Unmanned aerial vehicle rotor rotation frequency estimation method based on multi-parameter linear regression algorithm

Abstract

The invention discloses an unmanned aerial vehicle rotor rotation frequency estimation method based on a multi-parameter linear regression algorithm, and belongs to the field of signal processing and analysis. The method comprises the following steps: step 1, establishing a multi-point scattering rotor wing double-blade model; 2, based on the rotor wing double-blade model, estimating the rotor wing rotation frequency through a periodic method and a maximum frequency shift method; and 3, on the basis of estimating the rotation frequency of the rotor by a periodic method and a maximum frequency shift method, weighting the results of the two methods to estimate the rotation frequency of the rotor, which is called a linear regression algorithm. Through an unmanned aerial vehicle rotor micro-Doppler feature detection experiment, the effectiveness and the accuracy of estimating the unmanned aerial vehicle rotor frequency by the multiple linear regression algorithm are verified. According to the method, the spin frequency of the rotor wing of the unmanned aerial vehicle can be estimated more accurately by comprehensively utilizing the existing periodic method and the maximum frequency shift method through the multiple linear regression algorithm. The method provides a novel and effective way for extracting the micro-Doppler features of the unmanned aerial vehicle, and has relatively high application potential.

Description

Technical Field

[0001] The invention belongs to the field of signal processing and analysis, and in particular relates to a method for estimating the rotation frequency of a UAV rotor based on a multi-parameter linear regression algorithm. Background Art

[0002] For rotor UAVs, rotor blades are their main power components and the key source of micro-Doppler effect. At the same time, their micro-motion characteristics are also an important indicator of the type and model of UAVs. When describing the structural characteristics of the rotor, they are usually represented in a parametric way. Currently, the main parameters used to identify UAVs include rotor rotation frequency, rotor length, number of blades, and number of rotors. Among them, the rotor rotation frequency is the basic parameter, which affects the other three parameters and the accuracy of frequency shift extraction.

[0003] At present, there are two main methods for estimating the rotation frequency of rotor blades. One method is to obtain the rotation frequency of rotor blades by the inverse of the time taken by the rotor blades to complete one cycle. When extracting the cycle of the trough in the time-frequency graph and calculating the inverse, the extraction of the cycle is limited by the time resolution, and the error is greater when the rotor blades rotate too fast. The other method is to derive the rotation frequency of rotor blades from the micro-Doppler maximum frequency shift formula. When this method estimates the maximum micro-Doppler frequency shift in the time-frequency graph, it is affected by the external environment and the internal noise of the experimental equipment, and the estimated maximum frequency shift has a large error. At the same time, when the rotation frequency is low, the error is large due to insufficient resolution. Summary of the invention

[0004] In order to solve the above-mentioned problems existing in the background technology, the present invention proposes a method for estimating the rotor rotation frequency of a UAV based on a multi-parameter linear regression algorithm. The measurement results of the periodic method and the maximum frequency shift method are used to increase specific weight values, thereby reducing the measurement error. The multi-parameter linear regression algorithm is an excellent means to achieve this function.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for estimating the rotation frequency of a UAV rotor based on a multi-parameter linear regression algorithm, the method comprising the following steps:

[0007] Step 1: Establish a rotor double-blade model with multi-point scattering;

[0008] Step 2: Based on the rotor double-blade model, estimate the rotor rotation frequency by using the period method and the maximum frequency shift method;

[0009] Step 3: Based on the estimation of the rotor rotation frequency by the period method and the maximum frequency shift method, the rotor rotation frequency is estimated by weighting the results of the two.

[0010] Furthermore, in step 1, the process of establishing the multi-point scattering rotor double-blade model is as follows:

[0011] The center of the rotor blade is located at the coordinate origin O. When the azimuth angle α is zero and the pitch angle is β, the distance from the radar Q to the rotor center is R0, and the distance from the scattering point M on the rotor blade to the rotor center is l M , the scattering point M rotates around the Z axis at a constant angular velocity ω; let the initial phase of the rotor blade be The rotor blade reaches point M' from the scattering point M after time t, and its phase is After the scattering point M rotates, the distance from the scattering point to the radar is as follows:

[0012]

[0013] Where: z0 represents the height of radar Q relative to the coordinate origin O;

[0014] Since R0>>l M , then formula (1) is expressed as:

[0015]

[0016] Since the height z0 of the rotor blade relative to the radar and the pitch angle β between the rotor blade and the laser radar Q are not zero, formula (2) is modified as follows:

[0017]

[0018] Where: z0 represents the height of radar Q relative to the coordinate origin O;

[0019] At this time, the laser radar echo signal at the scattering point M is:

[0020]

[0021] Where: f0 represents the carrier frequency of the laser radar, λ represents the wavelength of the laser, and the phase term is derived to obtain the micro-Doppler frequency shift caused by the rotation of the rotor scattering point M, that is:

[0022]

[0023] in: represents phase, t represents time;

[0024] The angular velocity of the rotor is calculated as:

[0025]

[0026] Assume that the coordinates of each scattering point are (x i ,y j ,z k), where i, j, k are integers; the distance from the rotor center O to each scattering point is l M (x,y,z)=(x 2 +y 2 +z 2 ) 1 / 2 , the echo signal of the rotor double blades is:

[0027]

[0028] Where R'0=R0+l M (x,y,z),

[0029] Formula (7) is the obtained rotor double-blade model.

[0030] Furthermore, in step 2, based on the rotor double-blade model, the rotor rotation frequency is estimated by the periodic method and the maximum frequency shift method. The idea of ​​the periodic method is to extract the repetitive moment of the characteristic point from the micro-Doppler time-frequency spectrum of the rotor rotation; the maximum frequency shift method estimates the rotor rotation frequency as:

[0031]

[0032] Where: l p represents the distance from the scattering point P on the rotor blade to the center of the rotor, f M-max Indicates the maximum frequency shift produced by the rotor.

[0033] Furthermore, in step 3, based on the estimation of the rotor rotation frequency by the period method and the maximum frequency shift method, the rotor rotation frequency is estimated by weighting the results of the two; specifically:

[0034] For a sample with n features, the regression equation is:

[0035]

[0036] in: Represents the predicted value of the target variable, x1,x2,x3...x n Represents different characteristics of the sample, w0 represents the intercept, w1, w2, w3...w n Represents the regression coefficient; written in matrix form as follows:

[0037]

[0038] Abbreviated as Where X is the feature matrix with a structure of (m, n+1), and w is the weight matrix with a structure of (n+1, 1);

[0039] Let the true value of the target variable be y i, the error between the predicted value and the true value is expressed by the loss function J(w):

[0040]

[0041] To solve the optimal weight matrix, J(w) needs to be minimized. The stochastic gradient descent method is used to achieve this goal. The specific steps are as follows:

[0042] First, the loss function is averaged to eliminate the influence of the sample size m. Formula (10) is rewritten as:

[0043]

[0044] Derivative with respect to parameter w:

[0045]

[0046] Assume the learning rate is σ, and continuously iterate and update until J(w) is minimized to find the optimal weight matrix;

[0047]

[0048] The weight matrix contains three parameters ω0, ω1 and ω2. According to the simulation data, the linear regression algorithm is used to calculate the following results:

[0049]

[0050] The rotor rotation frequency f is thus estimated.

[0051] The beneficial effect of the present invention relative to the prior art is that accurate estimation of the rotor spin frequency of the UAV is of great significance for the detection and identification of the UAV. However, the existing methods are difficult to achieve accurate spin frequency estimation in different frequency bands. The current periodic method relies on the estimation of the rotor period, and the rotation period of the rotor is determined by the number of maximum peaks. However, the accuracy of the periodic method is limited by the time resolution, especially when the rotor blades rotate at high speed, the error increases significantly. On the other hand, the maximum frequency shift method derives the rotation frequency of the rotor through the frequency shift formula, but its result is interfered by external environmental factors and internal noise of the experimental equipment, resulting in a large error in the frequency estimation. To solve these problems, the present invention proposes a method for estimating the rotor rotation frequency of the UAV based on a multi-parameter linear regression algorithm for the laser radar UAV rotor target echo model. The method uses a multivariate linear regression algorithm to comprehensively utilize the existing periodic method and the maximum frequency shift method, so that the spin frequency of the UAV rotor can be estimated more accurately. This method provides a novel and effective way to extract the micro-Doppler features of UAVs, and has high application potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a map of the locations of the LiDAR and the UAV rotors.

[0053] Figure 2 It is a schematic diagram of micro-Doppler time-frequency signal simulation.

[0054] Figure 3 It is a schematic diagram of the rotor rotation direction.

[0055] Figure 4 It is the absolute error diagram of the simulation estimation error of the maximum frequency shift method and the period method.

[0056] Figure 5 It is the relative error diagram of the simulation estimation error of the maximum frequency shift method and the period method.

[0057] Figure 6 It is a linear regression calculation result diagram of the present invention.

[0058] Figure 7 It is the error analysis diagram of the linear regression algorithm of the present invention.

[0059] Figure 8 It is a schematic diagram of the UAV rotor micro-Doppler signal detection experimental system.

[0060] Fig. 9 It is the absolute error diagram of the experimental estimation error of the present invention.

[0061] Fig.10 It is a relative error diagram of the experimental estimation error of the present invention. DETAILED DESCRIPTION

[0062] Specific implementation method 1: This implementation method discloses a method for estimating the rotation frequency of a UAV rotor based on a multi-parameter linear regression algorithm, and the method comprises the following steps:

[0063] Step 1: Establish a multi-point scattering rotor double-blade model (i.e., laser radar UAV rotor target echo model);

[0064] Step 2: Based on the rotor double-blade model, the rotor rotation frequency is estimated by the period method and the maximum frequency shift method (the idea of ​​the period method is to extract the repetitive moment of the characteristic point from the micro-Doppler time-frequency spectrum of the rotor rotation, and the maximum frequency shift method is derived by the maximum frequency shift formula);

[0065] Step 3: Based on the estimation of the rotor rotation frequency by the period method and the maximum frequency shift method, the rotor rotation frequency is estimated by weighting the results of the two, which is called the linear regression algorithm.

[0066] Furthermore, the effectiveness and accuracy of the multivariate linear regression algorithm in estimating the UAV rotor frequency were verified through the UAV rotor micro-Doppler feature detection experiment.

[0067] Further, such as Figure 1 As shown, in step 1, the process of establishing a multi-point scattering rotor double-blade model is as follows:

[0068] The center of the rotor blade is located at the coordinate origin O. When the azimuth angle α is zero and the pitch angle is β, the distance from the radar Q to the rotor center is R0, and the distance from the scattering point M on the rotor blade to the rotor center is l M , the scattering point M rotates around the Z axis at a constant angular velocity ω; let the initial phase of the rotor blade be The rotor blade reaches point M' from the scattering point M after time t, and its phase is After the scattering point M rotates, the distance from the scattering point to the radar is as follows:

[0069]

[0070] Where: z0 represents the height of radar Q relative to the coordinate origin O;

[0071] Since R0>>l M , then formula (1) is expressed as:

[0072]

[0073] Since the height z0 of the rotor blade relative to the radar and the pitch angle β between the rotor blade and the laser radar Q are not zero, formula (2) is modified as follows:

[0074]

[0075] Where: z0 represents the height of radar Q relative to the coordinate origin O;

[0076] At this time, the laser radar echo signal at the scattering point M is:

[0077]

[0078] Where: f0 represents the carrier frequency of the laser radar, λ represents the wavelength of the laser, and the phase term is derived to obtain the micro-Doppler frequency shift caused by the rotation of the rotor scattering point M, that is:

[0079]

[0080] in: represents phase, t represents time;

[0081] The angular velocity of the rotor is calculated as:

[0082]

[0083] Assume that the coordinates of each scattering point are (x i ,y j ,zk ), where i, j, k are integers; the distance from the rotor center O (i.e., the origin of the coordinate system) to each scattering point is l M (x,y,z)=(x 2 +y 2 +z 2 ) 1 / 2 , the echo signal of the rotor double blades is:

[0084]

[0085] Where R'0=R0+l M (x,y,z),

[0086] Formula (7) is the obtained rotor double-blade model.

[0087] Furthermore, in step 2, based on the rotor double-blade model, the rotor rotation frequency is estimated by the periodic method and the maximum frequency shift method. The idea of ​​the periodic method is to extract the repetitive moment of the characteristic point from the micro-Doppler time-frequency spectrum of the rotor rotation; the maximum frequency shift method estimates the rotor rotation frequency as:

[0088]

[0089] Where: l p represents the distance from the scattering point P on the rotor blade to the center of the rotor, f M-max Indicates the maximum frequency shift produced by the rotor.

[0090] Analysis of the periodic method and the maximum frequency shift method for estimating the rotor rotation frequency. The idea of ​​the periodic method is to extract the repetitive moment of the characteristic point from the micro-Doppler of the rotor rotation. The sub-sideband points in the time-frequency distribution of the micro-Doppler of the UAV rotor are selected as the extraction reference points, such as Figure 2 The secondary sideband points correspond to the smallest micro-Doppler shift of the rotor, which is more convenient and accurate for matrix extraction. Figure 2 The secondary sideband points marked in the figure correspond to Figure 3 The direction of the scattering unit P at time t1. After the time interval of each spin cycle of the scattering unit P, the corresponding sub-sideband point will appear in the time spectrum. By extracting the time corresponding to the sub-sideband point, the rotation period of the rotor can be estimated. The rotation period is the inverse of the rotation frequency of the drone rotor.

[0091] Furthermore, in step 3, based on the estimation of the rotor rotation frequency by the period method and the maximum frequency shift method, the rotor rotation frequency is estimated by weighting the results of the two; specifically:

[0092] Regression analysis studies the relationship between independent variables and dependent variables, indicating the influence of multiple independent variables on a dependent variable. For a sample with n characteristics, the regression equation is:

[0093]

[0094] in: Represents the predicted value of the target variable, x1,x2,x3...x n Represents different characteristics of the sample, w0 represents the intercept, w1, w2, w3...w n Represents the regression coefficient; written in matrix form as follows:

[0095]

[0096] Abbreviated as Where X is the feature matrix with a structure of (m, n+1), and w is the weight matrix with a structure of (n+1, 1);

[0097] Let the true value of the target variable be y i , the error between the predicted value and the true value is expressed by the loss function J(w):

[0098]

[0099] To solve the optimal weight matrix, J(w) needs to be minimized. The stochastic gradient descent method is used to achieve this goal. The specific steps are as follows:

[0100] First, the loss function is averaged to eliminate the influence of the sample size m. Formula (10) is rewritten as:

[0101]

[0102] Derivative with respect to parameter w:

[0103]

[0104] Assume the learning rate is σ, and continuously iterate and update until J(w) is minimized to find the optimal weight matrix;

[0105]

[0106] The weight matrix contains three parameters ω0, ω1 and ω2. According to the simulation data, the linear regression algorithm is used to calculate the following results:

[0107]

[0108] The rotor rotation frequency f is thus estimated.

[0109] Furthermore, in step 4, the effectiveness and accuracy of estimating the rotor frequency of the drone by the multivariate linear regression algorithm is verified through the drone rotor micro-Doppler feature detection experiment. The specific process is as follows:

[0110] The rotor blade model with a length × width = 9mm × 3mm was obtained by 3D printing. The rotation frequency of the rotor blade was controlled by changing the rotation speed. The experiment selected the measurement results of the rotor blade rotation speed of 120 to 1500r / min, and its rotation frequency was in the range of 1 to 25Hz. The UAV rotor micro-Doppler signal detection experimental system (such as Figure 8 As shown in the figure, the model surface is irradiated with laser to obtain echo data, and the time-frequency diagram is obtained after data processing; the time-frequency diagram of 25 groups of data are collected, and the rotor rotation frequency is extracted based on the periodic method and the maximum micro-Doppler frequency shift method respectively; and the two methods are subjected to multivariate linear regression processing, and f0=14Hz is selected as the dividing point to obtain the multivariate linear regression formula. The measurement results after processing by the linear regression algorithm are more accurate than those of the above two methods.

[0111] Embodiment 1:

[0112] This embodiment discloses a method for estimating the rotation frequency of a UAV rotor based on a multi-parameter linear regression algorithm, the method comprising the following steps:

[0113] Step 1: The UAV rotor is usually composed of two or three blades. The model in the present invention is a double-blade rotor, and the two blades are symmetrical with respect to the rotation center. Figure 1 The figure shows the rotor double-blade simulation model, which simulates the echo model of the UAV rotor under the lidar system. The model parameters are shown in Table 1.

[0114] Table 1 UAV rotor micro-Doppler signal simulation parameters

[0115]

[0116] Figure 1 In the figure, D represents the rotor blade width and L represents the rotor blade length.

[0117] Since the echo signal of the UAV rotor is a non-stationary signal, the short-time Fourier transform (STFT) is used to analyze the echo model. Figure 2 The time-frequency distribution (TFD) of the simulated UAV rotor micro-Doppler signal is shown. The micro-Doppler frequency shift changes symmetrically with respect to the fundamental frequency on the time line. This is because the simulation uses a single rotor with two blades. The scattering units on the two blades always rotate at equal speeds and in opposite directions, and the micro-Doppler frequency shifts are equal in magnitude but opposite in direction.

[0118] Step 2: Analysis of the period method and maximum frequency shift method to estimate the rotor rotation frequency. Figure 2 In the example, the identified secondary sidebands are located at the troughs of the envelope, corresponding to Figure 3 This is point P in the graph, which is also the point with the smallest frequency shift. Figure 2The maximum frequency shift determined in is the micro-Doppler shift caused by the scattering point at the far edge of the rotor, corresponding to Figure 3 Point P' in. From formula (5), we can see that;

[0119]

[0120] This equation corresponds to the maximum micro-Doppler frequency shift f of the rotor blades. M-max , then the rotor spin frequency estimated by the maximum frequency shift method can be expressed as:

[0121]

[0122] in, L represents the length of the rotor blade and D represents the width of the rotor blade.

[0123] Figure 4 and Figure 5 The curves are the nonlinear fitting results of the two methods of extracting errors. f1 represents the error of the frequency value estimated by the period method, and f2 represents the error of the frequency value estimated by the maximum frequency shift method. Figure 4 and Figure 5 It can be seen that there are significant differences in the measurement effects of the two methods in different frequency ranges: in the frequency range less than 14 Hz, the absolute error estimated by the period method increases slowly with the increase of frequency, and the absolute error of the maximum micro-Doppler frequency shift method decreases with the increase of frequency and is greater than the absolute error of the period method; in the frequency range greater than 14 Hz, the absolute error of the period method increases rapidly with the increase of frequency, and the absolute error of the maximum micro-Doppler frequency shift method decreases slowly with the increase of frequency. In the frequency range less than 10 Hz, the relative error measured by the period method increases with the increase of frequency, and the relative error of the maximum micro-Doppler frequency shift method decreases rapidly with the increase of frequency, but is greater than the relative error of the period method; when the frequency is greater than 10 Hz, the relative error of the period method still increases with the increase of frequency and is greater than the relative error of the maximum micro-Doppler frequency shift method, and the relative error of the maximum micro-Doppler frequency shift method decreases slowly with the increase of frequency. In summary, the period method and the maximum frequency shift method have good frequency estimation accuracy within a specific range, but the overall performance is poor, and it is difficult to meet the high-precision requirements under complex conditions.

[0124] Step 3: The weight matrix in the present invention includes three parameters ω0, ω1 and ω2. According to the simulation data, the linear regression algorithm is used to calculate the following results:

[0125]

[0126] like Figure 6 is the result of linear regression calculation, the ordinate represents the measured value of the linear regression algorithm, and the straight line in the figure is the result of least squares fitting. The slope of the straight line is 1, and the residual sum of squares is 0.0326. The error of the multivariate linear regression algorithm is as follows Figure 7 As shown in the figure, it can be seen that the absolute error of the result obtained by the linear regression algorithm fluctuates around 0.02Hz, and the maximum does not exceed 0.1Hz. The relative error is about 0.18%, and the maximum value is 1.6%. Therefore, the linear regression algorithm is used to weight the results of the maximum frequency shift method and the period method, ensuring the high accuracy of the drone's spin frequency in the full frequency band.

[0127] Step 4: Experimental schematic diagram Figure 8 As shown in the figure, the laser beam emitted by the seed laser (i.e., laser light source) with an emission power of 100mW is divided into two parts, signal light and reference light, by the fiber beam splitter. The signal light with a total power of 90% is irradiated to the rotor blade target by the transmitting optical system and then scattered; the scattered micro-Doppler echo signal enters the fiber beam combiner through the receiving optical system, the reference light enters the acousto-optic modulator and shifts the frequency by 70MHz, and the output light enters the fiber beam combiner through the fiber attenuator. The two beams of light are mixed in the fiber beam combiner and transmitted to the balanced detector to form heterodyne interference and retain the difference frequency part. The optical signal is converted into an electrical signal and collected by the data acquisition card, and finally processed by the computer to obtain the time-frequency diagram.

[0128] The 3D printed rotor was used, and the experimental parameters are shown in Table 2. The maximum speed of the motor was 3000r / min, and the rotation frequency of the rotor blades was controlled by changing the speed. The arithmetic progression adjusted the speed of the rotor rotation in turn to verify the correctness of the linear regression algorithm.

[0129] Table 2 Experimental parameters

[0130]

[0131]

[0132] The absolute error of experimental data is Fig. 9 As shown in Figure 2, it can be seen that the absolute error of the period method increases with the increase of f0, and the absolute error of the maximum frequency shift method decreases with the increase of f0. The two curves intersect at f0 = 14.07 Hz. Fig.10 It can be seen that the relative error of the periodic method increases slowly with the increase of f0, the average relative error of the periodic method is 5.98%, and the average relative error of the maximum frequency shift method is 9.80%. Specifically, the relative error in the low-frequency region is relatively large, and with the increase of f0, the relative error decreases rapidly, and the two fitting nonlinear curves intersect at f0 = 14.28 Hz.

[0133] Analyze the estimation errors of the two methods and select f0 = 14 Hz as the dividing line. Weight the estimation results of the above two methods and use the multivariate linear regression algorithm for weighting. The final estimation results are as follows:

[0134]

[0135] Substituting f1 and f2 into formula (16), the estimated error result is Fig. 9 As shown. Fig. 9 In the figure, the spin frequency f3 weighted by the multivariate linear regression method shows the smallest absolute error in almost the entire spectrum, with a maximum value of 0.35 Hz. This shows that the absolute error is effectively reduced after the absolute error is weighted by the multivariate linear regression algorithm. Fig.10 It shows that the relative error processed by the multivariate linear regression algorithm is in the lowest range in almost the entire frequency band. The average relative error is 1.07%, and the maximum relative error does not exceed 4.05%. The results show that the weighted estimation results of the multivariate linear regression algorithm are generally better than the results of the period method and the maximum frequency shift method.

[0136] The above are only preferred specific implementation modes of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical solutions and inventive concepts of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for estimating the rotation frequency of a UAV rotor based on a multi-parameter linear regression algorithm, characterized in that: The method comprises the following steps: Step 1: Establish a rotor double-blade model with multi-point scattering; Step 2: Based on the rotor double-blade model, estimate the rotor rotation frequency by using the period method and the maximum frequency shift method; Step 3: Based on the estimation of the rotor rotation frequency by the period method and the maximum frequency shift method, the rotor rotation frequency is estimated by weighting the results of the two.

2. The method for estimating the rotor frequency of a UAV based on a multi-parameter linear regression algorithm according to claim 1, characterized in that: In step 1, the process of establishing a multi-point scattering rotor double-blade model is as follows: The center of the rotor blade is located at the coordinate origin O. When the azimuth angle α is zero and the pitch angle is β, the distance from the radar Q to the rotor center is R0, and the distance from the scattering point M on the rotor blade to the rotor center is l M , the scattering point M rotates around the Z axis at a constant angular velocity ω; let the initial phase of the rotor blade be The rotor blade reaches point M' from the scattering point M after time t, and its phase is After the scattering point M rotates, the distance from the scattering point to the radar is as follows: Where: z0 represents the height of radar Q relative to the coordinate origin O; Since R0>>l M , then formula (1) is expressed as: Since the height z0 of the rotor blade relative to the radar and the pitch angle β between the rotor blade and the laser radar Q are not zero, formula (2) is modified as follows: Where: z0 represents the height of radar Q relative to the coordinate origin O; At this time, the laser radar echo signal at the scattering point M is: Where: f0 represents the carrier frequency of the laser radar, λ represents the wavelength of the laser, and the phase term is derived to obtain the micro-Doppler frequency shift caused by the rotation of the rotor scattering point M, that is: in: represents phase, t represents time; The angular velocity of the rotor is calculated as: Assume that the coordinates of each scattering point are (x i ,y j ,z k ), where i, j, k are integers; the distance from the rotor center O to each scattering point is l M (x,y,z)=(x 2 +y 2 +z 2 ) 1 / 2 , the echo signal of the rotor double blades is: Where R'0=R0+l M (x,y,z), Formula (7) is the obtained rotor double-blade model.

3. The method for estimating the rotor rotation frequency of a UAV based on a multi-parameter linear regression algorithm according to claim 1, characterized in that: In step 2, based on the rotor double-blade model, the rotor rotation frequency is estimated by the period method and the maximum frequency shift method. The idea of ​​the period method is to extract the repetitive moment of the characteristic point from the micro-Doppler time-frequency spectrum of the rotor rotation; the maximum frequency shift method estimates the rotor rotation frequency as: Among them: p represents the distance from the scattering point P on the rotor blade to the center of the rotor, f M-max Indicates the maximum frequency shift produced by the rotor.

4. The method for estimating the rotor rotation frequency of a UAV based on a multi-parameter linear regression algorithm according to claim 1, characterized in that: In step 3, based on the estimation of the rotor rotation frequency by the period method and the maximum frequency shift method, the rotor rotation frequency is estimated by weighting the results of the two; specifically, as follows: For a sample with n features, the regression equation is: in: Represents the predicted value of the target variable, x1,x2,x3...x n Represents different characteristics of the sample, w0 represents the intercept, w1, w2, w3...w n Represents the regression coefficient; written in matrix form as follows: Abbreviated as Where X is the feature matrix with a structure of (m, n+1), and w is the weight matrix with a structure of (n+1, 1); Let the true value of the target variable be y i , the error between the predicted value and the true value is expressed by the loss function J(w): To solve the optimal weight matrix, J(w) needs to be minimized. The stochastic gradient descent method is used to achieve this goal. The specific steps are as follows: First, the loss function is averaged to eliminate the influence of the sample size m. Formula (10) is rewritten as: Derivative with respect to parameter w: Assume the learning rate is σ, and continuously iterate and update until J(w) is minimized to find the optimal weight matrix; The weight matrix contains three parameters ω0, ω1 and ω2. According to the simulation data, the linear regression algorithm is used to calculate the following results: The rotor rotation frequency f is thus estimated.

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