Multi-object separation method and device based on copeland decomposition and adaptive boosting

Abstract

The application provides a multi-target separation method and device based on Copeland decomposition and adaptive promotion, obtains radar point cloud observation data, and establishes a corresponding nonlinear dynamic relationship expression; the observation data is mapped to a promotion space to obtain first data and make the nonlinear dynamic relationship expression satisfy an approximate linear evolution relationship function in the promotion space; a promotion space matrix is constructed according to the first data, and second data is obtained through compression matrix calculation; a first data matrix and a second data matrix are constructed according to the second data, and Copeland operators are calculated; feature decomposition is performed according to the Copeland operators to obtain a candidate mode set, the optimal mode number is adaptively determined, and an effective mode set is obtained; the first data is projected to the effective mode set to obtain a multi-target separation point set. The nonlinear dynamic process is converted into a spectral decomposition problem under the action of a linear operator, and multi-target separation without explicit clustering or data association is realized in combination with adaptive selection.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and in particular to a multi-target separation method and apparatus based on Kopman decomposition and adaptive enhancement. Background Technology

[0002] With the rapid development of the low-altitude economy, drones, manned aircraft, and various low-altitude operation platforms are widely used in urban inspection, agricultural monitoring, logistics transportation, and passenger travel. As an important sensing means for low-altitude platforms, radar systems play an irreplaceable role in target detection and separation in complex environments due to their advantages such as all-weather operation and strong anti-interference capabilities.

[0003] Compared to traditional ground-based or high-altitude radars, radar systems designed for low-altitude platforms are used in a wider variety of scenarios. These include urban environments with roads and buildings, agricultural settings with farmland and vegetation, and open airspace and complex dynamic environments in manned flight scenarios. In these different scenarios, radar observation targets may encompass various entities such as vehicles, pedestrians, agricultural machinery, vegetation, surface structures, and aerial targets. Their scattering characteristics and motion patterns differ significantly and often overlap or intersect in the observation space.

[0004] Furthermore, low-altitude platforms typically possess strong maneuverability, exhibiting characteristics such as attitude changes, velocity variations, and trajectory nonlinearity during flight. This causes the radar observation geometry to dynamically change over time, resulting in significant nonlinear coupling between the target's range, angle, and Doppler parameters. In agricultural scenarios, wind-induced vegetation swaying and rough ground scattering introduce complex dynamic clutter. In urban environments, buildings and ground structures generate significant multipath reflections. In manned flight or open airspace scenarios, target motion is even more diverse, potentially including acceleration, turning, and even higher-order maneuvers. These factors combined result in radar echoes exhibiting strong nonlinearity, multi-target aliasing, and spatiotemporal nonstationarity.

[0005] Existing multi-target separation methods largely rely on spatial distribution or statistical characteristics for modeling. For example, density-based clustering methods divide point clouds based on spatial proximity, but are prone to misclassification or omission when target distributions are sparse or heavily overlapping. Probabilistic model-based methods typically require pre-setting the number or distribution of targets, making them difficult to adapt to dynamically changing scenarios. On the other hand, data association methods based on target tracking rely on explicit matching processes and usually assume linear or weakly nonlinear target motion, making it difficult to maintain stable performance under complex maneuvering conditions on low-altitude platforms.

[0006] Furthermore, traditional signal processing methods based on subspace decomposition (such as MUSIC and ESPRIT) are usually built on linear or stationary signal models, making it difficult to effectively handle the nonlinear dynamics and multipath coupling effects commonly found in low-altitude platform radars. When multiple targets and multipath coexist, the characteristics of different targets in the frequency domain or subspace often overlap, thus limiting the separation accuracy.

[0007] Therefore, existing methods generally suffer from the following shortcomings: First, they mainly rely on spatial or statistical features and lack the ability to characterize the dynamic evolution of targets; second, their model expressive power is insufficient under nonlinear and coupled dynamic conditions; and third, the stability and generalization ability of the separation results are limited in the case of mixed scenarios and types of targets. Especially when multiple low-altitude application scenarios such as agriculture, urban areas, and manned flight coexist, traditional methods struggle to construct a unified and effective processing framework.

[0008] In recent years, Koopman operator theory has provided a new approach to the linearization analysis of nonlinear dynamical systems. By mapping the original state to a high-dimensional observation function space, complex nonlinear systems can be described by linear operators in this space. However, existing methods still suffer from problems in practical applications, such as the dependence of observation function selection on experience, difficulty in controlling model dimensionality, and difficulty in directly applying them to multi-objective separation.

[0009] Therefore, there is an urgent need for a multi-objective separation method and apparatus based on Kopman decomposition and adaptive boosting to improve the above problems. Summary of the Invention

[0010] The purpose of this invention is to provide a multi-objective separation method and apparatus based on Copman decomposition and adaptive boosting, which can achieve multi-objective separation without explicit clustering or data association.

[0011] In a first aspect, the present invention provides a multi-target separation method based on Koppman decomposition and adaptive lifting, comprising the steps of: acquiring radar point cloud observation data and establishing a corresponding nonlinear dynamic relational expression; mapping the observation data to a lifting space to obtain first data and an approximately linear evolutionary relational function that the nonlinear dynamic relational expression satisfies in the lifting space; constructing a lifting space matrix based on the first data and calculating second data through a compression matrix; constructing a first data matrix and a second data matrix based on the second data, and calculating a Koppman operator; performing eigenvalue decomposition based on the Koppman operator to obtain a candidate mode set, adaptively determining the optimal number of modes, and obtaining an effective mode set; and projecting the first data onto the effective mode set to obtain a multi-target separation point set.

[0012] Optionally, acquiring radar point cloud observation data and establishing corresponding nonlinear dynamic relationship expressions includes: acquiring radar point cloud observation data, constructing observation vectors based on the observation data, and establishing corresponding nonlinear dynamic relationship expressions based on the observation vectors; the observation vectors include range, Doppler velocity, angle, and amplitude.

[0013] Optionally, mapping the observation data to the lift space to obtain the first data and the approximate linear evolutionary relation function that the nonlinear dynamic relation expression satisfies in the lift space includes: mapping the observation vector constructed based on the observation data to the lift space through the observation function and the constructed candidate lift function dictionary to obtain the first data and the approximate linear evolutionary relation function that the nonlinear dynamic relation expression satisfies in the lift space; the lift function dictionary includes polynomial terms, trigonometric function terms, coupling terms, and amplitude terms.

[0014] Optionally, constructing a first data matrix and a second data matrix based on the second data and calculating the Copman operator includes: constructing a first data matrix and a second data matrix based on the second data, and calculating the Copman operator through least squares estimation.

[0015] Optionally, obtaining a candidate mode set by performing eigenvalue decomposition based on the Kopman operator, and adaptively determining the optimal number of modes to obtain an effective mode set includes: obtaining a candidate mode set by performing eigenvalue decomposition based on the Kopman operator, and adaptively determining the optimal number of modes based on the reconstruction error and information criteria to obtain an effective mode set.

[0016] Optionally, projecting the first data onto the set of effective modes to obtain a set of multi-target separation points includes: calculating the projection coefficients of the observation points in the first data onto each effective mode, selecting the mode with the largest absolute value of the projection coefficient as the basis for target attribution, performing point-level target division, and obtaining a set of multi-target separation points.

[0017] Secondly, the present invention provides a multi-objective separation device based on Kopman decomposition and adaptive boosting, the device comprising modules / units for executing any of the possible design methods described in the first aspect above. These modules / units can be implemented in hardware or by hardware executing corresponding software.

[0018] Thirdly, the present invention provides an electronic device including a memory and a processor, wherein the memory stores a program executable on the processor, and when the program is executed by the processor, the electronic device implements a method for performing any of the possible designs described above.

[0019] Fourthly, the present invention provides a readable storage medium storing a program, which, when executed, implements a method of any possible design of any of the above aspects.

[0020] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0021] The beneficial effects of the method of this invention are as follows: It acquires radar point cloud observation data and establishes a corresponding nonlinear dynamic relational expression; it maps the observation data to a lift space to obtain first data and an approximately linear evolutionary relational function that satisfies the nonlinear dynamic relational expression in the lift space; it constructs a lift space matrix based on the first data and calculates second data through a compression matrix; it constructs a first data matrix and a second data matrix based on the second data and calculates the Kopman operator; it performs eigenvalue decomposition based on the Kopman operator to obtain a candidate mode set, adaptively determines the optimal number of modes, and obtains an effective mode set; it projects the first data onto the effective mode set to obtain a multi-target separation point set. This transforms the nonlinear multi-target dynamic process in radar observation into a spectral decomposition problem under the action of a linear operator, and, combined with the adaptive selection of the lift space structure, achieves multi-target separation without explicit clustering or data association. Attached Figure Description

[0022] Figure 1 A flowchart illustrating a multi-objective separation method based on Kopman decomposition and adaptive boosting provided in an embodiment of the present invention;

[0023] Figure 2 A schematic diagram of a multi-objective separation device based on Copman decomposition and adaptive lifting provided in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by those skilled in the art. The terms "comprising" and similar expressions used herein mean that the element or object preceding the word covers the element or object listed following the word and its equivalents, but do not exclude other elements or objects.

[0026] The technical solutions of the embodiments of the present invention will be described below with reference to the accompanying drawings. In the description of the embodiments of the present invention, the terminology used in the following embodiments is for the purpose of describing specific embodiments only and is not intended to limit the present invention. The singular expressions “a,” “the,” “the,” and “this” are intended to include expressions such as “one or more,” unless the context clearly indicates otherwise. It should also be understood that in the following embodiments of the present invention, “at least one” and “one or more” refer to one or more (including two). The term “and / or” is used to describe the relationship expression of related objects, indicating that three relationship expressions can exist; for example, A and / or B can represent: A alone, A and B simultaneously, and B alone, where A and B can be singular or plural. The character “ / ” generally indicates that the preceding and following related objects are in an “or” relationship expression.

[0027] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in connection with that embodiment is included in one or more embodiments of the invention. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," and "in still other embodiments" appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including, but not limited to," unless otherwise specifically emphasized. The term "connection" includes both direct and indirect connections, unless otherwise stated. "First" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated.

[0028] In embodiments of the present invention, "exemplarily" or "for example" are used to indicate that they are examples, illustrations, or descriptions. Any embodiment or design described as "exemplarily" or "for example" in embodiments of the present invention should not be construed as being more preferred or advantageous than other embodiments or design solutions. Rather, the use of "exemplarily" or "for example" is intended to present the relevant concepts in a specific manner.

[0029] like Figure 1 As shown, this invention provides a multi-objective separation method based on Kopman decomposition and adaptive boosting, comprising the following steps:

[0030] S101: Acquire radar point cloud observation data and establish corresponding nonlinear dynamic relationship expressions.

[0031] In some embodiments, acquiring radar point cloud observation data and establishing corresponding nonlinear dynamic relationship expressions includes: acquiring radar point cloud observation data, constructing observation vectors based on the observation data, and establishing corresponding nonlinear dynamic relationship expressions based on the observation vectors; the observation vectors include range, Doppler velocity, angle, and amplitude.

[0032] S102, the observed data is mapped to the lift space to obtain the first data and an approximate linear evolutionary relationship function that the nonlinear dynamic relationship expression satisfies in the lift space.

[0033] In some embodiments, mapping the observation data to a lift space to obtain first data and an approximate linear evolutionary relation function that satisfies the nonlinear dynamic relation expression in the lift space includes: mapping the observation vector constructed based on the observation data to the lift space through the observation function and a constructed candidate lift function dictionary to obtain the first data and an approximate linear evolutionary relation function that satisfies the nonlinear dynamic relation expression in the lift space; the lift function dictionary includes polynomial terms, trigonometric function terms, coupling terms, and amplitude terms.

[0034] S103, construct a lifting space matrix based on the first data, and calculate the second data through a compression matrix.

[0035] S104, construct a first data matrix and a second data matrix based on the second data, and calculate the Kopman operator.

[0036] In some embodiments, constructing a first data matrix and a second data matrix based on the second data and calculating the Copman operator includes: constructing a first data matrix and a second data matrix based on the second data, and calculating the Copman operator by least squares estimation.

[0037] S105, perform eigenvalue decomposition based on the Kopman operator to obtain a candidate mode set, adaptively determine the optimal number of modes, and obtain an effective mode set.

[0038] In some embodiments, obtaining a candidate mode set by performing eigenvalue decomposition based on the Kopman operator, and adaptively determining the optimal number of modes to obtain an effective mode set includes: obtaining a candidate mode set by performing eigenvalue decomposition based on the Kopman operator, and adaptively determining the optimal number of modes based on reconstruction error and information criteria to obtain an effective mode set.

[0039] S106, Project the first data onto the effective mode set to obtain a multi-target separation point set.

[0040] In some embodiments, projecting the first data onto the set of effective modes to obtain a set of multi-target separation points includes: calculating the projection coefficients of the observation points in the first data onto each effective mode, selecting the mode with the largest absolute value of the projection coefficient as the basis for target attribution, performing point-level target division, and obtaining a set of multi-target separation points.

[0041] The advantage of this invention is that it transforms the nonlinear multi-target dynamic process in radar observation into a spectral decomposition problem under the action of linear operators, and combines it with the adaptive selection of improved spatial structure to achieve multi-target separation without explicit clustering or data association.

[0042] To facilitate understanding, this embodiment further elaborates on the specific implementation process of the above method in conjunction with a specific application scenario. Taking point cloud observation data acquired by a low-altitude platform radar as an example, the specific steps include:

[0043] (1) Radar observation data modeling

[0044] Assume the low-altitude platform radar is at the... The point cloud observation data obtained in the frame are as follows:

[0045]

[0046] Construct an observation vector based on the observation data:

[0047]

[0048] These represent distance, Doppler velocity, angle, and amplitude information, respectively. Due to factors such as maneuvering flight, changes in observation geometry, and multipath reflections on low-altitude platforms, a corresponding nonlinear dynamic relationship expression is established based on the observation vectors:

[0049]

[0050] Furthermore, different targets correspond to different dynamic modes, resulting in the overall observation exhibiting nonlinear superposition characteristics of multi-target mixture.

[0051] (2) Koopman Lifting Space Structure

[0052] To characterize the above nonlinear dynamic process, the observation function is defined as follows:

[0053]

[0054] And map each observation point to obtain the first data:

[0055]

[0056] To ensure that nonlinear systems can be described by linear operators in the lift space, a dictionary of candidate lifting functions is constructed:

[0057]

[0058] These include:

[0059] Polynomial terms: , used to characterize higher-order motion properties;

[0060] Trigonometric function terms: , used to describe angle changes and observational geometric relationships;

[0061] Coupling terms: It is used to characterize the nonlinear coupling relationship between distance, velocity, and angle;

[0062] Amplitude Item: , used to distinguish different scattering characteristics.

[0063] By combining the above functions, the original nonlinear dynamic relation expression satisfies an approximately linear evolution relation function in the lift space, that is, it satisfies:

[0064]

[0065] Nonlinear dynamics are transformed into an approximately linear evolutionary relationship in the lift space.

[0066] (3) Frame-level lifting representation construction and compression matrix design

[0067] Construct the first data according to the first data Frame lift space matrix:

[0068]

[0069] in, For the first Frame count. Since the number of frames varies between different frames, a compression matrix is ​​introduced to obtain a temporal representation with uniform dimensions:

[0070]

[0071] Second data obtained:

[0072]

[0073] Wherein, the compression matrix Constructed using random projection, its elements satisfy:

[0074]

[0075] Alternatively, the compressed matrix may be generated using an equivalent zero-mean, unit-variance normalized distribution.

[0076] This random projection maps the high-dimensional representation of the original point cloud in the boosted space to a low-dimensional subspace, satisfying the Johnson–Lindenstrauss lemma, which preserves the Euclidean distance relationship between any two points with high probability.

[0077]

[0078] This ensures that the geometric structure of the point cloud in the lift space is maintained after compression.

[0079] Furthermore, since the compression operation is a linear transformation, and the Kopman model is based on the effect of linear operators on the lifting space representation, random projection does not change the linear superposition relationship between the dynamic modes, that is, it still satisfies:

[0080]

[0081] Therefore, the compressed representation maintains the point cloud structure without destroying the original Copman dynamics structure, thus ensuring the effectiveness of subsequent spectral decomposition and multi-object separation.

[0082] (4) Kopman linear dynamics modeling

[0083] Construct a first data matrix based on the second data. Second data matrix :

[0084]

[0085]

[0086] The overall observation in the lift space can be represented as a superposition of multiple dynamic modes:

[0087]

[0088] The Koopman operator is obtained through least squares estimation:

[0089]

[0090] (5) Copman spectral mode screening and decomposition

[0091] In obtaining the Kopman operator:

[0092]

[0093] Then, perform feature decomposition on it:

[0094]

[0095] Obtain the candidate mode set .

[0096] Modal validity assessment based on reconstruction error

[0097] To avoid the influence of noise or redundant modes on the separation results, an error assessment is performed for each mode.

[0098] The overall representation is written as a modal expansion:

[0099]

[0100] Before selection The modal construction approximation is as follows:

[0101]

[0102] Define reconstruction error:

[0103]

[0104] Modal quantity selection using information criteria

[0105] Introducing information criteria:

[0106]

[0107] in:

[0108] Number of modes

[0109] Total number of samples

[0110] By solving:

[0111]

[0112] The optimal number of modes is obtained.

[0113] By retaining the set of valid modes, we obtain the set of valid modes:

[0114]

[0115] After this step:

[0116] Noise modes were eliminated

[0117] Each mode corresponds to a stable dynamic component (usually an objective).

[0118] (6) Point-level modal projection and multi-object separation

[0119] For each observation point in the first dataset:

[0120]

[0121] The set of valid modes after screening Projecting onto the surface yields the projection coefficients:

[0122]

[0123] Projection structure

[0124] In the lift space, a point can be represented as:

[0125]

[0126] Since different targets correspond to different dynamic modes, the observation point is dominant in the direction of the corresponding mode, that is:

[0127]

[0128] Target attribution determination

[0129] definition:

[0130]

[0131] Output

[0132] The target partitioning is obtained, resulting in a set of multi-target separation points:

[0133]

[0134] in:

[0135] : No. The set of points corresponding to each target;

[0136] .

[0137] The key technical points of the embodiments of the present invention are as follows:

[0138] (1) Unified modeling mechanism for nonlinear dynamics based on Kopman lifting space

[0139] This invention maps the original radar observation data from the state space to a high-dimensional enhanced space by constructing an observation function, so that the nonlinear dynamic process caused by maneuvering flight, multipath propagation and target motion in low-altitude platform radar can be uniformly described by linear operators in this space.

[0140] Compared with traditional methods, existing Kalman filtering or multi-model methods usually rely on linear or weakly nonlinear assumptions, making it difficult to characterize high-order motion or complex maneuvers. This invention constructs a lifting function to make polynomial motion, angle changes, and spatial coupling relationships satisfy approximate closure in the lifting space, thereby transforming the nonlinear problem into a linear dynamics problem. Therefore, this invention still has stable modeling capabilities in complex nonlinear scenarios.

[0141] (2) Multi-objective implicit separation mechanism based on Kopman spectral modes

[0142] This invention utilizes the spectral decomposition of the Kopman operator to represent multi-target mixed observations as a linear superposition of multiple dynamic modes:

[0143]

[0144] Different targets correspond to different eigenvalues ​​and modal orientations, thus forming a natural separation structure in the spectral domain.

[0145] Compared with existing methods: spatial clustering-based methods rely on the distance or density between points, making it difficult to handle spatially overlapping targets; data association-based tracking methods rely on cross-frame matching processes, which are computationally complex and susceptible to occlusion; this invention directly decomposes the target at the dynamic level without explicit clustering or matching processes; therefore, stable separation can still be achieved even when targets are spatially overlapping or irregularly distributed.

[0146] (3) Modal adaptive screening mechanism based on reconstruction error and information criterion

[0147] This invention introduces reconstruction error based on Copman spectral decomposition:

[0148]

[0149] In conjunction with information guidelines:

[0150]

[0151] Achieve adaptive selection of the number of modes.

[0152] This mechanism enables:

[0153] Noise modes and redundant modes are automatically eliminated;

[0154] The number of effective modes should be consistent with the number of actual targets;

[0155] Compared to traditional methods that require a preset target number or rely on heuristic thresholds, and subspace methods that typically cannot stably distinguish between signal and noise subspaces, this invention achieves an adaptive balance between model complexity and fitting accuracy through information criteria, thereby improving system robustness.

[0156] (4) Point-level target attribution mechanism based on modal projection dominance

[0157] In this invention, the projection coefficients of the observation points in each modal direction are calculated within the filtered modal space.

[0158]

[0159] And utilize the dominant criterion:

[0160]

[0161] Achieve point-level target attribution.

[0162] The key to this method is:

[0163] Different objectives correspond to different modal orientations in the boost space;

[0164] The projection of a point of the same target onto the corresponding mode has significant advantages;

[0165] Compared with existing methods: it does not rely on spatial proximity, thus avoiding misclassification caused by uneven density; it does not rely on cross-frame data association, thus reducing computational complexity; and it can directly complete target segmentation within a single frame. Therefore, this invention can achieve stable separation under complex point cloud structures and target overlap conditions.

[0166] (5) Point cloud structure preservation compression mechanism based on random projection

[0167] This invention uses a random projection matrix to compress the lifting space representation:

[0168]

[0169] in, It is a random matrix.

[0170] This compression method has the following characteristics:

[0171] It satisfies the Johnson–Lindenstrauss property, preserving the distance relationship between points with high probability;

[0172] It is a linear transformation that does not change the linear superposition structure of the Kopman modes;

[0173] It can reduce computational complexity while maintaining the dynamic characteristics without distortion;

[0174] Compared to simple dimensionality reduction or aggregation methods, this invention ensures computational efficiency without destroying the point cloud structure and dynamic information.

[0175] (6) Information-based adaptive selection mechanism for lifting structure

[0176] This invention constructs a dictionary of candidate lifting functions and uses information criteria:

[0177]

[0178] Automatically select the optimal lifting structure.

[0179] This mechanism is able to:

[0180] Adaptive determination of model order;

[0181] Automatically select whether to introduce variable coupling terms;

[0182] Avoid biases caused by manually designing lifting functions;

[0183] Compared with existing Kopman methods, traditional methods rely on experience to select observation functions, resulting in limited generalization ability. This invention improves the model's adaptability and stability by using a data-driven approach to enhance structural optimization.

[0184] The advantages of this invention are that, by introducing Kopman lift space modeling, spectral mode decomposition, and adaptive lift selection mechanisms, the following beneficial effects are achieved in the multi-target separation problem of low-altitude platform radar:

[0185] (1) Achieve stability modeling and separation under nonlinear dynamic conditions

[0186] This invention constructs a Kopman lift space, transforming the nonlinear dynamic processes in low-altitude platform radar observations into an evolution problem under the action of linear operators. This allows target motion, which includes complex nonlinear factors such as acceleration, turning, and multipath coupling, to be effectively characterized within a unified framework. Compared to traditional methods based on linear or weakly nonlinear assumptions (such as Kalman filtering), this invention maintains stable modeling capabilities even under highly maneuvering targets and complex observation conditions, thereby improving the accuracy of multi-target separation.

[0187] (2) Achieve effective separation when the target spaces overlap.

[0188] This invention, based on Koppman spectral mode decomposition, represents multi-target mixed observations as a linear superposition of multiple dynamic modes. Different targets correspond to different eigenvalues ​​and mode directions in the spectral domain, thereby achieving separation based on dynamic characteristics. Compared to clustering methods that rely on spatial distance or density, this invention can still distinguish targets based on their dynamic characteristics even when their spatial locations are close or even overlapping, significantly reducing misclassification and omission.

[0189] (3) No explicit clustering or data association is required, reducing system complexity.

[0190] This invention achieves target attribution through point-level modal projection and dominant criteria, eliminating the need to construct explicit clustering structures or perform cross-frame data association. Compared to clustering-based methods that rely on parameter settings (such as distance thresholds) and tracking-based methods that require complex data association and trajectory maintenance, this invention can achieve multi-target separation under single-frame or limited-frame data conditions, reducing computational complexity and improving real-time performance.

[0191] (4) Automatically determine the number of targets to improve the system's adaptability. This invention combines reconstruction error with information criteria to achieve adaptive selection of the number of modes, so that the number of effective modes matches the actual number of targets. Compared with traditional methods that require pre-setting the number of targets or relying on heuristic judgment, this invention can automatically adjust the model complexity according to the data characteristics, thereby maintaining stable performance in different scenarios.

[0192] (5) Maintain the structural characteristics of point clouds while reducing computational complexity

[0193] This invention employs random projection compression to enhance spatial representation, reducing data dimensionality while preserving the geometric relationships and dynamic structural characteristics between point clouds. Since random projection satisfies the distance-preserving property and is a linear transformation, it does not disrupt the Kopman mode structure, thus significantly reducing computational complexity while maintaining separation accuracy and improving the algorithm's deployability in practical systems.

[0194] (6) Improve the model’s generalization ability and robustness

[0195] This invention achieves a balance between model fitting accuracy and complexity by adaptively selecting the enhancement structure, enabling the constructed model to fully characterize nonlinear dynamics while avoiding overfitting. Compared to the traditional Kopman method, which relies on human experience to select observation functions, this invention demonstrates good adaptability and stability in various low-altitude application scenarios (including urban environments, agricultural areas, and open airspace).

[0196] (7) Applicable to low-altitude platform radar applications in multiple scenarios

[0197] This invention does not rely on the spatial structure or target distribution characteristics of a specific scenario, and can uniformly process radar observation data in various low-altitude application environments such as urban areas, agriculture, and manned flight. Even in the presence of multipath interference, clutter, and complex background interference, it can still achieve effective separation based on dynamic characteristics, thereby improving the system's perception capability in complex environments.

[0198] like Figure 2 As shown, based on the above method, the present invention provides a multi-target separation device based on Kopman decomposition and adaptive lifting, comprising: an acquisition unit 201, used to acquire radar point cloud observation data and establish a corresponding nonlinear dynamic relation expression; a mapping unit 202, used to map the observation data to a lifting space to obtain first data and an approximate linear evolution relation function satisfied by the nonlinear dynamic relation expression in the lifting space; a construction unit 203, used to construct a lifting space matrix based on the first data and calculate second data through a compression matrix; a construction unit 204, used to construct a first data matrix and a second data matrix based on the second data and calculate a Kopman operator; a decomposition unit 205, used to perform eigenvalue decomposition based on the Kopman operator to obtain a candidate mode set, adaptively determine the optimal number of modes, and obtain an effective mode set; and an output unit 206, used to project the first data onto the effective mode set to obtain a multi-target separation point set.

[0199] It should be understood that all relevant content of each step involved in the above method embodiments can be referenced to the functional description of the corresponding functional module, and will not be repeated here. Furthermore, the use of suffixes such as "module," "component," or "unit" to represent elements is merely for the purpose of illustrative purposes and has no specific meaning in itself. Therefore, "module," "component," or "unit" can be used interchangeably. Terminals can be implemented in various forms. For example, the terminals described in this invention may include mobile terminals such as mobile phones, tablets, laptops, handheld computers, personal digital assistants (PDAs), portable media players (PMPs), navigation devices, wearable devices, smart bracelets, pedometers, etc., as well as fixed terminals such as digital TVs and desktop computers. The following description will use mobile terminals as examples; those skilled in the art will understand that, in addition to elements specifically designed for mobile purposes, the construction according to embodiments of the present invention can also be applied to fixed-type terminals.

[0200] In other embodiments of the present invention, an electronic device 300 is disclosed, such as... Figure 3As shown, the device may include: one or more processors 301; memory 302; display 303; one or more application programs (not shown); and one or more computer programs 304. These devices can be connected via one or more communication buses 305. The one or more computer programs 304 are stored in the memory 302 and configured to be executed by the one or more processors 301. The one or more computer programs 304 include instructions that can be used to perform actions such as... Figure 1 Each step in the corresponding embodiment.

[0201] Processor 301 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0202] The memory 302 can be an internal storage unit of the electronic device 300, such as a hard disk or RAM of the electronic device 300. The memory 302 can also be an external storage device of the electronic device 300, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or FlashCard equipped on the electronic device 300. Furthermore, the memory 302 can include both internal and external storage units of the electronic device 300. The memory 302 is used to store computer programs and other programs and data required by the electronic device. The memory 302 can also be used to temporarily store data that has been output or will be output.

[0203] The computer program 304 can be divided into one or more modules / units. The one or more modules / units can be a series of computer program instruction segments that can perform a specific function. The instruction segments are used to describe the execution process of the computer program 304 in the electronic device 300.

[0204] In addition to the above-described structure, those skilled in the art will understand that Figure 3This is merely an example of electronic device 300 and does not constitute a limitation on electronic device 300. Electronic device 300 may include more or fewer components than shown, or combine certain components, or different components. For example, electronic device may also include input / output devices, network access devices, buses, etc.

[0205] Those skilled in the art will understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the functions described above can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0206] Based on the above embodiments, the present invention also discloses a computer-readable storage medium having at least one computer program stored thereon, wherein the computer program, when executed by a processor, implements the methods described in the foregoing embodiments.

[0207] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing a processor. The program can be stored in a computer-readable storage medium, which is a non-transitory medium, such as random access memory, read-only memory, flash memory, hard disk, solid-state drive, magnetic tape, floppy disk, optical disk, and any combination thereof. The storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. This available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., digital video disc (DVD)), or a semiconductor medium (e.g., solid-state drive (SSD)).

[0208] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0209] Although the embodiments of the present invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and variations can be made to these embodiments. The above descriptions are merely embodiments of the present invention and do not limit the patent scope of the present invention. However, it should be understood that such modifications and variations fall within the scope and spirit of the present invention. Moreover, the present invention described herein may have other embodiments and can be implemented or realized in various ways. All equivalent transformations made based on the description and drawings of the present invention, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A multi-objective separation method based on Kopman decomposition and adaptive boosting, characterized in that, Including the following steps: Acquire radar point cloud observation data and establish corresponding nonlinear dynamic relationship expressions; The observed data is mapped to the lift space to obtain the first data and an approximate linear evolution relationship function that the nonlinear dynamic relationship expression satisfies in the lift space; A lifting space matrix is ​​constructed based on the first data, and the second data is obtained by calculating the compression matrix. Based on the second data, construct a first data matrix and a second data matrix, and calculate the Kopman operator; The candidate mode set is obtained by performing eigenvalue decomposition based on the Kopman operator, and the optimal number of modes is adaptively determined to obtain the effective mode set. The first data is projected onto the effective mode set to obtain a multi-target separation point set.

2. The method according to claim 1, characterized in that, Acquiring radar point cloud observation data and establishing corresponding nonlinear dynamic relationship expressions includes: Acquire radar point cloud observation data, and construct observation vectors based on the observation data; A corresponding nonlinear dynamic relationship expression is established based on the observed vector; The observation vector includes distance, Doppler velocity, angle, and amplitude.

3. The method according to claim 2, characterized in that, Mapping the observed data to the lift space to obtain the first data and the approximate linear evolutionary relationship function that the nonlinear dynamic relationship expression satisfies in the lift space includes: The observation vector constructed based on the observation data is mapped to the lift space by the observation function and the constructed candidate lift function dictionary, so as to obtain the first data and the approximate linear evolution relationship function that the nonlinear dynamic relationship expression satisfies in the lift space; The lifting function dictionary includes polynomial terms, trigonometric function terms, coupling terms, and amplitude terms.

4. The method according to claim 1, characterized in that, Based on the second data, a first data matrix and a second data matrix are constructed, and the Kopman operator is calculated, including: Based on the second data, construct a first data matrix and a second data matrix, and calculate the Kopman operator using least squares estimation.

5. The method according to claim 1, characterized in that, Based on the Kopman operator, an eigenvalue decomposition is performed to obtain a candidate mode set. The optimal number of modes is adaptively determined, resulting in an effective mode set including: The candidate mode set is obtained by performing eigenvalue decomposition based on the Kopman operator, and the optimal number of modes is adaptively determined based on the reconstruction error and information criteria to obtain the effective mode set.

6. The method according to any one of claims 1-5, characterized in that, Projecting the first data onto the effective mode set yields a multi-target separation point set, including: By calculating the projection coefficients of the observation points in the first data onto each effective mode, the mode with the largest absolute value of the projection coefficient is selected as the basis for target attribution, and point-level target division is performed to obtain a multi-target separation point set.

7. A multi-objective separation device based on Copman decomposition and adaptive lifting, used in the method of any one of claims 1-6, characterized in that, include: The acquisition unit is used to acquire radar point cloud observation data and establish corresponding nonlinear dynamic relationship expressions; A mapping unit is used to map the observed data to the lift space to obtain the first data and make the nonlinear dynamic relationship expression satisfy an approximate linear evolution relationship function in the lift space; A construction unit is used to construct a lifting space matrix based on the first data and calculate the second data through a compression matrix. A construction unit is used to construct a first data matrix and a second data matrix based on the second data, and to calculate the Kopman operator. The decomposition unit is used to perform feature decomposition based on the Kopman operator to obtain a candidate mode set, adaptively determine the optimal number of modes, and obtain an effective mode set. The output unit is used to project the first data onto the set of effective modes to obtain a set of multi-target separation points.

8. An electronic device, characterized in that, The device includes a memory and a processor, wherein the memory stores a program that can run on the processor, and when the program is executed by the processor, causes the electronic device to perform the method of any one of claims 1-6.

9. A readable storage medium storing a program, characterized in that, When the program is executed, it implements the method of any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-6.

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