CN109471095B  FMCW radar distance estimation method based on fast iterative interpolation  Google Patents
FMCW radar distance estimation method based on fast iterative interpolation Download PDFInfo
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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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 G—PHYSICS
 G01—MEASURING; TESTING
 G01S—RADIO DIRECTIONFINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCEDETECTING 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 phasemodulated, 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 onvehicle anticollision radar in a multitarget environment is easily interfered by frequency spectrums. The algorithm provided by the simulation verification has higher estimation accuracy in a multitarget 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 realtime property and is easy to realize in engineering.
Description
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 TransformDiscretetime Fourier Transform (FFTDTFT) combined correction method, a ChirpZ 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): 14.) 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): 123125.) 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): 351354), so that the precision is improved, but the problem of nonuniform Estimation error exists; the document (frequency iterative interpolation estimation algorithm based on the refined frequency spectrum, electronic and informatics newspaper, 2017,39 (9): 21412147.) proposes a method for interpolating signals by using the refined frequency spectrum, thereby solving the problem of nonuniform estimation errors. The method proposed by the above document has a good effect on the deviation estimation of the singlefrequency signal, but when the method is applied to a multitarget environment, the deviation of the distance estimation is increased due to interspectrum interference. In order to solve the problem, the literature (DFT Interpolation Algorithm for KaiserBessel and DolphChebyshev Windows, IEEE Transactions on Instrumentation & Measurement,2011,60 (3): 784790) proposes a method for compensating estimation deviation based on highorder polynomial Interpolation, and the method uses highorder 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): 245250.) 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 singlesnapshot DOA estimation, IEEE Geoscience and Remote Sensing Letters,2017,14 (4): 574578) 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 interspectrum interference in a multitarget environment, in particular to a method which can eliminate the interspectrum 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 multitarget 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 deviationi =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 iterationAnd amplitude estimatorCarry out initialization toi＝1,2…P；
Step 2.3: by usingCalculating the frequency spectrum interference generated by the p target to the i target
Step 2.5: using spectral peaksCalculating a deviation correction factorDeviation from the spectral unit
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 2.22.5; if Q is greater than Q, executing step 3;
and step 3: using spectral units m _{i} And spectral unit deviationCalculate 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:
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 pth target is located _{p} The expression is as follows:
2. the number of iterations Q in step 2.1 is set to 2.
3. Intensity of reflected signal of pth target in step 2.2The estimated value expression of (c) satisfies:
whereinIs 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 pth target _{p} Spectral unit m corresponding to the lth 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 pth targetDeviation of spectral unit corresponding to the lth targetThe distance in the frequency domain is expressed as follows:
Δδ _{pl} ＝Δδ _{p} Δδ _{l} 。
4. step 2.3, the pth target generates spectrum interference to the ith targetThe expression satisfies:
wherein Δ m _{ip} Indicating the frequency spectrum unit m corresponding to the ith target _{i} M of the spectrum unit corresponding to the pth 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 targetDeviation of spectral unit corresponding to pth targetAt a distance in the frequency domain, the expression satisfies:
Δδ _{ip} ＝Δδ _{i} Δδ _{p} 。
5. after the interference is removed in step 2.4Spectral peaks of spectral unitsThe expression satisfies:
wherein S _{i,±0.5} Representing direct Fourier transform of an intermediate frequency signalSpectral peak of spectral unit, S _{i,±0.5} The device consists of two parts: the ith target reflected signal isThe 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:
6. deviation correction factor in step 2.5Deviation from the spectral unitThe expressions respectively satisfy:
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:
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 nonuniform 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 signaltonoise ratios;
FIG. 3 is the distance root mean square error of the target 2 at different signaltonoise 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 mth in the frequency domain _{i} Spectral peaks of the individual spectral units, thenThe spectral peaks of individual spectral units can be expressed as:
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
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 kth 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 deviationAnd (4) a foundation.
The spectral unit m in which the pth target is located _{p} The expression is as follows
And 2, step: calculating the spectral unit m of the ith target _{i} Corresponding deviation of spectral uniti＝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 iterationAnd the intensity of the reflected signal of the ith targetCarry out initialization toi＝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.
Directly using intermediate frequency signals atThe spectrum peak obtained by FFT conversion of the spectrum unit comprises three parts: the pth target reflection signal is processed by FFT to obtain the amplitude, and other target reflection signals are processed by FFTLeakage of spectral cells and noisetoamplitude interference, where the interference of noise has a less negligible effect on the spectral peaks. The first target isThe leakage of the spectrum unit can be reflected at the target through the targetThe position of the frequency spectrum unit is obtained by FFT, and the expression is as follows
WhereinIs 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, thereforeThe 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 pth target _{p} M of the spectrum unit corresponding to the lth 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 pth targetDeviation of spectral unit corresponding to the lth targetThe distance in the frequency domain is expressed as follows
Δδ _{pl} ＝Δδ _{p} Δδ _{l}
step 2.3: by usingCalculating the frequency spectrum interference generated by the p target to the i target
The p target generates spectrum interference to the i targetCan pass through the pth target intermediate frequency signal s _{bp} (n) is inThe spectrum unit is obtained by FFT conversion, but s _{bp} (n) is not directly available and therefore needs to be utilizedObtainingThe expression is as follows
Wherein Δ m _{ip} Indicating the frequency spectrum unit m corresponding to the ith target _{i} M of the spectrum unit corresponding to the pth 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 targetDeviation of spectral unit corresponding to pth targetThe distance in the frequency domain is expressed as follows
Δδ _{ip} ＝Δδ _{i} Δδ _{p}
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 isThe spectral peak obtained by FFT of the spectral unit and the pth target reflection signal are FFTEnhancement of spectral cells, from whichExpression (2)
Step 2.5: using spectral peaksCalculating a deviation correction factorDeviation from the spectral unit
Spectral peaks from step 2.4Can be approximated as being present in the reflected signal only at the ith targetSpectral 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): 12371242.) method to obtain the offset correction factor for the ith targetDeviation from the spectral unitThe expression is as follows
Step 2.5: q ← Q +1, judging whether Q is less than Q, if Q is less than or equal to Q, repeating steps 2.22.5
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 deviationCalculating 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 unitThen, the real frequency spectrum unit corresponding to the ith target reflection signalThereby utilizingCalculating 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
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 localamplified Fourier algorithm (ZoomFFT) (see the modified ZFT algorithm For improving LFMCW radar ranging accuracy, 2015, (2): 14.), noniterative 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): 351354.), and spectral leakage suppression algorithm based on Hamming window (Hanmingwindow 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 SignaltoNoise 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 MonteCarlo 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 ZoomFFT 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 sameIs less subject to peak variations, and therefore does not affect the biasTherefore, the estimation performance of the two algorithms is better. In addition, the Hanmingwindow 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 Hanmingwindow algorithm and the ZoomFFT 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
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 ZoomFFT algorithm estimation error appears as a random error because the interpolation mode of ZoomFFT 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 ZoomFFT 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 ZoomFFT 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 realtime.
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 uniti＝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 iterationAnd amplitude estimatorCarry out initialization toi＝1,2…P。
Step 2.3: by usingCalculating the frequency spectrum interference generated by the p target to the i target
Step 2.5: using spectral peaksCalculating a deviation correction factorDeviation from the spectral unit
Step 2.6: q ← Q +1, judging whether Q is smaller than Q, if Q is not larger than Q, repeating steps 2.22.5.
And step 3: using spectral units m _{i} And spectral cell deviationCalculating 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
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 kth 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 pth target is located _{p} The expression is as follows
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.
WhereinIs 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 pth 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 pth targetDeviation of spectral unit corresponding to the lth targetThe distance in the frequency domain is expressed as follows
Δδ _{pl} ＝Δδ _{p} Δδ _{l}
Step 2.3 the pth target generates spectrum interference to the ith targetThe expression is as follows
Wherein Δ m _{ip} Indicating the frequency spectrum unit m corresponding to the ith target _{i} M of the spectrum unit corresponding to the pth 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 targetDeviation of spectral unit corresponding to pth targetThe distance in the frequency domain is expressed as follows
Δδ _{ip} ＝Δδ _{i} Δδ _{p}
After the interference is removed in step 2.4Spectral peaks of spectral unitsThe expression is as follows
Wherein S _{i,±0.5} Representation of direct FFT acquisition of an intermediate frequency signalSpectral peak of spectral unit, S _{i,±0.5} The device consists of two parts: the ith target reflection signal isThe 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
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
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 multitarget distance estimation algorithm based on iterative interpolation, aiming at the problem that the distance measurement precision of an onvehicle anticollision radar in a multitarget 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 nonuniform 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 multitarget 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 realtime 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 unitP, 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 iterationAnd amplitude estimatorProceed initialization to enable
Step 2.3: by usingCalculating the frequency spectrum interference generated by the p target to the i target
Step 2.5: using spectral peaksCalculating a deviation correction factorDeviation from the spectral unit
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 2.22.5; if Q is more than Q, executing step 3;
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:
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 pth target is located _{p} The expression is as follows:
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 pth target in step 2.2The estimated value expression of (c) satisfies:
whereinIs 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 pth 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 pth targetDeviation of spectral unit corresponding to the lth targetThe 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 pth target generates spectrum interference to the ith targetThe expression satisfies:
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 pth 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 targetDeviation of spectral unit corresponding to pth targetAt 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 2.4Spectral peaks of spectral unitsThe expression satisfies:
wherein S _{i，±0.5} Representation obtained by direct Fourier transform of intermediate frequency signalSpectral peak of spectral unit, S _{i，±0.5} The device consists of two parts: the ith target reflected signal isThe spectral peak and the pth target obtained by Fourier transform of the frequency spectrum unit generate frequency spectrum interference on the ith target, and the expression meets the following requirements:
wherein s is _{b} (N) represents the intermediate frequency signal after AD sampling, and N represents the number of points of 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:
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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