Method for estimating parameters of a rotating object and for analyzing stability based on whirling electromagnetic waves

Abstract

The application discloses a kind of based on vortex electromagnetic wave's rotating object parameter estimation and stability analysis method, method includes: the rotating object is regarded as ideal scattering point, the electric field intensity expression of this scattering point is established;Mixing frequency is carried out to echo signal, and the baseband signal containing radial velocity and angular velocity is obtained;The double-domain dictionary consisting of radial velocity dictionary and angular velocity dictionary is established, and the radial velocity and angular velocity are preliminarily estimated by matching double-domain dictionary with baseband signal;Correlation function is constructed based on preliminary estimation result, and dynamic step iterative optimization is designed until convergence, and the final parameter estimation of high precision is obtained;The final parameter estimation obtained is used to construct regularization objective function, and the stability of rotating object movement is quantified by calculating the entropy value of scattering coefficient probability distribution through iterative optimization.This application has higher parameter estimation precision and robustness under the condition that signal-to-noise ratio exists.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of machine learning, and particularly relates to a rotating object parameter estimation and stability analysis method based on vortex electromagnetic waves. BACKGROUND

[0002] As a new economic form, the low-altitude economy has broad application prospects in urban transportation, emergency rescue, logistics transportation and other fields. Among them, helicopters play an irreplaceable important role in medical rescue, emergency rescue, outdoor search and rescue and other scenes due to their vertical take-off and landing, maneuverability and other advantages. Safe and efficient take-off and landing and hovering operation in complex environment is the key prerequisite for safe operation of low-altitude economy. Especially in the complex urban environment, the stability of helicopter take-off directly affects the development of rescue, rescue and other tasks. Therefore, accurately sensing and estimating the motion parameters of rotating flight targets such as helicopters, and judging the stability of the take-off process are of great significance to ensure the safety of operation.

[0003] Vortex electromagnetic wave is a special electromagnetic wave carrying orbital angular momentum, and its wave front has a spiral structure, which can produce a spatial phase modulation effect on the target. In recent years, especially at microwave frequencies, the use of vortex electromagnetic waves to detect rotating objects has gradually attracted attention, and preliminary progress has been made in theoretical modeling and verification. However, in some application scenarios, rotating objects are often accompanied by compound motion, such as axial rotation and radial motion. In this case, the coupling effect of axial rotation and radial motion is significantly aggravated, making the decoupling ability of traditional estimation methods insufficient and plagued by high precision requirements. In addition, existing research has not analyzed the stability of target motion. Therefore, how to fully utilize the physical properties of vortex electromagnetic waves to achieve synchronous and high-precision estimation of the motion parameters of rotating objects under compound motion conditions, and further to quantitatively evaluate the motion stability has important research significance. SUMMARY

[0004] The main purpose of the present application is to overcome the shortcomings and deficiencies of the prior art, and to provide a rotating object parameter estimation and stability analysis method based on vortex electromagnetic waves. First, a uniform circular array antenna is used to generate vortex electromagnetic waves, and the rotating object is regarded as an ideal scattering point, and the electric field intensity expression of the scattering point is established. Second, the echo signal is mixed to obtain a baseband signal containing radial velocity and angular velocity. Then, by constructing a dual-domain dictionary model and designing a dynamic step optimization, the motion parameters of the rotating object under compound motion conditions are effectively separated and accurately estimated. Finally, by iteratively optimizing the regularization objective function, the scattering coefficient is obtained and the entropy value of the probability distribution of the scattering coefficient is calculated to realize the stability analysis of the motion.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] In a first aspect, the present application provides a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method, comprising the following steps:

[0007] A vortex electromagnetic wave is generated by using a uniform circular array antenna, a rotating object is regarded as an ideal scattering point, and an electric field intensity expression of the scattering point is established;

[0008] The echo signal is mixed to obtain a baseband signal containing radial velocity and angular velocity;

[0009] A dual-domain dictionary composed of a radial velocity dictionary and an angular velocity dictionary is established, and the radial velocity and the angular velocity are preliminarily estimated by matching the dual-domain dictionary with the baseband signal;

[0010] Based on the preliminary estimation result, a correlation function is constructed, and a dynamic step iteration optimization is designed until convergence, so as to obtain a high-precision final parameter estimation;

[0011] The obtained final parameter estimation is used to construct a regularization objective function, the stability of the rotating object motion is quantified by iteratively optimizing and calculating the entropy value of the scattering coefficient probability distribution, and the lower the entropy value, the higher the motion stability.

[0012] As a preferred technical solution, the electric field intensity expression is specifically:

[0013] ;

[0014] wherein, E s E represents the electric field intensity, B N represents the number of antenna units, j represents an imaginary number, j Im represents the imaginary part of a complex number, k k represents a wave number, l m represents a mode of the vortex electromagnetic wave, f 0 represents a carrier frequency, t t represents a variable of the electric field changing with time, θ and φ θ and φ respectively represent a pitch angle and an azimuth angle, α R represents the radius of the antenna, J l J kα n θ ( x ) is the first kind l Bessel function of order n.

[0015] As a preferred technical solution, the baseband signal expression is:

[0016] ;

[0017] wherein, Er denotes a baseband signal, denotes a scattering coefficient, j denotes the imaginary part of a complex number, v and Ω denote radial and angular velocity, respectively, λ denotes a wavelength, l denotes a mode of a vortex electromagnetic wave, t denotes a variable of a baseband signal over time, n t denotes additive white Gaussian noise.

[0018] As a preferred technical solution, the dual-domain dictionary is defined as:

[0019] ;

[0020] wherein D denotes a dual-domain dictionary, denotes a matrix with dimension 1 x NM ; denotes a dictionary candidate set composed of radial velocities, f D v N = 2 v N λ , v denotes a radial velocity, λ denotes a wavelength, t 1,..., t N denotes a discrete representation of a radial velocity dictionary candidate set, denotes a matrix with dimension 1 x N ; denotes a dictionary candidate set composed of angular velocities, l denotes a mode of a vortex electromagnetic wave, and Ω denotes an angular velocity, t 1,..., t M denotes a discrete representation of an angular velocity dictionary candidate set, denotes a matrix with dimension 1 x M ; j denotes the imaginary part of a complex number, denotes a tensor product.

[0021] As a preferred technical solution, the matching is:

[0022] ;

[0023] wherein Z NM denotes a degree of matching between the dual-domain dictionary and the baseband signal, U ​​​NM represents the weighting factor, E r represents the baseband signal, D Represents a dual-domain dictionary, N and M Indicates the dimensions of different dictionaries, v represents radial velocity, and Ω represents angular velocity.

[0024] As a preferred technical solution, the correlation function and dynamic step size are:

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] in, F ( v , Ω) represents the correlation function, E r represents the baseband signal, E r(0) represents the baseband signal after preliminary estimation of parameters, v s Indicates the s The radial velocity of the iteration, v s+1 Indicates the s+ Radial velocity at 1 iteration, μ s Indicates the s The step size of the iteration, μ s+1 Indicates the s+ The step size of 1 iteration, Denotes the correlation function of radial velocity variables v The differential of Ω s Indicates the s The angular velocity of the iteration, Ω s+1 Indicates the s+ Angular velocity at 1 iteration, represents the differential of the correlation function with respect to the angular velocity variable Ω, F s Indicates the s The correlation function of the iteration, F s+1 Indicates the s+ The correlation function for 1 iteration, β and δ Is the adjustment factor, the value is between 0 and 1,δ Ensure that the equation does not converge to zero when the condition is met F s+1 - F s | ε , ε is a set threshold, get v and the final parameter estimate of Ω.

[0030] As a preferred technical solution, the obtained final parameter estimate is used to construct a regularization objective function, the scattering coefficient is solved by iterative optimization, and the entropy value of the scattering coefficient probability distribution is calculated, and the stability of the rotating object motion is quantified according to the entropy value, specifically:

[0031] Construct the objective function Q :

[0032] ;

[0033] Among them, D denotes a two-domain dictionary, A' denotes a scattering coefficient, E r denotes a baseband signal, L denotes a smoothing operator, O 1 and O 2 denote regularization terms, and min denotes the scattering coefficient A' , denotes the square of the Euclidean norm, denotes the Manhattan norm;

[0034] Iterative optimization to solve the objective function:

[0035] ;

[0036] Among them,

[0037] ;

[0038] ;

[0039] soft denotes a soft threshold function, O 1 and O 2 denote regularization terms, q denotes an adjustment factor, and its value should be greater than W the maximum eigenvalue of the matrix, O 1 / q denotes a threshold value, m denotes the m th iteration, m+ 1 denotes the m+ 1th iteration, β ​is a regulation factor, taking a value between 0 and 1, A' denotes the scattering coefficient, and A' denotes the scattering coefficient of the m denotes the difference between the current iteration value and the previous iteration value at the D denotes the dual-domain dictionary, H denotes the matrix transpose, E r denotes the baseband signal, L denotes the smoothing operator, when the difference between the first iteration value and the m+ second iteration value of the scattering coefficient is less than a threshold value, the iteration is stopped and the scattering coefficient is obtained; m The entropy value is calculated according to the scattering coefficient:

[0040]

[0041] ;

[0042] wherein, is the probability distribution of the scattering coefficient.

[0043] In a second aspect, the present application provides a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system, characterized in that it is applied to the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method and comprises a mathematical model construction module, a return baseband signal acquisition module, a dual-domain dictionary construction module, a dynamic step optimization module, and a stability analysis module.

[0044] The mathematical model construction module is used to generate vortex electromagnetic waves by using a uniform circular array antenna, to regard a rotating object as an ideal scattering point, and to establish an electric field intensity expression of the scattering point.

[0045] The return baseband signal acquisition module is used to mix the return signal to obtain a baseband signal containing radial velocity and angular velocity.

[0046] The dual-domain dictionary construction module is used to establish a dual-domain dictionary composed of a radial velocity dictionary and an angular velocity dictionary, to preliminarily estimate the radial velocity and the angular velocity by matching the dual-domain dictionary with the baseband signal.

[0047] The dynamic step optimization module is used to construct a correlation function based on the preliminary estimation result, to design a dynamic step iteration optimization until convergence, and to obtain a high-precision final parameter estimation.

[0048] The stability analysis module is used to construct a regularization objective function by using the obtained final parameter estimation, to quantize the stability of the rotating object motion by iteratively optimizing and calculating the entropy value of the scattering coefficient probability distribution, and to indicate that the lower the entropy value, the higher the motion stability.

[0049] ​In a third aspect, the present application provides an electronic device, comprising:

[0050] at least one processor; and,

[0051] a memory connected to the at least one processor in communication; wherein,

[0052] the memory stores computer program instructions executable by the at least one processor, and the computer program instructions are executed by the at least one processor to enable the at least one processor to perform the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method.

[0053] In a fourth aspect, the present application provides a computer-readable storage medium storing a program, which, when executed by a processor, implements the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method.

[0054] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0055] The conventional rotating object compound motion (rotation + radial) parameter estimation method usually needs to emit a pair of modal opposite vortex electromagnetic wave beams, first estimates the radial velocity, and then further estimates the angular velocity. Therefore, it is necessary to process in sequence to separate the parameters. This processing process not only has complex steps, but also the parameter estimation accuracy is easily affected in the presence of signal-to-noise ratio, and it is difficult to realize efficient and synchronous parameter extraction.

[0056] In view of the above problems, the present application proposes an innovative rotating object compound motion parameter estimation method. The core step of the method is to construct a dual-domain dictionary model and introduce a dynamic step optimization mechanism to realize the separation and synchronous estimation of radial velocity and angular velocity, which significantly improves the parameter estimation efficiency. The method still has high parameter estimation accuracy and robustness under the condition of containing additive white Gaussian noise. In addition, in order to further represent the dynamic characteristics of object motion, the present application also designs a target function based on regularization, which combines iterative optimization to accurately estimate the scattering coefficient of the target. On this basis, the entropy value of the scattering coefficient is introduced as a measure index of motion stability, and the numerical value of the entropy can effectively reflect the motion stability degree of the target in a period of time. The smaller the entropy value, the more stable the motion state, thereby providing a reliable basis for long-term monitoring and abnormal identification of the target state.

[0057] In summary, the present application has obvious advantages in synchronous estimation of rotating object compound motion parameters and quantitative evaluation of stability, breaks through the technical bottleneck of the conventional method, and has wide application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and all other drawings obtained by those of ordinary skill in the art without creative effort based on these drawings are within the scope of protection of the present application.

[0059] Figure 1 is an application scenario diagram of the embodiment;

[0060] Figure 2 is a method flowchart of the embodiment;

[0061] Figure 3 is a two-dimensional color map of the radial velocity and angular velocity parameter synchronous estimation of the embodiment;

[0062] Figure 4 is a relative error map of the parameter estimation under different candidate sets of the dictionary in the embodiment;

[0063] Figure 5 is a relative error map of the radial velocity and angular velocity under different signal-to-noise ratios in the embodiment;

[0064] Figure 6 is a reconstructed amplitude map, i.e., a scattering coefficient map, of the embodiment;

[0065] Figure 7 is a reconstructed phase map of the embodiment;

[0066] Figure 8 is a block diagram of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system of the embodiment of the present application;

[0067] Figure 9 is a structural diagram of the electronic device of the embodiment of the present application. DETAILED DESCRIPTION

[0068] In order to make those skilled in the art better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0069] Reference to an "embodiment" in this application means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are they necessarily mutually exclusive of one another. As will be apparent to those of ordinary skill in the art, embodiments described in this application can be combined with one another.

[0070] The application relates to a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method. The method is based on the Doppler effect generated by the interaction between a vortex electromagnetic wave and a rotating object. First, a signal model under the complex motion (rotation + radial) of a rotating target is constructed, and a mixing frequency processing is performed to obtain the baseband signal. Subsequently, a dual-domain dictionary model is constructed, and a dynamic step optimization and regularization constraint are designed to effectively decouple the complex motion parameters and realize accurate estimation. At the same time, the method covers the analysis process of the stability of the target motion. Even under the condition of additive white Gaussian noise, the method still maintains high parameter estimation accuracy and robustness, and is suitable for low-altitude target parameter estimation, state monitoring (especially for rotary-wing rotating targets such as helicopters), and other application scenarios (such as Figure 1 ), and has significant engineering application value and promotion potential.

[0071] As Figure 2 shown, a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method of the application specifically includes the following steps:

[0072] S1, constructing a mathematical model: a vortex electromagnetic wave is generated by using a uniform circular array antenna, a rotating object is regarded as an ideal scattering point, and the electric field intensity of the scattering point is established. E s Expression.

[0073] In this embodiment, the rotating object is the rotor of a helicopter, and the rotor is regarded as an ideal scattering point. The electric field intensity generated by the scattering point in space is expressed as: E s

[0074] ; (1)

[0075] wherein, E s represents the electric field intensity, B represents the number of antenna elements, represents an imaginary number, j represents the imaginary part of a complex number, k represents a wave number, l represents the mode of the vortex electromagnetic wave, f 0 represents a carrier frequency, t represents a variable of the electric field changing with time,​θ and φ denote the pitch angle and azimuth angle, respectively, α denotes the radius of the antenna, J l kα sin θ is the first kind l Bessel function of order

[0076] S2, obtaining the echo baseband signal: mixing the received echo signal to obtain the baseband signal containing radial velocity and angular velocity E r .

[0077] Further, considering the case of a rotating object in a compound motion, including the rotation of the helicopter rotor around the axis and the radial motion of the helicopter relative to the antenna array. The rotating object is located above the uniform circular array antenna, which produces a return signal under the illumination of the vortex electromagnetic wave, which carries the motion parameter information of the target. Assuming that the initial azimuth angle of the vortex electromagnetic wave is zero, the received echo signal is mixed to obtain its corresponding baseband signal E r denotes as follows:

[0078] ; (2)

[0079] wherein, E r denotes the baseband signal, denotes the scattering coefficient, j denotes the imaginary part of a complex number, v and Ω denote the radial velocity and angular velocity, respectively, λ denotes the wavelength, l denotes the mode of the vortex electromagnetic wave, t denotes the variable of the baseband signal changing with time, n t denotes the additive white Gaussian noise.

[0080] S3, constructing a dual-domain dictionary model, establishing a dual-domain dictionary composed of a radial velocity dictionary and an angular velocity dictionary, and preliminarily estimating the radial velocity and angular velocity by matching the dual-domain dictionary with the baseband signal.

[0081] Further, step S3 includes the following steps:

[0082] S31, the dual-domain dictionary is denoted as follows:

[0083] ; (3)

[0084] wherein D denotes the dual-domain dictionary, denotes the dimension is 1 x​​NM Matrix of represents the dictionary candidate set composed of radial velocities, f D ( v N )=2 v N / λ , v represents the radial velocity, λ represents the wavelength, t 1, ..., t N represents the discrete representation of the radial velocity dictionary candidate set, Indicates that the dimension is 1× N Matrix of Represents the dictionary candidate set composed of angular velocity, l represents the mode of the vortex electromagnetic wave, Ω represents the angular velocity, t 1, ..., t M represents the discrete representation of the candidate set of angular velocity dictionary, Indicates that the dimension is 1× M Matrix of j represents the imaginary part of a complex number, Represents a tensor product.

[0085] S32. Evaluate the degree of match between the dictionary and the signal Z NM :

[0086] ; (4)

[0087] in, Z NM Indicates the matching degree between the dual-domain dictionary and the baseband signal, U NM represents the weighting factor, E r represents the baseband signal, D Represents a dual-domain dictionary, N and M Indicates the dimensions of different dictionaries, v represents radial velocity, and Ω represents angular velocity.

[0088] S33. Preliminary estimation of radial velocity and angular velocity based on the matching degree , the formula is as follows:

[0089] ; (5)

[0090] in, N and M Indicates different dictionary dimensions,Z NM Indicates the matching degree between the dual-domain dictionary and the baseband signal, argmax indicates the value used to return the Z NM The index at which the maximum value is obtained ( N , M ), v (0) represents a preliminary estimate of the radial velocity, Ω (0) Represents a preliminary estimate of the angular velocity.

[0091] S4. Dynamic step size optimization: Construct a correlation function based on the preliminary estimation results, and design a dynamic step size iterative optimization until convergence to obtain a high-precision final parameter estimate.

[0092] Furthermore, step S4 is specifically as follows:

[0093] ;(6)

[0094] ;

[0095] ;

[0096] ;(7)

[0097] in, F ( v , Ω) represents the correlation function, E r represents the baseband signal, E r(0) represents the baseband signal after preliminary estimation of parameters, v s Indicates the s The radial velocity of the iteration, v s+1 Indicates the s+ Radial velocity at 1 iteration, μ s Indicates the s The step size of the iteration, μ s+1 Indicates the s+ The step size of 1 iteration, Denotes the correlation function of radial velocity variables v The differential of Ω s Indicates the s The angular velocity of the iteration, Ω s+1 Indicates the s+ Angular velocity at 1 iteration, represents the differential of the correlation function with respect to the angular velocity variable Ω, F s Indicates thes The correlation function of the iteration, F s+1 Indicates the s+ The correlation function for 1 iteration, β and δ Is the adjustment factor, the value is between 0 and 1, δ To ensure that the equation does not converge to zero, when | F s+1 - F s |< ε , ε When is the set threshold, we get v and the final parameter estimates of Ω.

[0098] S5. Stability analysis: The final parameter estimate is used to construct a regularized objective function. The stability of the rotating object's motion is quantified by iterative optimization and calculation of the entropy value of the scattering coefficient probability distribution. The lower the entropy value, the higher the motion stability.

[0099] Furthermore, step S5 is specifically as follows:

[0100] S51. Constructing the objective function Q ;

[0101] ; (8)

[0102] in, D Represents a dual-domain dictionary, A' represents the scattering coefficient, E r represents the baseband signal, L represents the smoothing operator, O 1 and O 2 represents the regularization term, and min represents the scattering coefficient that minimizes the value of the entire expression. A' , represents the square of the Euclidean norm, represents the Manhattan norm;

[0103] S52, iterative optimization to solve the objective function; Due to the regularization term, directly solving the objective function cannot obtain the optimal closed-form solution. Therefore, this embodiment uses the following iterative optimization to solve the objective function:

[0104] ; (9)

[0105] in,

[0106] ;

[0107] ; (10)

[0108] soft denotes a soft threshold function, O 1 and O 2 denotes a regularization term, q denotes an adjustment factor, which should be greater than W the largest eigenvalue of the matrix, O 1 / q denotes a threshold value, m denotes the m th iteration, m+ 1 denotes the m+ 1th iteration, β is an adjustment factor, which is between 0 and 1, A' denotes a scattering coefficient, △ A' denotes the m th iteration, the difference between the current iteration value and the previous iteration value, D denotes a dual-domain dictionary, H denotes a matrix transpose, E r denotes a baseband signal, L denotes a smoothing operator, when the difference between the m+ 1th iteration value and the m th iteration value of the scattering coefficient is less than the threshold value, the iteration is stopped and the scattering coefficient is obtained.

[0109] S53, calculate the entropy value of the scattering coefficient.

[0110] ; (11)

[0111] wherein, is the probability distribution of the scattering coefficient. The entropy is used here as a measure of instability, a lower entropy value indicates that the motion is regular and stable, thereby inferring the stability of the rotating object motion.

[0112] In the simulation, it is assumed that the helicopter experiences a compound motion during landing. The landing of the helicopter is mainly achieved by adjusting the angle of attack of the rotor blades, therefore, the angular velocity is usually kept constant. In addition to the rotation of the rotor blades, it also includes the radial velocity relative to the antenna array. During the landing process, the rotating object is located above the uniform circular array antenna, and the vortex electromagnetic wave beam effectively irradiates the helicopter. Within a certain distance range, the intensity of the reflected signal becomes stronger, which ensures that the signal can be detected. Assuming that the frequency of the antenna is 2.4 GHz, the antenna radiates a vortex electromagnetic wave with a mode of 1, the angular velocity of the rotating object is 10π rad / s, the radial velocity is 0.2 m / s, and the additive Gaussian white noise is introduced to evaluate the robustness of the method.

[0113] The signal in step S2 is mixed, and then the obtained baseband signal is processed by step S3 and step S4,Figure 3 The final estimates of the radial velocity and the angular velocity obtained by the processing of steps S3 and S4 are shown. Specifically, a two-dimensional color plot shows the distribution over the set of candidates of the radial velocity and the angular velocity, and the estimate of (v, Ω) is obtained by the two-domain dictionary model and the dynamic step optimization, which is shown as a bright spot in the two-dimensional color plot, corresponding to the estimate of the radial velocity and the angular velocity. In addition, the estimation accuracy of the parameters is related to the size of the dictionary candidate set. v v The relative error of the parameters under different candidate set sizes is shown. It can be observed that the relative error of the radial velocity and the angular velocity gradually decreases with the increase of the dictionary candidate set. This trend confirms that the embodiment can converge with higher accuracy when considering more dictionary candidates. Figure 4

[0114] In order to evaluate the robustness of the embodiment, the signal-to-noise ratio is set to 5 dB to 20 dB, and the size of the dictionary candidate set is 300. It can be seen from Figure 5 that at 5 dB, the relative error between the reference value and the estimated value is 0.35% for the radial velocity and 0.25% for the angular velocity; with the increase of the signal-to-noise ratio, the error of the radial velocity and the angular velocity is further reduced to 0.25% and 0.17% respectively. These results confirm that the embodiment has reliable performance, and the accuracy is improved with the increase of the signal-to-noise ratio. The improvement of accuracy is due to the dynamic step optimization, which improves the accuracy of parameter estimation by prioritizing high correlation areas in the parameter space. At low signal-to-noise ratio, the accuracy of parameter estimation will also decrease due to the decrease of correlation in dictionary matching.

[0115] After obtaining the parameters of the radial velocity and the angular velocity, the phase of the signal can be reconstructed, which is the basis for solving the scattering coefficient. Subsequently, according to step S5, the scattering coefficient, i.e. the amplitude of the signal, is solved by using iterative optimization of the regularization objective function. Figure 6 Figure 7 The reconstructed amplitude and phase over time at a signal-to-noise ratio of 20 dB are shown, and it can be seen that the amplitude stabilizes around the expected value, while the phase becomes more continuous. Since the relative error produced by parameter estimation at a signal-to-noise ratio of 20 dB is the lowest, and the amplitude fluctuation is relatively small, the entropy of the scattering coefficient calculated under this condition is selected as the basis for stability estimation during the landing process of the helicopter. The scattering coefficient is discretized and the entropy is calculated, and the entropy value is 0.69. Since entropy can be regarded as a measure of instability, a lower entropy value means more stable motion. It can be seen that the entropy value is relatively small, indicating the stability of the helicopter during landing.

[0116] Compared with existing methods, the method of the present application not only realizes the simultaneous estimation of the parameters of the rotating object, but also has higher accuracy and robustness, and also has the ability to analyze the stability of the motion of the rotating object.​​​

[0117] It should be noted that for the foregoing method embodiments, for the convenience of description, they are all expressed as a combination of a series of actions, but those skilled in the art should know that the present application is not limited by the order of the described actions, because according to the present application, certain steps can be performed in other orders or simultaneously.

[0118] Based on the same idea as the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method in the above embodiment, the present application also provides a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system, which can be used to execute the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method described above. For the convenience of description, in the structural schematic diagram of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system embodiment, only the parts related to the embodiments of the present application are shown, and those skilled in the art can understand that the illustrated structure does not constitute a limitation on the device, which can include more or fewer components than the illustration, or combine certain components, or different component arrangements.

[0119] Please refer to Figure 8 In another embodiment of the present application, a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system 100 is provided, which comprises a mathematical model construction module 101, an echo baseband signal acquisition module 102, a dual-domain dictionary construction module 103, a dynamic step optimization module 104, and a stability analysis module 105.

[0120] The mathematical model construction module 101 is configured to generate vortex electromagnetic waves using a uniform circular array antenna, and to establish an electric field intensity expression of the scattering point by regarding the rotating object as an ideal scattering point.

[0121] The echo baseband signal acquisition module 102 is configured to perform mixing processing on the received echo signal to obtain a baseband signal containing radial velocity and angle.

[0122] The dual-domain dictionary construction module 103 is configured to establish a dual-domain dictionary composed of a radial velocity dictionary and an angular velocity dictionary, and to preliminarily estimate the radial velocity and the angular velocity by matching the dual-domain dictionary with the baseband signal.

[0123] The dynamic step optimization module 104 is configured to construct a correlation function based on the preliminary estimation result, and to design a dynamic step iteration optimization until convergence to obtain a high-precision final parameter estimation.

[0124] The stability analysis module 105 is configured to construct a regularization objective function using the obtained final parameter estimation, to solve the scattering coefficient by iteration optimization, to calculate the entropy value of the probability distribution of the scattering coefficient, and to quantify the stability of the rotating object motion according to the entropy value, wherein the lower the entropy value, the higher the motion stability.

[0125] It should be noted that the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system of the present application corresponds to the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method of the present application, and the technical features and advantages described in the above embodiment of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method are applicable to the embodiment of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method, and the specific content can be referred to the description in the method embodiment of the present application, which will not be described here again, and hereby declared.

[0126] In addition, in the implementation of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system in the above embodiment, the logical division of each program module is only illustrative, and in actual application, the above function allocation can be completed by different program modules according to needs, for example, for the configuration requirements of the corresponding hardware or the convenience of software implementation, that is, the internal structure of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis system is divided into different program modules to complete all or part of the functions described above.

[0127] Please refer to Figure 9 In one embodiment, an electronic device implementing the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis method is provided, and the electronic device 200 can include a first processor 201, a first memory 202 and a bus, and can further include a computer program stored in the first memory 202 and executable on the first processor 201, such as a vortex electromagnetic wave-based rotating object parameter estimation and stability analysis program 203.

[0128] The first memory 202 includes at least one type of readable storage medium, such as flash memory, mobile hard disk, multimedia card, card-type memory (e.g., SD or DX memory, etc.), magnetic memory, disk, optical disk, etc. In some embodiments, the first memory 202 can be an internal storage unit of the electronic device 200, such as a mobile hard disk of the electronic device 200. In other embodiments, the first memory 202 can also be an external storage device of the electronic device 200, such as a plug-in mobile hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. Further, the first memory 202 can include both an internal storage unit and an external storage device of the electronic device 200. The first memory 202 can be used to store application software and various data installed in the electronic device 200, such as the code of the vortex electromagnetic wave-based rotating object parameter estimation and stability analysis program 203, and can also be used to temporarily store data that has been output or will be output.

[0129] The first processor 201 can be composed of an integrated circuit in some embodiments, such as a single packaged integrated circuit, or a plurality of packaged integrated circuits with the same or different functions, including one or more combinations of central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips, etc. The first processor 201 is the control unit of the electronic device, which connects various components of the entire electronic device through various interfaces and lines, and executes various functions and processes data of the electronic device 200 by running or executing programs or modules stored in the first memory 202 and calling data stored in the first memory 202.

[0130] Figure 9 Only the electronic device with components is shown, and those skilled in the art can understand that, Figure 9 The structure shown does not constitute a limitation on the electronic device 200, and can include fewer or more components than shown, or combine certain components, or different component arrangements.

[0131] The vortex electromagnetic wave-based rotating object parameter estimation and stability analysis program 203 stored in the first memory 202 of the electronic device 200 is a combination of a plurality of instructions, which, when running in the first processor 201, can achieve:

[0132] The vortex electromagnetic wave is generated by using a uniform circular array antenna, a rotating object is regarded as an ideal scattering point, and an electric field intensity expression of the scattering point is established;

[0133] The echo signal is mixed to obtain a baseband signal containing radial velocity and angular velocity;

[0134] A dual-domain dictionary composed of a radial velocity dictionary and an angular velocity dictionary is established, and the radial velocity and the angular velocity are preliminarily estimated by matching the dual-domain dictionary with the baseband signal;

[0135] A correlation function is constructed based on the preliminary estimation result, and a dynamic step iteration optimization is designed until convergence, so that a high-precision final parameter estimation is obtained;

[0136] A regularization objective function is constructed by using the obtained final parameter estimation, and the stability of the rotating object motion is quantified by iteratively optimizing and calculating an entropy value of a scattering coefficient probability distribution, wherein the lower the entropy value, the higher the motion stability.

[0137] Further, the modules / units of the electronic device 200 are stored in a nonvolatile computer readable storage medium if they are realized in the form of software function units and sold or used as independent products. The computer readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory).

[0138] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The program can be stored in a non-volatile computer readable storage medium, and when the program is executed, the processes of the above-mentioned embodiment methods can be included. Any reference to memory, storage, database or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0139] Any combination of the technical features of the above embodiments can be made. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

[0140] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations and simplifications of the embodiments of the present application without departing from the spirit and principles of the present application are equivalent replacement methods, and are included in the protection scope of the present application.

Claims

1. A method for parameter estimation and stability analysis of rotating objects based on vortex electromagnetic waves, characterized in that: The steps include: Using a uniform circular array antenna to generate vortex electromagnetic waves, the rotating object is regarded as an ideal scattering point, and the electric field intensity expression of the scattering point is established; Mixing the echo signal to obtain a baseband signal containing radial velocity and angular velocity; A dual-domain dictionary consisting of a radial velocity dictionary and an angular velocity dictionary is established, and the radial velocity and angular velocity are preliminarily estimated by matching the dual-domain dictionary with the baseband signal; Based on the preliminary estimation results, a correlation function is constructed, and a dynamic step size is designed for iterative optimization until convergence, resulting in a high-precision final parameter estimate. The obtained final parameter estimate is used to construct a regularized objective function, and the stability of the rotating object's motion is quantified by iterative optimization and calculation of the entropy value of the scattering coefficient probability distribution. The lower the entropy value, the higher the motion stability. The correlation function and dynamic step size are: ； ； ； ； in, F ( v , Ω) represents the correlation function, E r represents the baseband signal, E r(0) represents the baseband signal after preliminary estimation of parameters, v s Indicates the s The radial velocity of the iteration, v s+1 Indicates the s+ Radial velocity at 1 iteration, μ s Indicates the s The step size of the iteration, μ s+1 Indicates the s+ The step size of 1 iteration, Denotes the correlation function of radial velocity variables v The differential of Ω s Indicates the s The angular velocity of the iteration, Ω s+1 Indicates the s+ Angular velocity at 1 iteration, represents the differential of the correlation function with respect to the angular velocity variable Ω, F s Indicates the s The correlation function of the iteration, F s+1 Indicates the s+ The correlation function for 1 iteration, β and δ Is the adjustment factor, the value is between 0 and 1, δ To ensure that the equation does not converge to zero, when | F s+1 - F s |< ε , ε When is the set threshold, we get v and the final parameter estimates of Ω.

2. The method for parameter estimation and stability analysis of rotating objects based on vortex electromagnetic waves according to claim 1, characterized in that: The electric field strength expression is specifically: ； in, E s represents the electric field strength, B Indicates the number of antenna units, represents an imaginary number, j represents the imaginary part of a complex number, k represents the wave number, l represents the mode of vortex electromagnetic wave, f 0 indicates the carrier frequency, t is the variable that represents the time-varying electric field, θ and denote the elevation angle and azimuth angle respectively, α represents the radius of the antenna, J l ( kα sin θ ) is the first category l Bessel function of order.

3. The method for parameter estimation and stability analysis of rotating objects based on vortex electromagnetic waves according to claim 1, characterized in that: The baseband signal expression is: ； in, E r represents the baseband signal, represents the scattering coefficient, j represents the imaginary part of a complex number, v and Ω represent radial velocity and angular velocity respectively, λ represents the wavelength, l represents the mode of vortex electromagnetic wave, t represents the time-varying variable of the baseband signal, n ( t ) represents additive white Gaussian noise.

4. The method for parameter estimation and stability analysis of rotating objects based on vortex electromagnetic waves according to claim 1, characterized in that: The dual-domain dictionary is defined as: ； in D Represents a dual-domain dictionary, Indicates that the dimension is 1× NM Matrix of represents the dictionary candidate set composed of radial velocities, f D ( v N )=2 v N / λ , v represents the radial velocity, λ represents the wavelength, t 1, ..., t N represents the discrete representation of the radial velocity dictionary candidate set, Indicates that the dimension is 1× N Matrix of Represents the dictionary candidate set composed of angular velocity, l represents the mode of the vortex electromagnetic wave, Ω represents the angular velocity, t 1, ..., t M represents the discrete representation of the candidate set of angular velocity dictionary, Indicates that the dimension is 1× M Matrix of j represents the imaginary part of a complex number, Represents a tensor product.

5. The method for parameter estimation and stability analysis of rotating objects based on vortex electromagnetic waves according to claim 4, characterized in that: The matching is: ； in, Z NM Indicates the matching degree between the dual-domain dictionary and the baseband signal, U NM represents the weighting factor, E r represents the baseband signal, D Represents a dual-domain dictionary, N and M Indicates the dimensions of different dictionaries, v represents radial velocity, and Ω represents angular velocity.

6. The method for parameter estimation and stability analysis of rotating objects based on vortex electromagnetic waves according to claim 5, characterized in that: The final parameter estimate is used to construct a regularized objective function. The scattering coefficient is solved through iterative optimization, and the entropy of the probability distribution of the scattering coefficient is calculated. The stability of the rotating object motion is quantified based on the entropy value, specifically: Constructing the objective function Q : ； in, D Represents a dual-domain dictionary, A' represents the scattering coefficient, E r represents the baseband signal, L represents the smoothing operator, O 1 and O 2 represents the regularization term, and min represents the scattering coefficient that minimizes the value of the entire expression. A' , represents the square of the Euclidean norm, represents the Manhattan norm; Iterative optimization solves the objective function: ； in, ； ； soft represents the soft threshold function, O 1 and O 2 represents the regularization term, q Represents the adjustment factor, its value should be greater than W The largest eigenvalue of the matrix, O 1 / q represents the threshold value, m Indicates the m iterations, m+ 1 means the m+ 1 iteration, β Is the adjustment factor, the value is between 0 and 1, A' represents the scattering coefficient, △ A' Indicates the m At the iteration, the difference between the current iteration value and the previous iteration value, D Represents a dual-domain dictionary, H represents the matrix transpose, E r represents the baseband signal, L represents the smoothing operator, when the scattering coefficient m+ 1 iteration value and m When the difference between the iteration values ​​is less than the threshold, the iteration is stopped and the scattering coefficient is obtained; Calculate the entropy value based on the scattering coefficient: ； in, is the probability distribution of the scattering coefficient.

7. A rotating object parameter estimation and stability analysis system based on vortex electromagnetic waves, characterized in that: A method for parameter estimation and stability analysis of a rotating object based on vortex electromagnetic waves, applied to any one of claims 1-6, comprising a mathematical model construction module, an echo baseband signal acquisition module, a dual-domain dictionary construction module, a dynamic step size optimization module, and a stability analysis module; The mathematical model building module is used to generate vortex electromagnetic waves using a uniform circular array antenna, regard the rotating object as an ideal scattering point, and establish an expression for the electric field intensity of the scattering point; The echo baseband signal acquisition module is used to mix the echo signal to obtain a baseband signal containing radial velocity and angular velocity; The dual-domain dictionary building module is used to establish a dual-domain dictionary consisting of a radial velocity dictionary and an angular velocity dictionary, and preliminarily estimate the radial velocity and angular velocity by matching the dual-domain dictionary with the baseband signal; The dynamic step size optimization module is used to construct a correlation function based on the preliminary estimation results, and to design a dynamic step size iterative optimization until convergence, thereby obtaining a high-precision final parameter estimate; The stability analysis module is used to construct a regularized objective function using the obtained final parameter estimate, and quantify the stability of the rotating object's motion by iterative optimization and calculating the entropy value of the scattering coefficient probability distribution. The lower the entropy value, the higher the motion stability.

8. An electronic device, characterized in that: The electronic device comprises: at least one processor; and, a memory communicatively connected to the at least one processor; wherein, The memory stores computer program instructions that can be executed by the at least one processor, and the computer program instructions are executed by the at least one processor so that the at least one processor can execute the rotating object parameter estimation and stability analysis method based on vortex electromagnetic waves as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a program, characterized in that: When the program is executed by a processor, the method for parameter estimation and stability analysis of a rotating object based on vortex electromagnetic waves according to any one of claims 1 to 6 is implemented.

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