Micro-motion parameter extraction method of flapping-wing UAV based on time-frequency characteristics of laser echo

Abstract

A method for extracting micro-motion parameters of flapping-wing UAVs based on the time-frequency characteristics of laser echoes belongs to the field of laser radar application detection. The method comprises the following steps: Step 1: Establishing a rectangular one-segment flapping-wing UAV motion model based on multiple scattering centers and a rectangular-triangular composite two-segment flapping-wing UAV motion model based on multiple scattering centers; Step 2: Simulating and obtaining the time-frequency spectrum of a one-segment flapping-wing UAV and a two-segment flapping-wing UAV at different azimuths and pitch angles; Step 3: Parameter extraction for flapping-wing UAVs with different structures. The method of the present invention can effectively realize the extraction of micro-motion parameters of the upper arm, forearm length and flapping angle of flapping-wing UAVs, and provides a new technical approach for the application of laser micro-Doppler system detection technology in target precise detection and identification.

Description

Technical Field

[0001] The invention relates to a method for extracting micro-motion parameters of a flapping-wing unmanned aerial vehicle, in particular to a method for extracting micro-motion parameters of a flapping-wing unmanned aerial vehicle based on a coherent laser radar micro-Doppler detection system, and belongs to the field of laser radar application detection. Background Art

[0002] At present, micro-Doppler technology has been widely used in the research field of micro-motion parameters of rotary-wing UAVs, and researchers have made great progress in this direction. The rotors of rotary-wing UAVs produce significant and regular micro-motion effects during flight, which makes micro-Doppler technology widely used in the analysis of their motion characteristics. However, compared with the popularity of rotary-wing UAV research, the research on micro-motion parameters of flapping-wing UAVs is relatively lagging. Due to its unique flight mechanism (completely different from rotary-wing UAVs), flapping-wing UAVs generate lift and propulsion by simulating the flapping of birds or insects in nature. This flight action not only shows nonlinear and unstable complex changes in time, but also forms multi-dimensional dynamic characteristics in space. The micro-Doppler signal brought by flapping wing motion has greater uncertainty in multiple dimensions such as frequency, amplitude, and phase, which makes it extremely difficult to extract parameters of flapping wing motion. The periodic flapping of the wings of flapping-wing UAVs will produce more complex and variable micro-motion signals, resulting in more complex frequency and amplitude characteristics of its micro-motion signals. Although flapping-wing UAVs have potential advantages in certain application fields, the research on their micro-motion characteristics is still in its infancy and requires further systematic exploration and research.

[0003] How to quickly and accurately detect and identify flapping-wing drones is a problem that needs to be explored in the field of detection and identification. At present, most of the existing flapping-wing drones are of one-stage structure, and a small number of flapping-wing drones are of two-stage structure. In this regard, the present invention proposes a method for extracting micro-motion parameters of flapping-wing drones based on the time-frequency characteristics of laser echoes by using the characteristics of laser micro-Doppler, thereby realizing the extraction of micro-motion parameters of flapping-wing drones. Summary of the invention

[0004] In order to solve the above problems existing in the background technology, the present invention proposes a method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo. The method uses the micro-Doppler time-frequency spectrum characteristics of flapping-wing UAV motion to solve the required micro-motion parameters.

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

[0006] A method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo, the method comprising the following steps:

[0007] Step 1: Establish a motion model of a rectangular one-segment flapping-wing UAV based on multiple scattering centers and a motion model of a rectangular-triangular composite two-segment flapping-wing UAV based on multiple scattering centers;

[0008] Step 2: Under different azimuth and pitch angles, the time-frequency spectra of the one-stage flapping-wing UAV and the two-stage flapping-wing UAV are obtained by simulation;

[0009] Step 3: Extract parameters for flapping-wing UAVs with different structures.

[0010] Furthermore, in step 1, the wings of the motion model of the rectangular-triangular composite two-stage flapping-wing drone based on multiple scattering centers are simplified into two parts, namely, an upper arm and a forearm; the upper arm is equivalent to a rectangle with thickness, the forearm is equivalent to a triangle with thickness, the two ends of the upper arm are connected to the shoulder joint and the elbow joint, and the two ends of the forearm are connected to the elbow joint and the wrist joint;

[0011] The motion model of the rectangular one-stage flapping-wing UAV has only one upper arm, and both ends of the upper arm are connected to the shoulder joint and the elbow joint.

[0012] Furthermore, in step 1, the process of establishing the motion model of the rectangular one-stage flapping-wing UAV is:

[0013] The position of the elbow joint is expressed as P1 = [x1, y1, z1], where:

[0014] x1(t)=v·t (17)

[0015] y1(t)=L1cos[ψ1(t)·π / 180] (18)

[0016] z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19)

[0017] Where: v represents the speed in the horizontal direction flying towards the radar, L1 represents the length of the upper arm, and ψ1 represents the flapping angle of the upper arm changing with time;

[0018] The expression of the flapping angle of the upper arm changing with time is shown in the following formula (1):

[0019] ψ1(t)=A1cos(2πf flap t)+ψ 10 (1)

[0020] Where: A1 represents the maximum flapping angle of the upper arm, f flap represents the flapping frequency, Ψ 10 Indicates the lag angle of the upper arm flap.

[0021] Furthermore, in step 1, the process of establishing the motion model of the two-stage flapping-wing UAV is:

[0022] The position of the elbow joint is expressed as P1 = [x1, y1, z1], where:

[0023] x1(t)=v·t (17)

[0024] y1(t)=L1cos[ψ1(t)·π / 180] (18)

[0025] z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19)

[0026] Where: v represents the speed in the horizontal direction flying towards the radar, L1 represents the length of the upper arm, and ψ1 represents the flapping angle of the upper arm changing with time;

[0027] The position of the wrist joint is expressed as P2 = [x2, y2, z2], where:

[0028] x2(t)=v·t (20)

[0029] y2(t)=L1cos[ψ1(t)·π / 180]+L2·cos[ψ1(t)-ψ2(t)] (21)

[0030] z2(t)=z1(t)+[y2(t)-y1(t)]·tan{[ψ1(t)-ψ2(t)]·π / 180} (22)

[0031] Where: L1 represents the length of the upper arm, L2 represents the length of the forearm, and ψ2 represents the flapping angle of the forearm changing with time;

[0032] The expression of the flapping angle of the upper arm changing with time is shown in the following formula (1):

[0033] ψ1(t)=A1cos(2πf flap t)+ψ 10 (1)

[0034] Where: A1 represents the maximum flapping angle of the upper arm, f flap represents the flapping frequency, Ψ 10 Indicates the hysteresis angle of the upper arm flapping;

[0035] The expression of the flapping angle of the forearm changing with time is shown in the following formula (2):

[0036] ψ2(t)=A2cos(2πf flap t)+ψ 20 (2)

[0037] Where: A2 represents the maximum flapping angle of the forearm, Ψ 20represents the lag angle of the forearm flapping, and ψ2(t) represents the flapping angle of the forearm changing with time.

[0038] Furthermore, in step 2, the time-frequency spectra of a one-stage flapping-wing UAV and a two-stage flapping-wing UAV are obtained by simulation at different azimuth angles and pitch angles; which includes the following steps:

[0039] Step 21: Simulate and obtain the time spectrum of a one-stage flapping-wing UAV;

[0040] The radar coordinate system is XYZ. Assume that the radar Q is located at the origin O, the flapping-wing UAV coordinate system is xyz, the center of the upper arm is the origin o, the flapping-wing target flaps around the x-axis, and the flapping-wing UAV is initially located at point o (x0, y0, z0). At this time, the distance from the origin o of the flapping-wing target to the radar Q is R0, the azimuth angle is α, and the pitch angle is β;

[0041] The movement direction of the flapping-wing target in the XOY plane is along the positive direction of the X axis. The target position of the flapping-wing UAV at time t is o′(x0+vt·,y0,z0). At this time, the distance from the origin o′ of the flapping-wing target to the radar Q is:

[0042]

[0043] Where: R is the distance from the origin o′ of the flapping-wing target to the radar Q, v is the speed of the flapping-wing UAV flying towards the radar in the horizontal direction;

[0044] At time t, in order to obtain the echo signal at a certain moment, assuming that a certain scattering point is p, the line of sight vector of radar Q is The distance from the origin o′ of the flapping wing target to the radar Q is R, and the vector and The angle between the radar Q and the scattering point p is γ, assuming that the distance between the radar Q and the scattering point p at time t is r p (t); Calculate the distance modulus r from the scattering point p to the laser radar Q using the triangular cosine theorem p (t):

[0045]

[0046] Where: l p is the distance from the scattering point p to the target origin o′, cosγ is the vector and The cosine of the angle between

[0047] Simplify formula (4) to:

[0048]

[0049] vector and The projection cosγ is expressed as:

[0050]

[0051] The final distance formula is expressed as:

[0052]

[0053] Since the outer contour peak of the time-frequency characteristics of the laser frequency band represents the micro-Doppler peak of the vertex, the left elbow joint point and the left wrist joint point are selected for calculation;

[0054] Distance from left elbow joint to radar Q It is expressed as:

[0055]

[0056] in:

[0057] The calculation formula of the micro-Doppler frequency shift of the left elbow joint is expressed as:

[0058]

[0059] in:

[0060] The frequency shift caused by translation is f t It is expressed as:

[0061]

[0062] Similarly, the calculation formula of the micro-Doppler frequency shift of the right elbow joint is expressed as:

[0063]

[0064] Step 22: Simulate and obtain the time-frequency spectrum of the two-stage flapping-wing UAV;

[0065] Based on the time spectrum of a one-stage flapping-wing UAV obtained by the above simulation,

[0066] Distance from left wrist joint to radar Q It is expressed as:

[0067]

[0068] in:

[0069] The calculation formula of the micro-Doppler frequency shift of the left wrist joint is expressed as:

[0070]

[0071] Where: L2 represents the length of the forearm, ψ1 represents the flapping angle of the upper arm changing with time, and ψ2 represents the flapping angle of the forearm changing with time;

[0072] Similarly, the calculation formula of the micro-Doppler frequency shift of the right wrist joint is expressed as:

[0073]

[0074] Furthermore, the simulated wavelength is 1064 nm, the simulated azimuth angle range is 30° to 80°, and the elevation angle range is 20° to 80°.

[0075] Furthermore, in step 3, the parameters of flapping-wing drones with different structures are extracted, and the specific extraction steps are:

[0076] Step 31: Extracting micro-motion parameters of a one-stage flapping-wing UAV;

[0077] In the time-frequency spectrum, the maximum frequency shift caused by the upper arm movement of the left and right flapping-wing UAV motion models is

[0078] n=1,2,3...there is an intersection point;

[0079] In the formula, t represents time, T represents the period of flapping motion, and n represents a positive integer starting from 1;

[0080] By extracting the maximum micro-Doppler frequency shift of the intersection and substituting it into the expression of the intersection frequency shift, the product of the length of the upper arm and the flapping angle of the upper arm can be obtained. Then, through the expressions of the two elbow joints (9) and (13), the length of the upper arm and the flapping angle of the upper arm can be obtained respectively.

[0081] The calculation formula of the micro-Doppler frequency shift of the left elbow joint is expressed as:

[0082]

[0083] in:

[0084] Where: λ represents the wavelength, A1 represents the maximum flapping angle of the upper arm, L1 represents the length of the upper arm, and f flap represents the flapping frequency;

[0085] Similarly, the calculation formula of the micro-Doppler frequency shift of the right elbow joint is expressed as:

[0086]

[0087] Step 32: Extracting micro-motion parameters of two-stage flapping-wing UAV;

[0088] Step 321: extracting micro-motion parameters of the upper arm of the two-stage flapping-wing UAV;

[0089] According to the micro-Doppler frequency shift expressions (9) and (13) of the elbow joint, the expression of the time when the maximum frequency shift of the inner contour occurs is derived, and then the maximum flapping angle and the length of the upper arm are obtained;

[0090] Step 322: extracting micro-motion parameters of the forearm of the two-stage flapping-wing UAV;

[0091] The maximum frequency shift generated by the forearm movement of the flapping-wing UAV motion model satisfies:

[0092] This type of function form,

[0093] According to this form of functional expression, the mathematical relationship between the length of the upper arm, the length of the forearm and the maximum flapping angle of the forearm can be approximately obtained.

[0094] Furthermore, in step 31, the expression of the intersection frequency shift is:

[0095]

[0096] Where: λ represents the wavelength, A1 represents the maximum flapping angle of the upper arm, L1 represents the length of the upper arm, and f flap represents the flapping frequency, α represents the azimuth angle, β represents the elevation angle, t represents the time, and f i represents the crossover frequency shift;

[0097] The expression for the product of L1 and A1 obtained by the expression of the crossover frequency shift is:

[0098]

[0099] Through formula (15), the expression of the maximum flapping angle A1 of the upper arm is derived as follows:

[0100]

[0101] Where: Indicates the time when the maximum frequency shift of the main peak frequency band occurs;

[0102] The expression of the length L1 of the upper arm is:

[0103]

[0104] Furthermore, in step 321, the time when the maximum frequency shift of the inner contour occurs is determined by the following expression:

[0105] g(t)=sin2πf flap t·sin[A1cos(cos2πf flap t)-φ] (26)

[0106] The point where the first-order derivative is zero is the extreme point of the function. The derivative of the above function is set to zero to find the extreme point. By solving equation (26), the maximum flapping angle A1 of the upper arm is determined;

[0107]

[0108] According to formula (15), the expression of the product of L1 and A1 can be derived as follows:

[0109]

[0110] The length L1 of the upper arm is calculated by formula (25).

[0111] Furthermore, in step 322, the This type of function form, according to this type of function form, the maximum frequency shift expression generated by the forearm movement is approximately expressed as:

[0112]

[0113] Through formula (16), we can get:

[0114]

[0115] Since there is a lag angle of forearm flapping in the flapping wing motion model, the effective length of the flapping wing motion model is approximately expressed as:

[0116] L≈(L1+L2)cosΨ 20 (30)

[0117] Where: L1 represents the length of the upper arm, L2 represents the length of the forearm, Ψ 20 represents the hysteresis angle of the forearm flapping;

[0118] Based on the above formula, the mathematical relationship between the length of the upper arm, the length of the forearm and the maximum flapping angle of the forearm is approximately obtained, and its expression is:

[0119] LA2≈L2′A2′(32).

[0120] The beneficial effects of the present invention over the prior art are as follows: the method of the present invention proposes a micro-motion parameter extraction method based on the time-frequency intersection, main peak frequency shift profile time approximation and maximum frequency shift expression approximation according to the variation law of the micro-Doppler time-frequency spectrum of a flapping-wing UAV with the azimuth and pitch angle, which is used to estimate the length of the upper arm and forearm and the flapping angle of the flapping-wing UAV. The method of the present invention can effectively realize the extraction of micro-motion parameters of the length of the upper arm and forearm and the flapping angle of the flapping-wing UAV, and provides a new technical approach for the application of laser micro-Doppler system detection technology in target precise detection and identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] Figure 1 This is a simplified diagram of the flapping wing motion model of a flapping wing drone;

[0122] Figure 2 It is a schematic diagram of the geometric relationship between radar and flapping wing motion model;

[0123] Figure 3 It is a time-frequency diagram of a segmented flapping motion;

[0124] Figure 4 It is the time-frequency diagram of the two-stage flapping motion.

[0125] The names and reference numerals of the components involved in the above drawings are as follows:

[0126] Upper arm 1, forearm 2, shoulder joint 3, elbow joint 4, wrist joint 5. DETAILED DESCRIPTION

[0127] Specific implementation method 1: This implementation method discloses a method for extracting micro-motion parameters of a flapping-wing UAV based on the time-frequency characteristics of laser echoes, and the method comprises the following steps:

[0128] Step 1: Establish a motion model of a rectangular one-segment flapping-wing UAV based on multiple scattering centers and a motion model of a rectangular-triangular composite two-segment flapping-wing UAV based on multiple scattering centers;

[0129] Step 2: Under different azimuth and pitch angles, the time-frequency spectra of the one-stage flapping-wing UAV and the two-stage flapping-wing UAV are obtained by simulation;

[0130] Step 3: Extract parameters for flapping-wing UAVs with different structures.

[0131] Furthermore, in step 1, the wings of the motion model of the rectangular-triangular composite two-stage flapping-wing drone based on multiple scattering centers are simplified into two parts, namely, an upper arm 1 and a forearm 2; the upper arm 1 is equivalent to a rectangle with thickness, the forearm 2 is equivalent to a triangle with thickness, the two ends of the upper arm 1 are connected to the shoulder joint 3 (joint one) and the elbow joint 4 (joint two), and the two ends of the forearm 2 are connected to the elbow joint 4 (joint two) and the wrist joint 5 (joint three);

[0132] The motion model of the rectangular one-stage flapping-wing UAV has only one upper arm 1, and both ends of the upper arm 1 are connected to the shoulder joint 3 (joint one) and the elbow joint 4 (joint two) (according to the structural characteristics of the current flapping-wing UAV, it is simplified and only the connection part between the elbow joint 4 and the wrist joint 5 is retained, that is, the motion model of the one-stage flapping-wing UAV is obtained).

[0133] Furthermore, in step 1, the process of establishing the motion model of the rectangular one-stage flapping-wing UAV is:

[0134] The position of the elbow joint 4 is expressed as P1 = [x1, y1, z1], where:

[0135] x1(t)=v·t (17)

[0136] y1(t)=L1cos[ψ1(t)·π / 180] (18)

[0137] z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19)

[0138] Where: v represents the speed in the horizontal direction flying toward the radar, L1 represents the length of upper arm 1, ψ1 represents the flapping angle of upper arm 1 changing with time (ψ1 and ψ1(t) have the same meaning);

[0139] The expression of the flapping angle of the upper arm 1 changing with time is shown in the following formula (1):

[0140] ψ1(t)=A1cos(2πf flap t)+ψ 10 (1)

[0141] Where: A1 represents the maximum flapping angle of upper arm 1, f flap represents the flapping frequency, Ψ 10 Indicates the hysteresis angle of the upper arm 1 flapping.

[0142] Furthermore, in step 1, the process of establishing the motion model of the two-stage flapping-wing UAV is:

[0143] The position of the elbow joint 4 is expressed as P1 = [x1, y1, z1], where:

[0144] x1(t)=v·t (17)

[0145] y1(t)=L1cos[ψ1(t)·π / 180] (18)

[0146] z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19)

[0147] Where: v represents the speed in the horizontal direction flying toward the radar, L1 represents the length of upper arm 1, ψ1 represents the flapping angle of upper arm 1 changing with time (ψ1 and ψ1(t) have the same meaning);

[0148] The position of wrist joint 5 is expressed as P2 = [x2, y2, z2], where:

[0149] x2(t)=v·t (20)

[0150] y2(t)=L1cos[ψ1(t)·π / 180]+L2·cos[ψ1(t)-ψ2(t)] (21)

[0151] z2(t)=z1(t)+[y2(t)-y1(t)]·tan{[ψ1(t)-ψ2(t)]·π / 180} (22)

[0152] Where: L1 represents the length of the upper arm 1, L2 represents the length of the forearm 2, ψ2 represents the flapping angle of the forearm 2 changing with time (ψ2 and ψ2(t) have the same meaning);

[0153] The expression of the flapping angle of the upper arm 1 changing with time is shown in the following formula (1):

[0154] ψ1(t)=A1cos(2πf flap t)+ψ 10 (1)

[0155] Where: A1 represents the maximum flapping angle of upper arm 1, f flap represents the flapping frequency, Ψ 10 represents the hysteresis angle of the upper arm 1 flapping;

[0156] The expression of the flapping angle of the forearm 2 changing with time is shown in the following formula (2):

[0157] ψ2(t)=A2 cos(2πf flap t)+ψ 20 (2)

[0158] Where: A2 represents the maximum flapping angle of forearm 2, Ψ 20 represents the hysteresis angle of the flapping of forearm 2, and ψ2(t) represents the flapping angle of forearm 2 changing with time.

[0159] Furthermore, in step 2, the time-frequency spectra of a one-stage flapping-wing UAV and a two-stage flapping-wing UAV are obtained by simulation at different azimuth angles and pitch angles; which includes the following steps:

[0160] Step 21: Simulate and obtain the time spectrum of a one-stage flapping-wing UAV;

[0161] The radar coordinate system is XYZ. Assume that the radar Q is located at the origin O, the flapping-wing drone coordinate system is xyz, the center of the upper arm 1 is the origin o, the flapping-wing target flaps around the x-axis, and the flapping-wing drone is initially located at point o (x0, y0, z0). At this time, the distance from the origin o of the flapping-wing target to the radar Q is R0, the azimuth angle is α, and the pitch angle is β;

[0162] The movement direction of the flapping-wing target in the XOY plane is along the positive direction of the X axis. The target position of the flapping-wing UAV at time t is o′(x0+vt·,y0,z0). At this time, the distance from the origin o′ of the flapping-wing target to the radar Q is:

[0163]

[0164] Where: R is the distance from the origin o′ of the flapping-wing target to the radar Q, v is the speed of the flapping-wing UAV flying towards the radar in the horizontal direction;

[0165] At time t, in order to obtain the echo signal at a certain moment, assuming that a certain scattering point is p, the line of sight vector of radar Q is The distance from the origin o′ of the flapping wing target to the radar Q is R, and the vector and The angle between the radar Q and the scattering point p is γ, assuming that the distance between the radar Q and the scattering point p at time t is r p (t); Calculate the distance modulus r from the scattering point p to the laser radar Q using the triangular cosine theorem p (t):

[0166]

[0167] Where: l p is the distance from the scattering point p to the target origin o′, cosγ is the vector and The cosine of the angle between

[0168] Simplify formula (4) to:

[0169]

[0170] vector and The projection cosγ is expressed as:

[0171]

[0172] The final distance formula is expressed as:

[0173]

[0174] Since the outer contour peak of the time-frequency characteristics of the laser frequency band represents the micro-Doppler peak of the vertex, 4 points of the left elbow joint and 5 points of the left wrist joint were selected for calculation;

[0175] The distance between the left elbow joint and the radar Q It is expressed as:

[0176]

[0177] in:

[0178] The calculation formula of the micro-Doppler frequency shift of the left elbow joint is expressed as:

[0179]

[0180] in:

[0181] The frequency shift caused by translation is f t It is expressed as:

[0182]

[0183] Similarly, the calculation formula of the micro-Doppler frequency shift of the right elbow joint is expressed as:

[0184]

[0185] Step 22: Simulate and obtain the time spectrum of the two-stage flapping-wing UAV;

[0186] Based on the time spectrum of a one-stage flapping-wing UAV obtained by the above simulation,

[0187] Distance from left wrist joint to radar Q It is expressed as:

[0188]

[0189] in:

[0190] The calculation formula of the 5-point micro-Doppler frequency shift of the left wrist joint is expressed as:

[0191]

[0192] Where: L2 represents the length of forearm 2, ψ1 represents the flapping angle of upper arm 1 changing with time, ψ2 represents the flapping angle of forearm 2 changing with time;

[0193] Similarly, the calculation formula of the micro-Doppler frequency shift of the right wrist joint is expressed as:

[0194]

[0195] The obtained micro-Doppler frequency shift is displayed on a time-frequency diagram, with the horizontal axis being time and the vertical axis being the micro-Doppler frequency shift.

[0196] Furthermore, the simulated wavelength is 1064 nm, the simulated azimuth angle range is 30° to 80°, and the elevation angle range is 20° to 80°.

[0197] Furthermore, in step 3, the parameters of flapping-wing drones with different structures are extracted, and the specific extraction steps are:

[0198] Step 31: Extracting micro-motion parameters of a one-stage flapping-wing UAV;

[0199] In the time-frequency spectrum, the maximum frequency shift caused by the movement of the upper arm 1 of the left and right flapping-wing UAV motion models is

[0200] n=1,2,3...there is an intersection;

[0201] In the formula, t represents time, T represents the period of flapping motion, and n represents a positive integer starting from 1;

[0202] By extracting the maximum micro-Doppler frequency shift of the intersection and substituting it into the expression of the intersection frequency shift, the product of the length of the upper arm 1 and the flapping angle of the upper arm 1 can be obtained. Then, through the expressions of the two elbow joints 4, equations (9) and (13), the length of the upper arm 1 and the flapping angle of the upper arm 1 can be obtained respectively.

[0203] The calculation formula of the micro-Doppler frequency shift of the left elbow joint is expressed as:

[0204]

[0205] in:

[0206] Where: λ represents the wavelength, A1 represents the maximum flapping angle of upper arm 1, L1 represents the length of upper arm 1, f flap represents the flapping frequency;

[0207] Similarly, the calculation formula of the micro-Doppler frequency shift of the right elbow joint is expressed as:

[0208]

[0209] Step 32: Extracting micro-motion parameters of two-stage flapping-wing UAV;

[0210] Step 321: Extracting micro-motion parameters of upper arm 1 of a two-stage flapping-wing UAV;

[0211] According to the characteristics of the inner and outer contours in the time-frequency diagram, the time when the maximum frequency shift of the main peak frequency band occurs Approximately equivalent to the time when the maximum frequency shift of the contour within the main peak occurs According to the micro-Doppler frequency shift expressions (9) and (13) of the elbow joint 4, the expression of the time when the maximum frequency shift of the inner contour occurs is derived, and then the maximum flapping angle of the upper arm 1 and the length of the upper arm 1 are obtained;

[0212] Step 322: extracting micro-motion parameters of the forearm 2 of the two-stage flapping-wing UAV;

[0213] The expression of the maximum frequency shift generated by the movement of forearm 2 of the flapping-wing UAV motion model is complex. By analyzing the characteristics of the inner and outer contours of the time-frequency graph, it can be seen that the maximum frequency shift generated by the movement of forearm 2 of the flapping-wing UAV motion model satisfies:

[0214] This type of function form,

[0215] According to this form of function expression, the mathematical relationship between the length of upper arm 1, the length of forearm 2 and the maximum flapping angle of forearm 2 can be approximately obtained (the maximum frequency shift expression generated by the movement of forearm 2 in the flapping-wing UAV motion model is relatively complex, but by analyzing the characteristics of the inner and outer contours of the time-frequency graph, it can be seen that it satisfies This type of function form. According to this form of function expression, the mathematical relationship between the length of the upper arm 1, the length of the forearm 2 and the maximum flapping angle of the forearm 2 can be approximately obtained).

[0216] Furthermore, in step 31, the expression of the intersection frequency shift is:

[0217]

[0218] Where: λ represents the wavelength, A1 represents the maximum flapping angle of upper arm 1, L1 represents the length of upper arm 1, f flap represents the flapping frequency, α represents the azimuth angle, β represents the elevation angle, t represents the time, and f i represents the crossover frequency shift;

[0219] The expression for the product of L1 and A1 obtained by the expression of the crossover frequency shift is:

[0220]

[0221] Through formula (15), the expression of the maximum flapping angle A1 of the upper arm 1 is derived as follows:

[0222]

[0223] Where: Indicates the time when the maximum frequency shift of the main peak frequency band occurs;

[0224] The expression of the length L1 of the upper arm 1 is:

[0225]

[0226] Furthermore, in step 321, the time when the maximum frequency shift of the inner contour occurs is determined by the following expression:

[0227] g(t)=sin2πf flap t·sin[A1cos(cos2πf flap t)-φ] (26)

[0228] The point where the first-order derivative is zero is the extreme point of the function. The derivative of the above function is set to zero to find the extreme point. By solving equation (26), the maximum flapping angle A1 of the upper arm 1 is determined;

[0229]

[0230] According to formula (15), the expression of the product of L1 and A1 can be derived as follows:

[0231]

[0232] The length L1 of the upper arm 1 is calculated by formula (25).

[0233] Furthermore, in step 322, the This type of function form, according to this type of function form, the maximum frequency shift expression generated by the movement of the forearm 2 is approximately expressed as:

[0234]

[0235] Through formula (16), we can get:

[0236]

[0237] Since there is a lag angle of forearm 2 flapping in the flapping wing motion model during the motion process, the effective length of the flapping wing motion model is approximately expressed as:

[0238] L≈(L1+L2)cosΨ 20 (30)

[0239] Where: L1 represents the length of the upper arm 1, L2 represents the length of the forearm 2, Ψ 20 represents the hysteresis angle of forearm 2 flapping;

[0240] Based on the above formula, the mathematical relationship between the length of the upper arm 1, the length of the forearm 2 and the maximum flapping angle of the forearm 2 is approximately obtained, and its expression is:

[0241] LA2≈L2′A2′(32).

[0242] Embodiment 1:

[0243] This embodiment discloses a method for extracting micro-motion parameters of a flapping-wing UAV based on the time-frequency characteristics of laser echoes, and the method comprises the following steps:

[0244] Step 1: In the traditional flapping-wing motion radar echo model, the shape is mostly an ellipsoid, which is very different from the shape of the actual flapping-wing UAV and ignores many factors such as the information carried by the wing spread surface. Therefore, the upper arm 1 of the flapping-wing motion model is equivalent to a rectangle with a certain thickness, and the forearm 2 is equivalent to a triangle with a certain thickness.

[0245] The existing geometric models of flapping-wing UAVs treat the motion of multiple segments connected by joints as rigid body motion. Figure 1 The figure shows a simplified diagram of the flapping wing motion model of a flapping wing drone. The flapping wing motion model simplifies the wing into two parts, namely the upper arm 1 and the forearm 2. The two ends of the upper arm 1 are connected to the shoulder joint 3 (joint 1) and the elbow joint 4 (joint 2), and the two ends of the forearm 2 are connected to the elbow joint 4 (joint 2) and the wrist joint 5 (joint 3). Among them, the elbow joint 4 and the wrist joint 5 have only one degree of freedom, and perform up and down flapping motion.

[0246] The flapping angle expression of the upper arm 1 is shown in the following formula (1):

[0247] ψ1(t)=A1cos(2πf flap t)+ψ 10 (1)

[0248] Where: A1 represents the maximum flapping angle of upper arm 1, f flap represents the flapping frequency, Ψ 10 represents the hysteresis angle of the upper arm 1 flapping;

[0249] The flapping angle expression of forearm 2 is shown in the following formula (2):

[0250] ψ2(t)=A2cos(2πf flap t)+ψ 20 (2)

[0251] Where: A2 represents the maximum flapping angle of forearm 2, f flap represents the flapping frequency, Ψ 20 Indicates the hysteresis angle of forearm 2 flapping.

[0252] Step 2: The radar coordinate system is XYZ, and the radar Q is located at the coordinate origin O. The flapping-wing drone coordinate system is xyz. For the convenience of analysis, the ox axis direction of the flapping-wing drone coordinate system is the same as the OX axis direction of the radar coordinate system, the oz axis direction is the same as the OZ axis direction of the radar coordinate system, and the oy axis and OY axis directions are determined according to the right-hand rule.

[0253] The geometric relationship between radar Q and the flapping motion model is as Figure 2 shown. Establish the coordinate system x - y - z of the flapping UAV, with the center of the upper arm 1 as the origin o. The flapping target (i.e., the target of the flapping UAV) makes a flapping motion around the x - axis. At the initial moment of the flapping UAV, it is located at point o(x0, y0, z0). At this time, the distance from the origin o of the flapping target to radar Q is R0, the azimuth angle is α, and the pitch angle is β.

[0254] If the moving direction of the flapping target in the X - O - Y plane is along the positive direction of the X - axis, then the position of the flapping UAV target at time t is o′(x0 + vt, y0, z0). At this time, the distance from the origin o′ of the flapping target to radar Q is:

[0255]

[0256] where: R represents the distance from the origin o′ of the flapping target to radar Q, and v represents the speed of the flapping UAV flying towards the radar in the horizontal direction;

[0257] Due to the short observation time (the observation time is generally about 1 s), the change in the position of the flapping target is not significant (at this time, α′≈α, β′≈β). When the emission wavelength is fixed, the micro - Doppler frequency shift is mainly related to the distance from the flapping target to the radar. The time - frequency characteristics obtained through laser detection and information processing are the superposed time - frequency characteristics of each scattering point on the surface of the flapping target.

[0258] At time t, to obtain the echo signal at a certain moment, assume that a certain scattering point is p, and the line - of - sight vector of radar Q is The distance from the flapping target to radar Q is denoted as R (i.e., the distance from the origin o′ of the flapping target to radar Q), and the angle between the vector and is γ. Assume that the distance between radar Q and the scattering point p at time t is r p (t).

[0259] According to the cosine theorem of a triangle, the distance modulus r p (t) from the scattering point p to lidar Q can be calculated as:

[0260]

[0261] where: l p represents the distance from the scattering point p to the origin o′ of the flapping target, and cosγ represents the cosine of the angle between the vector and .

[0262] Generally, the size of the flapping target is much smaller than the distance R0 between it and radar Q. It can be known that l p <<R0, and the distance formula can be simplified as:

[0263]

[0264] vector and The projection cosγ can be expressed as:

[0265]

[0266] The final distance formula can be expressed as:

[0267]

[0268] Since the outer contour peak of the time-frequency characteristics of the laser frequency band represents the micro-Doppler peak of the vertex, the left elbow joint point and the left wrist joint point are selected for calculation.

[0269] The distance from the left elbow joint to the radar Q It can be expressed as:

[0270]

[0271] in:

[0272] The calculation formula of the micro-Doppler frequency shift of the left elbow joint can be expressed as:

[0273]

[0274] in:

[0275] The frequency shift caused by translation is f t It can be expressed as:

[0276]

[0277] The distance between the left wrist joint and the radar Q It can be expressed as:

[0278]

[0279] in:

[0280] The calculation formula of the micro-Doppler frequency shift of the left wrist joint can be expressed as:

[0281]

[0282] Where: L2 represents the length of forearm 2, ψ1 and ψ2 represent the flapping angles of upper arm 1 and forearm 2 respectively that change with time;

[0283] Similarly, the calculation formulas for the micro-Doppler frequency shift of the right elbow joint and the right wrist joint are:

[0284]

[0285] in: It indicates the micro-Doppler shift of the right elbow joint;

[0286]

[0287] in: Indicates the micro-Doppler shift at the right wrist joint.

[0288] Step 3: Extract micro-motion parameters for flapping-wing UAVs with different structures;

[0289] Step 3.1: Extraction of micro-motion parameters of one-stage flapping-wing UAV;

[0290] At different azimuth and pitch angles, if only the radar echo simulation of the upper arm 1 of the left and right flapping wing motion model is performed, the following Figure 3 By observing the time-frequency diagram, it can be seen that the maximum frequency shift caused by the movement of the upper arm 1 of the left and right flapping wing motion models is n=1,2,3... There is an intersection. Analyzing equations (9) and (13), we can see that the intersection frequency shift expression is:

[0291]

[0292] Where: λ represents the wavelength, A1 represents the maximum flapping angle of upper arm 1, L1 represents the length of upper arm 1, f flap represents the flapping frequency, α represents the azimuth angle, β represents the elevation angle, t represents the time, and f i represents the crossover frequency shift;

[0293] Step 3.2: Extraction of micro-motion parameters of two-stage flapping-wing UAV;

[0294] Step 3.2.1: Since the radar echo simulation of the complete left and right flapping wing motion model is performed at different azimuths and pitch angles, it is difficult to obtain the intersection frequency shift of the upper arm 1 motion of the left and right flapping wing motion model by obtaining the time-frequency diagram. Figure 4 As shown, according to Figure 4 The characteristics of the inner and outer contours in the image can be used to roughly equate the time when the maximum frequency shift of the main peak band occurs to the time when the maximum frequency shift of the inner contour of the main peak occurs. The flapping angle of the upper arm 1 and the length of the upper arm 1 of the two-stage flapping-wing UAV can be approximately calculated.

[0295] Step 3.2.2: The maximum frequency shift expression produced by the forearm 2 movement in the flapping wing motion model is relatively complex, but can be obtained by analyzing Figure 4 (Time-frequency diagram) The characteristics of the inner and outer contours show that they satisfy This type of function form. Therefore, the maximum frequency shift expression generated by the forearm 2 movement can be approximately expressed as:

[0296]

[0297] This expression can be used to approximately infer the expression for the product of the maximum flapping angle of the forearm 2 and the length of the forearm 2.

[0298] Embodiment 2:

[0299] This embodiment discloses a method for extracting micro-motion parameters of a flapping-wing UAV based on the time-frequency characteristics of laser echoes, and the method comprises the following steps:

[0300] Step 1: Figure 1 As shown in the figure, the motion geometry model of the flapping-wing UAV is constructed. The specific model is as follows Figure 2 As shown, the x-axis is the motion axis, and the motion parameters of the motion model of the flapping-wing UAV are shown in Table 1.

[0301] Table 1 Flapping motion parameters

[0302]

[0303] The position of elbow joint 4 (joint 2) can be expressed as P1 = [x1, y1, z1], where:

[0304] x1(t)=v·t (17)

[0305] y1(t)=L1cos[ψ1(t)·π / 180] (18)

[0306] z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19)

[0307] Where: v represents the speed in the horizontal direction flying towards the radar.

[0308] The position of wrist joint 5 (joint 3) can be expressed as P2 = [x2, y2, z2], where:

[0309] x2(t)=v·t (20)

[0310] y2(t)=L1cos[ψ1(t)·π / 180]+L2·cos[ψ1(t)-ψ2(t)] (21)

[0311] z2(t)=z1(t)+[y2(t)-y1(t)]·tan{[ψ1(t)-ψ2(t)]·π / 180} (22)

[0312] According to the structural characteristics of the current flapping-wing UAV, Figure 1 The flying bird motion diagram shown is simplified by retaining only the connection between the shoulder joint 3 (joint one) and the elbow joint 4 (joint two), and the motion model of a one-stage flapping-wing UAV can be obtained.

[0313] Step 2: Set the radar wavelength to 1064nm, the sampling frequency to 200MHz, the azimuth angle to 60°, the elevation angle to 30°, and the movement direction to Figure 2 shown.

[0314] The effect of flapping wing motion on radar echo is mainly considered, and the flapping wing model is set to move at a speed of 0 m / s relative to the radar. Figure 3 It can be seen that the maximum frequency shift caused by the movement of upper arm 1 in the left and right flapping wing motion models has an intersection at t=0.05s, and the intersection frequency shift is 4.1MHz.

[0315] Step 3: Extract micro-motion parameters for flapping-wing UAVs with different structures.

[0316] Step 3.1: Extract the micro-motion parameters of a one-stage flapping-wing UAV. The expression of the product of L1 and A1 can be obtained through the intersection frequency shift expression:

[0317]

[0318] According to formula (15), the expression of the maximum flapping angle A1 of the upper arm 1 can be derived as:

[0319]

[0320] It is known that The left elbow joint 4 produces the largest frequency shift When the signal-to-noise ratio SNR=5, the flapping angle of the upper arm 1 of the one-stage flapping-wing UAV is estimated to be 38.1°.

[0321] Combining the above formula, the expression of the length L1 of the upper arm 1 can be further derived as follows:

[0322]

[0323] From this, the estimated value of the length of the upper arm 1 can be calculated to be 0.22 m.

[0324] Step 3.2.1: According to formula (12),

[0325]

[0326] The time when the maximum frequency shift of the inner contour occurs is determined by the following expression:

[0327] g(t)=sin2πfflap t·sin[A1cos(cos2πf flap t)-φ] (26)

[0328] The point where the first-order derivative is zero is the extreme point of the function. The derivative of the above function is set to zero to find the extreme point. By solving equation (26), the maximum flapping angle A1 of the upper arm 1 can be determined.

[0329]

[0330] According to formula (15), the expression of the product of L1 and A1 can be derived as follows:

[0331]

[0332] The length L1 of the upper arm 1 can be obtained by formula (25). When the signal-to-noise ratio SNR=5, it is estimated that the maximum flapping angle of the upper arm 1 of the two-stage flapping-wing drone is 37.4°, and the length of the upper arm 1 is 0.22m.

[0333] Step 3.2.2: Obtain the maximum frequency shift and corresponding time through the time-frequency diagram According to formula (16),

[0334]

[0335] We can obtain:

[0336]

[0337] Since the flapping lag angle of forearm 2 exists in the flapping motion model during the motion process, the effective length of the flapping motion model can be approximately expressed as:

[0338] L≈(L1+L2)cosΨ 20 (30)

[0339] Based on the above formula, the mathematical relationship between the length of the upper arm 1, the length of the forearm 2 and the maximum flapping angle of the forearm 2 can be approximately obtained, and the expression is:

[0340] LA2≈L2′A2′(32)

[0341] When the signal-to-noise ratio SNR=5, the estimated relationship between the length of the upper arm 1, the length of the forearm 2 and the maximum flapping angle of the forearm 2 of the two-stage flapping-wing UAV is 0.155 (the theoretical value is 0.16).

[0342] 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 extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo, characterized by: The method comprises the following steps: Step 1: Establish a motion model of a rectangular one-segment flapping-wing UAV based on multiple scattering centers and a motion model of a rectangular-triangular composite two-segment flapping-wing UAV based on multiple scattering centers; Step 2: Under different azimuth and pitch angles, the time-frequency spectra of the one-stage flapping-wing UAV and the two-stage flapping-wing UAV are obtained by simulation; Step 3: Extract parameters for flapping-wing drones with different structures; the specific extraction steps are: Step 31: Extracting micro-motion parameters of a one-stage flapping-wing UAV; In the time-frequency spectrum, the maximum frequency shift produced by the upper arm (1) motion of the left and right flapping-wing UAV motion model is There is an intersection; In the formula, t represents time, T represents the period of flapping motion, and n represents a positive integer starting from 1; By extracting the maximum micro-Doppler frequency shift of the intersection and substituting it into the expression of the intersection frequency shift, the product value of the length of the upper arm (1) and the flapping angle of the upper arm (1) can be obtained, and then through the expressions of the two elbow joints (4) of formula (9) and formula (13), the length of the upper arm (1) and the flapping angle of the upper arm (1) can be obtained respectively; The calculation formula of the micro-Doppler frequency shift of the left elbow joint is expressed as: in: Where: λ represents the wavelength, A1 represents the maximum flapping angle of the upper arm (1), L1 represents the length of the upper arm (1), and f flap represents the flapping frequency; Similarly, the calculation formula of the micro-Doppler frequency shift of the right elbow joint is expressed as: Step 32: Extracting micro-motion parameters of two-stage flapping-wing UAV; Step 321: Extracting micro-motion parameters of the upper arm (1) of the two-stage flapping-wing UAV; According to the micro-Doppler frequency shift expressions (9) and (13) of the elbow joint (4), the expression of the time when the maximum frequency shift of the inner contour occurs is derived, and then the maximum flapping angle of the upper arm (1) and the length of the upper arm (1) are obtained; Step 322: Extracting micro-motion parameters of the two-stage flapping-wing UAV forearm (2); The maximum frequency shift generated by the forearm (2) movement of the flapping-wing UAV motion model satisfies: This type of function form, According to the functional expression of this form, the mathematical relationship between the length of the upper arm (1), the length of the forearm (2) and the maximum flapping angle of the forearm (2) can be approximately obtained.

2. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 1 is characterized in that: In step 1, the wings of the motion model of the rectangular-triangular composite two-stage flapping-wing drone based on multiple scattering centers are simplified into two parts, namely, an upper arm (1) and a forearm (2); the upper arm (1) is equivalent to a rectangle with thickness, the forearm (2) is equivalent to a triangle with thickness, the two ends of the upper arm (1) are connected to the shoulder joint (3) and the elbow joint (4), and the two ends of the forearm (2) are connected to the elbow joint (4) and the wrist joint (5); The motion model of the rectangular one-stage flapping-wing UAV has only one upper arm (1), and two ends of the upper arm (1) are connected to a shoulder joint (3) and an elbow joint (4).

3. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 2 is characterized in that: In step 1, the process of establishing the motion model of the rectangular one-stage flapping-wing UAV is: The position of the elbow joint (4) is expressed as P1 = [x1, y1, z1], where: x1(t)=v·t (17) y1(t)=L1cos[ψ1(t)·π / 180] (18) z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19) Where: v represents the speed in the horizontal direction flying toward the radar, L1 represents the length of the upper arm (1), ψ1 represents the flapping angle of the upper arm (1) changing with time; The expression of the flapping angle of the upper arm (1) changing with time is shown in the following formula (1): ψ1(t)=A1cos(2πf flap t)+ψ 10 (1) Where: A1 represents the maximum flapping angle of the upper arm (1), f flap represents the flapping frequency, Ψ 10 It represents the hysteresis angle of the upper arm (1) flapping.

4. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 2 is characterized in that: In step 1, the process of establishing the motion model of the two-stage flapping-wing UAV is: The position of the elbow joint (4) is expressed as P1 = [x1, y1, z1], where: x1(t)=v·t (17) y1(t)=L1cos[ψ1(t)·π / 180] (18) z1(t)=y1(t)·tan[ψ1(t)·π / 180] (19) Where: v represents the speed in the horizontal direction flying toward the radar, L1 represents the length of the upper arm (1), ψ1 represents the flapping angle of the upper arm (1) changing with time; The position of the wrist joint (5) is expressed as P2 = [x2, y2, z2], where: x2(t)=v·t (20) y2(t)=L1cos[ψ1(t)·π / 180]+L2·cos[ψ1(t)-ψ2(t)] (21) z2(t)=z1(t)+[y2(t)-y1(t)]·tan{[ψ1(t)-ψ2(t)]·π / 180} (22) Where: L1 represents the length of the upper arm (1), L2 represents the length of the forearm (2), ψ2 represents the flapping angle of the forearm (2) changing with time; The expression of the flapping angle of the upper arm (1) changing with time is shown in the following formula (1): ψ1(t)=A1cos(2πf flap t)+ψ 10 (1) Where: A1 represents the maximum flapping angle of the upper arm (1), f flap represents the flapping frequency, Ψ 10 represents the hysteresis angle of the upper arm (1) flapping; The expression of the flapping angle of the forearm (2) changing with time is shown in the following formula (2): ψ2(t)=A2cos(2πf flap t)+ψ 20 (2) Where: A2 represents the maximum flapping angle of the forearm (2), Ψ 20 represents the hysteresis angle of the flapping of the forearm (2), and ψ2(t) represents the flapping angle of the forearm (2) changing with time.

5. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 1 is characterized in that: In step 2, the time-frequency spectra of a one-stage flapping-wing UAV and a two-stage flapping-wing UAV are obtained by simulation at different azimuth angles and pitch angles; It includes the following steps: Step 21: Simulate and obtain the time spectrum of a one-stage flapping-wing UAV; The radar coordinate system is XYZ. Assume that the radar Q is located at the origin O, the flapping-wing drone coordinate system is xyz, the center of the upper arm (1) is the origin o, the flapping-wing target performs flapping motion around the x-axis, and the flapping-wing drone is initially located at point o (x0, y0, z0). At this time, the distance from the origin o of the flapping-wing target to the radar Q is R0, the azimuth angle is α, and the pitch angle is β; The movement direction of the flapping-wing target in the XOY plane is along the positive direction of the X axis. The target position of the flapping-wing UAV at time t is o′(x0+vt·,y0,z0). At this time, the distance from the origin o′ of the flapping-wing target to the radar Q is: Where: R is the distance from the origin o′ of the flapping-wing target to the radar Q, v is the speed of the flapping-wing UAV flying towards the radar in the horizontal direction; At time t, in order to obtain the echo signal at a certain moment, assuming that a certain scattering point is p, the line of sight vector of radar Q is The distance from the origin o′ of the flapping wing target to the radar Q is R, and the vector and The angle between the radar Q and the scattering point p is γ, assuming that the distance between the radar Q and the scattering point p at time t is r p (t); Calculate the distance modulus r from the scattering point p to the laser radar Q using the triangular cosine theorem p (t): Where: l p is the distance from the scattering point p to the target origin o′, cosγ is the vector and The cosine of the angle between Simplify formula (4) to: vector and The projection cosγ is expressed as: The final distance formula is expressed as: Since the outer contour peak of the time-frequency characteristics of the laser frequency band represents the micro-Doppler peak of the vertex, the left elbow joint (4) and the left wrist joint (5) are selected for calculation; Distance from left elbow joint (4) to radar Q It is expressed as: in: The calculation formula of the micro-Doppler frequency shift of the left elbow joint is expressed as: in: The frequency shift caused by translation is f t It is expressed as: Similarly, the calculation formula of the micro-Doppler frequency shift of the right elbow joint is expressed as: Step 22: Simulate and obtain the time spectrum of the two-stage flapping-wing UAV; Based on the time spectrum of a one-stage flapping-wing UAV obtained by the above simulation, Distance from left wrist joint to radar Q It is expressed as: in: The calculation formula of the micro-Doppler frequency shift of the left wrist joint (5) is expressed as: Wherein: L2 represents the length of the forearm (2), ψ1 represents the flapping angle of the upper arm (1) changing with time, ψ2 represents the flapping angle of the forearm (2) changing with time; Similarly, the calculation formula of the micro-Doppler frequency shift of the right wrist joint is expressed as:

6. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 5 is characterized in that: The simulation wavelength is 1064nm, the simulation azimuth angle range is 30°~80°, and the elevation angle range is 20°~80°.

7. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 1 is characterized in that: In step 31, the expression of the intersection frequency shift is: Where: λ represents the wavelength, A1 represents the maximum flapping angle of the upper arm (1), L1 represents the length of the upper arm (1), and f flap represents the flapping frequency, α represents the azimuth angle, β represents the elevation angle, t represents the time, and f i represents the crossover frequency shift; The expression for the product of L1 and A1 obtained by the expression of the crossover frequency shift is: Through formula (15), the expression of the maximum flapping angle A1 of the upper arm (1) is derived as follows: Where: t p1 Indicates the time when the maximum frequency shift of the main peak frequency band occurs; The length L1 of the upper arm (1) is expressed as:

8. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 1 is characterized in that: In step 321, the time when the maximum frequency shift of the inner contour occurs is determined by the following expression: g(t)=sin2πf flap t·sin[A1cos(cos2πf flap t)-φ] (26) The point where the first-order derivative is zero is the extreme point of the function. The derivative of the above function is set to zero to find the extreme point. By solving equation (26), the maximum flapping angle A1 of the upper arm (1) is determined; According to formula (15), the expression of the product of L1 and A1 can be derived as follows: The length L1 of the upper arm (1) is calculated by formula (25).

9. The method for extracting micro-motion parameters of flapping-wing UAV based on the time-frequency characteristics of laser echo according to claim 1, characterized in that: In step 322, the This type of function form, according to this type of function form, the maximum frequency shift expression generated by the forearm (2) movement is approximately expressed as: Through formula (16), we can get: Since the flapping motion model has a lag angle of the forearm (2) during the motion process, the effective length of the flapping motion model is approximately expressed as: L≈(L1+L2)cosΨ 20 (30) Where: L1 represents the length of the upper arm (1), L2 represents the length of the forearm (2), Ψ 20 represents the hysteresis angle of the forearm (2) flapping; Based on the above formula, the mathematical relationship between the length of the upper arm (1), the length of the forearm (2) and the maximum flapping angle of the forearm (2) is approximately obtained, and the expression is: LA2≈L2′A2′(32).

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