Ship scattering point three-degree-of-freedom rotation micro-doppler frequency extraction method

Abstract

The application discloses a ship scattering point three-freedom rotation micro-Doppler frequency extraction method, belongs to the technical field of radar signal processing and target identification, is used for micro-Doppler frequency extraction, and comprises the following steps: constructing a ship motion geometric model, and constructing a three-component amplitude modulation and frequency modulation micro-Doppler frequency model; performing generalized S transformation on a one-dimensional echo in the azimuth direction of a range cell, synchronously compressing the generalized S transformation in combination with a time-frequency track and an instantaneous frequency operator, and calculating a micro-Doppler frequency estimation value; constructing an adaptive ridge filter, decomposing the micro-Doppler frequency estimation value to obtain a micro-Doppler frequency estimation value subcomponent, and linearly superimposing the subcomponent to obtain an unoptimized micro-Doppler frequency estimation value. Through the construction of the three-freedom rotation micro-Doppler frequency model and the synchronous compression generalized S transformation and adaptive ridge filter method, high-precision and high-resolution extraction of the rotation micro-Doppler frequency of the ship scattering point is realized, and the problems of multi-component time-frequency cross and noise interference are effectively solved.

Description

Technical Field

[0001] This invention discloses a method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point, belonging to the field of radar signal processing and target recognition technology. Background Technology

[0002] In recent years, enhancement methods combining high-resolution time-frequency representation, adaptive time-frequency distribution, and synchronous compression transform have been developed to further improve energy concentration and estimate ridge parameters through robust fitting. However, these algorithms suffer from high computational complexity and still belong to the posterior trajectory search paradigm, exhibiting limitations in stability under complex and highly non-stationary scenarios. One instantaneous frequency estimation method combines time-frequency representation enhancement with path optimization. First, it utilizes a generative adversarial network to reconstruct the time-frequency distribution to enhance energy concentration. Then, it combines the Viterbi algorithm for globally optimal path tracking to extract multi-component instantaneous frequencies. This method requires additional network training and inference processes, resulting in significant overall computational overhead. Furthermore, the final trajectory estimation still depends on the energy distribution quality of the enhanced time-frequency map, and performance is easily affected by severe energy aliasing or training model mismatch. Another method detects time-frequency ridges based on the Wignerville distribution, constructs a training dataset using these ridges, and reconstructs the instantaneous frequency trajectory through a parameterized model. This method relies on ridge detection accuracy and model assumptions, and is prone to fitting bias when ridges are falsely detected or components overlap severely. Moreover, the multi-stage processing increases computational complexity. A method combining the Generalized S-Transform (GST) with Linear Micro-Doppler Trajectory Tracking (LMDT) is used to alleviate the insufficient resolution of the GST in non-stationary signals with a large frequency span by performing correlation and filtering operations on the coarsely estimated time-frequency curves. However, this method lacks robustness under noise interference. Noise interference and missed detection of effective signals in the time-frequency domain can easily lead to trajectory correlation errors and breaks, thereby disrupting the continuity of the micro-motion trajectory and affecting the stability of feature extraction. Summary of the Invention

[0003] The purpose of this invention is to provide a method for extracting the micro-Doppler frequencies of three-degree-of-freedom rotation of ship scattering points, so as to solve the problem in the prior art that it is difficult to accurately separate and estimate the micro-Doppler frequencies of each scattering point from the complex three-degree-of-freedom rotational echo of a ship.

[0004] A method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point includes:

[0005] S1. Construct a geometric model of ship motion, including radar coordinate system, carrier coordinate system, and carrier body coordinate system at the imaging center time.

[0006] S2. Introduce amplitude modulation and frequency modulation expressions for three-degree-of-freedom rotational angular velocity to construct a three-component amplitude modulation and frequency modulation micro-Doppler frequency model;

[0007] S3. Based on the deskewing processing of the linear frequency modulated signal, calculate the echo signal of the ship in the azimuth, time and range frequency domains, and based on the echo signal, calculate the azimuth one-dimensional echo of the range unit.

[0008] S4. Perform a generalized S-transform on the azimuth one-dimensional echo of the range cell to obtain the time-frequency trajectory of several scattering points contained in the range cell. Calculate the instantaneous frequency operator of the signal based on the time-frequency trajectory. Combine the time-frequency trajectory and the instantaneous frequency operator to synchronously compress the generalized S-transform. Introduce the Viterbi method to calculate the micro-Doppler frequency estimate.

[0009] S5. Based on the bandwidth control parameters and center frequency, construct an adaptive ridge filter, perform band-limited filtering decomposition on the micro-Doppler frequency estimate, obtain the micro-Doppler frequency estimate sub-components and sub-component frequency domains, and linearly superimpose the sub-components to obtain the unoptimized micro-Doppler frequency estimate.

[0010] S6. The frequency domain of the sub-components is iteratively updated using a weighted average method. A comprehensive evaluation function is constructed using singular spectral entropy and energy alignment. The bandwidth control parameters are optimized using the comprehensive evaluation function. The optimized bandwidth control parameters are substituted into step S5 to calculate the final micro-Doppler frequency estimate.

[0011] S1 includes constructing the ship's motion geometry model and coordinate system. Radar coordinate system The origin is , This is the projection of the radar onto the plane.

[0012] coordinate system For the carrier coordinate system The origin is the center of rotation of the ship. coordinate axes and parallel;

[0013] coordinate system The carrier body coordinate system at the imaging center time The origin is , When the axis points to the center, the direction of the ship's bow is... The axis points to the port side of the ship at the center moment. The orientation of the axis is determined by the right-hand rule.

[0014] S2 includes the introduction of amplitude modulation and frequency modulation expressions for three-degree-of-freedom rotational angular velocities, and the construction of a three-component amplitude modulation and frequency modulation micro-Doppler frequency model. :

[0015] ;

[0016] In the formula, Indices for the ship's three rotational degrees of freedom. , For the first The instantaneous amplitude of each component, For the first The instantaneous phase of each component, for The first derivative with respect to time, For the first The instantaneous angular frequency of each component.

[0017] S3 includes S3.1, the echo signal of the ship in the azimuth, time, and range frequency domains. for:

[0018] ;

[0019] ;

[0020] ;

[0021] In the formula, and To replace the variable, For direction and time, For range frequency, For a rectangular function, T int To accumulate time, For carrier frequency, Where C is the signal bandwidth and C is the speed of light. This represents the time-varying vector from the radar phase center to the ship's rotation center. express The model, for unit vector, Let be the vector from the ship's center of rotation to a scattering point on the ship. In order to be in Normalized radar cross section at the location, For and The relevant amplitude modulation function, It is the transpose symbol. It is the imaginary unit.

[0022] S3 includes S3.2, the distance-compressed first... One-dimensional echo in azimuth direction of a distance cell for:

[0023] ;

[0024] In the formula, For the first The number of scattering points contained in a distance cell. For the kth scattering point , For the first Backscattering coefficient at each scattering point For the first Two-way delay time corresponding to each distance unit For the first The shortest two-way delay time corresponding to each scattering point This refers to the bandwidth of the radar's transmitted signal.

[0025] S4 includes, S4.1, for the echo signal... Perform a generalized S-transform on the nth distance unit to obtain the nth distance unit. Time-frequency trajectory of scattering point of each distance unit:

[0026] ;

[0027] In the formula, Indicates to The signal after performing the generalized S-transform operation For Doppler frequency, and Two parameters for adjusting the width of the Gaussian window;

[0028] For any and At that time, the instantaneous frequency operator of the signal for:

[0029] ;

[0030] In the formula, for right Find the partial derivative. To take the real part of the complex number;

[0031] Synchronous compression of generalized S-transform for:

[0032] ;

[0033] In the formula, To synchronously compress the final output of the generalized S-transform, Dirac function, The frequency of the original generalized S-transform.

[0034] S4 includes, S4.2, which covers all time points. Values ​​are arranged in non-increasing order:

[0035] ;

[0036] In the formula, For discrete azimuth time. , For discrete orientation, The position of the time-frequency point in the sequence. , The number of time-frequency points;

[0037] Based on the criterion of maximizing time-frequency energy corresponding to ridges, an energy penalty function is defined. :

[0038] ;

[0039] In the formula, To The energy penalty function;

[0040] Based on the continuity constraint of ridge frequency changes at adjacent time points, a frequency transfer penalty function is defined. :

[0041] ;

[0042] In the formula, for The ridge frequency value at time t. for The ridge frequency value at time t. For discrete frequency indexing, The constant coefficient, The choice is based on Selection of frequency resolution for the transformation;

[0043] Introducing Viterbi's core formula to calculate micro-Doppler frequency estimates:

[0044] ;

[0045] In the formula, For the set of all possible paths, , This is the estimated value of the micro-Doppler frequency.

[0046] S5 includes constructing an adaptive ridge filter based on physical prior constraints of a three-component amplitude-modulated and frequency-modulated micro-Doppler frequency model. ,right Perform band-limited filtering decomposition:

[0047] ;

[0048] In the formula, For the first Frequency domain representation of each component for The frequency domain representation, For the first The center frequency of each component For bandwidth control parameters, Indices for the ship's three rotational degrees of freedom. , ;

[0049] The three frequency components obtained after filtering and decomposition , The unoptimized micro-Doppler frequency estimate is obtained by linear superposition:

[0050] .

[0051] S6 includes S6.1, center frequency. Through iterative updates:

[0052] ;

[0053] In the formula, For the number of iterations, To prevent division by zero constants, For the minimum center frequency, The maximum center frequency;

[0054] Constructing the Singular Spectral Entropy :

[0055] ;

[0056] In the formula, for singular values, Indicates the number of singular values. for The index;

[0057] Building energy alignment :

[0058] ;

[0059] In the formula, The width is half the width of the window. For frequency offset index, .

[0060] S6 includes S6.2, in bandwidth control parameters. During the optimization process, utilizing and Two quality metrics were used to construct a comprehensive evaluation function. Optimize bandwidth control parameters :

[0061] ;

[0062] In the formula, for corresponding , for corresponding ;

[0063] Global optimization is performed using the Crowned Porcupine optimization algorithm:

[0064] ;

[0065] In the formula, The optimized bandwidth parameters;

[0066] Will Substitute the values ​​into step S5 to obtain the final micro-Doppler frequency estimate.

[0067] Compared with the prior art, the present invention has the following beneficial effects: By constructing a three-degree-of-freedom rotating micro-Doppler frequency model and integrating synchronous compression generalized S-transform and adaptive ridge filtering, the present invention significantly improves the time-frequency resolution and noise resistance of micro-Doppler frequency, and effectively solves the technical problem of severe cross-over and difficulty in separating multi-component micro-Doppler signals from multiple scattering points of ships in the time-frequency domain. Attached Figure Description

[0068] Figure 1 This is the motion geometry model of the present invention;

[0069] Figure 2 This is a flowchart of the method of the present invention;

[0070] Figure 3 It is the high-aggregation time-frequency diagram obtained by SSGST in the first embodiment;

[0071] Figure 4 This is the coarse frequency trajectory obtained using the Viterbi method in the first embodiment;

[0072] Figure 5 This is a frequency estimation result diagram after optimizing the coarse frequency trajectory using the LMDT method in the first embodiment;

[0073] Figure 6 This is a frequency estimation result diagram after optimizing the coarse frequency trajectory using the method of the present invention in the first embodiment;

[0074] Figure 7 This is the high-aggregation time-frequency diagram obtained by SSGST in the second embodiment;

[0075] Figure 8This is the coarse frequency trajectory obtained using the Viterbi method in the second embodiment;

[0076] Figure 9 This is the coarse frequency trajectory obtained using the LMDT method in the second embodiment;

[0077] Figure 10 This is the coarse frequency trajectory map obtained using the method of the present invention in the second embodiment;

[0078] Figure 11 This is the high-aggregation time-frequency diagram obtained by SSGST in the third embodiment;

[0079] Figure 12 This is the coarse frequency trajectory obtained using the Viterbi method in the third embodiment;

[0080] Figure 13 This is the coarse frequency trajectory obtained using the LMDT method in the third embodiment;

[0081] Figure 14 This is a coarse frequency trajectory diagram obtained using the method of the present invention in the third embodiment. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0083] A method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point includes:

[0084] S1. Construct a geometric model of ship motion, including radar coordinate system, carrier coordinate system, and carrier body coordinate system at the imaging center time.

[0085] S2. Introduce amplitude modulation and frequency modulation expressions for three-degree-of-freedom rotational angular velocity to construct a three-component amplitude modulation and frequency modulation micro-Doppler frequency model;

[0086] S3. Based on the deskewing processing of the linear frequency modulated signal, calculate the echo signal of the ship in the azimuth, time and range frequency domains, and based on the echo signal, calculate the azimuth one-dimensional echo of the range unit.

[0087] S4. Perform a generalized S-transform on the azimuth one-dimensional echo of the range cell to obtain the time-frequency trajectory of several scattering points contained in the range cell. Calculate the instantaneous frequency operator of the signal based on the time-frequency trajectory. Combine the time-frequency trajectory and the instantaneous frequency operator to synchronously compress the generalized S-transform. Introduce the Viterbi method to calculate the micro-Doppler frequency estimate.

[0088] S5. Based on the bandwidth control parameters and center frequency, construct an adaptive ridge filter, perform band-limited filtering decomposition on the micro-Doppler frequency estimate, obtain the micro-Doppler frequency estimate sub-components and sub-component frequency domains, and linearly superimpose the sub-components to obtain the unoptimized micro-Doppler frequency estimate.

[0089] S6. The frequency domain of the sub-components is iteratively updated using a weighted average method. A comprehensive evaluation function is constructed using singular spectral entropy and energy alignment. The bandwidth control parameters are optimized using the comprehensive evaluation function. The optimized bandwidth control parameters are substituted into step S5 to calculate the final micro-Doppler frequency estimate.

[0090] S1 includes constructing the ship's motion geometry model and coordinate system. Radar coordinate system The origin is , This is the projection of the radar onto the plane.

[0091] coordinate system For the carrier coordinate system The origin is the center of rotation of the ship. coordinate axes and parallel;

[0092] coordinate system The carrier body coordinate system at the imaging center time The origin is , When the axis points to the center, the direction of the ship's bow is... The axis points to the port side of the ship at the center moment. The orientation of the axis is determined by the right-hand rule.

[0093] S2 includes the introduction of amplitude modulation and frequency modulation expressions for three-degree-of-freedom rotational angular velocities, and the construction of a three-component amplitude modulation and frequency modulation micro-Doppler frequency model. :

[0094] ;

[0095] In the formula, Indices for the ship's three rotational degrees of freedom. , For the first The instantaneous amplitude of each component, For the first The instantaneous phase of each component, for The first derivative with respect to time, For the first The instantaneous angular frequency of each component.

[0096] S3 includes S3.1, the echo signal of the ship in the azimuth, time, and range frequency domains. for:

[0097] ;

[0098] ;

[0099] ;

[0100] In the formula, and To replace the variable, For direction and time, For range frequency, For a rectangular function, T int To accumulate time, For carrier frequency, Where C is the signal bandwidth and C is the speed of light. This represents the time-varying vector from the radar phase center to the ship's rotation center. express The model, for unit vector, Let be the vector from the ship's center of rotation to a scattering point on the ship. In order to be in Normalized radar cross section at the location, For and The relevant amplitude modulation function, It is the transpose symbol. It is the imaginary unit.

[0101] S3 includes S3.2, the distance-compressed first... One-dimensional echo in azimuth direction of a distance cell for:

[0102] ;

[0103] In the formula, For the first The number of scattering points contained in a distance cell. For the kth scattering point , For the first Backscattering coefficient at each scattering point For the first Two-way delay time corresponding to each distance unit For the first The shortest two-way delay time corresponding to each scattering point This refers to the bandwidth of the radar's transmitted signal.

[0104] S4 includes, S4.1, for the echo signal... Perform a generalized S-transform on the nth distance unit to obtain the nth distance unit. Time-frequency trajectory of scattering point of each distance unit:

[0105] ;

[0106] In the formula, Indicates to The signal after performing the generalized S-transform operation For Doppler frequency, and Two parameters for adjusting the width of the Gaussian window;

[0107] For any and At that time, the instantaneous frequency operator of the signal for:

[0108] ;

[0109] In the formula, for right Find the partial derivative. To take the real part of the complex number;

[0110] Synchronous compression of generalized S-transform for:

[0111] ;

[0112] In the formula, To synchronously compress the final output of the generalized S-transform, Dirac function, The frequency of the original generalized S-transform.

[0113] S4 includes, S4.2, which covers all time points. Values ​​are arranged in non-increasing order:

[0114] ;

[0115] In the formula, For discrete azimuth time. , For discrete orientation, The position of the time-frequency point in the sequence. , The number of time-frequency points;

[0116] Based on the criterion of maximizing time-frequency energy corresponding to ridges, an energy penalty function is defined. :

[0117] ;

[0118] In the formula, To The energy penalty function;

[0119] Based on the continuity constraint of ridge frequency changes at adjacent time points, a frequency transfer penalty function is defined. :

[0120] ;

[0121] In the formula, for The ridge frequency value at time t. for The ridge frequency value at time t. For discrete frequency indexing, The constant coefficient, The choice is based on Selection of frequency resolution for the transformation;

[0122] Introducing Viterbi's core formula to calculate micro-Doppler frequency estimates:

[0123] ;

[0124] In the formula, For the set of all possible paths, , This is the estimated value of the micro-Doppler frequency.

[0125] S5 includes constructing an adaptive ridge filter based on physical prior constraints of a three-component amplitude-modulated and frequency-modulated micro-Doppler frequency model. ,right Perform band-limited filtering decomposition:

[0126] ;

[0127] In the formula, For the first Frequency domain representation of each component for The frequency domain representation, For the first The center frequency of each component For bandwidth control parameters, Indices for the ship's three rotational degrees of freedom. , ;

[0128] The three frequency components obtained after filtering and decomposition , The unoptimized micro-Doppler frequency estimate is obtained by linear superposition:

[0129] .

[0130] S6 includes S6.1, center frequency. Through iterative updates:

[0131] ;

[0132] In the formula, For the number of iterations, To prevent division by zero constants, For the minimum center frequency, The maximum center frequency;

[0133] Constructing the Singular Spectral Entropy :

[0134] ;

[0135] In the formula, for singular values, Indicates the number of singular values. for The index;

[0136] Building energy alignment :

[0137] ;

[0138] In the formula, The width is half the width of the window. For frequency offset index, .

[0139] S6 includes S6.2, in bandwidth control parameters. During the optimization process, utilizing and Two quality metrics were used to construct a comprehensive evaluation function. Optimize bandwidth control parameters :

[0140] ;

[0141] In the formula, for corresponding , for corresponding ;

[0142] Global optimization is performed using the Crowned Porcupine optimization algorithm:

[0143] ;

[0144] In the formula, The optimized bandwidth parameters;

[0145] Will Substitute the values ​​into step S5 to obtain the final micro-Doppler frequency estimate.

[0146] The derivation process of unifying the micro-Doppler frequency into a three-cosine sum form in this invention includes, after constructing a geometric model of ship motion, setting the ship's scattering point at the center time. exist Position vector in for , , and for exist coordinate system axis, shaft and Axial component, via azimuth to time , exist coordinates in for:

[0147] ;

[0148] In the formula, , and for exist coordinate system axis, shaft and Axial components, , , They represent in The rotation angles corresponding to roll, pitch, and yaw at all times. , , These represent the roll, pitch, and yaw rotation matrices of the ship, respectively.

[0149] Instantaneous distance to radar for:

[0150] ;

[0151] ;

[0152] In the formula, The position vector from the ship's rotation center to the radar at the moment of imaging center. Position vector from the ship's rotation center to the radar The corresponding unit vector, For the Euclidean norm, It is the transpose symbol;

[0153] Micro Doppler frequency value for:

[0154] ;

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] In the formula, , , To replace the variable, For wavelength, Angular velocity, These are the ship's roll, pitch, and yaw angular velocities, respectively.

[0160] The angular velocities of the ship's roll, pitch, and yaw can be approximated as constant-amplitude single-frequency cosine forms:

[0161] ;

[0162] In the formula, , , These represent the magnitudes of roll, pitch, and yaw angular velocities, respectively. , , For the corresponding period, , , This corresponds to the initial phase;

[0163] Will , and Substitution The calculation formula yields the three-component amplitude-modulated and frequency-modulated micro-Doppler frequency models:

[0164] .

[0165] The process of constructing the three-component amplitude-modulated and frequency-modulated micro-Doppler frequency model includes, to characterize the slowly varying envelope and phase evolution characteristics of wave excitation, modeling it as a narrow-band non-stationary process, and denoting the wave excitation input as:

[0166] ;

[0167] In the formula, To excite the amplitude envelope, Wave direction angle, As the excitation frequency, all three change slowly over time. For the instantaneous input of wave excitation, The instantaneous phase of wave excitation for The first derivative;

[0168] According to the principle of dynamic equilibrium, the total torque acting on the ship's roll degree of freedom satisfies the equilibrium relationship. The inertial torque, damping torque, and restoring torque of the roll motion together resist the excitation torque caused by the waves, thus allowing the ship's roll angle under the action of waves to be adjusted. The response is described as a second-order forced system:

[0169] ;

[0170] in, Roll characteristic angular frequency, The attenuation coefficients are both approximated as constant parameters. for The second derivative, for The first derivative;

[0171] Within any sufficiently short time window , as well as The relative fluctuation period changes slowly and can be considered constant. Therefore, non-stationary sea state can be equivalent to a single-frequency regular wave excitation within this short time window, with its equivalent amplitude and frequency taken as the instantaneous values ​​within the window. , and Therefore, the roll response within a short time window can be written in the form of a forced system with constant coefficients:

[0172] ;

[0173] Its particular solution is represented as follows:

[0174] ;

[0175] get:

[0176] ;

[0177] Based on the quasi-steady-state approximation, by performing a time-varying parametric generalization on the steady-state amplitude and phase results of the local regular wave, the roll response under non-stationary sea states can be obtained:

[0178] ;

[0179] ;

[0180] Let the roll rate be defined as Differentiating, we get:

[0181] ;

[0182] make:

[0183] ;

[0184] ;

[0185] ;

[0186] but for:

[0187] ;

[0188] ;

[0189] remember:

[0190] ;

[0191] ;

[0192] but for:

[0193] ;

[0194] ;

[0195] ;

[0196] Further utilize trigonometric identities:

[0197] ;

[0198] ;

[0199] ;

[0200] Therefore, It is no longer a constant-amplitude, single-frequency cosine wave, but exhibits a time-varying amplitude-phase structure, displaying amplitude-frequency modulation (AM–FM) characteristics. Similarly, and It can also be derived in AM–FM form. Therefore, by introducing the AM–FM expression for the 3-DOF rotational angular velocity, the Tri-AMFM micro-Doppler frequency model can be obtained:

[0201] .

[0202] The following description, in conjunction with embodiments and accompanying drawings, further illustrates the invention. The ship motion geometry model of the present invention is as follows: Figure 1 As shown, including the coordinate system Radar coordinate system , With the origin as the point, The horizontal axis is... The vertical axis is For the vertical axis, the vertical axis The blue triangle above represents the radar; coordinate system For the carrier coordinate system , With the origin as the point, The horizontal axis is... The vertical axis is Vertical axis; coordinate system The carrier body coordinate system at the imaging center time The origin is , When the axis points to the center, the direction of the ship's bow is... The axis points to the port side of the ship at the center moment. The orientation of the axis is determined by the right-hand rule; It is the position vector from the ship's rotation center to the radar at the moment of imaging center. It is the first The position vector of each scattering point , , These represent the angular velocities of the ship's roll, pitch, and yaw axes, respectively.

[0203] The process of this invention is as follows Figure 2As shown, this invention first receives the radar echo, performs range compression processing on the echo, takes the one-dimensional azimuth signal corresponding to the current range cell, and simultaneously compresses the generalized S-transform time-frequency representation and extracts the global ridge trajectory using the Viterbi algorithm. Then, it performs Tri-AMFM adaptive ridge filtering, including initializing the filtering parameters, then performing ridge filtering decomposition, updating the center frequency, calculating the evaluation function, and determining whether it is less than a threshold. If it is not less than the threshold, it determines whether the maximum number of iterations has been reached. If the maximum number of iterations has not been reached, it performs the CPO algorithm to update the bandwidth control parameters and returns to the ridge filtering decomposition step. If it is less than the threshold, it outputs the optimal bandwidth control parameters, and finally performs micro-Doppler frequency reconstruction.

[0204] The parameter values ​​in the embodiments of the present invention include, , , , .

[0205] In the first embodiment of this invention, a micro-Doppler simulation signal of a scattering point is constructed using real three-axis rotational angular velocity data of a ship. The azimuth signal of the same range cell is processed using Viterbi, LMDT, and the method of this invention, respectively. Figure 3 , Figure 4 , Figure 5 and Figure 6 The processing results of three methods are presented. It can be observed that Viterbi coarse extraction still exhibits local jumps and shifts under the influence of cross terms and noise; LMDT can improve trajectory continuity to some extent, but deviations are still prone to occur in the energy diffusion region; the method of this invention, under the physical prior constraints of Tri-AMFM, achieves band-limited filtering decomposition and reconstruction through adaptive updates of center frequency and bandwidth control parameters, thereby obtaining a more stable trajectory shape and a more consistent physical evolution trend. Table 1 presents the quantitative evaluation results of the three methods in the first embodiment:

[0206] Table 1. Evaluation of Results of the First Embodiment

[0207] ;

[0208] The RMSE of the method in this invention is 1.28 Hz, which is significantly lower than that of Viterbi and LMDT. Meanwhile, the singular spectral entropy and fuzzy entropy of the method in this invention are 0.051 and 0.023, respectively, both lower than the comparative methods, indicating that the frequency trajectory structure obtained by the method in this invention is more regular and has weaker random fluctuations. In terms of time consumption, the method in this invention is slightly longer than Viterbi, but shorter than LMDT, demonstrating a relatively balanced trade-off between improved accuracy and computational cost.

[0209] The radar equipment parameters of the second and third embodiments of the present invention are shown in Table 2:

[0210] Table 2. Radar Equipment Parameters

[0211] ;

[0212] The second embodiment of this invention is an experiment on a small unmanned surface vessel (USV) in a microwave anechoic chamber water tank (observed by an intelligent vehicle-mounted radar). The USV is placed inside the water tank, and the intelligent vehicle-mounted radar is located on a lifting platform on one side of the tank. Waves and water flow are generated by wave-generating equipment to excite the USV to sway and exhibit attitude disturbances. After preprocessing the echoes, frequency extraction is performed on selected range cells using Viterbi, LMDT, and the method of this invention, respectively. The processing results are as follows: Figure 7 , Figure 8 , Figure 9 and Figure 10 As shown, since it is difficult to obtain the true micro-Doppler frequency of the scattering point under actual measurement conditions, the extracted micro-Doppler curves are superimposed on the time-frequency plot to visually demonstrate the extraction accuracy. The results show that the Viterbi method can track the main energy ridge to a certain extent, but mistracking still occurs in areas with strong noise interference and intersections, resulting in insufficient continuity and stability of the extraction results. The LMDT method can further enhance the continuity of the trajectory and generally fits the main time-frequency ridge better, but it still has limitations in characterizing detailed changes in areas with weak local energy or component intersections. The method of this invention can stably track the main time-frequency energy ridge throughout the entire time domain and maintains good robustness in intersection and weak energy regions, enabling it to more accurately characterize the dynamic changes in micro-Doppler frequency. To quantitatively evaluate the performance improvement of the method of this invention in micro-Doppler frequency extraction caused by the rotation of the ship's scattering point, Table 3 summarizes the singular spectral entropy, fuzzy entropy, and algorithm time of different methods in the water tank experimental scenario.

[0213] Table 3. Evaluation of the results of the unmanned surface vessel experiment in the water tank

[0214] ;

[0215] It can be seen that the singular spectral entropy and fuzzy entropy of the method of the present invention are 0.169 and 0.066, respectively, which are significantly lower than those of Viterbi and LMDT. This indicates that even when real noise, non-ideal scattering, and cross-term interference are present, the method of the present invention can still obtain more regular frequency trajectories, while its time consumption is lower than that of LMDT.

[0216] The third embodiment of this invention further designs an observation experiment of a UAV-borne radar on a small unmanned surface vessel near the coast. After preprocessing the echo data, such as range compression, micro-Doppler frequency estimation is performed on selected range cells using Viterbi, LMDT, and the method of this invention, respectively. The processing results are as follows: Figure 11 , Figure 12 , Figure 13and Figure 14 As shown, the background was also set to the time-frequency map obtained using SSGST. It can be seen from the figure that due to the weak target echo energy and low signal-to-noise ratio, the energy advantage of the main ridge line in the time-frequency map is not obvious, and the reliability of the observation information is insufficient. The trajectory extracted by the Viterbi method has certain local offsets, and the trajectory stability is relatively weak, especially with a large number of false tracking errors in the initial time period. The LMDT method improves the trajectory continuity, and the extraction results are smoother overall, but there are still deviations in local areas with weak energy. In contrast, the method of this invention can still effectively identify the evolution trend of the main ridge line under low signal-to-noise ratio conditions, demonstrating stronger noise resistance and trajectory self-correction ability. Table 4 presents the quantitative evaluation results under the near-shore experimental scenario:

[0217] Table 4. Evaluation of Nearshore Unmanned Vessel Experiment Results

[0218] ;

[0219] The method of this invention achieves minimum values ​​for both singular spectral entropy and fuzzy entropy, indicating that under more complex nearshore sea conditions and platform observation conditions, the proposed method can still effectively suppress trajectory jitter and local jumps, and obtain more stable frequency estimation results.

[0220] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point, characterized in that, include: S1. Construct a geometric model of ship motion, including radar coordinate system, carrier coordinate system, and carrier body coordinate system at the imaging center time. S2. Introduce amplitude modulation and frequency modulation expressions for three-degree-of-freedom rotational angular velocity to construct a three-component amplitude modulation and frequency modulation micro-Doppler frequency model; S3. Based on the deskewing processing of the linear frequency modulated signal, calculate the echo signal of the ship in the azimuth, time and range frequency domains, and based on the echo signal, calculate the azimuth one-dimensional echo of the range unit. S4. Perform a generalized S-transform on the azimuth one-dimensional echo of the range cell to obtain the time-frequency trajectory of several scattering points contained in the range cell. Calculate the instantaneous frequency operator of the signal based on the time-frequency trajectory. Combine the time-frequency trajectory and the instantaneous frequency operator to synchronously compress the generalized S-transform. Introduce the Viterbi method to calculate the micro-Doppler frequency estimate. S5. Based on the bandwidth control parameters and center frequency, construct an adaptive ridge filter, perform band-limited filtering decomposition on the micro-Doppler frequency estimate, obtain the micro-Doppler frequency estimate sub-components and sub-component frequency domains, and linearly superimpose the sub-components to obtain the unoptimized micro-Doppler frequency estimate. S6. The frequency domain of the sub-components is iteratively updated using a weighted average method. A comprehensive evaluation function is constructed using singular spectral entropy and energy alignment. The bandwidth control parameters are optimized using the comprehensive evaluation function. The optimized bandwidth control parameters are substituted into step S5 to calculate the final micro-Doppler frequency estimate.

2. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 1, characterized in that, S1 includes constructing the ship's motion geometry model and coordinate system. Radar coordinate system The origin is , This is the projection of the radar onto the plane. coordinate system For the carrier coordinate system The origin is the center of rotation of the ship. coordinate axes and parallel; coordinate system The carrier body coordinate system at the imaging center time The origin is , When the axis points to the center, the direction of the ship's bow is... The axis points to the port side of the ship at the center moment. The orientation of the axis is determined by the right-hand rule.

3. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 2, characterized in that, S2 includes the introduction of amplitude modulation and frequency modulation expressions for three-degree-of-freedom rotational angular velocities, and the construction of a three-component amplitude modulation and frequency modulation micro-Doppler frequency model. : ； In the formula, Indices for the ship's three rotational degrees of freedom. , For the first The instantaneous amplitude of each component, For the first The instantaneous phase of each component, for The first derivative with respect to time, For the first The instantaneous angular frequency of each component.

4. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 3, characterized in that, S3 includes S3.1, the echo signal of the ship in the azimuth, time, and range frequency domains. for: ； ； ； In the formula, and To replace the variable, For direction and time, For range frequency, For a rectangular function, T int To accumulate time, For carrier frequency, Where C is the signal bandwidth and C is the speed of light. This represents the time-varying vector from the radar phase center to the ship's rotation center. express The model, for unit vector, Let be the vector from the ship's center of rotation to a scattering point on the ship. In order to be in Normalized radar cross section at the location, For and The relevant amplitude modulation function, It is the transpose symbol. It is the imaginary unit.

5. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 4, characterized in that, S3 includes S3.2, the distance-compressed first... One-dimensional echo in azimuth direction of a distance cell for: ； In the formula, For the first The number of scattering points contained in a distance cell. For the kth scattering point , For the first Backscattering coefficient at each scattering point For the first Two-way delay time corresponding to each distance unit For the first The shortest two-way delay time corresponding to each scattering point This refers to the bandwidth of the radar's transmitted signal.

6. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 5, characterized in that, S4 includes, S4.1, for the echo signal... Perform a generalized S-transform on the nth distance unit to obtain the nth distance unit. Time-frequency trajectory of scattering point of each distance unit: ； In the formula, Indicates to The signal after performing the generalized S-transform operation For Doppler frequency, and Two parameters for adjusting the width of the Gaussian window; For any and At that time, the instantaneous frequency operator of the signal for: ； In the formula, for right Find the partial derivative. To take the real part of the complex number; Synchronous compression of generalized S-transform for: ； In the formula, To synchronously compress the final output of the generalized S-transform, Dirac function, The frequency of the original generalized S-transform.

7. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 6, characterized in that, S4 includes, S4.2, which covers all time points. Values ​​are arranged in non-increasing order: ； In the formula, For discrete azimuth time. , For discrete orientation, The position of the time-frequency point in the sequence. , The number of time-frequency points; Based on the criterion of maximizing time-frequency energy corresponding to ridges, an energy penalty function is defined. : ； In the formula, To The energy penalty function; Based on the continuity constraint of ridge frequency changes at adjacent time points, a frequency transfer penalty function is defined. : ； In the formula, for The ridge frequency value at time t. for The ridge frequency value at time t. For discrete frequency indexing, The constant coefficient, The choice is based on Selection of frequency resolution for the transformation; Introducing Viterbi's core formula to calculate micro-Doppler frequency estimates: ； In the formula, For the set of all possible paths, , This is the estimated value of the micro-Doppler frequency.

8. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 7, characterized in that, S5 includes constructing an adaptive ridge filter based on physical prior constraints of a three-component amplitude-modulated and frequency-modulated micro-Doppler frequency model. ,right Perform band-limited filtering decomposition: ； In the formula, For the first Frequency domain representation of each component for The frequency domain representation, For the first The center frequency of each component For bandwidth control parameters, Indices for the ship's three rotational degrees of freedom. , ; The three frequency components obtained after filtering and decomposition , The unoptimized micro-Doppler frequency estimate is obtained by linear superposition: 。 9. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 8, characterized in that, S6 includes S6.1, center frequency. Through iterative updates: ； In the formula, For the number of iterations, To prevent division by zero constants, For the minimum center frequency, The maximum center frequency; Constructing the Singular Spectral Entropy : ； In the formula, for singular values, Indicates the number of singular values. for The index; Building energy alignment : ； In the formula, The width is half the width of the window. For frequency offset index, .

10. The method for extracting the three-degree-of-freedom rotational micro-Doppler frequency of a ship's scattering point according to claim 9, characterized in that, S6 includes S6.2, in bandwidth control parameters. During the optimization process, utilizing and Two quality metrics were used to construct a comprehensive evaluation function. Optimize bandwidth control parameters : ； In the formula, for corresponding , for corresponding ; Global optimization is performed using the Crowned Porcupine optimization algorithm: ； In the formula, The optimized bandwidth parameters; Will Substitute the values ​​into step S5 to obtain the final micro-Doppler frequency estimate.

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