Unmanned aerial vehicle height measurement method based on millimeter wave radar

Abstract

The invention discloses an unmanned aerial vehicle height measurement method based on a millimeter wave radar, and the method comprises the steps: carrying out the FFT conversion of an intermediate frequency signal received by the millimeter wave radar, calculating the amplitude of the signal, and extracting an FFT frequency spectrum; traversing the FFT frequency spectrum and finding out a frequency f0 corresponding to a maximum amplitude point in a spectrogram, setting a frequency refining interval (fl, fh) by taking the frequency f0 as a center and taking a frequency resolution delta f as a frequency radius, performing complex modulation, low-pass filtering and down-sampling on signals in the frequency refining interval (fl, fh), and then performing FFT transformation again and extracting a refined frequency spectrum; traversing the refined frequency spectrum, finding out a spectral line with the maximum amplitude and two adjacent spectral lines, performing polynomial fitting and fitting parameter solution, and calculating an extreme point of a fitting curve; and taking the frequency corresponding to the extreme point as a deviation frequency, trimming the frequency f0, and determining a target distance according to the corrected frequency. The method has the advantages that the fence effect caused by FFT can be effectively relieved, and the millimeter wave radar height measurement precision and stability can be improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned aerial vehicle control, in particular to an unmanned aerial vehicle height measurement method based on millimeter wave radar. BACKGROUND

[0002] With the rapid development of science and technology, unmanned aerial vehicles (UAV) are widely used in military reconnaissance, environmental monitoring, agricultural plant protection and other fields due to their high efficiency, low cost and flexibility. In many application scenarios, the autonomous flight capability of unmanned aerial vehicles is particularly important, and the ground simulation flight technology is one of the important research directions. Ground simulation flight requires the unmanned aerial vehicle to perceive the change of the terrain in real time and maintain a height above the ground at all times. How to accurately measure the height of the unmanned aerial vehicle from the ground is the key to ground simulation flight.

[0003] At present, the common height measurement methods of unmanned aerial vehicles mainly include visual measurement method, laser ranging method and ultrasonic ranging method. Among them, the visual measurement method relies on image recognition and ground feature extraction, which can achieve high accuracy in environments with sufficient light and obvious terrain features, but its performance decreases significantly in complex weather conditions such as night, strong light reflection and fog, and it requires high computing resources, which is not suitable for small flight platforms with strong real-time performance and limited resources. Although the laser ranging method has high accuracy, it has relatively high cost and high power consumption, and it is easy to have measurement errors in dense vegetation or terrain with dramatic reflectivity changes. Ultrasonic ranging is limited by range and ground material, and is prone to echo interference and response delay in complex terrain or high flight speed.

[0004] Millimeter wave radar has gradually become the preferred height measurement solution in the field of unmanned aerial vehicles due to its strong penetration, good anti-interference ability and strong environmental adaptability. Millimeter wave radar extracts target distance by performing fast Fourier transform on the echo signal. The traditional FFT algorithm is affected by the fence effect, which will cause errors in distance estimation. Therefore, an algorithm is needed to effectively alleviate the fence effect caused by FFT, improve the height measurement accuracy and stability of millimeter wave radar, and adapt to the operation requirements of unmanned aerial vehicles in low-altitude and high-dynamic environments. SUMMARY

[0005] In view of the above problems of the prior art, the technical problem to be solved by the present application is to provide an unmanned aerial vehicle height measurement method based on millimeter wave radar, which can effectively alleviate the fence effect caused by FFT and improve the height measurement accuracy and stability of millimeter wave radar.

[0006] To solve the above technical problems, the present application adopts the following technical solutions:

[0007] An unmanned aerial vehicle height measurement method based on millimeter wave radar, characterized in that it comprises the following steps:

[0008] S1, performing FFT transformation on the intermediate frequency signal x(n) received by the millimeter wave radar, calculating the amplitude |X(k)| of the signal, and extracting the FFT spectrum;

[0009] S2, traversing the FFT spectrum and finding the frequency f0 corresponding to the maximum amplitude point in the spectrum graph, setting a frequency refinement interval (f l ,f h ) with the frequency f0 as the center and the frequency resolution Δf as the frequency radius, determining the refined target spectrum, and extracting a narrowband signal;

[0010] S3, performing complex modulation, low-pass filtering and downsampling on the signal in the frequency refinement interval (f l ,f h ), performing FFT transformation again, and extracting the refined spectrum;

[0011] S4, traversing the refined spectrum and finding the spectrum line with the maximum amplitude and the two adjacent spectrum lines, and performing polynomial fitting;

[0012] S5, solving the fitting parameters of the polynomial fitting function and calculating the extreme point of the fitting curve;

[0013] S6, taking the frequency corresponding to the extreme point as the deviation frequency, adjusting the frequency f0, and determining the target distance according to the corrected frequency.

[0014] In the above method, on the basis of the FFT spectrum, the frequency refinement interval is determined by taking the frequency f0 corresponding to the maximum amplitude point as the center and the frequency resolution Δf as the radius, then the signal in the refined frequency range is complex modulated, low-pass filtered and downsampled, and then FFT transformation is performed and the refined spectrum is extracted, finally the refined spectrum is polynomial fitted, the error of the estimated frequency is compensated, the influence of the fence effect is reduced, and the frequency estimation accuracy is improved.

[0015] Further, in the step S4, the amplitude point of the spectrum line with the maximum amplitude is (f i ,y i ), the amplitude points of the two adjacent spectrum lines are (f i-1 ,y i-1 ) and (f i+1 ,y i+1 ) respectively, a quadratic polynomial fitting is adopted, and a quadratic polynomial function is constructed as:

[0016] R(x)=ax 2 +bx+c

[0017] In the formula, a, b, and c are the fitting parameters of the quadratic polynomial.

[0018] Further, in the step S5, the solving step of the fitting parameter is:

[0019] S51, the mean square error is used to evaluate the deviation between the fitting curve R(x) and the actual data points, and the expression is:

[0020]

[0021] S52, according to the extremum principle of multivariate function, the partial derivative of the mean square error with respect to the fitting parameters a, b and c satisfies the following formula:

[0022]

[0023] S53, the fitting equation of the quadratic polynomial function is obtained according to the expression of step S52:

[0024]

[0025] S54, the fitting parameters a, b and c of the quadratic polynomial are solved according to the fitting equation.

[0026] Further, in the step S5, the frequency of the extreme point is:

[0027]

[0028] Further, the correction frequency is:

[0029] f0' = f0 + f r

[0030] The target distance is:

[0031]

[0032] In the formula, c is the speed of light, T is the millimeter wave radar frequency sweeping time, and Δf is the frequency resolution.

[0033] Further, in the step S3, the complex modulation of the intermediate frequency signal x(n) in the frequency refinement interval (f l ,f h ) satisfies the following formula:

[0034]

[0035] In the formula, n is the sampling point number.

[0036] Further, in the step S3, the expression of the low-pass filtering of the complex modulated signal is:

[0037] x filter (n) = x move (n)·h(n)

[0038] wherein h(n) is the impulse response of the filter.

[0039] Further, the expression for down-sampling the low-pass filtered signal in step S3 is:

[0040] x resample (m)=x filter (n·D)

[0041] wherein D is the refinement factor.

[0042] Further, the FFT transform of the down-sampled signal x resample (m) in step S3 is:

[0043]

[0044] wherein N zoom is the number of sampling points of the FTT transform in step S6.

[0045] In summary, the present application has the advantages of effectively alleviating the fence effect caused by FFT, and improving the accuracy and stability of millimeter wave radar height measurement. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is the FFT spectrum of the discrete intermediate frequency signal.

[0047] Figure 2 is the flow chart of the Zoom-FFT algorithm.

[0048] Figure 3 is the flow chart of the improved Zoom-FFT algorithm.

[0049] Figure 4 is the root mean square error of frequency estimation under different signal-to-noise ratios.

[0050] Figure 5 is the standard deviation of frequency estimation under different signal-to-noise ratios.

[0051] Figure 6 is the root mean square error of frequency estimation under different frequencies when SNR=1.

[0052] Figure 7 is the standard deviation of frequency estimation under different frequencies when SNR=1.

[0053] Figure 8 is the schematic diagram of the 2m flight test results in the earth simulation.

[0054] Figure 9 is the schematic diagram of the 2m flight test results in the complex environment during the day.

[0055] Figure 10This is a schematic diagram of the results of a 2m ground-mimicking flight experiment in a complex environment at night. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to the embodiments.

[0057] In FMCW radar systems, target range information is contained in the intermediate frequency (IF) signal. Since range is related to the frequency of the IF signal, target range information can be calculated by performing spectral analysis on the IF signal. In practical engineering, the IF signal is typically processed using Discrete Fourier Transform (DFT), and then the spectrum is analyzed to obtain its spectral characteristics, thereby calculating the target range information. Based on the spectral analysis theory of FFT, the IF signal is sampled by an ADC at a sampling frequency of f0. s Given n sampling points, the discrete sequence of the intermediate frequency signal expressed by Euler's formula is:

[0058]

[0059] The n-point FFT expression for the discrete sequence of the intermediate frequency signal is:

[0060]

[0061] The spectrum of the intermediate frequency signal after FFT processing is as follows Figure 1 As shown, in Figure 1 In the diagram, the solid lines represent the envelopes of the individual spectral lines obtained through the FFT, and the vertical dashed lines represent the spectral lines after FFT processing. real The frequency corresponding to the highest point of the envelope, i.e., the true frequency of the target object, is then represented by the following frequency resolution:

[0062]

[0063] The FFT algorithm, limited by its discrete nature, can only obtain n discrete spectral lines. Because the signal is truncated aperiodically during actual processing, there are intervals between the spectral lines; this phenomenon is called the picket fence effect. The discrete nature of the FFT algorithm leads to a slight deviation δ between the frequency position corresponding to the maximum amplitude and the target's true frequency. Since the intermediate frequency signal is proportional to the target distance, this also introduces a certain deviation in distance estimation. Therefore, the accuracy of frequency estimation directly affects the accuracy of target distance estimation, which is the main source of error in FFT algorithm frequency estimation. To reduce the impact of the picket fence effect, spectrum subdivision algorithms have emerged.

[0064] In the field of millimeter wave radar ranging, the spectrum subdivision algorithm is improved and optimized on the basis of FFT algorithm. The commonly used spectrum subdivision algorithms mainly include zero padding FFT algorithm, CZT (Chirp-Z transform) algorithm and Zoom-FFT algorithm. These algorithms refine the frequency resolution in different ways, thereby reducing the frequency measurement deviation caused by the fence effect.

[0065] The process of the traditional Zoom-FFT algorithm is shown in Figure 2 Firstly, the frequency band of interest is selected for complex modulation, and the frequency band of interest is moved to the vicinity of zero frequency. Then, the low-pass filter is used to extract the narrowband signal after complex modulation. Subsequently, the down-sampling processing is performed on the modulated signal to realize the refinement of the spectrum. Finally, the FFT analysis is performed on the down-sampled signal, and the frequency corresponding to the maximum amplitude point, i.e. the target frequency, is found by traversing the spectrum.

[0066] After the signal is processed by the down-sampling and then by the FFT, the frequency resolution will indeed be improved. However, the calculated frequency has a certain error with the real frequency of the target due to the influence of the fence effect. Therefore, the Zoom-FFT algorithm still has defects.

[0067] In order to reduce the influence of the fence effect on the frequency estimation accuracy, the embodiment improves the traditional Zoom-FFT algorithm, thereby further improving the accuracy of frequency estimation. The improved algorithm mainly includes three steps: frequency coarse estimation, spectrum refinement and frequency correction. Through this improvement, the error caused by the fence effect can be effectively reduced, and the accuracy of frequency estimation can be improved.

[0068] Frequency coarse estimation: firstly, the FFT algorithm is used for the intermediate frequency signal x(n), and the amplitude |X(k)| of the signal is calculated. The frequency f0 corresponding to the maximum amplitude point of the spectrum is found by traversing the spectrum, and the frequency refinement interval (f l ,f h ) is set with the frequency resolution Δf as the frequency radius:

[0069] f l = f0+ Δf (4)

[0070] f h = f0- Δf (5)

[0071] Frequency refinement: high-resolution spectrum analysis is performed on the intermediate frequency discrete signal x(n) in (f l ,f h ). Firstly, the complex modulation is performed on the signal in the refined frequency range, so as to realize the translation of the target spectrum and move it to the vicinity of zero frequency, thereby facilitating the subsequent refinement analysis and processing. The complex modulation operation can be realized by multiplying the discrete intermediate frequency signal by the complex exponential signal, and the formula is as follows:

[0072]

[0073] where n is the number of sampling points. To further remove irrelevant frequency components outside the target frequency band, low-pass filtering is needed for the complex modulated signal, which can effectively suppress high-frequency noise and interference signals in non-target frequency bands, and only retain the spectrum of interest. The specific implementation is as follows:

[0074] x filter (n)=x move (n)·h(n) (7)

[0075] where h(n) is the impulse response of the filter. After complex modulation and low-pass filtering, the bandwidth of the target frequency band has been effectively compressed, and data redundancy is further reduced by downsampling, thereby reducing computational complexity and improving processing efficiency. Downsampling not only reduces the overhead of data storage and transmission, but also optimizes subsequent signal processing steps, making the system run more efficiently while maintaining effective information extraction of the target frequency band. The mathematical expression of downsampling is as follows:

[0076] x resample (m)=x filter (n·D) (8)

[0077] where D is the refinement factor. It determines the step size of downsampling, i.e., the interval of the sampling points retained during downsampling. After completing the downsampling, the signal x resample (m) is subjected to FFT analysis, using more sampling points N zoom to improve frequency resolution, making the target frequency components more clear and helping to improve the accuracy of frequency estimation:

[0078]

[0079] The frequency resolution is:

[0080]

[0081] Frequency correction: When correcting the refined frequency spectrum, first perform peak search on the entire spectrum to find the spectrum line with the largest amplitude and its two adjacent spectrum lines. To further improve the accuracy of frequency estimation, a quadratic polynomial fitting is used to accurately locate the peak frequency. Assume that the amplitude points of the three spectrum lines are (f i-1 ,y i-1 ), (f i ,y i ), and (f i+1 ,y i+1 ). Let's construct a quadratic polynomial function as follows:

[0082] R(x)=ax2 + bx + c (11)

[0083] In the formula, a, b, and c are fitting parameters of the polynomial. In order to measure the matching degree of the fitting curve and the original data points, the mean squared error (MSE) is used to evaluate the deviation between the fitting curve R(x) and the actual data points, and the mathematical expression is:

[0084]

[0085] In order to make the fitting curve more consistent with the actual situation, that is, to obtain the optimal fitting parameters, the mean squared error needs to be minimized. According to the extremum principle of multivariate function, the partial derivative of the mean squared error with respect to the parameters a, b, and c must be zero, that is, the following equation is satisfied:

[0086]

[0087] The fitting equation of the quadratic polynomial function is obtained by arranging formula (13):

[0088]

[0089] The quadratic polynomial parameters a, b, and c are solved by formula (14), and then the extreme point of the quadratic polynomial, that is, the vertex position of the parabola, is obtained. The extreme point of the quadratic polynomial can be obtained by derivation, and the calculation formula is:

[0090]

[0091] Real frequency compensation:

[0092] f0' = f0+ f r (16)

[0093] The traditional FFT is limited by the fixed frequency resolution, and it is difficult to obtain more detailed spectral information under limited computing resources. However, during the FFT calculation and analysis process when processing signals, the fence effect will still introduce a certain frequency deviation, affecting the measurement accuracy. In order to further improve the spectral resolution and improve the accuracy of frequency estimation, the embodiment further introduces a spectral line calibration algorithm based on Zoom-FFT, which corrects the refined spectral peak value to improve the accuracy of frequency estimation. The improved algorithm process is as shown in Figure 3 , and the specific process is:

[0094] S1, perform FFT transformation on the intermediate frequency signal x(n) received by the millimeter wave radar to calculate the amplitude |X(k)| of the signal and extract the FFT spectrum;

[0095] S2, traverse the FFT spectrum and find the frequency f0 corresponding to the maximum amplitude point in the spectrum graph, set the frequency refinement interval (f l ,f h ) with frequency resolution Af as the frequency radius, determine the refined target spectrum, and extract the narrowband signal;

[0096] S3, after complex modulation, low-pass filtering and down-sampling of the signal in the frequency refinement interval (f l ,f h ), perform FFT transform again, and extract the refined spectrum;

[0097] S4, traverse the refined spectrum and find the two adjacent spectral lines with the maximum amplitude, and perform polynomial fitting;

[0098] S5, solve the fitting parameters of the polynomial fitting function, and calculate the extreme point of the fitting curve;

[0099] S6, take the frequency corresponding to the extreme point as the deviation frequency, adjust the frequency f0, and determine the target distance according to the corrected frequency.

[0100] Compared with the traditional FFT method, the improved Zoom-FFT combined with the spectral line calibration algorithm can effectively reduce the error caused by the fence effect in FFT frequency estimation, thereby improving the accuracy of frequency estimation. This method has important application value in FMCW millimeter wave radar, precise ranging and high-resolution signal analysis fields.

[0101] Analysis of algorithm calculation amount: In engineering applications, the calculation amount of the algorithm will directly affect the real-time performance and feasibility. In embedded systems with limited computing resources or signal processing tasks with high real-time requirements, the size of the calculation amount directly determines the practicality of the algorithm. Under normal circumstances, the calculation complexity of complex multiplication is much higher than that of complex addition, so when analyzing the calculation complexity, the influence of complex addition can be ignored, and the operation amount of complex multiplication is focused on.

[0102] In order to comprehensively evaluate the calculation complexity of the improved Zoom-FFT frequency estimation algorithm proposed in this embodiment, the main calculation steps are analyzed, and the calculation amount of the traditional FFT and other algorithms is compared. Table 1 lists the calculation amount of FFT algorithm, zero padding FFT algorithm, CZT algorithm, Zoom-FFT algorithm and improved Zoom-FFT algorithm under the same signal processing task.

[0103] Table 1 Comparison of algorithm calculation amount

[0104]

[0105] Zero-padding FFT improves frequency resolution by extending the signal length to a larger value (usually 2-3 times the original signal length) by adding zero values at the end of the signal. The computational complexity of the algorithm is directly related to the signal length, so the computational complexity of the zero-padding FFT algorithm is relatively higher than that of several other algorithms.

[0106] CZT algorithm is a frequency spectrum estimation method based on Z-transform, which is suitable for scenarios that require fine analysis of a specific frequency range. CZT achieves frequency refinement by adjusting the sampling points of the signal, but its computational complexity is relatively high, especially when the interpolation point number M is large, the computational complexity is close to O(MlogM), so the calculation cost is high.

[0107] Zoom-FFT algorithm is an improvement based on standard FFT algorithm, its main advantage is that it can significantly improve the frequency resolution and only increase a small amount of calculation, especially in local frequency range analysis. This algorithm can provide higher frequency resolution without excessive increase in computational burden.

[0108] The algorithm proposed in this embodiment is further optimized on the basis of Zoom-FFT, and the spectrum error is compensated to improve the accuracy of frequency estimation. The improved Zoom-FFT algorithm of this embodiment is very close to the traditional Zoom-FFT algorithm in terms of computational complexity, but the frequency estimation accuracy is improved, and the practicality of the algorithm is improved.

[0109] In order to better evaluate the differences between different algorithms, simulation analysis is carried out on each algorithm, including comparing the algorithm running time of each algorithm, the algorithm performance under different signal-to-noise ratios, the algorithm performance under different frequencies and ranging simulation experiments, and the specific analysis is as follows.

[0110] Algorithm running time: In order to evaluate the computational efficiency of different spectrum subdivision algorithms, this embodiment sets the frequency f c = 2000Hz of the signal s(n) when the signal-to-noise ratio is 1dB, compares the actual running time of each algorithm under different sampling point numbers, sets the zero padding length of the zero padding FFT algorithm to N, and the refinement multiple of the CZT algorithm, Zoom-FFT algorithm and improved Zoom-FFT algorithm is 2, and the experimental results are shown in Table 2.

[0111] Table 2 Running time of each algorithm under different sampling points (s)

[0112]

[0113] As can be seen from Table 2, the running time of the zero-padding FFT algorithm is the longest, and the operation time of the CZT algorithm, the Zoom-FFT algorithm and the improved Zoom-FFT algorithm is slightly increased compared with the standard FFT algorithm. The experimental results show that the improved Zoom-FFT algorithm proposed in the embodiment is basically consistent with the traditional Zoom-FFT algorithm in running time, and does not significantly affect the calculation speed.

[0114] Performance comparison of algorithms under different signal-to-noise ratios: In order to verify the performance of the improved algorithm, the MATLAB software is used to simulate and analyze the optimized improved algorithm, and the improved algorithm proposed in the embodiment is compared with the FFT algorithm, the zero-padding FFT algorithm, the CZT algorithm and the Zoom-FFT algorithm. At the same time, in order to evaluate the theoretical limit of different algorithms in frequency estimation, the Cramer-Rao Lower Bound (CRLB) is introduced as a reference standard in the embodiment. The Cramer-Rao Lower Bound is a theoretical tool commonly used in statistical signal processing to evaluate the performance of unbiased estimators, which gives the minimum variance that the estimated parameter can reach under a specific signal model. For unbiased estimation of a single frequency complex sinusoidal signal, the expression of the Cramer-Rao Lower Bound is:

[0115]

[0116] In the formula, f s is the sampling frequency, N is the number of sampling points, and SNR (Signal to Noise Ratio, SNR) is the signal-to-noise ratio, which is an important indicator in signal processing, used to measure the ratio of signal strength to noise strength. SNR is usually expressed in decibels (dB), reflecting the quality of the signal and the performance of the system.

[0117] In order to evaluate the accuracy of frequency estimation, the Root Mean Square Error (RMSE) is used as an evaluation index. RMSE is used to measure the deviation between predicted values and actual values, which can effectively measure the prediction error of the model and intuitively reflect the accuracy of the model in fitting data. The smaller the RMSE value, the higher the accuracy of frequency estimation. The calculation formula is as follows:

[0118]

[0119] In the formula, L is the number of simulations. In order to evaluate the stability of the algorithm, the standard deviation (Standard Deviation, SD) is used as a measurement index. Standard deviation is used to describe the dispersion of data, and the smaller the value, the more stable the estimation results of the algorithm. The calculation formula is as follows:

[0120]

[0121] In simulation, the sampling frequency f s = 100 x 10 3 Hz, the initial phase is a random value, the amplitude A = 1, and 10000 independent Monte Carlo simulation experiments are performed. The frequency f c of the signal s(n) is set to 2000 Hz, and the number of sampling points N = 1024. The frequency estimation accuracy and stability of the FFT algorithm, the zero-padding FFT algorithm, the CZT algorithm, the Zoom-FFT algorithm, and the improved Zoom-FFT algorithm under different signal-to-noise ratios are compared when the signal-to-noise ratio is in the range of [-20 dB, 20 dB], and the results are shown in Figure 4 and Figure 5 .

[0122] As can be seen from Figure 4 , when the signal-to-noise ratio is low (SNR < 0 dB), the root mean square errors of various algorithms differ greatly, among which the FFT and zero-padding FFT algorithms have higher errors, while the CZT, Zoom-FFT, and improved Zoom-FFT algorithms have better estimation accuracy. When SNR > 0 dB, the FFT algorithm, the zero-padding FFT algorithm, and the Zoom-FFT algorithm are gradually stabilized due to the influence of the fence effect, while the CZT algorithm and the improved Zoom-FFT algorithm are not affected by the fence effect. Overall, the root mean square error of the improved Zoom-FFT algorithm is better than that of other algorithms.

[0123] Figure 5 The results reflect the frequency estimation stability (SD) of each algorithm under different signal-to-noise ratios. As can be seen from the results, under low signal-to-noise ratio, the standard deviation of the FFT algorithm and the zero-padding FFT algorithm is much higher than that of other algorithms, indicating that the frequency estimation results of the two algorithms fluctuate greatly. The CZT algorithm, the Zoom-FFT algorithm, and the improved Zoom-FFT algorithm have better stability.

[0124] In summary, the improved Zoom-FFT algorithm can reduce the influence of the fence effect while maintaining good stability and ensuring calculation accuracy.

[0125] Performance comparison of algorithms under different frequencies: In order to evaluate the performance of the improved Zoom-FFT algorithm proposed in this embodiment under different frequencies, a set of simulation experiments are designed under the condition of a signal-to-noise ratio of 1 dB. In the experiment, the number of sampling points is kept constant, and the frequency of the simulation signal is gradually increased from 1950 Hz to 2050 Hz with a step size of 1 Hz. Through this simulation, the estimation accuracy and stability of different algorithms under different signal frequencies can be analyzed. The final simulation results are shown in Figure 6 and Figure 7 .

[0126] From Figure 6 and Figure 7 It can be seen that the root mean square error and the standard deviation of the frequency estimation of the FFT algorithm, the zero-padding FFT algorithm, and the Zoom-FFT algorithm show periodic changes as the signal gradually increases, while the CZT algorithm and the improved Zoom-FFT algorithm do not show regular fluctuations. Overall, the root mean square error of the improved Zoom-FFT algorithm is closer to the CRLB than other algorithms, meaning that the accuracy of the improved Zoom-FFT algorithm is less affected by the change in frequency, and the standard deviation of the improved algorithm is better than other algorithms, meaning that it is also more stable.

[0127] Overall, the FFT algorithm and the zero-padding FFT algorithm have larger errors under low SNR conditions and are not suitable for high-precision frequency estimation. The CZT algorithm, the Zoom-FFT algorithm, and the improved Zoom-FFT algorithm are stable in the entire frequency range and can effectively reduce RMSE and SD, especially the improved Zoom-FFT algorithm, which performs best, has high estimation accuracy and stability.

[0128] Distance simulation test: In order to verify the reliability and effectiveness of the improved Zoom-FFT algorithm in FMCW millimeter wave radar ranging, this embodiment evaluates the ranging performance of the algorithm through simulation experiments. In the experiment, the millimeter wave radar transmits a sawtooth wave frequency modulation signal, and sets the corresponding signal parameters according to the actual application scenario, as shown in Table 3:

[0129] Table 3 Sawtooth wave signal parameter settings

[0130]

[0131] In order to ensure the universality and objectivity of the experiment, the intermediate frequency signal is processed using the FFT algorithm, the zero-padding FFT algorithm, the CZT algorithm, the Zoom-FFT algorithm, and the improved Zoom-FFT algorithm for distance calculation. The experiment sets the initial target distance to 2m, and then gradually increases by 1m step by step to simulate the ranging of multiple target points. In order to reduce the influence of random errors on the simulation experiment, we perform 10 repeated simulation experiments to obtain the average value, and reduce the influence of random errors. The experimental results are shown in Table 4:

[0132] Table 4 Simulation experiment results (m)

[0133]

[0134] From the overall error analysis of the experimental results, the overall measurement error of the FFT algorithm is larger, the zero-padding FFT algorithm, the CZT algorithm and the Zoom-FFT algorithm have smaller error, and the error of the improved Zoom-FFT algorithm of the embodiment is the smallest, all the calculated values are almost accurate to the target values, and the maximum error is also relatively small. Overall, the improved algorithm of the embodiment performs best, has the smallest error and better stability, which shows that the accuracy and stability of the improved algorithm are better than those of the other algorithms.

[0135] In order to better verify the algorithm of the embodiment, the embodiment builds a complete unmanned aerial vehicle flight simulation test platform based on the ZD850 unmanned aerial vehicle developed by YH Far Travel Technology Model Company, integrates a height measurement module, a flight control unit and a data processing system, can collect unmanned aerial vehicle flight height information in real time, and adjust the flight height through the control system to realize the flight simulation function. The height measurement module uses a millimeter wave radar sensor, and the main technical parameters of the unmanned aerial vehicle are shown in Table 5.

[0136] Table 5 Main technical parameters of ZD850 unmanned aerial vehicle

[0137]

[0138] In order to verify the height measurement accuracy of the improved Zoom-FFT algorithm in the unmanned aerial vehicle flight simulation process, and the effectiveness and stability of the entire flight simulation system, a series of experiments are designed and carried out to evaluate the ranging performance of different algorithms under various environmental conditions. The experiments mainly compare and analyze the traditional FFT algorithm, the standard Zoom-FFT algorithm and the improved Zoom-FFT algorithm of the embodiment, and focus on the measurement error and anti-interference ability under different heights, different light and weather conditions.

[0139] Self-stable height measurement experiment: This experiment aims to evaluate the ranging accuracy of the millimeter wave radar using the improved Zoom-FFT algorithm under different environmental conditions. In the daytime, at night and in heavy fog, the millimeter wave radar is used to measure the ranging of six different height targets (1.5 m, 1.7 m, 1.9 m, 2.1 m, 2.3 m, 2.5 m). By conducting experiments in different environments to simulate the complex environment that the unmanned aerial vehicle may encounter in actual operation, the environmental adaptability of the algorithm is comprehensively verified. During the experiment, the measurement results of the traditional FFT algorithm, the standard Zoom-FFT algorithm and the improved Zoom-FFT algorithm are recorded respectively, and error analysis is carried out. The experimental results show that the measurement accuracy of the improved Zoom-FFT algorithm under different environments is significantly better than that of the traditional algorithm, and the specific results are as follows:

[0140] Table 6 Millimeter wave radar daytime height measurement results

[0141]

[0142] Table 7 Millimeter-wave radar height measurement results in night

[0143]

[0144] Table 8 Millimeter-wave radar height measurement results in heavy fog

[0145]

[0146] To measure the accuracy and stability of the algorithm, the mean absolute error (MAE) and the root mean square error (RMSE) are introduced as performance indicators. The mean absolute error reflects the average deviation of the algorithm calculation value from the true distance, and the smaller the value, the smaller the measurement error and the higher the measurement accuracy; RMSE is the average of the square of the error and then takes the square root, the smaller the value, the smaller the overall measurement error and the higher the ranging accuracy. The expression of the mean absolute error is:

[0147]

[0148] In the formula, y i is the true value, is the calculation value obtained by the algorithm, and n is the total number of measurement data points. The self-stable height measurement results are shown in Tables 9, 10 and 11.

[0149] Table 9 RMSE and MAE in daytime environment

[0150]

[0151] Table 10 RMSE and MAE in night environment

[0152]

[0153] Table 11 RMSE and MAE in heavy fog environment

[0154]

[0155] The experimental results show that the improved Zoom-FFT algorithm can provide higher ranging accuracy and more stable height measurement performance in different environments compared with traditional FFT and standard Zoom-FFT. Especially in heavy fog environment, the RMSE is only 2.11 mm and the MAE is only 1.85 mm, which shows excellent anti-interference ability and verifies its feasibility in unmanned aerial vehicle ground simulation flight. It has shown high accuracy and strong stability in different environments.

[0156] Dynamic height measurement experiment: In order to further verify the real-time height measurement performance and stability of the improved Zoom-FFT algorithm in the process of unmanned aerial vehicle flight simulation, a dynamic height measurement experiment is designed in this embodiment. In the experiment, the unmanned aerial vehicle flies along the predetermined route at a set height of 2m, and continuously collects millimeter wave radar ranging data during flight. The height measurement performance of the traditional FFT algorithm, the standard Zoom-FFT algorithm and the improved Zoom-FFT algorithm in the flight process is compared and analyzed to evaluate the measurement accuracy and error fluctuation. The experimental results are shown in Table 12 and Table 13. Figure 8 and Table 12.

[0157] Table 12 RMSE and MAE (m) of 2m flight simulation

[0158]

[0159] From the experimental results, it can be seen that the RMSE of the improved Zoom-FFT algorithm is 0.0103m, and the MAE is 0.0087m, which are smaller than those of the traditional FFT algorithm (RMSE is 0.0218m, and MAE is 0.0184m) and the standard Zoom-FFT algorithm (RMSE is 0.0157m, and MAE is 0.0133m). This indicates that the improved Zoom-FFT algorithm has the smallest measurement error and good stability in the dynamic process of unmanned aerial vehicle flight simulation, and can more accurately reflect the change of flight height, verifying the superiority of the algorithm in real-time height measurement of unmanned aerial vehicle flight simulation, and providing strong support for precise height control of unmanned aerial vehicle flight simulation.

[0160] Complex environment flight simulation: In order to verify the height measurement results of the improved algorithm in different environments, a 50cm high obstacle is set on the flight route of the unmanned aerial vehicle. In the daytime and at night, the unmanned aerial vehicle always maintains a height of 2m from the ground to compare and analyze the height measurement performance of the traditional FFT algorithm, the standard Zoom-FFT algorithm and the improved Zoom-FFT algorithm in the flight process, and evaluate the measurement accuracy and error fluctuation. The experimental results are shown in Table 13 and Table 14. Figure 9 、 Figure 10 , Table 13 and Table 14.

[0161] Table 13 RMSE and MAE (m) of 2m flight simulation in the daytime

[0162]

[0163] Table 14 RMSE and MAE (m) of 2m flight simulation at night

[0164]

[0165] From the measurement accuracy and error fluctuation, the RMSE of the improved Zoom-FFT algorithm is 0.0154 m and the MAE is 0.0103 m in the daytime environment; the RMSE is 0.0163 m and the MAE is 0.0112 m in the night environment. Both are better than the traditional FFT algorithm (RMSE is 0.0263 m and MAE is 0.0192 m in the daytime; RMSE is 0.0278 m and MAE is 0.0203 m in the night) and the standard Zoom-FFT algorithm (RMSE is 0.0196 m and MAE is 0.0146 m in the daytime; RMSE is 0.0183 m and MAE is 0.0145 m in the night).

[0166] The experimental results show that the improved Zoom-FFT algorithm has smaller measurement error in complex environments (different light and containing obstacles), exhibits stronger anti-interference ability, and can measure height more accurately, providing reliable height measurement guarantee for the hover flight of unmanned aerial vehicles in complex environments, and effectively supporting the application of unmanned aerial vehicles in complex scenes.

[0167] Self-stable slope detection experiment: In this experiment, in order to verify the slope detection ability of the multi-millimeter wave radar in static environment, the unmanned aerial vehicle is hovered at a height of 1.5 meters from the ground, and the millimeter wave radar is used to measure the slope land with slope of 15°, 20°, 25° and 30° respectively. During the test, the traditional FFT algorithm, the Zoom-FFT algorithm and the improved Zoom-FFT algorithm are used for data processing respectively to evaluate the accuracy of different algorithms in slope measurement, and the experimental results are shown in Table 15.

[0168] Table 15 Self-stable terrain slope detection results

[0169]

[0170] The improved Zoom-FFT algorithm shows higher accuracy in slope detection, and its measurement value is closest to the true value under all slope conditions, especially in 15° and 30° slope measurement. In contrast, the error of the traditional FFT algorithm is larger, and although the standard Zoom-FFT algorithm is better than the traditional FFT algorithm, it still has certain deviation. The experimental results show that the improved Zoom-FFT algorithm has higher precision and reliability in slope detection in static environment, and also verifies the effectiveness of the multi-millimeter wave radar slope measurement.

[0171] Flight slope detection experiment: In order to further verify the slope detection ability of the millimeter wave radar in the dynamic environment, the experiment is carried out when the unmanned aerial vehicle is in flight. The unmanned aerial vehicle flies forward at a flight height of 2m, and synchronously collects the data of two millimeter wave radars and flight control IMU to measure the terrain slope and the yaw angle of the unmanned aerial vehicle. Under the same slope conditions (15°, 20°, 25°, 30°), the measured data is processed by using FFT algorithm, Zoom-FFT algorithm and improved Zoom-FFT algorithm, and the experimental measurement results are shown in Table 16.

[0172] Table 5.14 Dynamic terrain slope detection results

[0173]

[0174]

[0175] From the experimental results, compared with the hovering state, the error measured in the dynamic flight state is obviously greater than the measurement result in the self-stable state. The reason for this situation is mainly affected by the following two factors: in the process of unmanned aerial vehicle flight, the unmanned aerial vehicle is disturbed by airflow and the vibration caused by its own motor, which leads to the fluctuation of millimeter wave radar measurement data, and further reduces the precision of terrain slope measurement. In the process of unmanned aerial vehicle flight, the IMU is affected by the change of acceleration and the adjustment of attitude, which will introduce additional measurement error. The experimental results also show that the terrain slope precision calculated by using the improved Zoom-FFT algorithm is higher than that of FFT algorithm and Zoom-FFT algorithm, which verifies the application value of millimeter wave radar in the complex terrain flight of unmanned aerial vehicle. This provides solid technical support for realizing accurate terrain perception and adaptive flight control, and further promotes the application potential of unmanned aerial vehicle in complex environment.

[0176] The above only describes the preferred embodiments of the present application, and does not limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1.A method for measuring the height of a drone based on millimeter wave radar, characterized in that, The method comprises the following steps: S1, performing FFT transformation on the intermediate frequency signal x(n) received by the millimeter wave radar, calculating the amplitude |X(k)| of the signal, and extracting the FFT spectrum; S2, traverse the FFT spectrum and find the frequency f0 corresponding to the maximum amplitude point in the spectrum diagram, set the frequency refinement interval (f l ,f h ) with frequency resolution Δf as the frequency radius with the frequency f0 as the center, determine the refined target spectrum, and extract the narrowband signal; S3, re-modulating, low-pass filtering and down-sampling the signal in the frequency refinement interval (f l ,f h ) and then performing FFT transform again and extracting the refined frequency spectrum; S4, traversing the refined spectrum and finding the spectrum line with the largest amplitude and the two adjacent spectrum lines, and performing polynomial fitting; S5, solving the fitting parameters of the polynomial fitting function and calculating the extreme point of the fitting curve; S6, taking the frequency corresponding to the extreme point as the deviation frequency, correcting the frequency f0, and determining the target distance according to the corrected frequency. 2.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 1, wherein, The amplitude point of the spectral line with the largest amplitude in the step S4 is (f i ,y i ), and the amplitude points of the two spectral lines adjacent to it are (f i-1 ,y i-1 ) and (f i+1 ,y i+1 ), a quadratic polynomial function is constructed by using quadratic polynomial fitting. R(x) = ax + bx + c 2 + bx + c In the formula, a, b, and c are fitting parameters of the quadratic polynomial. 3.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 2, wherein, In the step S5, the solving step of the fitting parameters is: S51, using the mean square error to evaluate the deviation between the fitting curve R(x) and the actual data points, and the expression is: S52, according to the extreme value principle of the multivariate function, the partial derivative of the mean square error with respect to the fitting parameters a, b, and c satisfies the following formula: S53, the fitting equation of the quadratic polynomial function is obtained according to the expression of step S52: S54, the fitting parameters a, b, and c of the quadratic polynomial are solved according to the fitting equation. 4.The unmanned aerial vehicle height measurement method based on millimeter wave radar of claim 3, wherein, In the step S5, the frequency of the extreme point is: 5.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 4, wherein, The corrected frequency is: f0' = f0 + f r The target distance is: In the formula, c is the speed of light, T is the frequency sweeping time of the millimeter wave radar, and Δf is the frequency resolution. 6.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 1, wherein, The complex modulation of the intermediate frequency signal x(n) in the frequency refinement interval (f l ,f h ) in the step S3 satisfies the following equation: In the formula, n is the number of sampling points. 7.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 6, wherein, In the step S3, the expression for performing low-pass filtering on the complex modulated signal is: x filter (n) = x move (n) · h(n) In the formula, h(n) is the impulse response of the filter. 8.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 7, wherein, In the step S3, the expression for performing downsampling on the low-pass filtered signal is: x resample (m) = x filter (n-D) In the formula, D is the refinement multiple. 9.The unmanned aerial vehicle height measurement method based on millimeter wave radar according to claim 8, wherein, In the step S3, the down-sampled signal x resample (m) performing an FFT transform: In the formula, N zoom is the number of sampling points of the FTT transform in step S6.

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