High-orbit bistatic radar aerial target detection method based on multi-dimensional manifold constraint

Abstract

The invention provides a high-orbit bistatic radar aerial target detection method based on multi-dimensional manifold constraint, and relates to the technical field of bistatic radar target detection, and the method comprises the following steps: calculating the ground coverage area of a high-orbit satellite irradiation source; establishing an echo signal model; dividing the echo signal in the long observation time period into a plurality of short-time subframes, and ensuring that the Doppler walking of the target in each subframe time is limited in a single resolution unit; estimating the Doppler center frequency and the Doppler change rate of the target in each sub-frame; carrying out distance-crossing unit walking correction and high-order motion phase compensation in the sub-frame, and realizing coherent energy focusing in the sub-frame; and performing incoherent accumulation on the cross-frame target energy to obtain detection statistics. According to the method, coherent gain and compensation complexity are balanced through a framing strategy, the operand is reduced by using cross-frame parameter evolution constraint, and robust detection of a long-distance weak maneuvering target can be realized.

Description

Technical Field

[0001] This invention relates to the field of bistatic radar target detection technology, and specifically to a high-orbit bistatic radar air target detection method based on multidimensional manifold constraints. Background Technology

[0002] With the rapid development of integrated air-space information networks, bistatic radar based on high-orbit satellite illumination sources has shown significant potential in long-range, wide-area aerial target detection. However, high-orbit bistatic radar faces the dual challenges of extremely weak target echo signals and high target maneuverability in practical applications. Existing detection methods are mainly divided into two categories: one is detection methods based on low-order motion models, such as using Keystone transform to correct the linear range migration of uniformly moving targets. However, when the target has high maneuverability, it is difficult to accurately compensate for high-order phase errors, resulting in ineffective energy focusing. The other category is high-order motion matching methods based on long-term coherent accumulation, such as the generalized Radon-Fourier transform. However, these methods require grid search of unknown high-dimensional parameter spaces, resulting in extremely high computational complexity and making it difficult to meet real-time processing requirements.

[0003] Existing technical solutions have significant drawbacks: methods based on low-order models are difficult to adapt to highly maneuverable targets, resulting in severe divergence of signal energy over long coherence times and a sharp decline in detection performance; while methods based on high-order model matching can theoretically achieve precise focusing, their huge parameter search space brings an exponentially increasing computational burden and is prone to getting trapped in local optima, resulting in poor engineering practicality.

[0004] Therefore, how to significantly reduce the complexity and computational load of parameter estimation while ensuring effective focusing on highly maneuverable weak targets has become a key technical challenge that urgently needs to be solved in the field of high-orbit bistatic radar. Summary of the Invention

[0005] To address the challenges of high-orbit bistatic radar systems, where aerial targets exhibit significant range-crossing movement (RCM) and Doppler shift over long coherence intervals due to their high maneuverability, and where extremely weak target signals render conventional detection methods ineffective and multidimensional parameter search computationally complex, this invention provides a high-orbit bistatic radar aerial target detection method based on multidimensional manifold constraints. This invention aims to balance coherence gain and compensation complexity through a framing strategy and reduce computational load by utilizing cross-frame parameter evolution constraints, thereby achieving robust detection of long-range, weakly maneuvering targets.

[0006] To achieve the above objectives, the technical solution adopted by the present invention includes:

[0007] According to a first aspect of the present invention, a method for detecting high-orbit bistatic radar airborne targets based on multidimensional manifold constraints is provided, comprising:

[0008] Step S1: Calculate the ground coverage area of ​​the high-orbit satellite illumination source, and determine the geometric layout of the radar network and the geometric resolution performance of the observation area in combination with the observation requirements;

[0009] Step S2: Based on the bistatic distance history between the high-orbit satellite and the receiving platform, establish an echo signal model of a highly maneuverable aerial target under the bistatic system and analyze its echo characteristics;

[0010] Step S3: Based on the system range resolution and Doppler resolution, divide the echo signal of the long observation period into multiple short time subframes, and ensure that the Doppler movement of the target is limited to a single resolution cell within each subframe.

[0011] Step S4: To address the issues of migration and weak target echo caused by high maneuverability, a modeling and optimization problem is established. A multi-dimensional parameter space manifold constraint strategy is adopted, and the particle swarm optimization method is improved to estimate the Doppler center frequency and Doppler rate of change of the target in each sub-frame.

[0012] Step S5: Using the parameters estimated in step S4, perform distance cell movement correction and higher-order motion phase compensation within the subframe, and achieve coherent energy focusing within the subframe through deslope Fourier transform;

[0013] Step S6: Extract the features of each subframe in the range-Doppler domain, and perform incoherent accumulation of the target energy across frames to obtain the detection statistics.

[0014] Optionally, in step S1, the calculation of the ground coverage area of ​​the high-orbit satellite illumination source specifically includes: establishing the relationship between the satellite's viewing angle and the geocentric angle using the sine theorem, calculating the range coverage width and the azimuth coverage width respectively, and defining the effective illumination area using the ellipse area formula;

[0015] Wherein, the distance coverage width The azimuth coverage width is obtained by calculating the arc length difference from the edge point of the coverage area to the sub-satellite point. According to the slope distance and azimuth beamwidth Calculated as The final coverage area S is calculated as follows: .

[0016] Optionally, in step S2, establishing the echo signal model of a highly maneuverable aerial target under a dual-base system specifically includes:

[0017] Historical bistatic distance between the target and the high-orbit satellite and receiving platform In slow time Perform a second-order Taylor series expansion at this point, which is expressed as: In the formula, Indicates slow time The bistatic distance between the target and the high-orbit satellite and receiving platform. In slow time The bistatic distance between the target and the high-orbit satellite and receiving platform. For slow time The first derivative at that point, This represents a slow-time variable, used to describe the time offset in the slow-time dimension. For higher-order infinitesimal terms in Taylor expansion.

[0018] Optionally, in step S3, the criterion for dividing short-time subframes is:

[0019] Ensure that within the preset subframe duration, the residual distance error caused by the second-order Taylor expansion is less than the system distance resolution unit, and the residual Doppler frequency shift error is less than 1 / 3 of the system Doppler frequency resolution.

[0020] Optionally, in step S4, the multidimensional parameter space manifold constraint strategy specifically includes:

[0021] Utilizing the continuity of target motion over a short timescale, a linear evolution correlation model of Doppler parameters across subframes is established. The entire observation period is divided into n subframes, and the originally independent 2n motion parameters to be determined, namely the Doppler center frequency of each subframe, are... and Doppler rate of change The parameters are jointly estimated by projecting the multidimensional parameter space manifold constraint onto a constraint subspace of dimension n+2.

[0022] Optionally, in step S5, a phase compensation operator is constructed using the stationary phase principle to eliminate linear and higher-order range migration within the subframe, and spectral broadening caused by Doppler frequency variations is eliminated using the deslope Fourier transform; wherein, the expression for the deslope Fourier transform is: In the formula, This indicates that in the nth subframe, the distance is R and the Doppler frequency is... The signal after deslope processing, This indicates that in the nth subframe, the distance is R and the slow time is... The original echo signal, This represents the exponential function, used to construct the kernel function for Fourier transform and phase compensation. The imaginary unit, For Doppler frequency, For slow time, The rate of change of Doppler frequency within the nth subframe.

[0023] Optionally, in step S5, after intra-frame coherent accumulation, the signal expression of the nth subframe in the range-Doppler domain is:

[0024]

[0025] In the formula, For the target echo signal amplitude, This is a rectangular window function used to represent the effective duration or frequency range of a signal in the Doppler domain. and These are the estimated Doppler center frequency and Doppler frequency slope of the target within the nth subframe, respectively. The duration of the subframe. This is a range pulse compression function used to describe the main lobe and side lobe characteristics of a signal in the range domain. The initial slant distance of the target. For radar signal wavelength, and These are the estimated Doppler center frequency and the estimated Doppler frequency change rate of the target within the entire frame, respectively. This is the range-phase offset term of the target within the nth subframe.

[0026] Optionally, in step S6, the incoherent accumulation of the target energy across frames specifically includes:

[0027] Based on the accumulated results of the intermediate reference subframes, the energy peak positions of each subframe in the range-Doppler domain are compensated for motion trajectory and then summed to obtain the final detection statistics. The expression is:

[0028]

[0029] In the formula, This represents summing over all subframes n and taking the modulus of the signal, indicating a noncoherent accumulation operation across frames, used to improve the signal-to-noise ratio of the target energy. This represents the signal amplitude in the range-Doppler domain of the nth subframe.

[0030] Optionally, in step S6, the echo is moved by utilizing the mathematical mapping relationship between the distance migration of the target echo and the Doppler parameters to achieve inter-frame echo accumulation.

[0031] According to a second aspect of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, is capable of implementing the steps of the high-orbit bistatic radar air target detection method based on multidimensional manifold constraints as described in any of the technical solutions of the first aspect of the present invention.

[0032] Beneficial effects:

[0033] 1. Through the above technical solution, firstly, the method of the present invention can effectively achieve a balance in the face of technical contradictions. Specifically, the method of the present invention constructs a hierarchical processing architecture by organically combining step S3 (data framing processing) with steps S5 (intra-frame coherent focusing) and S6 (inter-frame incoherent accumulation). This hierarchical processing architecture transforms the continuous observation time, which was originally impossible to achieve effective long coherent accumulation due to the high maneuverability of the target, into a series of short sub-frames in which the target motion can be regarded as "quasi-stationary". Coherent processing is performed within each sub-frame (step S5), which can obtain a signal-to-noise ratio gain relative to single-pulse processing; while incoherent accumulation across sub-frames (step S6) can further accumulate energy. In this way, through this strategy of "intra-frame coherence + inter-frame incoherence", the pursuit of high accumulation gain and overcoming the extreme complexity of motion compensation caused by high maneuverability can be effectively balanced, thereby effectively achieving reliable detection of weak signals.

[0034] Second, the method of this invention can improve the overall efficiency of parameter estimation and signal processing. Specifically, step S4 (using a multi-dimensional manifold constraint strategy to improve particle swarm optimization for parameter estimation) is not isolated; it is a key link embedded in the aforementioned frame-segmentation processing framework. Thus, for each subframe requiring motion compensation, an efficient parameter estimation method can be provided. Simultaneously, step S2 (establishing an echo model based on bibase distance history) provides an accurate physical and mathematical model foundation for the entire process, ensuring the effectiveness of subsequent frame segmentation, parameter estimation, and compensation correction (step S5). Therefore, the method of this invention, through a sequential process of modeling, then frame segmentation, and subsequently efficient parameter estimation and compensation, can effectively improve the feasibility and efficiency of accurately focusing on the echoes of highly maneuvering targets, thereby enabling reliable detection under low signal-to-noise ratio conditions (step S6 outputs detection statistics).

[0035] In summary, the method of this invention provides a systematic solution framework. This framework, through a specific combination of steps, innovatively designs two dimensions: processing strategy (frame accumulation) and core algorithm (manifold constraint estimation). Ultimately, it achieves a good balance between computational complexity and detection performance, thereby enabling effective detection of long-range, highly maneuverable, and weakly reflective aerial targets under high-orbit bistatic radar systems.

[0036] 2. Other beneficial effects or advantages of the present invention will be described in detail in the specific embodiments. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the 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.

[0038] in:

[0039] Figure 1 This is a flowchart illustrating the steps of a high-orbit bistatic radar air target detection method based on multidimensional manifold constraints, provided by an exemplary embodiment of the present invention.

[0040] Figure 2 This is a geometrical diagram of the coverage area of ​​a high-orbit satellite provided in an exemplary embodiment of the present invention;

[0041] Figure 3 This is an example embodiment of the present invention providing a range-Doppler domain image of an airborne moving target echo after range pulse compression;

[0042] Figure 4 and Figure 5 This is a simulation result diagram of target echo characteristic analysis provided by an exemplary embodiment of the present invention, wherein, Figure 4 This is a graph showing the error results of different Taylor expansion orders for Doppler frequency shift. Figure 5 This is a graph showing the distance error results for different orders of Taylor expansion;

[0043] Figure 6 This is a schematic diagram of the PSO iterative signal-to-noise ratio optimization curve of the multidimensional parameter space manifold reduction method provided in an exemplary embodiment of the present invention;

[0044] Figure 7 and Figure 8 This is an accumulation result diagram of a highly maneuverable weak target in the air provided by an exemplary embodiment of the present invention, wherein, Figure 7 It is a target distance-Doppler 2D map. Figure 8 It is a three-dimensional graph of target point distance-Doppler-amplitude;

[0045] Figure 9 and Figure 10 This is an example embodiment of the present invention providing a cross-sectional view of the accumulated target location, wherein, Figure 9 It is a normalized range profile of the target location. Figure 10 It is a normalized azimuth frequency profile of the target location. Detailed Implementation

[0046] To facilitate a clearer and more accurate understanding of the technical solutions of this invention by those skilled in the art, the existing related technologies and their technical problems will be described in more detail below.

[0047] With the rapid development of integrated air-space information networks, bistatic radar systems based on external radiation sources have attracted widespread attention. In particular, high-orbit bistatic radar systems using geostationary orbit (GEO) satellites as illumination sources and low-altitude mobile platforms as receiving stations have shown great potential in long-range aerial target detection. However, this system faces the dual challenges of extremely weak echo energy and high target mobility in practical applications, making it difficult for existing detection methods to achieve both high accuracy and efficiency.

[0048] For example, in the paper "A multi-frame fractional Fourier transform technique for moving target detection with space-based passive radar" (IEEE IET Radar Sonarand Navigation, 2016, 11(5):822-828.), a linear range-Doppler migration correction method for target echoes was proposed, which can effectively detect uniformly moving ship targets. Its core algorithm is based on the assumption of a low-order motion model. When facing targets with drastic acceleration and high-order motion components, such as highly maneuverable fighter jets or hypersonic vehicles, the Keystone transform is difficult to accurately correct high-order phase errors, resulting in severe defocusing of the detection statistics and ineffective energy accumulation.

[0049] For example, in the paper "Moving Target Detection for FDA-MIMO Radar Based on Two-Step Radon-Fourier Transform," (2024 International Radar Symposium (IRS), Wroclaw, Poland, 2024, pp. 144-149), a generalized Radon-Fourier transform (GRFT) algorithm is proposed, attempting to match high-order motion models through long-term coherent accumulation. However, when the target parameters are unknown, this method requires a blind grid search of multi-dimensional parameters. For the multi-order motion parameters of highly maneuverable targets, the search space explodes exponentially and is prone to getting trapped in local optima, resulting in extremely low computational efficiency, making it difficult to meet the real-time detection requirements of high-orbit bistatic radar.

[0050] Therefore, how to propose a method for stable detection of weak targets at long range for high-orbit bistatic radar systems that can effectively correct the complex migration caused by high maneuverability and reduce computational complexity by optimizing the search mechanism is a key technical problem that urgently needs to be solved in the field of radar signal processing.

[0051] In view of this, the present invention provides a high-orbit bistatic radar air target detection method based on multidimensional manifold constraints to solve the problems of large computational load and severe model mismatch of traditional long-term coherent accumulation methods, as well as the weak detection capability of conventional framing methods under low signal-to-noise ratio, thereby achieving robust detection of long-range, highly maneuverable, weak targets.

[0052] The technical concept of this invention lies in introducing a "multidimensional parameter space manifold constraint" mechanism. Utilizing the inherent continuity of the target trajectory at the physical level, the original parameter search problem, which was conducted independently in each subframe, is transformed into a holistic optimization problem with strong correlation constraints. In other words, the method of this invention no longer blindly estimates each subframe independently. Instead, it establishes a cross-frame parameter evolution model, projecting the high-dimensional search space onto a low-dimensional manifold subspace. This significantly reduces computational complexity while using high signal-to-noise ratio (SNR) information to assist low SNR subframes, achieving precise focusing of weak signals.

[0053] Specifically, firstly, this invention establishes a strict adaptive framing criterion based on an accurate second-order Taylor expansion bibasic distance history model, ensuring that the target motion satisfies the "quasi-stationary" condition within each subframe, thus avoiding mismatch in higher-order models from the source. Secondly, it constructs a cross-frame parameter linear evolution correlation model, compressing the originally independent 2n motion parameters (Doppler centroid and frequency modulation) of n subframes into a constrained subspace containing only n+2 core parameters through parameter space manifold constraints, and using this constraint strategy to improve the particle swarm optimization algorithm for efficient solution. Finally, it adopts a two-layer integration strategy of "intra-frame coherent focusing + inter-frame incoherent accumulation," achieving coherent gain within subframes through deslope Fourier transform, and performing energy fusion along the target's spatiotemporal evolution trajectory between frames.

[0054] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0055] like Figure 1 As shown in the figure, this embodiment provides a high-orbit bistatic radar air target detection method based on multidimensional manifold constraints, which includes the following steps:

[0056] S1. Calculate the ground coverage area of ​​the high-orbit satellite illumination source, and determine the geometric layout of the radar network and the geometric resolution performance of the observation area based on the observation requirements;

[0057] S2. Based on the bistatic distance history between the high-orbit satellite and the receiving platform, establish an echo signal model of highly maneuverable aerial targets under the bistatic system and analyze its echo characteristics.

[0058] S3. Based on the system range resolution and Doppler resolution, the echo signal of the long observation period is divided into multiple short time subframes. Through intra-frame keystone transformation, it is ensured that the Doppler movement of the target is limited to a single resolution cell within each subframe.

[0059] S4. To address the issues of migration and weak target echo caused by high maneuverability, a modeling and optimization problem is proposed. A multi-dimensional parameter space manifold constraint strategy is adopted, and the particle swarm optimization method is improved to estimate the Doppler center frequency and Doppler rate of change of the target in each subframe.

[0060] S5. Using the parameters estimated in step S4, perform range cell movement (RCM) correction and higher-order motion phase compensation within the subframe, and achieve coherent energy focusing within the subframe by using the proposed slope Fourier transform.

[0061] S6. Extract the features of each subframe in the range-Doppler domain, and perform incoherent accumulation of the target energy across frames to obtain the detection statistics.

[0062] Through the above technical solution, firstly, the method of the present invention can effectively achieve a balance in the face of technical contradictions. Specifically, the method of the present invention constructs a hierarchical processing architecture by organically combining step S3 (data framing processing) with steps S5 (intra-frame coherent focusing) and S6 (inter-frame incoherent accumulation). This hierarchical processing architecture transforms the continuous observation time, which was originally impossible to achieve effective long coherent accumulation due to the high maneuverability of the target, into a series of short sub-frames in which the target motion can be regarded as "quasi-stationary". Coherent processing is performed within each sub-frame (step S5), which can obtain a signal-to-noise ratio gain relative to single-pulse processing; while incoherent accumulation across sub-frames (step S6) can further accumulate energy. In this way, through this strategy of "intra-frame coherence + inter-frame incoherence", the pursuit of high accumulation gain and overcoming the extreme complexity of motion compensation caused by high maneuverability can be effectively balanced, thereby effectively achieving reliable detection of weak signals.

[0063] Second, the method of this invention can improve the overall efficiency of parameter estimation and signal processing. Specifically, step S4 (using a multi-dimensional manifold constraint strategy to improve particle swarm optimization for parameter estimation) is not isolated; it is a key link embedded in the aforementioned frame-segmentation processing framework. Thus, for each subframe requiring motion compensation, an efficient parameter estimation method can be provided. Simultaneously, step S2 (establishing an echo model based on bibase distance history) provides an accurate physical and mathematical model foundation for the entire process, ensuring the effectiveness of subsequent frame segmentation, parameter estimation, and compensation correction (step S5). Therefore, the method of this invention, through a sequential process of modeling, then frame segmentation, and subsequently efficient parameter estimation and compensation, can effectively improve the feasibility and efficiency of accurately focusing on the echoes of highly maneuvering targets, thereby enabling reliable detection under low signal-to-noise ratio conditions (step S6 outputs detection statistics).

[0064] In summary, the method of this invention provides a systematic solution framework. This framework, through a specific combination of steps, innovatively designs two dimensions: processing strategy (frame accumulation) and core algorithm (manifold constraint estimation). Ultimately, it achieves a good balance between computational complexity and detection performance, thereby enabling effective detection of long-range, highly maneuverable, and weakly reflective aerial targets under high-orbit bistatic radar systems.

[0065] The technical solution of the present invention will be further described below with reference to an exemplary embodiment.

[0066] For example, the steps of the method of the present invention can be simplified as follows: calculate the coverage area of ​​the high-orbit satellite → combine the motion parameters of the high-orbit satellite and the receiving platform to establish a signal echo model of the highly maneuverable target → data framing processing → target Doppler parameter estimation → intra-frame coherent accumulation and correction → inter-frame incoherent accumulation.

[0067] Specifically,

[0068] Step 1: Please refer to Figure 2 , Figure 2 In the diagram, A represents the location of the space-based radar. C represents the radar's flight direction, and C represents the Earth's center. Where B is the Earth's radius, H is the nadir point, H is the altitude of the space-based radar, and R is the distance from the center point of the space-based radar beam to the nadir point. The slant range of the radar beam reaching the center point on the ground. For the geocentric angle, From a satellite perspective, To wipe the corners of the floor, This refers to the range beamwidth.

[0069] In triangle ACD, we have, ;

[0070] Then, we can obtain: ;

[0071] Wipe the corner of the ground from point D : ;

[0072] We can obtain: ;

[0073] Similarly, the rubbing angle at point E can be obtained. :

[0074] Calculate the geocentric angles corresponding to the arc lengths from points D and E to the sub-satellite point B, respectively:

[0075]

[0076]

[0077] The arc lengths from points D and E to the sub-satellite point B are obtained respectively. , ;

[0078] The corresponding distance coverage width is: ;

[0079] Calculating the azimuth beam coverage width first requires calculating the slant range. In triangle ACD, according to the law of cosines: ;

[0080] It can be solved :

[0081]

[0082] Calculated based on actual conditions ;

[0083] The coverage width in the azimuth direction is obtained from the relationship between beamwidth and tan:

[0084]

[0085] According to the formula for calculating the area of ​​an ellipse, the coverage area of ​​the GEO satellite can be obtained as follows:

[0086]

[0087] In this step, by defining specific calculation methods for the ground coverage area (sine theorem, ellipse formula), the coverage area can be transformed from a concept into a precisely calculable geometric quantity. This ensures the accuracy and feasibility of radar observation area planning, provides a reliable spatial reference for the entire detection system, and avoids detection blind spots or resource waste caused by coverage area estimation errors.

[0088] Step 2: Perform an exact Taylor expansion on the bibase distance history, expressed as:

[0089]

[0090] in, The expansion coefficients are of order m. For expansion terms.

[0091] Substituting the bistatic distance history into the echo, the pulse-compressed target echo is represented as follows:

[0092]

[0093] Echo image of the distance-to-pulse compression distance-Doppler domain as shown in the image. Figure 3 As shown.

[0094] In this step, the core of the echo signal model is the second-order Taylor series expansion. In this way, the complex and continuous target motion history can be approximated as a concise parameterized mathematical model. While retaining the main motion characteristics (velocity, acceleration), it can effectively reduce the complexity of subsequent signal processing and lay an accurate mathematical foundation for frame processing and parameter estimation.

[0095] Step 3: Analyze the echo characteristics and improve particle swarm optimization, which greatly improves the efficiency of the algorithm.

[0096] To achieve effective detection of highly maneuverable, weak targets in the air, it is necessary to first analyze the range migration characteristics and Doppler characteristics of their echoes. Simulation parameters are shown in Table 1 below. The theoretical range resolution is 7.33m. When using a frame-by-frame accumulation detection strategy, with a frame duration of 3s, simulation diagrams of the range errors of different orders of the dual-base range history Taylor expansion and the errors of different orders of the Doppler frequency shift Taylor expansion are available. Figure 4 and Figure 5 .

[0097] Table 1 Simulation Parameter Table

[0098]

[0099] analyze Figure 4 and Figure 5 The second-order expansion can be used to satisfy the following conditions: the range history error is less than the theoretical resolution in the azimuth direction, and the Doppler error is less than 1 / 3 of its frequency resolution. (In this way, it can be ensured that the target motion in each subframe satisfies the "quasi-stationary" assumption, guaranteeing the effectiveness of subsequent intra-frame coherent processing from the source and avoiding compensation residue or gain loss caused by improper frame length selection.)

[0100] The bibase distance history is R(t). Based on its frame-segmentation characteristics, its second-order Taylor expansion at slow time t=0 yields: In the formula, Indicates slow time The bistatic distance between the target and the high-orbit satellite and receiving platform. In slow time At this point, the bistatic distance between the target and the high-orbit satellite and receiving platform, i.e., the zeroth-order term of the bistatic distance, For slow time The first derivative at that point, i.e., the rate at which the bibasic distance changes with slow time, This represents a slow-time variable, used to describe the time offset in the slow-time dimension. Let be the higher-order infinitesimal terms in the Taylor expansion, and represent the higher-order remainder terms above t² in the expansion, which can be ignored within the required accuracy range; where... ;

[0101] Based on the above expansion, the instantaneous Doppler frequency can be obtained as:

[0102]

[0103] The Doppler modulation frequency is:

[0104]

[0105] The above , (Doppler parameters of the intermediate reference frame), where, Consider it as a linear compensation factor approximation ,available:

[0106]

[0107] Furthermore, we can obtain:

[0108]

[0109] At the subframe processing scale, the instantaneous Doppler frequency within a frame can be approximated as having a linear mapping relationship with the Doppler modulation frequency, and the Doppler modulation frequency within the frame and the higher-order infinitesimal terms of the Taylor expansion satisfy a linear evolution law.

[0110] Accordingly, this invention uses the aforementioned linear evolution criterion as the physical constraint for parameter estimation: that is, within each subframe, both the Doppler centroid and the Doppler modulation frequency exhibit linear time-varying characteristics, and the parameter evolution between different subframes follows differentiated linear constraint logic. Based on this multidimensional parameter space manifold constraint mechanism, the n parameters to be estimated can be mapped to the slope of the linear evolution relationship within each subframe, thereby deriving the dual Doppler parameters corresponding to each subframe.

[0111] In this way, the high-dimensional parameter estimation problem can be transformed into a strongly constrained low-dimensional search problem. By utilizing the prior knowledge of the physical continuity of the target motion, the search space can be greatly compressed, fundamentally solving the core bottleneck of high computational complexity and poor real-time performance caused by the explosion of parameter dimensions in traditional methods.

[0112] In summary, if the entire observation period is divided into n subframes, this invention introduces a cross-frame parameter correlation model to project the originally redundant multidimensional search space into a constrained subspace containing only n+2 core parameters. By solving this reduced-dimensional parameter set using an optimization algorithm, the precise Doppler centroid and Doppler modulation frequency parameters of each subframe can be reconstructed.

[0113] By introducing the aforementioned multidimensional parameter space manifold constraint method, the optimization objective is the signal-to-noise ratio (SNR) of the target echo accumulated in the range-Doppler domain. The relationship between the number of optimization iterations and the SNR is as follows: Figure 6 As shown.

[0114] Step 4: Using the stationary phase principle, obtain the echo after intra-frame coherent accumulation in the range Doppler and domain.

[0115] To achieve coherent accumulation of intra-frame signals, and addressing the issue of high-speed aerial target movement and significant motion in the echo, a first-order Keystone motion correction is first applied to the intra-frame echo. The expression is as follows:

[0116]

[0117] The present invention then proposes a deslope Fourier transform to correct intra-frame Doppler migration. The expression for the deslope Fourier transform is as follows:

[0118]

[0119] In the formula, This indicates that in the nth subframe, the distance is R and the Doppler frequency is... The signal after deslope processing. It is at a specific Doppler slope. Below is the result of performing a de-Fourier transform on the original signal. This indicates that in the nth subframe, the distance is R and the slow time is... The original echo signal. Here It represents the azimuth time, indicating the timing of radar pulse transmissions. The slant range from the target to the radar is the path length of the electromagnetic wave from transmission to reception. Slow time, also called azimuth time, is the time axis that distinguishes different transmitted pulses and is used to describe the echo of the target at different times. This represents an exponential function, specifically a complex exponential phase term used to construct the kernel function for Fourier transform and phase compensation. The imaginary unit, The frequency is the Doppler frequency, generated by the relative radial motion between the target and the radar, and is a slow-time frequency. The corresponding frequency components, Let be the rate of change of Doppler frequency within the nth subframe, representing the Doppler frequency as a function of slow time. The rate of change is caused by the target's acceleration or the movement of the radar platform.

[0120] Applying the slope Fourier transform to the echo expression after range pulse compression, and combining it with the stationary phase principle, the expression for the signal after intra-frame coherent accumulation is obtained as follows:

[0121]

[0122] The amplitude of the target echo signal reflects the combined effects of target scattering characteristics, radar transmit power, and propagation loss. This is a rectangular window function used to represent the effective duration or frequency range of a signal in the Doppler domain. and These are the estimated Doppler center frequency and Doppler frequency slope of the target within the nth subframe, respectively. This refers to the subframe duration, i.e., the time length corresponding to a single subframe. This is a range pulse compression function used to describe the main lobe and side lobe characteristics of a signal in the range domain. This represents the initial slant range of the target, i.e., the slant range from the target to the radar at the start of the subframe. The radar signal wavelength is inversely proportional to the carrier frequency. and These are the estimated Doppler center frequency and the estimated Doppler frequency change rate of the target within the entire frame, respectively. This is the range-phase offset term of the target within the nth subframe, caused by the target's motion and radar geometry.

[0123] In this step, the closed-form expression of the signal after intra-frame coherent accumulation theoretically characterizes the ideal aggregation form of the target energy in the range-Doppler two-dimensional domain after precise motion compensation (manifested as a sharp main lobe). This not only proves the effectiveness of the aforementioned steps (model, framing, parameter estimation, compensation), but also provides a clear signal form for subsequent peak detection and inter-frame alignment.

[0124] Step 5: Obtain the result after inter-frame incoherent accumulation.

[0125] Subsequently, noncoherent ensemble processing is performed on the multi-frame signals after coherent accumulation to further improve the target detection gain. Considering the variation characteristics of the target Doppler centroid (fdc) with the sub-frame sequence, and the residual cross-range cell movement and range curvature effects at extremely long observation timescales, the spatial distribution of the energy peaks of each sub-frame after coherent processing exhibits spatial variability in the range-Doppler plane. Therefore, before performing multi-frame noncoherent ensemble, an inter-frame parameter compensation mechanism based on a reference frame must be established. Taking the coherent accumulation result of the intermediate sub-frame as a reference, the residual motion compensation and noncoherent accumulation process of the multi-frame signals can be specifically described as follows:

[0126]

[0127] In the formula, This represents summing over all subframes n and taking the modulus of the signal, indicating a noncoherent accumulation operation across frames, used to improve the signal-to-noise ratio of the target energy. This represents the signal amplitude of the nth subframe in the range-Doppler domain, i.e., the subframe signal output after intra-frame coherence accumulation and deslope processing.

[0128] After the above processing, the third-order range migration and higher-order Doppler migration present in the target echo over extremely long time are effectively corrected, thereby accumulating all target energy to the same location in the range-Doppler domain, while the noise remains diffuse in this domain after processing. Therefore, the target signal-to-noise ratio can be significantly improved, thus enabling effective detection of highly maneuverable, weak targets in the air. The accumulation results for highly maneuverable, weak targets in the air are as follows: Figure 7 and Figure 8 As shown.

[0129] In this way, by performing inter-frame incoherent accumulation (accumulation after compensation) and energy alignment and fusion along the target motion trajectory, signal-to-noise ratio accumulation across the time dimension can be achieved, thereby breaking through the detection threshold of single-frame processing and significantly improving the final detection capability of weak signals.

[0130] In one embodiment of the present invention, in step S6, the mathematical mapping relationship between the distance migration of the target echo and the Doppler parameters can be used to move the echo and achieve inter-frame accumulation of the echo.

[0131] To further analyze the fine structural features of the target after coherent accumulation, this invention, based on the obtained range-Doppler (RD) two-dimensional spectral matrix, obtains the grid coordinates of the target by searching for the energy peak center, and then performs normalized slice extraction along the range dimension and the Doppler frequency dimension respectively to obtain the range and Doppler profiles of the target location, as shown below. Figure 9 and Figure 10 As shown. This operation aims to visually characterize the energy focusing performance of the target signal in both time and frequency dimensions, providing a quantitative basis for subsequent evaluation of accumulation gain and resolution metrics.

[0132] As can be seen from the above exemplary embodiments, the method of the present invention can achieve robust detection of highly maneuverable weak targets in the air under a high-orbit bistatic radar system. Specifically, the method of the present invention introduces a multidimensional parameter space manifold constraint mechanism, which ensures precise motion compensation and coherent energy focusing for highly maneuverable targets, while utilizing the physical evolution law between parameters to achieve effective dimensionality reduction of the search space. Compared with traditional exhaustive search or high-dimensional optimization algorithms, it can effectively improve computational efficiency and reduce the false alarm rate.

[0133] In summary, this invention quantitatively characterizes the range migration and Doppler time-varying characteristics of highly maneuverable aerial targets, establishing an adaptive framing criterion based on a second-order motion model. Within the subframe scale, it restricts cross-range cell movement and Doppler frequency spread to a single resolution cell, ensuring the stability of weak signals over long coherent observation times. Building upon this, the invention innovatively proposes a multi-dimensional parameter space manifold constraint mechanism. Utilizing the physical continuity of the target trajectory, it establishes a linear evolutionary correlation model between the Doppler centroid and Doppler modulation frequency across subframes. This maps the originally redundant 2n-dimensional independent search space to a constrained subspace containing only n+2 core parameters. This strategy improves the particle swarm optimization algorithm for heuristic search, significantly reducing computational complexity while maintaining parameter estimation accuracy. Furthermore, this invention employs a two-layer integration strategy of intra-frame coherent focusing and cross-frame trajectory correlation non-coherent accumulation, effectively avoiding trajectory breakage caused by high maneuverability, breaking through the detection threshold of extremely weak targets under high-orbit dual-base systems, and significantly improving the robustness and real-time performance of the system detection in complex maneuvering scenarios.

[0134] It is understood that the frame-by-frame accumulation detection framework proposed in this invention can be widely applied in technical fields such as integrated air and space reconnaissance, long-range early warning detection, civil aviation safety monitoring, and new radar system algorithm design.

[0135] According to a second aspect of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, is capable of implementing the steps of the high-orbit bistatic radar air target detection method based on multidimensional manifold constraints in any of the technical solutions of the first aspect of the present invention.

[0136] In this embodiment, the computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), a register, a hard disk, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof, or any other form of computer-readable storage medium known in the art. An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium may also be a component of the processor. The processor and the storage medium may reside in an application-specific integrated circuit (ASIC). In embodiments of the present invention, a computer-readable storage medium may be any tangible medium that contains or stores a program that may be used by or in conjunction with an instruction execution system, apparatus, or device.

[0137] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for detecting high-orbit bistatic radar airborne targets based on multidimensional manifold constraints, characterized in that, include: Step S1: Calculate the ground coverage area of ​​the high-orbit satellite illumination source, and determine the geometric layout of the radar network and the geometric resolution performance of the observation area in combination with the observation requirements; Step S2: Based on the bistatic distance history between the high-orbit satellite and the receiving platform, establish an echo signal model of a highly maneuverable aerial target under the bistatic system and analyze its echo characteristics; Step S3: Based on the system range resolution and Doppler resolution, divide the echo signal of the long observation period into multiple short time subframes, and ensure that the Doppler movement of the target is limited to a single resolution cell within each subframe. Step S4: To address the issues of migration and weak target echo caused by high maneuverability, a modeling and optimization problem is established. A multi-dimensional parameter space manifold constraint strategy is adopted, and the particle swarm optimization method is improved to estimate the Doppler center frequency and Doppler rate of change of the target in each sub-frame. Step S5: Using the parameters estimated in step S4, perform distance cell movement correction and higher-order motion phase compensation within the subframe, and achieve coherent energy focusing within the subframe through deslope Fourier transform; Step S6: Extract the features of each subframe in the range-Doppler domain, and perform incoherent accumulation of the target energy across frames to obtain the detection statistics.

2. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 1, characterized in that, In step S1, calculating the ground coverage area of ​​the high-orbit satellite illumination source specifically includes: The relationship between satellite viewpoint and geocentric angle is established using the sine theorem. The range coverage width and azimuth coverage width are calculated separately, and the effective illumination area is defined by combining the ellipse area formula. Wherein, the distance coverage width The azimuth coverage width is obtained by calculating the arc length difference from the edge point of the coverage area to the sub-satellite point. According to the slope distance and azimuth beamwidth Calculated as The final coverage area S is calculated as follows: .

3. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 1, characterized in that, In step S2, establishing the echo signal model of a highly maneuverable aerial target under a dual-base system specifically includes: Historical bistatic distance between the target and the high-orbit satellite and receiving platform In slow time Perform a second-order Taylor series expansion at this point, which is expressed as: In the formula, Indicates slow time The bistatic distance between the target and the high-orbit satellite and receiving platform. In slow time The bistatic distance between the target and the high-orbit satellite and receiving platform. For slow time The first derivative at that point, This represents a slow-time variable, used to describe the time offset in the slow-time dimension. For higher-order infinitesimal terms in Taylor expansion.

4. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 3, characterized in that, In step S3, the criterion for dividing short-time subframes is: Ensure that within the preset subframe duration, the residual distance error caused by the second-order Taylor expansion is less than the system distance resolution unit, and the residual Doppler frequency shift error is less than 1 / 3 of the system Doppler frequency resolution.

5. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 1, characterized in that, In step S4, the multidimensional parameter space manifold constraint strategy specifically includes: Utilizing the continuity of target motion over a short timescale, a linear evolution correlation model of Doppler parameters across subframes is established. The entire observation period is divided into n subframes, and the originally independent 2n motion parameters to be determined, namely the Doppler center frequency of each subframe, are... and Doppler rate of change The parameters are jointly estimated by projecting the multidimensional parameter space manifold constraint onto a constraint subspace of dimension n+2.

6. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 1 or 5, characterized in that, In step S5, a phase compensation operator is constructed using the stationary phase principle to eliminate linear and higher-order range migrations within the subframe, and spectral broadening caused by Doppler frequency variations is eliminated using a deslope Fourier transform; wherein, the expression for the deslope Fourier transform is: In the formula, This indicates that in the nth subframe, the distance is R and the Doppler frequency is... The signal after slope removal processing This indicates that in the nth subframe, the distance is R and the slow time is... The original echo signal, This represents the exponential function, used to construct the kernel function for Fourier transform and phase compensation. The imaginary unit, For Doppler frequency, For slow time, The rate of change of Doppler frequency within the nth subframe.

7. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 6, characterized in that, In step S5, after intra-frame coherent accumulation, the signal expression of the nth subframe in the range-Doppler domain is: In the formula, For the target echo signal amplitude, This is a rectangular window function used to represent the effective duration or frequency range of a signal in the Doppler domain. and These are the estimated Doppler center frequency and Doppler frequency slope of the target within the nth subframe, respectively. The duration of the subframe. This is a range pulse compression function used to describe the main lobe and side lobe characteristics of a signal in the range domain. The initial slant distance of the target. For radar signal wavelength, and These are the estimated Doppler center frequency and the estimated Doppler frequency change rate of the target within the entire frame, respectively. This is the range-phase offset term of the target within the nth subframe.

8. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 7, characterized in that, In step S6, the incoherent accumulation of the target energy across frames specifically includes: Based on the accumulated results of the intermediate reference subframes, the energy peak positions of each subframe in the range-Doppler domain are compensated for motion trajectory and then summed to obtain the final detection statistics. The expression is: In the formula, This represents summing over all subframes n and taking the modulus of the signal, indicating a noncoherent accumulation operation across frames, used to improve the signal-to-noise ratio of the target energy. This represents the signal amplitude in the range-Doppler domain of the nth subframe.

9. The high-orbit bistatic radar air target detection method based on multidimensional manifold constraints according to claim 7, characterized in that, In step S6, the echo is shifted by utilizing the mathematical mapping relationship between the distance migration of the target echo and the Doppler parameters to achieve inter-frame echo accumulation.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it can implement the steps of the high-orbit bistatic radar air target detection method based on multidimensional manifold constraints as described in any one of claims 1-9.

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