Hrrp target micro-motion characteristic extraction method based on chaos optimization and polarization synthesis

Abstract

This invention proposes a method for extracting the micro-motion characteristics of HRRP targets based on chaotic optimization and polarization synthesis, targeting the high-resolution one-dimensional range image domain. The method includes: performing optimal polarization contrast enhancement on HRRP multi-channel polarization data, and optimal polarization fusion based on the maximum signal-to-noise ratio criterion; combining second harmonic backoff optimization and autocorrelation / amplitude difference enhancement processing to estimate the period of the polarization-fused data; and combining chaotic mapping with backpropagation to avoid the problem of traditional optimization easily getting trapped in local minima, thus obtaining the precession angle and size results of the space target. This invention significantly improves the feature contrast of HRRP data through polarization fusion, and simultaneously achieves high-precision estimation of the micro-motion characteristics of space targets under low signal-to-noise ratio conditions. It effectively improves the stability of period detection and the global search capability of parameter inversion within a limited observation time, significantly enhancing the accuracy and robustness of space target micro-motion estimation in complex environments.

Description

Technical Field

[0001] This invention relates to the field of target feature extraction in high-resolution one-dimensional range profiles (HRRP), and in particular to a method for extracting the micro-motion characteristics of HRRP targets based on chaotic optimization and polarization synthesis. Background Technology

[0002] High-resolution range profiles (HRRPs) are obtained from broadband radar signals and are projection vectors of the target's scattered echoes onto the radar ray direction. They can reflect characteristic parameters such as the target's structure, size, and motion state, thus having significant application value in the extraction and analysis of micro-motion features of space targets. When detecting moving targets, due to the relative motion between the radar and the target, echo information from multiple consecutive azimuth angles can be obtained, thereby constructing a continuous HRRP sequence. By modeling and analyzing the correlation of this sequence, the dynamic characteristics of the target can be effectively revealed, thereby achieving accurate estimation of the micro-motion features of space targets. However, existing HRRP-based micro-motion feature extraction methods still have certain limitations.

[0003] First, when using HRRP data to estimate the micro-motion characteristics of space targets, relying solely on single-polarization channel data often results in echo characteristics significantly influenced by the target's material, shape, and attitude, leading to incomplete and unstable micro-motion information. Single-polarization HRRP struggles to simultaneously capture the feature information carried by different scattering mechanisms, especially in complex space environments, easily resulting in insufficient feature extraction and thus limiting the accuracy and robustness of micro-motion parameter estimation. To overcome the limitations of single-polarization HRRP in micro-motion feature extraction, researchers proposed a multi-channel fusion method based on total polarization power (Span). Span weights or unweights the power of different polarization channels to obtain a comprehensive polarization power distribution. This method can enhance the difference between the target and the background to some extent, improving the overall utilization rate of target scattering information. However, traditional Span fusion is essentially a power superposition method, which fails to optimize and distinguish the scattering mechanisms of different polarization channels. This results in insufficient target feature enhancement in complex scenarios, especially under low signal-to-noise ratio conditions. Span fusion has limited noise suppression capabilities and cannot guarantee the stability and accuracy of micro-motion feature estimation.

[0004] Secondly, accurate estimation of the micro-motion period is a crucial step in the analysis of the micro-motion characteristics of space targets. In existing research, the traditional Fast Fourier Transform (FFT) method based on HRRP sequences, while intuitive and simple, suffers from frequency resolution dependence on observation duration, only guaranteeing accuracy when a sufficient number of complete periods are included. Under practical conditions of high-speed maneuvers and limited observation windows, obtaining long-term stable data is difficult, making this method prone to failure. Meanwhile, existing methods such as autocorrelation and the Average Magnitude Difference Function (AMDF) often suffer from frequency overtone or frequency division misidentification under low signal-to-noise ratios and limited observations, further limiting the reliability of the estimation. Especially in short-term observations, spectral leakage and the picket fence effect easily highlight harmonic components. If the second harmonic is misidentified as the fundamental frequency, the period estimate will be half its original value, making the frequency overtone error problem even more pronounced.

[0005] Finally, in the estimation of the precession angle and size of space targets, nonlinear optimization fitting methods have become an important approach in existing research due to their ability to jointly handle multiple parameters within a unified framework. However, these methods generally suffer from a prominent problem: the target scattering mechanism is complex, the cost function is highly nonconvex, and the optimization process is prone to getting trapped in local minima, leading to biased parameter inversion results or convergence failure. Existing research often uses Logistic mapping and Tent mapping to enhance the global search capability of the optimization process, but these methods suffer from limited chaotic intervals, uneven distribution, and insufficient search coverage, which may still lead to getting trapped in local minima or insufficient search in complex optimization problems. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a method for extracting the micro-motion characteristics of HRRP targets based on chaotic optimization and polarization synthesis. This method significantly improves the stability of space target micro-motion period detection and the global convergence of parameter inversion under low signal-to-noise ratio conditions in short-time observations, ultimately achieving excellent estimation accuracy and robust performance in complex environments.

[0007] The technical solution adopted by this invention to solve its technical problem is:

[0008] A method for extracting micro-motion characteristics of HRRP targets based on chaotic optimization and polarization synthesis, the method comprising:

[0009] S1. Obtain multi-channel polarization data from HRRP;

[0010] S2. Perform optimal polarization contrast enhancement and optimal polarization fusion based on the maximum signal-to-noise ratio criterion on the HRRP multi-channel polarization data;

[0011] S3. Perform FFT coarse estimation on HRRP polarization fusion data and frequency offset correction estimation based on second harmonic backoff optimization to estimate the target micro-motion period;

[0012] S4. Perform parameter inversion estimation of space targets based on chaotic mapping on HRRP polarization fusion data to estimate the precession angle and size of the targets.

[0013] Furthermore, S2 utilizes optimal polarization contrast enhancement and optimal polarization fusion of HRRP data based on the maximum signal-to-noise ratio criterion, including:

[0014] S21. First, calculate the total polarization power (Span) of the multi-channel polarization data to fuse the power information of each channel;

[0015] S22. The Optimization of Polarimetric Contrast Enhancement (OPCE) theory is used to optimize HRRP multi-channel data to enhance the contrast between the target of interest and the background, thereby achieving the function of target enhancement.

[0016] S23. Use the generalized optimization of polarimetric contrast enhancement (GOPCE) technique to fuse HRRP multi-channel data to further increase the contrast between the target and background clutter.

[0017] Furthermore, in S3, cross-correlation function analysis is performed on the HRRP sequence after optimal polarization fusion to obtain an initial estimate of the precession period. Based on this, a second harmonic backoff mechanism is introduced to overcome the misjudgment problem caused by the symmetrical structure of the space target and the distribution of scattering centers, which may lead to the main peak of the spectrum falling at the second harmonic position. When the power spectrum is at the main peak frequency... Nearby half-frequency location detected The spectral energy at the location satisfies:

[0018] (1)

[0019] The estimated frequency is corrected to:

[0020] (2)

[0021] in Represents frequency The power spectral amplitude at that point By setting a preset threshold parameter, the period estimation deviation caused by the second harmonic peak can be effectively avoided, and a more accurate precession period result can be obtained. For the frequency of correction, This indicates the result of the cycle estimation.

[0022] In S4, a precession scattering model of a space target is established, and the relationship expression of the radial length of the space target HRRP changing with time is derived, and the influence of high-speed translation during the precession process on the radial length is considered. On this basis, a cost function for the radial length is constructed, and an improved chaotic mapping combined with the backpropagation algorithm is used for optimization iteration to update the precession parameters such as the precession angle and the target size. The improved chaotic mapping is shown in Equation (3) below:

[0023]

[0024] (3)

[0025] In the formula, express The value of the moment. express The value after chaotic mapping. and These are chaos parameters, and the range of the chaos mapping is... ,parameter Compared to traditional Logistic and Tent mappings, this mapping has a wider range of chaotic parameters and a more uniform spatial ergodicity, thus exploring the parameter space more thoroughly during the optimization process, avoiding getting trapped in local minima, and improving the global search capability and convergence accuracy of precession parameter inversion.

[0026] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0027] In this invention, firstly, OPCE and GOPCE strategies are used to fuse multi-channel polarization data to improve the feature contrast between the target and the background. Subsequently, in the micro-motion period estimation stage, cross-correlation analysis and a second harmonic half-wave backoff mechanism are combined to effectively overcome the harmonic misjudgment problem caused by symmetrical structures and complex scattering center distributions, avoiding misjudging half-cycles as full cycles, thereby significantly improving the accuracy and stability of period estimation. Finally, in the precession angle and size parameter inversion process, a novel optimization strategy combining chaotic mapping and backpropagation is introduced to broaden the parameter search range, prevent getting trapped in local minima, and achieve higher accuracy and stronger robustness in the estimation of space target micro-motion features. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of the invention;

[0030] Figure 2 This is the HRRP data HH channel intensity map of the space target provided in the embodiment;

[0031] Figure 3 This is the HRRP data VV channel intensity map of the space target provided in the embodiment;

[0032] Figure 4 This is a Span fusion map of HRRP data for a space target provided in the embodiment;

[0033] Figure 5 This is an OPCE fusion map of HRRP data for a space target provided in the embodiment;

[0034] Figure 6 This is a GOPCE fusion map of HRRP data for a space target provided in the embodiment;

[0035] Figure 7 This is the period estimation result obtained using the HH channel when the signal-to-noise ratio is -20dB, as provided in the example.

[0036] Figure 8 This is the period estimation result obtained using the VV channel when the signal-to-noise ratio is -20dB, as provided in the example.

[0037] Figure 9 This is the period estimation result obtained by using Span fusion when the signal-to-noise ratio is -20dB, as provided in the example.

[0038] Figure 10 This is the period estimation result obtained by OPCE fusion when the signal-to-noise ratio is -20dB, as provided in the example.

[0039] Figure 11 This is the period estimation result obtained by using GOPCE fusion when the signal-to-noise ratio is -20dB, as provided in the example.

[0040] Figure 12 This is a comparison between the estimated micro-motion period of a space target obtained using different polarization fusion methods under different signal-to-noise ratios and the actual period, provided in the embodiments of the present invention.

[0041] Figure 13 This is the spatial target precession coordinate system provided in the embodiments of the present invention;

[0042] Figure 14 This is a novel chaotic mapping provided by the embodiments of the present invention. Follow A changing bifurcation diagram;

[0043] Figure 15This is a novel chaotic mapping provided by the embodiments of the present invention. Follow A changing bifurcation diagram;

[0044] Figure 16 This is a novel chaotic mapping provided by the embodiments of the present invention. A graph showing the changing Lyapunov index;

[0045] Figure 17 This is a novel chaotic mapping provided by the embodiments of the present invention. A graph showing the changing Lyapunov index;

[0046] Figure 18 This is an attractor graph of a novel chaotic mapping provided in the embodiments of the present invention. Detailed Implementation

[0047] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0048] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0049] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0050] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0051] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0052] This invention provides an application of HRRP data based on polarization fusion in the identification of micro-motions of space targets. This method combines optimal polarization fusion, period estimation optimization, and chaotic optimization to analyze HRRP data features and estimate the micro-motion characteristics of space targets. Figure 1The flowchart shown is for a method of identifying micro-motions of space targets based on HRRP data using polarization fusion. The processing flow of this method may include the following steps:

[0053] S1. Obtain HRRP multi-channel polarization data.

[0054] In one feasible implementation, the input HRRP sequence is: The dimension of the sequence is ,in, The length of the HRRP sequence, For the channel dimension of the HRRP sequence, Indicates the first HRRP data for each azimuth angle, This indicates the matrix transpose.

[0055] S2. Perform optimal polarization contrast enhancement on HRRP multi-channel polarization data and optimal polarization fusion based on the maximum signal-to-noise ratio criterion.

[0056] To improve the signal-to-noise ratio (SNR) and enhance the analysis of target micro-motion and size features, a multi-polarization channel fusion method based on optimal polarization synthesis is proposed. This method improves the SNR and provides optimal estimation of the target's micro-motion and size features, including:

[0057] S21. First, calculate the total polarization power (Span) of the multi-channel polarization data to fuse the power information of each channel.

[0058] Total polarimetric power is one of the most commonly used quantities in polarimetric SAR research, denoted by Span. If the target is given by the polarimetric scattering matrix, the total polarimetric power is as follows:

[0059]

[0060] in, Indicates incident polarization as Receiver polarization The scattering coefficient at that time. This indicates the horizontal polarization H for transmission and H for reception; This indicates that the transmitter is vertically polarized (V) and the receiver is horizontally polarized (H). This indicates that the transmitter is horizontally polarized (H) and the receiver is vertically polarized (V). This indicates that the transmitting vertical polarization V is V, and the receiving vertical polarization V is V. Under single-station reciprocity conditions, this is often the case. .

[0061] Total power of dual polarization:

[0062]

[0063] If the target is Matrix or Given the matrix, the total polarization power is as follows:

[0064]

[0065] in, and This represents the Huynen parameter. Represents the trace of a matrix.

[0066] Figure 2 and Figure 3 These are the HH channel intensity map and VV channel intensity map of this embodiment; the HRRP multi-channel data map of the first-stage booster target, fused using Span technology, is shown below. Figure 4 As shown.

[0067] S22. The Optimization of Polarimetric Contrast Enhancement (OPCE) theory is used to optimize the HRRP multi-channel data to enhance the contrast between the target of interest and the background, thereby achieving the function of target enhancement.

[0068] The Optical Optimization-Cut-Off (OPCE) problem includes three typical radar polarization channel fusion methods: co-polarization, cross-polarization, and matched polarization. If the polarization state of the receiving antenna and the transmitting antenna are interdependent, the only independent variable is the polarization state of the transmitting antenna. However, if the transmitting and receiving polarization states are independent, then there are two polarization states that can change independently, which can increase the radar's energy-to-receive ratio. Therefore, OPCE uses two independent variables in its modeling process. Here, we use a contrast-enhanced solution for OPCE based on the Sequential Unconstrained Minimization Technique (SUMT).

[0069] set up These represent the target scattering matrix that needs to be enhanced and the clutter scattering matrix that is to be suppressed as much as possible, respectively. Let represent the polarization states of the transmitting and receiving antennas, respectively. Then, the energies of the two targets received by the radar are respectively... and .

[0070] According to the polarization target zero theory, it can be deduced that there are infinitely many pairs of complex numbers in the real number field. This makes clutter The received power is equal to 0. Therefore, the optimal polarization contrast enhancement model is established as follows:

[0071] maximize:

[0072] Constraints

[0073]

[0074] according to matrix and matrix Relationship, assuming They are Based on the principle of scattering matrix transformation, the Stocks vector can be transformed from the above equation into the following equation:

[0075]

[0076] SUMT uses a series of sequences to transform a constrained optimization problem into an unconstrained optimization problem, which can then be solved numerically. The HRRP multi-channel data of the first-stage booster target, fused using SUMT technology, is shown in the following figure. Figure 5 As shown.

[0077] S23. The generalized optimization of polarimetric contrast enhancement (GOPCE) technique is used to fuse HRRP multi-channel data to further increase the contrast between the target and background clutter. The GOPCE model is shown below:

[0078]

[0079] In the formula, This is the polarization parameter vector; This is the vector of fusion coefficients that need to be obtained; .exist The three polarization parameters used in the model reflect different scattering characteristics of the target. We plan to use the similarity parameters of the target's plane scattering and dihedral scattering, as well as the polarization entropy of the target's polarization scattering characteristics, for analysis, and construct a polarization parameter vector. Simultaneously, other optimal polarization parameter characterizations will be investigated to enhance the target / clutter ratio. Under this model, the GOPCE problem is a problem with the following equations:

[0080]

[0081]

[0082] in, Represents all regions corresponding to the selected target area. The mean of a matrix; All of the selected clutter regions Matrix mean. The model consists of two parts: a polarization parameter fusion term. The optimal coefficient vector can be obtained by calculating the generalized eigenvalues. The optimization term of OPCE can be obtained by cross-iteration. The HRRP multi-channel data of the first-stage booster target fused using GOPCE technology is shown in the figure below. Figure 6 As shown.

[0083] S3. Perform FFT coarse estimation on HRRP polarization fusion data and frequency offset correction estimation based on second harmonic backoff optimization to estimate the target micro-motion period.

[0084] For any two frames , Within the allowed distance lag Take the maximum value of the linear cross-correlation within the inner range:

[0085]

[0086] Using frame 1 as a reference, the maximum cross-correlation with each frame is stacked over time:

[0087]

[0088] right Amplitude normalization is performed to obtain a similarity sequence that changes over time.

[0089] After normalization, detrending processing is performed to eliminate DC components and slow drift, resulting in the following form.

[0090]

[0091] To facilitate subsequent spectrum analysis, Multiply by a window function (such as the Hann window), specifically in the following form:

[0092]

[0093] It contains periodic information about the target's motion, but its spectrum is conjugate symmetric.

[0094] right Perform FFT:

[0095]

[0096] in, For frequency, Indicates a time interval.

[0097] Find the location of the maximum spectral line in the non-DC component. To obtain an initial estimate of the cycle .

[0098] It is worth noting that short-time observations and spectral leakage often lead to the second harmonic being more significant than the fundamental frequency. To avoid misjudgment by FFT, a "half-frequency backoff" criterion is proposed. Let the FFT roughly estimate the dominant peak as... If in place,

[0099]

[0100] Then it is believed Falling on the second harmonic, a backoff is executed:

[0101]

[0102] otherwise Second harmonic backoff can actively suppress the misjudgment of harmonic frequencies caused by "halving the period estimate".

[0103] Reset The analytic signal is in the following form:

[0104]

[0105] in This represents the Hilbert transform. In the frequency domain, the Hilbert transform adds -90° to the phase of positive frequency components and adds +90° to the phase of negative frequency components. The purpose of constructing an analytic signal is to facilitate down-conversion and phase extraction, thereby enabling frequency offset correction.

[0106] Will With frequency The mixing to baseband takes the following form:

[0107]

[0108] in, For frequency offset, This represents the sampling time interval. After expanding the phase, it can be obtained in the following form:

[0109]

[0110] in, Indicates the initial phase shift. For frequency offset, The sampling time interval is represented, and the frequency offset is obtained through linear fitting. The final correction frequency and period are:

[0111]

[0112] when When the value exceeds a threshold (e.g., half a frequency resolution), the correction result is discarded, and the FFT coarse estimate is retained.

[0113] calculate The autocorrelation function is used to find the first significant peak with a positive delay:

[0114]

[0115] in, Represents the total number of samples. The normalization factor representing the biased estimate is averaged using a fixed N. This represents the delay time. The delay index representing the first significant peak . This represents the micro-period estimated by the autocorrelation method. To more stably determine significant peaks, several criteria need to be set: First, a significant peak requires the first local maximum within the positive delay interval; second, the peak height... Furthermore, the significance peak must exceed a set threshold; finally, when finding the periodic peak in the autocorrelation function, the period is limited to the rough estimate by FFT. The surrounding area (e.g., 0.5-1.5 times) Search within the range to avoid selecting the wrong octave peak or a false peak.

[0116] when At that time, it can be considered Credible; when If the FFT segment is misjudged, then the second harmonic of the FFT segment is determined to be false. The final period; if the difference between the two is large and not an integer multiple, then the message "Insufficient data / Low signal-to-noise ratio / Improper observation" will be displayed. Maintain the main focus and keep the prompts.

[0117] This invention provides a period estimation for the first-stage booster target of the LGM-30G (Minuteman III). The LGM-30G ballistic missile is powered by a three-stage solid-propellant rocket engine. The first and second stage propulsion systems are essentially the same as those of the LGM-30F missile, with the main difference being the introduction of a new third-stage propulsion rocket. The first stage is 7.49 meters long, 1.67 meters in diameter, and weighs 22.68 tons. The solid propellant used is polybutadiene acrylonitrile / ammonium perchlorate / aluminum powder. Its precession period is 3 seconds, and its precession angle is 30°.

[0118] Under a low signal-to-noise ratio of -20 dB, the micro-motion period estimation results for different polarization modes are as follows: Figures 7 to 11 As shown. From Figures 7 to 11As can be seen, when relying solely on cross-correlation sequences, the periodic characteristics are often not obvious or are masked by noise. However, after FFT correction, the frequency domain spectral peaks significantly enhance the discernibility of the periodic components, forming a relatively stable criterion even at low signal-to-noise ratios, thus improving the robustness and accuracy of period estimation. Single-polarization HH and VV are affected by insufficient scattering information and noise interference, resulting in estimated periods of 1.50 s and 1.20 s respectively, deviating significantly from the true value of 3 s, and can only be used as references. Span fusion improves robustness by using total polarization power, yielding a result of 2.00 s, but with a systematic underestimation. OPCE utilizes polarization contrast optimization to highlight the micro-motion sensitive scattering unit, estimating a value of 2.77 s, which is closer to the true period. GOPCE achieves effective noise suppression and accurate preservation of the fundamental frequency component, ultimately yielding a result of 3.00 s, completely consistent with the true period, demonstrating an advantage in balancing accuracy and robustness.

[0119] Table 1. Period estimation results for different polarization modes at different signal-to-noise ratios.

[0120]

[0121] Figure 12 Table 1 shows the period estimation results of different polarization methods under different signal-to-noise ratios. The experimental results show that under high signal-to-noise ratio conditions, all methods can accurately extract the target micro-motion period. However, as the signal-to-noise ratio decreases, the single-polarization HH and VV are most severely affected by noise, and the period estimation is seriously underestimated at -20 dB. The Span method improves stability through energy superposition, but there is a systematic underestimation at extremely low SNR. OPCE can give a result closer to the true value (2.77s) at -20 dB, which reflects the enhancement effect on the fundamental frequency component. GOPCE can accurately output 3s in the entire range, showing the best robustness and accuracy, and is the optimal polarization feature fusion strategy under low signal-to-noise ratio conditions.

[0122] Table 2 shows the period estimation results of the Span feature under different signal-to-noise ratios without the introduction of the second harmonic backoff mechanism.

[0123] Table 2 shows the Span characteristic period estimation results without incorporating second harmonic backoff.

[0124]

[0125] As can be seen, when the signal-to-noise ratio is high (20 dB, 10 dB), although the estimated result is close to the true period (3 s), there is a significant deviation (1.763 s, 1.853 s, respectively), indicating that the spectral peak is easily affected by harmonic components. Under lower signal-to-noise ratios (-10 dB, -20 dB), the estimated result is further severely distorted, even converging to obviously erroneous period values ​​such as 1 s and 1.2 s. The root cause of this phenomenon is that, under limited observation and strong noise conditions, the FFT method often incorrectly identifies the second harmonic (or other harmonic components) as the fundamental frequency, resulting in the period estimation result being half or even more smaller. Therefore, introducing a "second harmonic backoff" mechanism is necessary and reasonable. This mechanism actively identifies the misjudged harmonic components by comparing the spectral peak significance of the fundamental frequency and its half-frequency point, and backs the period estimation result from the erroneous second harmonic position to the true fundamental frequency position. This design effectively avoids the estimation distortion problem shown in the table, enabling the period estimation to maintain stable tracking of the true value even under low signal-to-noise ratio and short-term observation conditions, thereby significantly improving the robustness and reliability of the method.

[0126] S4. Perform parameter inversion estimation of space targets based on chaotic mapping on HRRP polarization fusion data to estimate the precession angle and size of the targets.

[0127] The specific precession of the space target is as follows Figure 13 As shown. Precession involves two types of motion; the first is the space target's motion around the cone axis. The spin, and secondly the target's rotation around the orientation axis. The conical rotation. The angle between the radar line of sight and the precession axis. , which is the radar observation angle. The angle between the radar line of sight and the warhead's axis of symmetry. The angle is the radar line-of-sight angle. The angle between the precession axis and the main axis. , where is the precession angle. (See diagram) Indicates the height of the vertebral target. This represents the radius of the base of the cone-shaped target. This represents the precession rate. The precession of the target causes periodic changes in the radar line-of-sight angle, resulting in a periodic change in the one-dimensional range profile sequence over time. If the change in the radar observation angle is ignored over a short period, then the target's one-dimensional range profile will be periodically changing.

[0128] During the target's precession, the axis of symmetry The vector representation in the precessing coordinate system is:

[0129]

[0130] in It is the rotation angle of the body axis relative to the precession axis in the initial state.

[0131] The radar line of sight in the precession coordinate system is represented by the following vector:

[0132]

[0133] Then the radar line of sight and the axis of symmetry of the cone The included angle between them is denoted as .

[0134]

[0135] According to geometric diffraction theory, when a space target's structural features have significant edges or protruding areas, its main scattering points are usually concentrated at the intersection of the target surface and the radar line of sight, forming a significant geometric structure. Taking a typical conical target as an example, when its semi-cone angle is small (generally less than 10°), the visible strong scattering points are mainly distributed at the intersection of the cone's apex and bottom edge with the plane containing the radar line of sight and the target's principal axis (usually the other intersection point is invisible due to target obstruction). For more general space targets (such as satellites, spacecraft, or rocket sections), a similar distribution pattern of main scattering points exists when they have regularly rotating parts or end structures. Therefore, the radial length of the target in the radar line of sight direction can be approximated by the distance difference between the front and rear main scattering points and can serve as the input basis for inverting target structural parameters. Therefore, the radial length can be expressed as:

[0136]

[0137] The above expression for the radial range of a space target considers only precession and not high-speed translation, i.e., it does not account for changes in the radar observation angle. In reality, space targets (such as satellites, spacecraft, and rocket sections) often undergo high-speed translation during their orbital operation, causing their observation angle in the radar coordinate system to change over time. In this case, the angle between the radar line of sight and the target's principal axis is no longer constant but a dynamic result of both spatial translation and precession. By transforming the parameters of the radar line of sight vector changing over time in the radar coordinate system to the precession coordinate system, the influence of these two motions on the one-dimensional range image is resolved.

[0138] During the target's translational motion, its precession axis remains constant. Therefore, the coordinates of the cone's precession axis in the radar coordinate system are expressed as follows: And assume that the orientation angle of the precession axis in the radar coordinate system is... The tilt angle is Therefore, the vector representation of the precession axis in the radar coordinate system is:

[0139]

[0140] From the direction cosine transformation relationship between coordinate systems, the transformation matrix from the radar coordinate system to the precession coordinate system is:

[0141]

[0142] Assume that in the radar coordinate system, the target's spatial position coordinates are... The target's speed is The vector transformed from the radar line of sight to the precession coordinate system is:

[0143]

[0144] The radar line-of-sight angle after considering translation is expressed as:

[0145]

[0146] in,

[0147]

[0148] Then the radial length is expressed as:

[0149]

[0150] Since our spatial target data does not contain translational information, the radial length modeling directly adopts the geometric model of equation (24) in the paper, rather than equation (30) which depends on the target coordinates and motion state.

[0151] As can be seen from the expression for the radial length under precession during target flight in equation (30), this radial length is related to the precession angle. Precession period Cone length Base radius The direction angle of the precession axis in the radar coordinate system and pitch angle Parameter-dependent. Let the feature parameter vector be:

[0152]

[0153] Summing the residuals at each time step with equal weights makes them susceptible to low-amplitude / low signal-to-noise ratio segments. Therefore, this invention extends the cost function to weighted least squares, allowing reliable samples to play a greater role in parameter updates. The cost function is defined as follows:

[0154]

[0155] in It is the true radial length calculated using broadband echo at different precession attitude angles under simulated conditions in an assumed environment. The radial length is the predicted value estimated based on the parameters. The cost function is optimized, and the precession parameters that minimize the cost function are the optimal feature parameters. That is:

[0156]

[0157] Based on the radial length amplitude, the construction strictly falls within Initial weights:

[0158]

[0159] in, This is a smoothing coefficient. This naturally suppresses the influence of low-amplitude samples.

[0160] To further avoid getting trapped in local minima, we... A two-stage weight is obtained by applying a chaotic mapping. First, a normalization operation is performed, the specific expression of which is shown below:

[0161]

[0162] The chaotic mapping of the normalized weights is expressed as follows:

[0163]

[0164] in, This represents the value at time n. express The value after chaotic mapping. and These are chaos parameters, and the range of the chaos mapping is... , parameter d=1.1.

[0165] Bifurcation diagrams depict the process from bifurcation to chaos and are of great significance for analyzing chaotic characteristics; variables vary with parameters. The changing bifurcation diagram is as follows Figure 14 and Figure 15 As shown, the initial value is Bifurcation diagrams can clearly reflect the entire chaotic process. When a large number of irregularly distributed points appear in the bifurcation diagram, it indicates that the system is chaotic. The proposed method yields the system in... It exhibits a wider range of chaos parameters, providing a broader view of the entire... The intervals are traversed more evenly and comprehensively, as evidenced by the high upper bound and lack of large gaps in their chaotic regions.

[0166] Figure 16 and Figure 17 The system's Lyapunov exponent varies with parameters. And the change, from Figure 16 It can be observed in most The Lyapunov exponent remained positive throughout the interval, with only a few points showing brief dips. Overall, this indicates the system is highly sensitive to initial conditions and exhibits significant chaos; furthermore... Figure 17 Therefore, the Lyapunov index follows The chaos intensity increases and remains positive, rising with... The enhancement indicates that the system remains in a state of strong chaos.

[0167] System attractor graph as follows Figure 18 As shown in the figure, the particles are randomly and uniformly distributed throughout the entire area. The interval indicates a stronger pseudo-random effect. This chaotic mapping can help optimization algorithms, enabling models to exhibit chaotic behaviors such as uniform random ergodicity, and freeing the optimization process from local minima, thereby enhancing fitting accuracy.

[0168] Weights after chaotic mapping The mapping expression is as follows:

[0169]

[0170] For this nonlinear multidimensional cost function, an analytical solution for its minimum cannot be found; therefore, it can only be solved through optimization methods. In this invention, gradient descent is used for optimization. The gradient of the function at any point is the direction in which the function changes most rapidly at that point. The gradient of the cost function is expressed as:

[0171]

[0172] Since the cost function is defined as the sum of the mean square errors of the radial length at each time step,

[0173]

[0174] Therefore, calculating the gradient of this cost function can be expressed as summing the gradients of the mean squared error at each time step:

[0175]

[0176] In this invention, to make the cost function quickly approach its minimum, the negative gradient direction of the parameter change is chosen, wherein... :

[0177]

[0178] The change in the function is:

[0179]

[0180] The change in this function is always less than zero, ensuring that the cost function gradually decreases as the precession parameters are continuously updated, and follows the direction of the fastest descent of the objective function. The iteration process of the feature parameters is illustrated using the precession angle as an example.

[0181]

[0182] During the observation period, the precession parameters are updated. When the error rate on the test set falls below a certain set threshold, the estimated parameters are considered optimal. Training involves two phases: first using... Obtain the baseline solution, and then use Fine-tune in its vicinity; compare the error of the test set and output the best result.

[0183] Table 3. Precession angle estimation results for different polarization schemes at different signal-to-noise ratios.

[0184]

[0185] Table 3 shows that in precession angle estimation, different polarization methods exhibit relatively large errors without chaotic mapping: HH bias -2.80°, VV bias -2.83°, Span bias -1.87°, OPCE bias -1.72°, and GOPCE bias +1.56°. The overall error is concentrated in the range of 1.5°-2.9°, indicating limited accuracy. However, after introducing chaotic mapping, the estimation accuracy is significantly improved: HH bias -0.70°, VV bias +0.81°, Span bias -0.54°, OPCE bias +0.50°, and GOPCE bias +0.34°. The errors of all methods are controlled within ±1°. The results indicate that polarization fusion combined with chaotic mapping can not only effectively reduce estimation bias but also improve overall stability and robustness. Among them, the GOPCE method performs best, achieving a high-precision estimation of the true value of 30° with a tiny error of only 0.34°, demonstrating the significant advantage of the improved polarization fusion strategy in estimating the precession angle of space targets.

[0186] Table 4. Size estimation results for different polarization schemes at different signal-to-noise ratios.

[0187]

[0188] Table 4 shows that different polarization methods exhibit certain deviations under chaotic conditions: HH and VV have relatively large error rates (5.07% and 5.61%), while Span, OPCE, and GOPCE are relatively better (error rates of 4.27%, 4.01%, and 3.34%, respectively), but still have a systematic underestimation of 0.25-0.42 m. After introducing chaotic mapping, the accuracy of all methods is significantly improved, with error rates decreasing to 0.40%-2.14%. Span has a deviation of only 1.07%, OPCE reaches 0.93%, while GOPCE is the best, with an error rate of only 0.40% and an error range of only -0.03 m, almost perfectly matching the true value. The results indicate that polarization fusion combined with chaotic mapping can effectively reduce the systematic error in target size estimation and significantly improve accuracy and stability, with the GOPCE method showing the most significant improvement.

[0189] This invention proposes a method for extracting the micro-motion characteristics of HRRP targets based on chaotic optimization and polarization synthesis, specifically for the High Resolution Range Profile (HRRP) domain. The method includes: performing optimal polarization contrast enhancement on multi-channel HRRP polarization data, and optimal polarization fusion based on the maximum signal-to-noise ratio criterion; combining second harmonic backoff optimization and autocorrelation / amplitude difference enhancement processing to estimate the period of the polarization-fused data; and combining chaotic mapping with backpropagation to avoid the problem of traditional optimization easily getting trapped in local minima, thus obtaining the precession angle and size results of the space target. This invention significantly improves the feature contrast of HRRP data through polarization fusion, and simultaneously achieves high-precision estimation of the micro-motion characteristics of space targets under low signal-to-noise ratio conditions. It effectively improves the stability of period detection and the global search capability of parameter inversion within a limited observation time, significantly enhancing the accuracy and robustness of space target micro-motion estimation in complex environments.

[0190] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0191] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0192] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0193] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0194] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0195] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

Claims

1. A method for extracting micro-motion characteristics of HRRP targets based on chaotic optimization and polarization synthesis, characterized in that, The method includes: S1. Acquire multi-channel polarization data of high-resolution one-dimensional range image HRRP; S2. Perform optimal polarization contrast enhancement and optimal polarization fusion based on the maximum signal-to-noise ratio criterion on the HRRP multi-channel polarization data; S3. Perform FFT coarse estimation on HRRP polarization fusion data and frequency offset correction estimation based on second harmonic backoff optimization to estimate the target micro-motion period; In S3, cross-correlation function analysis is performed on the HRRP sequence after optimal polarization fusion to obtain the initial estimate of the precession period. Based on this, a second harmonic backoff mechanism is introduced to overcome the misjudgment problem that the main peak of the spectrum may fall on the second harmonic position due to the symmetrical structure of the space target and the distribution of the scattering center. When the power spectrum is at the main peak frequency Nearby half-frequency location detected The spectral energy at the location satisfies: （1） When the estimated frequency is corrected, it is then: （2） in Represents frequency The power spectral amplitude at that point For preset threshold parameters, For the frequency of correction, This indicates the period estimation result; S4. Perform parameter inversion based on chaotic mapping on HRRP polarization fusion data to estimate the precession angle and size of space targets; In S4, a precession scattering model of a space target is established, the relationship between the radial length of the space target's HRRP and time is derived, and the influence of high-speed translation during the precession process on the radial length is considered. Based on this, a cost function for the radial length is constructed, and an improved chaotic mapping combined with a backpropagation algorithm is used for optimization iteration to update precession parameters such as precession angle and target size. The improved chaotic mapping in S4 is shown in equation (3) below: ， （3） In the formula, express The value of the moment. express The value after chaotic mapping. and These are chaos parameters, and the range of the chaos mapping is... ,parameter .

2. The method for extracting HRRP target micro-motion characteristics based on chaotic optimization and polarization synthesis according to claim 1, characterized in that, S2 includes the following sub-steps: S21. Calculate the total polarization power Span of the multi-channel polarization data to fuse the power information of each channel; S22. The relative optimal polarization OPCE theory is used to optimize the HRRP multi-channel data to enhance the contrast between the target of interest and the background, thereby achieving the target enhancement function. S23. Use the generalized optimal polarization contrast enhancement (GOPCE) technique to fuse HRRP multi-channel data to further increase the contrast between the target and background clutter.

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