547225800000410
Deviation from the spectral unit
Figure BDA00018547225800000411
The expressions respectively satisfy:
Figure BDA00018547225800000412
Figure BDA00018547225800000413
7. frequency f of ith target reflection signal in step 3 i And the distance value R of the target i The expressions respectively satisfy:
Figure BDA00018547225800000414
wherein f is s Is the AD sampling frequency, c is the speed of light, B is the bandwidth of the modulation, T is the period of the modulated triangular wave.
The invention has the beneficial effects that:
the method firstly estimates the number of the targets and the rough position of the targets by utilizing fast Fourier transform and combining a constant false alarm detection algorithm, then carries out non-uniform iterative interpolation on the frequency spectrum of the targets, and eliminates interference between the frequency spectrums in the process of each iteration, thereby obtaining more accurate distance.
Drawings
FIG. 1 is a block diagram of an FMCW radar system;
FIG. 2 is the distance root mean square error of the target 1 at different signal-to-noise ratios;
FIG. 3 is the distance root mean square error of the target 2 at different signal-to-noise ratios;
FIG. 4 is the effect of target 2 sampling point on distance root mean square error;
FIG. 5 is a plot of distance root mean square error for different algorithms under multiple objectives;
FIG. 6 is the result of a local refinement of the target 3;
FIG. 7 is the result of a local refinement of the target 8;
FIG. 8 is a real environment test chart;
FIG. 9 is an FMCW radar system;
fig. 10 is the result of FMCW radar output versus the target true distance.
Detailed Description
Let S be for convenience of description i =S b (m i ),S b (m i ) Represents the m-th in the frequency domain i Spectral peaks of the individual spectral units, then
Figure BDA0001854722580000051
The spectral peaks of individual spectral units can be expressed as:
Figure BDA0001854722580000052
the specific implementation mode for realizing the aim of the invention is as follows:
step 1: performing Fast Fourier Transformation (FFT) on the intermediate frequency signal after AD sampling, and then performing Constant False Alarm detection (CFAR) to estimate the number P of targets and the spectrum unit m where the targets are located i ,i=1,2...P。
Fourier transform expression is as follows
Figure BDA0001854722580000053
Wherein s is b (N) represents the intermediate frequency signal after AD sampling, N represents the number of points of FFT conversion, S b (k) Representing the amplitude of the k-th element in the frequency domain. By pair S b (k) The power level of the background noise is estimated by CFAR processing, and then S is calculated b (k) Comparing with the background noise power level to estimate the target number P, the expression is as follows
P=Count{S b (k)>CFAR(S b (k))}
Wherein CFAR (S) b (k) Represents a pair S b (k) The result of the constant false alarm detection, i.e. the background noise power, count represents the pair S b (k) Greater than CFAR (S) b (k) The number of the spectrum peaks is counted, and the counted result is the number of the targets. In addition, it is necessary to extract the spectrum unit where the target is located and use the extracted spectrum unit as the estimated spectrum unit deviation
Figure BDA0001854722580000061
And (4) a foundation.
The spectral unit m in which the p-th target is located p The expression is as follows
Figure BDA0001854722580000062
And 2, step: calculating the spectral unit m of the ith target i Corresponding deviation of spectral unit
Figure BDA0001854722580000063
i=1,2…P。
Step 2.1: setting a target iteration number Q, and enabling the current iteration number Q =0; deviation estimate for ith target after single iteration
Figure BDA0001854722580000064
And the intensity of the reflected signal of the ith target
Figure BDA0001854722580000065
Carry out initialization to
Figure BDA0001854722580000066
i=1,2…P。
The iteration times Q is set to be 2, experiments show that when Q is 2, high distance precision can be achieved, and the distance estimation precision is slightly influenced when multiple iterations are carried out. And when the iteration is performed for multiple times, only the calculated amount is increased, and the influence on the distance estimation precision is small.
Step 2.2: estimating the reflected signal strength of the p-th target
Figure BDA0001854722580000067
p=1,2...P。
Directly using intermediate frequency signals at
Figure BDA0001854722580000068
The spectrum peak obtained by FFT conversion of the spectrum unit comprises three parts: the p-th target reflection signal is processed by FFT to obtain the amplitude, and other target reflection signals are processed by FFT
Figure BDA0001854722580000069
Leakage of spectral cells and noise-to-amplitude interference, where the interference of noise has a less negligible effect on the spectral peaks. The first target is
Figure BDA00018547225800000610
The leakage of the spectrum unit can be reflected at the target through the target
Figure BDA00018547225800000611
The position of the frequency spectrum unit is obtained by FFT, and the expression is as follows
Figure BDA00018547225800000612
Wherein
Figure BDA00018547225800000613
Is an estimate of the reflected signal strength of the first target, with an initial value of 0,s bl And (n) represents an intermediate frequency signal reflected by the l target. Due to s bl (n) is not available, therefore
Figure BDA00018547225800000614
The process of the true value is also continuously approached by iterating the successive updates. Δ m pl Indicating the frequency spectrum unit m corresponding to the p-th target p M of the spectrum unit corresponding to the l-th target l The distance in the frequency domain is expressed as follows
Δm pl =Δm p -Δm l
Δδ pl Indicating the deviation of the spectrum unit corresponding to the p-th target
Figure BDA00018547225800000615
Deviation of spectral unit corresponding to the l-th target
Figure BDA00018547225800000616
The distance in the frequency domain is expressed as follows
Δδ pl =Δδ p -Δδ l
Thereby obtaining the reflected signal intensity of the p-th target
Figure BDA0001854722580000071
The expression is as follows:
Figure BDA0001854722580000072
step 2.3: by using
Figure BDA0001854722580000073
Calculating the frequency spectrum interference generated by the p target to the i target
Figure BDA0001854722580000074
The p target generates spectrum interference to the i target
Figure BDA0001854722580000075
Can pass through the p-th target intermediate frequency signal s bp (n) is in
Figure BDA0001854722580000076
The spectrum unit is obtained by FFT conversion, but s bp (n) is not directly available and therefore needs to be utilized
Figure BDA0001854722580000077
Obtaining
Figure BDA0001854722580000078
The expression is as follows
Figure BDA0001854722580000079
Wherein Δ m ip Indicating the frequency spectrum unit m corresponding to the ith target i M of the spectrum unit corresponding to the p-th target p The distance in the frequency domain is expressed as follows
Δm ip =Δm i -Δm p
Δδ ip Indicating the deviation of the spectrum unit corresponding to the ith target
Figure BDA00018547225800000710
Deviation of spectral unit corresponding to p-th target
Figure BDA00018547225800000711
The distance in the frequency domain is expressed as follows
Δδ ip =Δδ i -Δδ p
Step 2.4: after calculating and removing interference
Figure BDA00018547225800000712
Spectral peaks of spectral units
Figure BDA00018547225800000713
Directly making FFT on the intermediate frequency signal to obtain the spectrum peak S i,±0.5 ,S i,±0.5 The device consists of two parts: the ith target reflection signal is
Figure BDA00018547225800000714
The spectral peak obtained by FFT of the spectral unit and the p-th target reflection signal are FFT
Figure BDA00018547225800000715
Enhancement of spectral cells, from which
Figure BDA00018547225800000716
Expression (2)
Figure BDA00018547225800000717
Step 2.5: using spectral peaks
Figure BDA0001854722580000081
Calculating a deviation correction factor
Figure BDA0001854722580000082
Deviation from the spectral unit
Figure BDA0001854722580000083
Spectral peaks from step 2.4
Figure BDA0001854722580000084
Can be approximated as being present in the reflected signal only at the ith target
Figure BDA0001854722580000085
Spectral peaks of the spectral unit. Thus, a single target frequency estimation (Iterative frequency estimation by interpolation on Fourier coeffients [ J ] may be utilized]IEEE Transactions on Signal Processing,2005,53 (4): 1237-1242.) method to obtain the offset correction factor for the ith target
Figure BDA0001854722580000086
Deviation from the spectral unit
Figure BDA0001854722580000087
The expression is as follows
Figure BDA0001854722580000088
Figure BDA0001854722580000089
Step 2.5: q ← Q +1, judging whether Q is less than Q, if Q is less than or equal to Q, repeating steps 2.2-2.5
And updating Q after the current iteration frequency is Q each time of iteration is finished, and judging the relation between Q and the set iteration frequency Q.
And step 3: using spectral cells m i And spectral cell deviation
Figure BDA00018547225800000810
Calculating the frequency f of the ith target reflected signal i And the distance value R of the target i
When obtaining the deviation of the spectrum unit
Figure BDA00018547225800000811
Then, the real frequency spectrum unit corresponding to the ith target reflection signal
Figure BDA00018547225800000812
Thereby utilizing
Figure BDA00018547225800000813
Calculating a frequency value f corresponding to the ith target i From f i Obtaining the distance value R of the ith target by the relation of the distance i The expression is as follows
Figure BDA00018547225800000814
Wherein f is s Is the AD sampling frequency, c is the speed of light, B is the bandwidth of the modulation, T is the period of the modulated triangular wave.
To verify the performance of the algorithm, three typical methods were chosen For comparison, modified local-amplified Fourier algorithm (Zoom-FFT) (see the modified ZFT algorithm For improving LFMCW radar ranging accuracy, 2015, (2): 1-4.), non-iterative Frequency Estimation Method based on discrete Fourier transform (Candan algorithm) (see A Method For Fine Resolution Frequency Estimation From DFT Samples [ J ]. IEEE Signal Processing Letters,2011,18 (6): 351-354.), and spectral leakage suppression algorithm based on Hamming window (Hanming-window algorithm) (see the Fine Resolution Estimation From Samples: e of wired data [ J ]. Signal Processing, 114). The simulation effects of distance Root Mean Square Error (RMSE) under different Signal-to-Noise Ratio (SNR) conditions, RMSE of different algorithms under multiple targets and the like are mainly given.
The effect of the invention can be illustrated by the following simulations:
simulation conditions and contents:
simulation experiment using c 24.125GHz, bandwidth B250 MHz, signal period T8 us, sampling rate 95KHz, and FFT point number N512. Two targets in FIGS. 2 and 3Signal intensity of (b) satisfies A 2 =0.5A 1 . The signal strength of the two targets in FIG. 4 satisfies A 2 =0.5A 1 And SNR =15dB. Table 1 shows that the signal intensity varies in the range of A.epsilon. [0.3,1]Where a =1 indicates no signal loss on target reflection. The simulation experiments all adopt 5000 Monte-Carlo simulations.
As can be seen from fig. 2, the algorithm proposed herein has better estimation performance at the same SNR than the other three algorithms. Furthermore, the Zoom-FFT algorithm RMSE curve tends to be flat because the estimation accuracy of the algorithm is limited by the local refinement factor, resulting in the deviation value of the distance not varying with SNR.
As can be seen from fig. 3, the offset estimation of the target 2 by the proposed algorithm and the Candan algorithm has better performance, because both algorithms estimate the offset by the spectral peaks near the target, the peak values of the left and right adjacent spectral peaks caused by the interference of the target 1 are almost the same, and the offset correction factor is almost the same
Figure BDA0001854722580000091
Is less subject to peak variations, and therefore does not affect the bias
Figure BDA0001854722580000092
Therefore, the estimation performance of the two algorithms is better. In addition, the Hanming-window algorithm affects the estimation of the bias correction factor under the interference of the target 1, resulting in the failure of the distance estimation.
Fig. 4 is a graph of the effect of the number of signal sample points for target 2 on RMSE. From fig. 2, it can be seen that the Hanming-window algorithm and the Zoom-FFT algorithm have large error in the estimation of the bias under the condition, and therefore the Candan algorithm is selected for comparison. As can be seen from fig. 4, the simulation results of target 1 and target 2 are the same, so that only the simulation result of target 2 is given. As can be seen from the figure, the algorithm proposed herein can achieve smaller RMSE with a smaller number of iterations Q, and the RMSE is smaller with the same number of sample points.
Table 1 shows the simulation results for 10 targets whose signal strength ranges are a e [0.3,1], where a =1 indicates no signal loss when the target is reflected; it can be seen from the table that the signal amplitude has little influence on the estimation performance of the algorithm proposed herein, and in addition, it can be seen from the table that the distance difference between the targets 6, 7, 8 is less than 0.5m, and the estimation error of the algorithm for each target is small because the algorithm suppresses the influence of the spectral interference on the bias estimation in the iterative process.
TABLE 1 simulation parameters and results for multiple targets
Figure BDA0001854722580000101
FIG. 5 is an RMSE for various algorithms simulating the targets in Table 1. As can be seen from the figure, the estimation error of the algorithm proposed herein is stable below 10cm, the estimation error is more uniform and the RMSE is smaller compared with the other two algorithms, and it is found by combining the signal strength in table 1 that the estimation deviation of the algorithm proposed herein is less affected by the signal strength, because the spectrum change caused by the signal interference can be suppressed by the algorithm proposed herein, and the distance error estimated by the spectrum without interference is smaller. It can also be seen from the figure that the Zoom-FFT algorithm estimation error appears as a random error because the interpolation mode of Zoom-FFT is a uniform interpolation, the error is smaller as the spectral peak of the target is closer to the interpolation point, and the error is the largest when the spectral peak of the target just falls between the interpolation points.
Fig. 6 and 7 show the result of partially amplifying the targets 3 and 8, and the algorithms used are the algorithm proposed herein and the Zoom-FFT algorithm, and it can be seen from the figures that the accuracy can be improved by changing the number of iterations Q, and compared with the Zoom-FFT algorithm, the proposed algorithm is closer to the real frequency and has higher accuracy.
FIGS. 8 and 9 are actual environment test charts and FMCW radar hardware systems, respectively, with target 1 held stationary at 14.6m and target 2 at [8,10 ]]In the meantime, the test results of the FMCW radar for two target detection and the true values of the targets are shown in FIG. 10, where R is shifted every 0.2m real Representing the true distance value, R, of the object est Is the target distance estimated using the algorithm presented herein.
As can be seen from fig. 10, the FMCW radar output results are very close to the true range of the target and the error remains within 10 cm. In addition, FMCW radar data can be updated 20 times per second, proving that the algorithm fully meets the requirements of real-time.
The specific implementation mode of the invention also comprises the following steps:
step 1: performing Fast Fourier Transformation (FFT) on the intermediate frequency signal after AD sampling, and then performing Constant False Alarm Rate (CFAR) to estimate the number P of targets and the spectrum unit m where the targets are located i ,i=1,2...P。
And 2, step: calculating the spectral unit m of the ith target i Corresponding deviation of spectral unit
Figure BDA0001854722580000111
i=1,2…P。
Step 2.1: setting a target iteration number Q, and enabling the current iteration number Q =0; deviation estimate for ith target after single iteration
Figure BDA0001854722580000112
And amplitude estimator
Figure BDA0001854722580000113
Carry out initialization to
Figure BDA0001854722580000114
i=1,2…P。
Step 2.2: estimating the reflected signal strength of the p-th target
Figure BDA0001854722580000115
p=1,2...P;
Step 2.3: by using
Figure BDA0001854722580000116
Calculating the frequency spectrum interference generated by the p target to the i target
Figure BDA0001854722580000117
Step 2.4: after calculating and removing interference
Figure BDA0001854722580000118
Spectral peaks of spectral units
Figure BDA0001854722580000119
Step 2.5: using spectral peaks
Figure BDA00018547225800001110
Calculating a deviation correction factor
Figure BDA00018547225800001111
Deviation from the spectral unit
Figure BDA00018547225800001112
Step 2.6: q ← Q +1, judging whether Q is smaller than Q, if Q is not larger than Q, repeating steps 2.2-2.5.
And step 3: using spectral units m i And spectral cell deviation
Figure BDA00018547225800001113
Calculating the frequency f of the ith target reflected signal i And the distance value R of the target i
The expression of performing fourier transform on the intermediate frequency signal after AD sampling in the processing of step 1 is as follows
Figure BDA00018547225800001114
Wherein s is b (N) represents the intermediate frequency signal after AD sampling, N represents the number of points of FFT conversion, S b (k) Representing the amplitude of the k-th element in the frequency domain. The expression for estimating the target number P is as follows
P=Count{S b (k)>CFAR(S b (k))}
Wherein CFAR (S) b (k) Represents a pair S b (k) The result of the constant false alarm detection, count represents the S pair b (k) Greater than CFAR(S b (k) The number of the amplitude values is counted, and the counted result is the number of the targets.
The spectral unit m where the p-th target is located p The expression is as follows
Figure BDA00018547225800001115
In the step 2.1, the iteration number Q is set to be 2, experiments show that when Q is 2, high distance precision can be achieved, and the distance estimation precision is slightly influenced when multiple iterations are carried out.
Reflected signal strength of the p-th target in step 2.2
Figure BDA00018547225800001116
Is expressed as follows
Figure BDA0001854722580000121
Wherein
Figure BDA0001854722580000122
Is the estimated value of the intensity of the reflected signal of the first target, and the initial value is 0, Δ m pl Indicating the frequency spectrum unit m corresponding to the p-th target p Spectral unit m corresponding to the ith target l The distance in the frequency domain is expressed as follows
Δm pl =Δm p -Δm l
Δδ pl Indicating the deviation of the spectrum unit corresponding to the p-th target
Figure BDA0001854722580000123
Deviation of spectral unit corresponding to the l-th target
Figure BDA0001854722580000124
The distance in the frequency domain is expressed as follows
Δδ pl =Δδ p -Δδ l
Step 2.3 the p-th target generates spectrum interference to the i-th target
Figure BDA0001854722580000125
The expression is as follows
Figure BDA0001854722580000126
Wherein Δ m ip Indicating the frequency spectrum unit m corresponding to the ith target i M of the spectrum unit corresponding to the p-th target p The distance in the frequency domain is expressed as follows
Δm ip =Δm i -Δm p
Δδ ip Indicating the deviation of the spectrum unit corresponding to the ith target
Figure BDA0001854722580000127
Deviation of spectral unit corresponding to p-th target
Figure BDA0001854722580000128
The distance in the frequency domain is expressed as follows
Δδ ip =Δδ i -Δδ p
After the interference is removed in step 2.4
Figure BDA0001854722580000129
Spectral peaks of spectral units
Figure BDA00018547225800001210
The expression is as follows
Figure BDA00018547225800001211
Wherein S i,±0.5 Representation of direct FFT acquisition of an intermediate frequency signal
Figure BDA00018547225800001212
Spectral peak of spectral unit, S i,±0.5 The device consists of two parts: the ith target reflection signal is
Figure BDA00018547225800001213
The spectral peak obtained by FFT of the spectrum unit and the frequency spectrum interference of the p target to the i target are generated, and the expression is as follows
Figure BDA0001854722580000131
Deviation correction factor in step 2.5
Figure BDA0001854722580000132
Deviation from the spectral unit
Figure BDA0001854722580000133
The expression is as follows
Figure BDA0001854722580000134
Figure BDA0001854722580000135
Frequency f of ith target reflection signal in step 3 i And the distance value R of the target i The expression is as follows
Figure BDA0001854722580000136
Wherein f is s Is AD sampling frequency, c is light speed, B is frequency modulation bandwidth, T is frequency modulation triangle wave period
The invention provides an improved multi-target distance estimation algorithm based on iterative interpolation, aiming at the problem that the distance measurement precision of an on-vehicle anti-collision radar in a multi-target environment is easily interfered by frequency spectrums. The method comprises the steps of firstly estimating the number of targets and the rough position of the targets by utilizing fast Fourier transform and combining a constant false alarm detection algorithm, then carrying out non-uniform iterative interpolation on the frequency spectrum of the targets, and eliminating interference between the frequency spectrums in the process of each iteration, thereby obtaining more accurate distance. The algorithm provided by the simulation verification has higher estimation accuracy in a multi-target environment and under the condition of low signal to noise ratio. And finally, the algorithm is realized by DSP, and the algorithm is proved to meet the requirement of real-time property and is easy to realize in engineering.

Claims (8)

1. An FMCW radar distance estimation method based on fast iterative interpolation is characterized by comprising the following steps:
step 1: fourier transform is carried out on the intermediate frequency signals after AD sampling, and then constant false alarm detection is carried out to estimate the number P of targets and the frequency spectrum unit m where the targets are located i ,i=1,2...P;
Step 2: calculating the spectral unit m of the ith target i Corresponding deviation of spectral unit
Figure FDA0003915250360000011
P, step 2 comprises the steps of:
step 2.1: setting a target iteration number Q, and enabling the current iteration number Q =0; deviation estimate for ith target after single iteration
Figure FDA0003915250360000012
And amplitude estimator
Figure FDA0003915250360000013
Proceed initialization to enable
Figure FDA0003915250360000014
Step 2.2: estimating the reflected signal strength of the p-th target
Figure FDA0003915250360000015
p=1,2...P;
Step 2.3: by using
Figure FDA0003915250360000016
Calculating the frequency spectrum interference generated by the p target to the i target
Figure FDA0003915250360000017
Step 2.4: after calculating and removing interference
Figure FDA0003915250360000018
Spectral peaks of spectral units
Figure FDA0003915250360000019
Step 2.5: using spectral peaks
Figure FDA00039152503600000110
Calculating a deviation correction factor
Figure FDA00039152503600000111
Deviation from the spectral unit
Figure FDA00039152503600000112
Step 2.6: q ← Q +1, judging whether Q is smaller than Q, if Q is smaller than or equal to Q, repeating the steps 2.2-2.5; if Q is more than Q, executing step 3;
and 3, step 3: using spectral cells m i And spectral cell deviation
Figure FDA00039152503600000113
Calculating the frequency f of the ith target reflected signal i And the distance value R of the target i
2. The FMCW radar distance estimation method based on fast iterative interpolation of claim 1, wherein: in step 1, the intermediate frequency signal after AD sampling is subjected to fourier transform expression as follows:
Figure FDA00039152503600000114
wherein s is b (N) represents an intermediate frequency signal after AD sampling, N represents the number of points of Fourier transform, S b (k) And expressing the amplitude of the kth unit in the frequency domain, and estimating that the expression of the target number P satisfies the following conditions:
P=Count{S b (k)>CFAR(S b (k))}
wherein CFAR (S) b (k) Represents a pair S b (k) The result of the constant false alarm detection, count represents the S pair b (k) Greater than CFAR (S) b (k) The number of the amplitude values is counted, and the counted result is the number of the targets;
the spectral unit m where the p-th target is located p The expression is as follows:
Figure FDA00039152503600000115
3. an FMCW radar distance estimation method based on fast iterative interpolation according to claim 1, characterized in that: the number of iterations Q in step 2.1 is set to 2.
4. An FMCW radar distance estimation method based on fast iterative interpolation according to claim 1, characterized in that: reflected signal strength of the p-th target in step 2.2
Figure FDA0003915250360000021
The estimated value expression of (c) satisfies:
Figure FDA0003915250360000022
wherein
Figure FDA0003915250360000023
Is the intensity of the reflected signal of the ith targetDegree estimate, with an initial value of 0, N representing the number of points of the Fourier transform, Δ m pl Indicating the frequency spectrum unit m corresponding to the p-th target p Spectral unit m corresponding to the ith target l At a distance in the frequency domain, the expression satisfies:
Δm pl =Δm p -Δm l
Δδ pl indicating the deviation of the spectrum unit corresponding to the p-th target
Figure FDA0003915250360000024
Deviation of spectral unit corresponding to the l-th target
Figure FDA0003915250360000025
The distance in the frequency domain is expressed as follows:
Δδ pl =Δδ p -Δδ l
5. the FMCW radar distance estimation method based on fast iterative interpolation of claim 1, wherein: step 2.3, the p-th target generates spectrum interference to the i-th target
Figure FDA0003915250360000026
The expression satisfies:
Figure FDA0003915250360000027
where N represents the number of Fourier transform points, Δ m ip Indicating the frequency spectrum unit m corresponding to the ith target i M of the spectrum unit corresponding to the p-th target p At a distance in the frequency domain, the expression satisfies:
Δm ip =Δm i -Δm p
Δδ ip indicating the deviation of the spectrum unit corresponding to the ith target
Figure FDA0003915250360000028
Deviation of spectral unit corresponding to p-th target
Figure FDA0003915250360000029
At a distance in the frequency domain, the expression satisfies:
Δδ ip =Δδ i -Δδ p
6. the FMCW radar distance estimation method based on fast iterative interpolation of claim 1, wherein: after the interference is removed in step 2.4
Figure FDA00039152503600000210
Spectral peaks of spectral units
Figure FDA00039152503600000211
The expression satisfies:
Figure FDA0003915250360000031
wherein S i,±0.5 Representation obtained by direct Fourier transform of intermediate frequency signal
Figure FDA0003915250360000032
Spectral peak of spectral unit, S i,±0.5 The device consists of two parts: the ith target reflected signal is
Figure FDA0003915250360000033
The spectral peak and the p-th target obtained by Fourier transform of the frequency spectrum unit generate frequency spectrum interference on the i-th target, and the expression meets the following requirements:
Figure FDA0003915250360000034
wherein s is b (N) represents the intermediate frequency signal after AD sampling, and N represents the number of points of fourier transform.
7. The FMCW radar distance estimation method based on fast iterative interpolation of claim 1, wherein: deviation correction factor in step 2.5
Figure FDA0003915250360000035
Deviation from the spectral unit
Figure FDA0003915250360000036
The expressions respectively satisfy:
Figure FDA0003915250360000037
Figure FDA0003915250360000038
where N represents the number of points of the fourier transform.
8. An FMCW radar distance estimation method based on fast iterative interpolation according to claim 1, characterized in that: frequency f of ith target reflection signal in step 3 i And the distance value R of the target i The expressions respectively satisfy:
Figure FDA0003915250360000039
wherein f is s Is the AD sampling frequency, c is the speed of light, B is the bandwidth of modulation, T is the period of the triangular wave of modulation, N represents the number of points of Fourier transform.
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