Fast direct positioning method and device based on deep structured tensor completion

Abstract

This application discloses a fast direct localization method and apparatus based on deep structured tensor completion. The method includes: discretizing the target state space of the target to be localized to construct a high-dimensional discrete grid framework corresponding to a high-order target localization likelihood tensor; sparsely sampling the high-dimensional discrete grid framework to obtain a sparse observation tensor; structurally decomposing the sparse observation tensor through a pre-set deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental interference; and determining the target state estimate of the target to be localized based on the maximum index of the factor vector of the main peak structure. This application eliminates the need for exhaustive full-grid search, significantly reduces computational complexity and the total amount of likelihood value calculations while maintaining the physical structure characteristics and localization accuracy of the deep structured tensor completion network, thereby improving localization robustness and generalization ability.

Description

Technical Field

[0001] This application relates to the field of radio positioning technology, and in particular to a fast direct positioning method and apparatus based on deep structured tensor completion. Background Technology

[0002] Direct Position Determination (DPD) technology is widely used in engineering fields such as electronic reconnaissance, emergency rescue, collaborative sensing of unmanned systems, and low-altitude monitoring. Unlike traditional two-step positioning techniques, DPD does not rely on the estimation of intermediate parameters such as time difference of arrival and angle difference of arrival. Instead, it directly constructs a likelihood function in the candidate state space and obtains the target state estimate by maximizing this likelihood function. Therefore, in low signal-to-noise ratio or complex propagation environments, DPD typically has higher positioning accuracy and stronger robustness.

[0003] However, existing DPD methods have significant technical bottlenecks, making it difficult to balance positioning accuracy, computational efficiency, and structural interpretability. Specific problems include:

[0004] First, the computational complexity remains high, making it difficult to meet real-time requirements. The core computational process of the DPD method relies on evaluating the likelihood value of each candidate point on a discretized high-dimensional state grid. As the state dimension increases (e.g., simultaneously estimating two-dimensional position and two-dimensional velocity), the number of candidate grids grows exponentially, leading to a sharp increase in computational burden. At the same time, the likelihood value calculation at each grid point usually involves complex numerical operations such as eigenvalue decomposition and generalized likelihood ratio testing, further increasing the cost of a single computation. This makes the traditional DPD method difficult to apply to real-time positioning systems and computationally limited scenarios under high-dimensional state space or high-resolution grid conditions.

[0005] Secondly, existing acceleration methods have significant drawbacks, failing to balance efficiency and accuracy. To reduce computational complexity, existing technologies have proposed several improvement schemes: one type employs coarse-to-fine search or hierarchical search strategies to reduce computation by narrowing down the candidate region; however, this type of method is prone to error propagation when the initial estimate is inaccurate, affecting positioning accuracy. Another type introduces deep neural networks to achieve end-to-end prediction, which can improve inference speed, but lacks modeling of the physical structure of the DPD, limiting its generalization ability and stability in complex environments. Some methods also utilize low-rank matrices or tensor decomposition to model the likelihood landscape; however, existing low-rank modeling methods struggle to characterize the significant and locally concentrated main peak structure in the DPD likelihood function, resulting in limited structural representation capabilities in high-dimensional cases and an inability to accurately separate the target main peak from background interference, leading to a decrease in positioning accuracy.

[0006] Furthermore, existing technologies lack effective structured modeling methods, making it difficult to achieve efficient completion and localization while preserving the physical structural characteristics of the DPD. Traditional DPD methods require likelihood calculation for all grid points, while existing sparse sampling related methods lack standardized structured decomposition and completion logic. This makes it impossible to accurately recover the main peak and background structure of the complete likelihood tensor from a small number of observation points, either resulting in difficulty in reducing computational load or failing to guarantee the identifiability of the main peak structure, thus affecting the accuracy of target state estimation.

[0007] In summary, existing DPD acceleration methods still present a significant contradiction between efficiency and accuracy. This technical bottleneck severely restricts the promotion and application of DPD technology in real-time positioning systems and scenarios with limited computing resources. Summary of the Invention

[0008] Therefore, it is necessary to provide a fast and direct localization method and apparatus based on deep structured tensor completion to address the above-mentioned technical problems, thereby solving at least one of the problems existing in the prior art.

[0009] In a first aspect, embodiments of this application provide a fast and direct localization method based on deep structured tensor completion, including:

[0010] The target state space of the target to be located is discretized, and a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor is constructed.

[0011] Sparse sampling is performed on the high-dimensional discrete grid framework to obtain the sparse observation tensor;

[0012] The sparse observation tensor is decomposed into a structured form by a pre-defined deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental disturbances.

[0013] Based on the maximum index of the factor vector of the main peak structure, the target state estimate of the target to be located is determined.

[0014] In one possible implementation, the discretization of the target state space of the target to be located, and the construction of a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor, includes:

[0015] Based on the number of parameter dimensions corresponding to the target state, each dimension of the state parameter is uniformly or non-uniformly divided into several discrete grid points to form a high-dimensional discrete state grid covering the range of target candidate states.

[0016] In this context, the grid dimension of the high-dimensional discrete state grid corresponds one-to-one with the dimension of the high-order target localization likelihood tensor, the grid point combination corresponds one-to-one with the candidate target state, and each element of the high-order target localization likelihood tensor corresponds to the target localization likelihood value under a candidate target state.

[0017] In one possible implementation, the sparse sampling of the high-dimensional discrete grid framework to obtain the sparse observation tensor includes:

[0018] According to the preset sampling rules, grid points with a preset sampling ratio are selected from all grid points of the high-dimensional discrete grid framework as observation grid points;

[0019] Calculate the location likelihood value corresponding to the observed grid point, and mark the likelihood value of the non-observed grid point as missing or set to zero;

[0020] The sparse observation tensor is obtained by combining the likelihood values ​​of the observed grid points with the corresponding grid dimension index information.

[0021] In one possible implementation, the step of structurally decomposing the sparse observation tensor using a pre-defined deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental disturbances includes:

[0022] The pre-defined deep structured tensor completion network recovers the structured decomposition result from the sparse observation tensor. The structured decomposition result is a superposition of a rank-one peak tensor and a low-rank background tensor.

[0023] The rank-one peak tensor is used to characterize the main peak structure corresponding to the true state of the target, and each modal factor vector has a single-peak characteristic; the low-rank background tensor is used to characterize the background changes and interference structure.

[0024] In one possible implementation, recovering the structured decomposition result from the sparse observation tensor using the preset deep structured tensor completion network includes:

[0025] The sparse observation tensor and auxiliary sensor information are subjected to feature fusion and global attention aggregation to obtain a global feature representation;

[0026] The global feature representation is decoded in multiple branches, and the set of rank factors of the rank-one peak tensor and the set of low-rank factors of the low-rank background tensor are output respectively.

[0027] In one possible implementation, the step of performing feature fusion and global attention aggregation on the sparse observation tensor and auxiliary sensor information to obtain a global feature representation includes:

[0028] The sparse observation tensor is decomposed into grid dimension index, grid position index, and observation value, and then encoded to obtain dimension features, position features, and observation value features.

[0029] The dimensional features, location features, and observation features are aggregated to obtain the observation features;

[0030] The auxiliary sensor information is encoded to obtain sensor features;

[0031] The observed features and the sensor features are concatenated and fused, and then processed by global attention aggregation to obtain the global feature representation.

[0032] In one possible implementation, the deep structured tensor completion network includes an encoding module, a peak branch decoding module, and a background branch decoding module; the encoding module is used to fuse sparse observation tensors with auxiliary sensor information to output a global feature representation; the peak branch decoding module is used to generate factor vectors corresponding to the main peak structure based on the global feature representation; and the background branch decoding module is used to generate factor vectors corresponding to the background interference structure based on the global feature representation.

[0033] In one possible implementation, the training process of the deep structured tensor completion network includes:

[0034] Construct a total loss function consisting of a weighted sum of a reconstruction error term and a unimodal regularization term;

[0035] Based on the total loss function, the parameters of the deep structured tensor completion network are iteratively updated through backpropagation;

[0036] The reconstruction error term is used to measure the deviation between the reconstructed high-order target localization likelihood tensor and the true high-order target localization likelihood tensor.

[0037] The single-peak regularization term is used to constrain the modal factor vectors of the rank-one peak tensor so that they exhibit a monotonically increasing trend before the peak position corresponding to the true state of the target in the corresponding dimension and a monotonically decreasing trend after the peak position.

[0038] Secondly, a fast direct positioning device based on deep structured tensor completion is provided, comprising:

[0039] High-dimensional discrete grid building units are used to discretize the target state space of the target to be located and construct the high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor.

[0040] A sparse observation tensor generation unit is used to perform sparse sampling on the high-dimensional discrete grid framework to obtain a sparse observation tensor.

[0041] The sparse observation tensor decomposition unit is used to perform structured decomposition of the sparse observation tensor through a preset deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental interference.

[0042] The target state estimation unit is used to determine the target state estimation value of the target to be located based on the maximum value index of the factor vector of the main peak structure.

[0043] Thirdly, a computer-readable storage medium is provided, which stores computer-readable instructions that, when executed by a processor, implement the steps of the fast direct positioning method based on deep structured tensor completion as described above.

[0044] The aforementioned fast direct positioning method and apparatus based on deep structured tensor completion includes the following steps: discretizing the target state space of the target to be located to construct a high-dimensional discrete grid framework corresponding to a high-order target positioning likelihood tensor; sparsely sampling the high-dimensional discrete grid framework to obtain a sparse observation tensor; structurally decomposing the sparse observation tensor through a pre-defined deep structured tensor completion network to obtain a main peak structure representing the true state of the target and a background structure representing environmental interference; and determining the target state estimate of the target to be located based on the maximum index of the factor vector of the main peak structure. In this application embodiment, a fast direct positioning method based on deep structured tensor completion (STC-DPD) is proposed. This method addresses the problem of traditional DPD requiring exhaustive likelihood search on a high-dimensional state grid by constructing a structured likelihood tensor modeling framework and combining it with a deep neural network for sparse observation completion, thereby recovering the complete likelihood structure under the condition of calculating only a small number of grid point likelihood values, achieving efficient state estimation. This method significantly reduces the total amount of likelihood value calculation by discretizing the target state space to construct a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor and performing sparse sampling. This solves the pain points of high computational complexity and poor real-time performance of traditional DPD methods. At the same time, by constructing a deep structured tensor completion network containing an encoding module and dual decoding branches, it achieves accurate separation of the target's main peak structure from background interference. Combined with single-peak regularization constraints, it enhances the identifiability of the main peak, allowing the target state to be directly determined by the maximum index of the factor vector without exhaustive search of the entire grid. This effectively solves the problems of existing acceleration methods that are difficult to balance accuracy and efficiency, have limited generalization ability, and lack structural representation. Ultimately, while maintaining the physical structure characteristics and localization accuracy of DPD, it significantly reduces computational complexity and improves localization robustness and generalization ability, providing effective support for the promotion and application of DPD technology in various engineering fields with real-time requirements and limited computational resources. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart illustrating a fast and direct localization method based on deep structured tensor completion in one embodiment of this application;

[0047] Figure 2This is a schematic diagram of a network architecture of a deep structured tensor completion network in one embodiment of this application;

[0048] Figure 3 This is a schematic diagram of a fast direct positioning device based on deep structured tensor completion in one embodiment of this application;

[0049] Figure 4 This is a schematic diagram of a computer device according to one embodiment of this application. Detailed Implementation

[0050] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0051] In one embodiment, such as Figure 1 As shown, a fast direct localization method based on deep structured tensor completion is provided, including the following steps:

[0052] In step S110, the target state space of the target to be located is discretized to construct a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor.

[0053] It should be noted that the target state space refers to a high-dimensional parameter space describing all key state parameters of the target in the observation space, and its dimension is determined by the physical quantity of the target to be estimated. The target to be located refers to an object whose position and state need to be estimated by receiving signals, such as personnel, vehicles, communication terminals, and drones carrying signal transmitting devices. These can all be received by sensor arrays through radiated or reflected signals, and then the direct positioning method of this application can be used to achieve state estimation. For example, the target state space can be a four-dimensional state space, including the target's position coordinates in a two-dimensional plane and its velocity along the corresponding direction. That is, the complete state of the target is jointly determined by its lateral position, longitudinal position, lateral velocity, and longitudinal velocity, used to simultaneously achieve joint estimation of the target's position and motion state.

[0054] Optionally, based on the state parameter dimensions corresponding to the target to be located, the state variables of each dimension, such as position and velocity, are uniformly or non-uniformly divided within a preset value range to obtain discrete grid points of the corresponding dimensions. These grid points together constitute a high-dimensional discrete state grid covering the states of all candidate targets. This high-dimensional discrete state grid is used to characterize the dimensional structure, indexing system, and spatial distribution of the high-order target localization likelihood tensor. As a unified grid carrier for subsequent sparse sampling and likelihood value calculation, it is merely a structured framework of dimensions and indexes, eliminating the need to pre-traverse and calculate the likelihood values ​​of all grid points. This reduces redundant calculations from the source and provides a fundamental support for achieving rapid and direct localization.

[0055] The higher-order target localization likelihood tensor is a high-order tensor data structure used to represent the direct localization likelihood function values ​​of each candidate target state after the target state space is discretized in multiple dimensions. Its number of dimensions is consistent with the number of target state parameters. Each dimension in the tensor corresponds to a state parameter of the target (such as two-dimensional position or two-dimensional velocity). Each element index in the tensor corresponds to a set of grid coordinates for a candidate state, and the element value is the target localization likelihood value for that candidate state, representing the probability that the state is the true state of the target. This higher-order tensor can completely describe the likelihood distribution landscape within the target state space, and its unique peak position corresponds to the true state of the target.

[0056] It should be noted that this application organizes the discretized direct location DPD likelihood function into a higher-order tensor form, denoted as . ,in Each of these represents the number of grid cells in its respective dimension, and the elements of this tensor are defined as follows: ,in For the corresponding candidate target state The DPD likelihood function under the tensor uniquely represents the probability that the candidate state is the true target state, thus providing a structured data foundation for subsequent sparse sampling, tensor completion and target state estimation.

[0057] For example, taking low-altitude UAV positioning as an example, the lateral and longitudinal positions within the monitoring area, as well as the lateral and longitudinal velocities of the UAV, are divided into multiple grid points to form a four-dimensional high-dimensional discrete grid. It is not necessary to traverse all combinations of grid points in this high-dimensional grid; only a subset of grid points are selected as candidate target states in the subsequent sparse sampling stage, and the target positioning likelihood values ​​corresponding to these sampled grid points are calculated based on the signals received by the sensor array. This high-dimensional discrete grid serves as a structured framework for the high-order target positioning likelihood tensor, providing the dimensionality and indexing basis for subsequent sparse sampling, tensor completion, and target state estimation.

[0058] In step S120, sparse sampling is performed on the high-dimensional discrete grid framework to obtain the sparse observation tensor;

[0059] Optionally, to avoid the computational explosion caused by performing full calculations on all candidate points in a high-dimensional discrete grid, a pre-defined sparse sampling strategy can be adopted (such as random uniform sampling to ensure that observation points are evenly distributed in the state space and avoid sampling bias that may miss the target's true state region). From all grid points corresponding to the high-dimensional discrete grid framework, only a small number of grid points are selected as observation grid points. After determining the observation grid points, the localization likelihood value calculation process is only performed on these selected grid points. For non-observation grid points that are not selected, the likelihood value is not calculated, and their corresponding likelihood values ​​are directly marked as missing or pre-set to zero to simplify the data structure of the sparse observation tensor. Subsequently, the retained observation grid points and their corresponding effective localization likelihood values ​​are associated and combined, and the specific position index of each observation grid point in the original high-order tensor is recorded. Finally, a sparse observation tensor containing only a small amount of effective observation information and with the rest of the positions being missing or zero values ​​is formed. This sparse sampling process not only preserves the core features of the target localization likelihood landscape, but also significantly reduces the computational load of subsequent data processing, effectively alleviating the real-time bottleneck in high-dimensional state space in traditional direct localization technology.

[0060] In step S130, the sparse observation tensor is decomposed into a structured form by a preset deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental interference.

[0061] Optionally, a pre-defined deep structured tensor completion network is used to perform structured modeling of the sparse observation tensor based on Canonical Polyadic Decomposition (CPD). The network learns and separates a single-peak factor vector containing the target's main peak feature and a low-rank background factor vector containing environmental interference. The CPD structured decomposition model explicitly decouples the high-order DPD likelihood tensor into three parts: a single-peak structure representing the target's true state, a low-rank background structure representing environmental interference, and a noise term isolating random errors. This model fully utilizes the inherent "single-peak" physical characteristic of the DPD likelihood landscape to mathematically achieve accurate separation of the target signal from background interference such as multipath propagation and noise, providing clean and interpretable core features for subsequent state estimation.

[0062] The Deep Structured Tensor Completion Network (DTP) is a neural network model built on deep learning and tensor decomposition theory, used for feature fusion, structured completion, and component separation of sparse observation tensors. It uses the CPD structured decomposition model as its core constraint, guiding the network to learn and fit the single-peak main factor vector and the low-rank background factor vector. To avoid the computational bottleneck caused by exhaustive full-grid calculation, this application only calculates the DPD likelihood value for a small number of grid points, obtains the sparse observation tensor through sampling mask and Hadamard product, and then inputs it into the Deep Structured Tensor Completion Network to complete the completion and component separation. This scheme retains the rigor and interpretability of CPD decomposition physical modeling, while leveraging the feature extraction and fitting capabilities of deep learning to efficiently recover the complete likelihood structure and separate the main peak from the background under sparse observation conditions. This significantly reduces the computational complexity in high-dimensional state spaces, effectively suppresses peak shift problems, and improves positioning accuracy and robustness in complex environments.

[0063] Specifically, the obtained sparse observation tensor, combined with auxiliary sensor information (such as environmental noise intensity and signal propagation path information) collected by the sensor array, is input into a deep structured tensor completion network for encoding. Then, through global attention aggregation, the fused global feature representation is extracted, effectively capturing the correlation between observation points, target state, and environmental interference. Subsequently, the global feature representation is input to two parallel decoding branches: the peak branch decoding module outputs a rank-one peak tensor correlation factor vector representing the true target state, which has a unimodal characteristic and corresponds to the main peak structure of the target's true state in the likelihood landscape; the background branch decoding module outputs a low-rank background tensor correlation factor vector representing environmental interference and noise, corresponding to the background interference structure other than the main peak in the likelihood landscape. This achieves structured component separation of the sparse observation tensor, accurately separating the main peak structure and the background structure. The main peak structure directly corresponds to the true position and velocity state of the target to be located, while the background structure corresponds to interference factors such as environmental noise and signal reflection, providing clear and pure core feature support for subsequent target state estimation while avoiding the impact of background interference on positioning accuracy.

[0064] It should be noted that this structured decomposition model can be expressed as:

[0065] ;

[0066] in, Locate the likelihood tensor for higher-order objectives; Represents the cross product of vectors; It is a unimodal factor vector. The number of grid points in the nth state dimension is given by n=1, 2, 3, 4, which correspond to different dimensions of the four-dimensional state (such as horizontal position, vertical position, horizontal velocity, and vertical velocity). This is the factor vector of the nth mode and the rth background component of the low-rank background factor vector, corresponding to background structures such as environmental interference and noise; The rank of the low-rank background tensor is the number of components of the background structure. This represents the noise term. The model utilizes the physical property of the DPD likelihood landscape having a single main peak structure to separate the main peak from the background structure.

[0067] In step S140, the target state estimate of the target to be located is determined based on the maximum value index of the factor vector of the main peak structure.

[0068] Optionally, since the factor vectors corresponding to the main peak structure have a distinct unimodal distribution characteristic, meaning that the factor vector representing the true state of the target has only one unique maximum point in the corresponding state dimension, the value monotonically increases before reaching this maximum point and monotonically decreases after passing the maximum point, exhibiting a single prominent peak distribution. This maximum point directly corresponds to the true state position of the target to be located. By extracting the maximum points of the factor vectors in each state dimension such as position and velocity of the main peak structure, and combining the grid parameters corresponding to these extreme points, the state estimate of the target to be located can be directly obtained without traversing and searching the high-dimensional grid. This method utilizes the separated pure main peak structure to complete state localization, effectively eliminating the influence of environmental interference and background noise, significantly improving localization efficiency while ensuring the accuracy and stability of target state estimation.

[0069] For example, taking a low-altitude monitoring scenario, the target to be located is a low-altitude flying drone. In the factor vector of its lateral position dimension, the peak value is found at 100 meters; in the factor vector of its longitudinal position dimension, the peak value is found at 200 meters; in the factor vector of its lateral velocity dimension, the peak value is found at 10 meters per second; and in the factor vector of its longitudinal velocity dimension, the peak value is found at 5 meters per second. By combining the parameters corresponding to the extreme points of each of these dimensions, the estimated target state of the drone to be located can be obtained (lateral position 100 meters, longitudinal position 200 meters, lateral velocity 10 meters per second, longitudinal velocity 5 meters per second).

[0070] It should be noted that after obtaining the target state estimate, this estimate can be output to the upper-level monitoring or control system for functions such as target position display, trajectory tracking, flight path warning, and situational awareness. To further ensure the reliability of the positioning results, the target state estimate can be validated. For example, the position and velocity information obtained in this estimation can be compared with the historical positioning results from previous moments to determine whether the changes in the target's position and velocity conform to the laws of physical motion; or the peak intensity of the factor vector corresponding to the main peak structure can be compared with a preset threshold. The higher the peak intensity, the more reliable the positioning result. If the peak intensity is lower than the threshold, the positioning result is considered unreliable, and a new sparse sampling and tensor completion process can be triggered; or multiple sets of positioning results at different sampling rates can be combined for cross-validation to ensure that the final output target state is stable and consistent. Through the above verification and post-processing operations, the accuracy and robustness of the positioning results in complex environments can be effectively improved, meeting the requirements of practical engineering systems for positioning reliability.

[0071] This application provides a fast direct positioning method based on deep structured tensor completion, comprising: discretizing the target state space of the target to be located to construct a high-dimensional discrete grid framework corresponding to a high-order target positioning likelihood tensor; sparsely sampling the high-dimensional discrete grid framework to obtain a sparse observation tensor; structurally decomposing the sparse observation tensor through a preset deep structured tensor completion network to obtain a main peak structure representing the true state of the target and a background structure representing environmental interference; and determining the target state estimate of the target to be located based on the maximum index of the factor vector of the main peak structure. This application proposes a fast direct positioning method based on deep structured tensor completion (STC-DPD). This method addresses the problem of traditional DPD requiring exhaustive likelihood search on a high-dimensional state grid by constructing a structured likelihood tensor modeling framework and combining it with a deep neural network for sparse observation completion, thereby recovering the complete likelihood structure under the condition of calculating only a small number of grid point likelihood values, achieving efficient state estimation. This method significantly reduces the total amount of likelihood value calculation by discretizing the target state space to construct a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor and performing sparse sampling. This solves the pain points of high computational complexity and poor real-time performance of traditional DPD methods. At the same time, by constructing a deep structured tensor completion network containing an encoding module and dual decoding branches, it achieves accurate separation of the target's main peak structure from background interference. Combined with single-peak regularization constraints, it enhances the identifiability of the main peak, allowing the target state to be directly determined by the maximum index of the factor vector without exhaustive search of the entire grid. This effectively solves the problems of existing acceleration methods that are difficult to balance accuracy and efficiency, have limited generalization ability, and lack structural representation. Ultimately, while maintaining the physical structure characteristics and localization accuracy of DPD, it significantly reduces computational complexity and improves localization robustness and generalization ability, providing effective support for the promotion and application of DPD technology in various engineering fields with real-time requirements and limited computational resources.

[0072] In one embodiment of this application, the discretization of the target state space of the target to be located, and the construction of a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor, includes:

[0073] Based on the number of parameter dimensions corresponding to the target state, each dimension of the state parameter is uniformly or non-uniformly divided into several discrete grid points to form a high-dimensional discrete state grid covering the range of target candidate states.

[0074] In this context, the grid dimension of the high-dimensional discrete state grid corresponds one-to-one with the dimension of the high-order target localization likelihood tensor, the grid point combination corresponds one-to-one with the candidate target state, and each element of the high-order target localization likelihood tensor corresponds to the target localization likelihood value under a candidate target state.

[0075] Optionally, the number of parameter dimensions corresponding to the target state of the target to be located is determined. Based on actual positioning needs and engineering accuracy requirements, each state parameter dimension is divided into several discrete grid points in a uniform or non-uniform manner, thereby constructing a high-dimensional discrete state grid covering all possible states of the target. For example, taking a low-altitude flying UAV as the target to be located, its target state space is a four-dimensional space, including four dimensions: lateral position, longitudinal position, lateral velocity, and longitudinal velocity. According to the preset accuracy, the position and velocity ranges are divided into multiple discrete grid points, forming a high-dimensional grid covering all possible states of the target. Considering the accuracy requirements of low-altitude monitoring, the lateral and longitudinal positions are divided uniformly, with the lateral position divided into several grid points at 10-meter intervals, and the longitudinal position divided into several grid points at 10-meter intervals, covering the preset monitoring area. The lateral and longitudinal velocities are also divided uniformly, with several grid points at 5-meter-per-second intervals, covering the possible flight speed range of the UAV. Finally, a four-dimensional discrete state grid is constructed, which contains all possible combinations of the UAV's position and velocity. Each set of grid points in the grid can be used as a candidate target state. For example, a horizontal position of 100 meters, a vertical position of 200 meters, a horizontal velocity of 10 meters per second, and a vertical velocity of 5 meters per second constitute a candidate target state. The likelihood value of this state is only calculated when it is selected during the sparse sampling stage.

[0076] In one embodiment of this application, the step of sparsely sampling the high-dimensional discrete grid framework to obtain a sparse observation tensor includes:

[0077] According to the preset sampling rules, grid points with a preset sampling ratio are selected from all grid points of the high-dimensional discrete grid framework as observation grid points;

[0078] Calculate the location likelihood value corresponding to the observed grid point, and mark the likelihood value of the non-observed grid point as missing or set to zero;

[0079] The sparse observation tensor is obtained by combining the likelihood values ​​of the observed grid points with the corresponding grid dimension index information.

[0080] Optionally, considering the target localization accuracy requirements, computational resource constraints, and the fitting capability of the subsequent tensor completion network, reasonable sampling rules, sampling ratios, and sampling masks are preset. The sampling mask is a binary tensor with dimensions completely identical to the high-order target localization likelihood tensor, where elements are only 0 or 1, used to mark whether a grid point is selected as an observation grid point. The preset sampling rules can be random sampling, uniform sampling, or adaptive sampling (prioritizing sampling grid points in areas where the target may exist). The element distribution of the sampling mask will strictly follow these sampling rules. The preset sampling ratio can be flexibly adjusted according to the actual engineering scenario.

[0081] The sampling mask generated according to the preset sampling rules selects grid points with a preset sampling ratio as valid observation grid points from all discrete grid points corresponding to the high-order target localization likelihood tensor. Specifically, grid points with a value of 1 in the sampling mask are selected as valid observation grid points. Only for these selected observation grid points, the localization likelihood value is recalculated or the stored value is called up using the sensor received signal and the preset DPD likelihood calculation model. Grid points with a value of 0 in the sampling mask are treated as non-observation grid points. No likelihood value calculation is required. Their corresponding likelihood values ​​are directly marked as missing or set to zero to distinguish between valid observation data and missing data. The sampling mask will also record the position information of all observation grid points and non-observation grid points simultaneously.

[0082] Then, a Hadamard product operation is performed using the sampling mask and the high-order target localization likelihood tensor. Only the likelihood values ​​of the observed grid points are retained, while the remaining positions remain missing or zero. The localization likelihood values ​​of all observed grid points are then combined one-to-one with their corresponding grid dimension index information (i.e., the coordinate positions of the grid point in each dimension of the high-dimensional discrete state grid), and arranged in a regularized manner according to the dimensional order of the original high-order target localization likelihood tensor, forming a sparse observation tensor containing only a small amount of valid observation data, with the rest being missing or zero values. This sparse observation tensor retains the core features of the target's main peak structure while significantly reducing the computational cost of likelihood values, effectively avoiding the computational bottleneck caused by full-grid computation. The sampling mask, as a core auxiliary tool for sparse sampling, not only achieves accurate selection of observed grid points but also provides crucial positional identification support for subsequent deep structured tensor completion network localization of missing data locations, and for completing structured completion and decomposition, while simultaneously meeting the requirements of computational efficiency and localization accuracy.

[0083] The likelihood value of each grid point can be calculated using the following formula:

[0084] ;

[0085] in For sampling mask, This is the Hadamard product. The sampling ratio satisfies... = ,in, .

[0086] In one embodiment of this application, the step of performing structured decomposition of the sparse observation tensor using a preset deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental disturbance includes:

[0087] The pre-defined deep structured tensor completion network recovers the structured decomposition result from the sparse observation tensor. The structured decomposition result is a superposition of a rank-one peak tensor and a low-rank background tensor.

[0088] The rank-one peak tensor is used to characterize the main peak structure corresponding to the true state of the target, and each modal factor vector has a single-peak characteristic; the low-rank background tensor is used to characterize the background changes and interference structure.

[0089] Optionally, based on the directly located physical priors and tensor decomposition structure, a deep structured tensor completion network constrained by canonical multilinear decomposition (CPD) is constructed. The acquired sparse observation tensors and corresponding sampling masks are then input into this network. The network performs global feature learning and structured fitting on the sparse data, directly outputting the tensor decomposition result that satisfies the physical priors. This structured decomposition result is represented as a superposition of a rank-one peak tensor and a low-rank background tensor. The rank-one peak tensor accurately characterizes the main peak structure corresponding to the target's true state; the factor vectors corresponding to each mode all exhibit obvious single-peak characteristics, and the peak position directly corresponds to the optimal state estimate of the target. The low-rank background tensor characterizes non-target components such as environmental noise, multipath reflection, and clutter interference, effectively separating and suppressing irrelevant interference structures, thereby achieving reliable decoupling of the target signal from background interference while preserving physical interpretability.

[0090] like Figure 2 As shown, this deep structured tensor completion network includes an encoding module, a peak branch decoding module, and a background branch decoding module. The encoding module comprises an embedding layer, a feature concatenation layer, a multi-head attention layer, and fully connected layers, used to fuse sparse observation tensors with auxiliary sensor information and output a global feature representation. The peak branch decoding module is used to generate factor vectors corresponding to the main peak structure based on the global feature representation. The background branch decoding module is used to generate factor vectors corresponding to the background interference structure based on the global feature representation. Both the peak branch decoding module and the background branch decoding module consist of several fully connected layers.

[0091] In one embodiment of this application, the step of recovering the structured decomposition result from the sparse observation tensor using the preset deep structured tensor completion network includes:

[0092] The sparse observation tensor and auxiliary sensor information are subjected to feature fusion and global attention aggregation to obtain a global feature representation;

[0093] The global feature representation is decoded in multiple branches, and the set of rank factors of the rank-one peak tensor and the set of low-rank factors of the low-rank background tensor are output respectively.

[0094] Optionally, the sparse observation tensor and auxiliary sensor information are input together into a deep structured tensor completion network. The encoder performs multi-source information feature fusion and global attention aggregation to fully explore the correlation features between observation data, auxiliary information, target state, and environmental interference, and obtain a global feature representation. Then, the peak branch decoding module and the background branch decoding module perform parallel decoding processing on the global feature representation, and output the set of rank factors for reconstructing the rank-one peak tensor and the set of low-rank factors for reconstructing the low-rank background tensor, respectively, thereby achieving decoupled output of the target main peak structure and the background interference structure.

[0095] In one embodiment of this application, the step of performing feature fusion and global attention aggregation on the sparse observation tensor and auxiliary sensor information to obtain a global feature representation includes:

[0096] The sparse observation tensor is decomposed into grid dimension index, grid position index, and observation value, and then encoded to obtain dimension features, position features, and observation value features.

[0097] The dimensional features, location features, and observation features are aggregated to obtain the observation features;

[0098] The auxiliary sensor information is encoded to obtain sensor features;

[0099] The observed features and the sensor features are concatenated and fused, and then processed by global attention aggregation to obtain the global feature representation.

[0100] Optionally, the input sparse observation tensor is structurally decomposed into three core components: grid position index, grid dimension index, and corresponding observation values. Adaptive encoding methods are used for each of these three data components based on their different characteristics. Specifically, the grid position index and grid dimension index are transformed into learnable low-dimensional vector features through embedding encoding, resulting in position features and index features. The observation values ​​(i.e., the DPD likelihood values ​​of the observed grid points) are encoded through a fully connected layer, transforming numerical observation information into high-dimensional feature vectors, resulting in observation value features. Then, a combination of feature concatenation and element-level fusion is used to aggregate the encoded position features, index features, and observation value features, fully integrating the positional and numerical information of the sparse observation tensor to form observation features that comprehensively characterize the sparse observation data. Simultaneously, after standardizing and preprocessing the auxiliary sensor information (such as environmental noise intensity, signal propagation path loss, and sensor array attitude information), environmental interference features and signal correlation features are extracted from the auxiliary information through a combined encoding structure of normalization layers and fully connected layers, resulting in sensor features. Finally, the observed features and sensor features obtained above are dimensionally aligned and then concatenated to obtain the initial fused features that integrate multi-source information. Then, they are processed through a global attention aggregation mechanism, which can adaptively capture the correlation between observed features and sensor features, focus on strengthening the weight of features related to the main peak of the target, suppress the influence of irrelevant interference features, realize the deep fusion and information enhancement of multi-source features, and finally output a global feature representation that is both complete and targeted.

[0101] The deep structured tensor completion network can be represented by the following formula:

[0102] ;

[0103] ;

[0104] in, For encoder networks; For peak branching networks; It is a low-rank background branch network; and For network parameters; The four modal factor vectors of the rank-one peak tensor (corresponding to the four-dimensional state space, such as lateral position, longitudinal position, lateral velocity, and longitudinal velocity) each have a unimodal characteristic, and the position of its maximum value directly corresponds to the true state of the target in that dimension. For sparse observation tensors.

[0105] Specifically, such as Figure 2As shown, a model structure diagram of a deep structured tensor completion network is presented, which can be divided into two main stages: a feature extraction encoder and a CPD-based tensor generation decoder. First, sparse observation tensors (such as sparse observation indices) are input into the input layer. , corresponding observation values ), and corresponding auxiliary sensor information (such as sensor position) and signal-to-noise ratio , (Index the sensor number). The encoder first performs a structured decomposition on the sparse observation tensor to obtain three types of data: grid position index, grid dimension index, and observation value. Each of these is encoded using an independent MLP module for local feature encoding. The encoded position features, index features, and observation value features are then aggregated to obtain the observation features. Simultaneously, auxiliary sensor information is encoded using an MLP module to obtain sensor features. The observation features and sensor features are concatenated and fused, then mapped by the MLP module into three vectors: query Q, key K, and value V. A masked scaling dot product global attention mechanism is then used to perform feature aggregation and information enhancement, outputting global features. These global features are then input into a CPD-based tensor generator decoder, which decodes them using two parallel MLP modules. One module outputs a set of rank-one factors for each modality used to construct the rank-one peak tensor, while the other outputs a set of low-rank factors for constructing the low-rank background tensor. The two sets of factors are then multiplied to generate a rank-one tensor representing the main peak structure of the target's true state and a low-rank tensor representing environmental interference. Finally, these two are superimposed to obtain the reconstructed complete high-order target localization likelihood tensor, completing the completion and structured decomposition of the sparse observation tensor.

[0106] In one embodiment of this application, the training process of the deep structured tensor completion network includes:

[0107] Construct a total loss function consisting of a weighted sum of a reconstruction error term and a unimodal regularization term;

[0108] Based on the total loss function, the parameters of the deep structured tensor completion network are iteratively updated through backpropagation;

[0109] The reconstruction error term is used to measure the deviation between the reconstructed high-order target localization likelihood tensor and the true high-order target localization likelihood tensor.

[0110] The single-peak regularization term is used to constrain the modal factor vectors of the rank-one peak tensor so that they exhibit a monotonically increasing trend before the peak position corresponding to the true state of the target in the corresponding dimension and a monotonically decreasing trend after the peak position.

[0111] Optionally, a total loss function for network training is constructed, which consists of a reconstruction error term and a unimodal regularization term weighted and summed with preset weights. The training sample set is composed of a sparse observation tensor labeled with the true high-order target localization likelihood tensor, the peak position of the true target state, and the corresponding auxiliary sensor information. Then, in each iteration, based on the total loss function, the gradient descent optimization algorithm is used to iteratively update the full-link learnable parameters of the deep structured tensor to complete the network through backpropagation until the total loss function converges to a preset convergence threshold, thus completing the full-process training of the network. The reconstruction error term measures the numerical deviation between the reconstructed high-order target localization likelihood tensor output by the network and the labeled true high-order target localization likelihood tensor. By minimizing this reconstruction error term, the network can be constrained to accurately reconstruct the overall numerical distribution of the complete likelihood tensor under sparse observation conditions, ensuring the accuracy and reliability of tensor completion. The single-peak regularization term is a constraint term designed based on the physical characteristic that the DPD likelihood landscape naturally possesses a single main peak in the direct localization scenario. It is used to impose monotonic constraints on the modal factor vectors corresponding to the rank-one peak tensor output by the network, forcing each factor vector to exhibit a monotonically increasing trend before the true peak position in the corresponding dimension and a monotonically decreasing trend after the true peak position. This can effectively avoid multi-peak interference, false peak misjudgment, or peak shift problems during network training, ensuring that the reconstructed rank-one peak tensor can accurately correspond to the true position and motion state of the target, while significantly improving the training stability and generalization performance of the network in low signal-to-noise ratio and strong multipath interference scenarios.

[0112] The total loss function can be expressed as:

[0113] ;

[0114] The unimodal regularization term is defined as follows: , This is the index corresponding to the actual location in this dimension. It is the reconstructed high-order target localization likelihood tensor output by the network, that is, the complete DPD likelihood tensor after completion, which is obtained by superimposing the rank-one peak tensor output by the decoder and the low-rank background tensor. It is the true high-order target localization likelihood tensor (training supervision label), which is the standard DPD likelihood tensor obtained by full-grid computation, serving as a benchmark for reconstruction accuracy. It is the square of the Frobenius norm. The weighting coefficient of the unimodal regularization term is a preset hyperparameter used to balance the optimization weights of the reconstruction error term and the unimodal regularization term, thereby controlling the strength of the unimodal physical constraint. The factor vector corresponding to the nth mode of the rank-one peak tensor. The constraint term to the left of the peak value is an increasing term, and the constraint factor vector shows a monotonically increasing trend before the actual peak position. The constraint term to the right of the peak value is a decreasing constraint factor vector that shows a monotonically decreasing trend after the actual peak value.

[0115] The final location is estimated to be ,in, Each of these corresponds to one of the four dimensions of the four-dimensional state space. The length of the vector is equal to the total number of discrete grids in the corresponding dimension, and its peak position directly corresponds to the true state of the target in that dimension.

[0116] To verify the effectiveness and technical advantages of the direct localization method based on deep structured tensor completion proposed in this application, a multi-station passive localization simulation experiment was constructed for comparative verification. First, a multi-station passive localization system with multiple fixed sensor nodes was constructed. In the experiment, the state parameters of the target to be localized included four dimensions: two-dimensional planar position and two-dimensional motion velocity. Each state dimension was discretized, with each dimension uniformly divided into 21 discrete grid points, corresponding to a fourth-order DPD likelihood tensor with dimensions 21×21×21×21, for a total of 21 grid points. 4 The experiment uses a modulation signal model for signal simulation. By adjusting the signal sampling rate and signal-to-noise ratio parameters within a preset range, test scenarios with different channel environments are constructed. For each test scenario, the full-grid complete DPD likelihood tensor is calculated as a benchmark for positioning accuracy. At the same time, only 5% of the grid points are randomly sampled, and the DPD likelihood value corresponding to the sampled grid points is calculated as the input observation data for the method of this application and the comparison methods.

[0117] To fully verify the technical effectiveness of the method proposed in this application, this embodiment selects three mainstream localization and tensor completion methods as a comparison group: 1. Traditional full-mesh DPD method, as the upper bound benchmark for localization accuracy; 2. Neural network method based on low-rank tensor reconstruction; 3. Tensor completion method based on multidimensional convolutional networks. The following metrics are used for performance evaluation: 1. State error: defined as the Euclidean distance between the estimated state and the true state; 2. Reconstruction error: defined as the normalized Frobenius norm error between the recovered tensor and the true tensor; 3. Computation time ratio: defined as the ratio of the time required by the proposed method to the time required by the full-mesh DPD method.

[0118] The experimental results are shown in Table 1 below:

[0119] Table 1: Comparison of results for different methods on the test set, where Pos.Err and Vel.Err are the state errors, and Recon.Loss is the reconstruction error.

[0120]

[0121] As shown in Table 1 above, under a low sampling ratio of 5%, the target state estimation error of the proposed method is significantly better than that of existing depth tensor completion methods, and the positioning accuracy is close to the upper bound of the full-mesh DPD method. Specifically, in terms of positioning accuracy, the root mean square error of the position of the method used in this application is significantly lower than that of the low-rank tensor reconstruction neural network method and the multidimensional convolutional tensor completion method used in the comparison group. Under the premise that the overall tensor reconstruction error is similar to that of the comparison methods, the method used in this application can more accurately recover the main peak position of the DPD likelihood landscape, effectively avoiding the peak shift problem. In terms of computational efficiency, the single-scene computation time of the method used in this application is only about 5% of that of the traditional full-mesh DPD method, which greatly reduces the computational burden and resource consumption of direct positioning in high-dimensional state space, and solves the pain points of high computational complexity and difficulty in adapting to real-time scenarios of the traditional full-mesh DPD method.

[0122] The experimental results further validate the rationality and advancement of the technical solution presented in this application: Existing methods that only use the overall tensor reconstruction error as the optimization objective can fit the overall numerical shape of the likelihood landscape well, but they cannot explicitly model and precisely constrain the core peak structure corresponding to the target. They often fail to accurately locate the true position of the peak and are prone to problems such as false peak interference and peak shift, ultimately leading to a large target state estimation error. In contrast, this application uses a structured decomposition model based on canonical multilinear decomposition (CPD) to explicitly decouple and model the rank-one peak tensor representing the true state of the target and the low-rank background tensor representing environmental interference. At the same time, it introduces a single-peak regularization term to impose physical property constraints on the peak factor vector, effectively improving the recovery accuracy of the likelihood peak and significantly improving the accuracy of target state estimation and robustness in complex scenarios from the root.

[0123] Furthermore, to verify the functional necessity of each core design and the synergistic effect between modules in this application, this embodiment sets up targeted ablation experiments. All ablation experiments are carried out under the same 5% low sampling ratio test conditions as the aforementioned main experiment. By performing targeted removal processing on the core structure of this application, the actual function of each module is verified. The specific experimental settings and results are as follows:

[0124] Remove the unimodal regularization term: Remove the unimodal regularization constraint term in the loss function and use only the reconstruction error term as the network optimization objective. Experimental results show that the target state estimation error of this ablation group is significantly increased compared with the complete scheme of this application, and the accuracy of the main peak position recovery is greatly reduced. This fully verifies that the unimodal regularization constraint plays an indispensable core role in ensuring the accurate recovery of the likelihood peak structure and improving the positioning accuracy.

[0125] Removing the global attention mechanism: The global attention aggregation module in the encoder was removed, and only the basic feature fusion method was used to process multi-source input data. Experimental results show that the localization performance and tensor completion accuracy of this ablation group under sparse observation conditions are significantly degraded. This verifies that the global attention mechanism can effectively improve the global information aggregation and effective feature mining capabilities of sparse observation data, and is a key design to ensure the performance of the method under low sampling ratio.

[0126] The above ablation experiment results fully verify that each core module designed in this application is an essential component of the scheme. The modules cooperate and work together to ensure the high positioning accuracy, strong robustness and high computational efficiency of the method in this application under low sampling ratio.

[0127] In this embodiment, by sparsely sampling the high-order target localization likelihood tensor and calculating the likelihood values ​​of only a small number of grid points, a pre-defined deep structured tensor completion network is used to structurally complete and decompose the sparse observation tensor, thus recovering the complete likelihood structure. This eliminates the need to traverse and calculate all candidate target states, significantly reducing computational complexity in high-dimensional state spaces. It effectively addresses the core pain points of traditional techniques, such as high computational overhead and poor real-time performance. This allows the application to flexibly adapt to various engineering scenarios with high real-time requirements and limited computational resources, providing lightweight support for the engineering implementation of direct localization technology. Furthermore, this application explicitly models the peak structure of the target localization likelihood, directly corresponding the target state estimate to the peak position of the rank-one factor vector. This fully preserves the inherent physical structure characteristics of direct localization technology. Compared to existing completion methods that rely solely on overall reconstruction errors, this approach offers stronger interpretability, clearly tracing the physical logic of target state estimation and facilitating subsequent technical optimization and engineering debugging. In terms of positioning performance, this application achieves accurate separation of the target's main peak structure from the environmental background interference structure through a dual-branch decoding structure of a deep structured tensor completion network. Simultaneously, the introduction of single-peak regularization constraints effectively avoids the main peak shift problem caused by overall reconstruction errors in existing acceleration methods, significantly improving target positioning accuracy and enhancing positioning robustness in complex interference environments, thus adapting to positioning needs in different scenarios. Furthermore, the structured modeling approach adopted in this application has excellent scalability, easily extending to high-dimensional state spaces containing more parameters such as position, velocity, and clock deviation without significant modifications to the core architecture, adapting to the needs of multi-parameter joint positioning and broadening its applicability. In summary, this application, while fully retaining the advantages of physical modeling in direct positioning technology, effectively solves the computational bottleneck problem caused by high-dimensional grid search, balancing computational efficiency, positioning accuracy, and scalability, providing an efficient, reliable, and scalable solution for the practical application of direct positioning technology in complex environments and multiple scenarios.

[0128] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0129] In one embodiment, a fast direct positioning device based on deep structured tensor completion is provided, which corresponds one-to-one with the fast direct positioning method based on deep structured tensor completion in the above embodiments. For example... Figure 3 As shown, this fast direct localization device based on deep structured tensor completion includes modules A, B, C, and D. Detailed descriptions of each functional module are as follows:

[0130] The high-dimensional discrete grid construction unit 10 is used to discretize the target state space of the target to be located and construct the high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor.

[0131] The sparse observation tensor generation unit 20 is used to perform sparse sampling on the high-dimensional discrete grid framework to obtain the sparse observation tensor.

[0132] The sparse observation tensor decomposition unit 30 is used to perform structured decomposition of the sparse observation tensor through a preset deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental interference.

[0133] The target state estimation generation unit 40 is used to determine the target state estimation value of the target to be located based on the maximum value index of the factor vector of the main peak structure.

[0134] In one embodiment of this application, the high-dimensional discrete mesh building unit 10 is further used for:

[0135] The process of discretizing the target state space of the target to be located and constructing a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor includes:

[0136] Based on the number of parameter dimensions corresponding to the target state, each dimension of the state parameter is uniformly or non-uniformly divided into several discrete grid points to form a high-dimensional discrete state grid covering the range of target candidate states.

[0137] In this context, the grid dimension of the high-dimensional discrete state grid corresponds one-to-one with the dimension of the high-order target localization likelihood tensor, the grid point combination corresponds one-to-one with the candidate target state, and each element of the high-order target localization likelihood tensor corresponds to the target localization likelihood value under a candidate target state.

[0138] The sparse observation tensor generation unit 20 is also used for:

[0139] According to the preset sampling rules, grid points with a preset sampling ratio are selected from all grid points of the high-dimensional discrete grid framework as observation grid points;

[0140] Calculate the location likelihood value corresponding to the observed grid point, and mark the likelihood value of the non-observed grid point as missing or set to zero;

[0141] The sparse observation tensor is obtained by combining the likelihood values ​​of the observed grid points with the corresponding grid dimension index information.

[0142] In one embodiment of this application, the sparse observation tensor decomposition unit 30 is further configured to:

[0143] The pre-defined deep structured tensor completion network recovers the structured decomposition result from the sparse observation tensor. The structured decomposition result is a superposition of a rank-one peak tensor and a low-rank background tensor.

[0144] The rank-one peak tensor is used to characterize the main peak structure corresponding to the true state of the target, and each modal factor vector has a single-peak characteristic; the low-rank background tensor is used to characterize the background changes and interference structure.

[0145] In one embodiment of this application, the sparse observation tensor decomposition unit 30 is further configured to:

[0146] The sparse observation tensor and auxiliary sensor information are subjected to feature fusion and global attention aggregation to obtain a global feature representation;

[0147] The global feature representation is decoded in multiple branches, and the set of rank factors of the rank-one peak tensor and the set of low-rank factors of the low-rank background tensor are output respectively.

[0148] In one embodiment of this application, the sparse observation tensor decomposition unit 30 is further configured to:

[0149] The sparse observation tensor is decomposed into grid dimension index, grid position index, and observation value, and then encoded to obtain dimension features, position features, and observation value features.

[0150] The dimensional features, location features, and observation features are aggregated to obtain the observation features;

[0151] The auxiliary sensor information is encoded to obtain sensor features;

[0152] The observed features and the sensor features are concatenated and fused, and then processed by global attention aggregation to obtain the global feature representation.

[0153] In one embodiment of this application, the deep structured tensor completion network includes an encoding module, a peak branch decoding module, and a background branch decoding module; the encoding module is used to fuse sparse observation tensors and auxiliary sensor information to output a global feature representation; the peak branch decoding module is used to generate factor vectors corresponding to the main peak structure based on the global feature representation; the background branch decoding module is used to generate factor vectors corresponding to the background interference structure based on the global feature representation.

[0154] In one embodiment of this application, the device further includes a network training unit, used for:

[0155] Construct a total loss function consisting of a weighted sum of a reconstruction error term and a unimodal regularization term;

[0156] Based on the total loss function, the parameters of the deep structured tensor completion network are iteratively updated through backpropagation;

[0157] The reconstruction error term is used to measure the deviation between the reconstructed high-order target localization likelihood tensor and the true high-order target localization likelihood tensor.

[0158] The single-peak regularization term is used to constrain the modal factor vectors of the rank-one peak tensor so that they exhibit a monotonically increasing trend before the peak position corresponding to the true state of the target in the corresponding dimension and a monotonically decreasing trend after the peak position.

[0159] In this embodiment, by sparsely sampling the high-order target localization likelihood tensor and calculating the likelihood values ​​of only a small number of grid points, a pre-defined deep structured tensor completion network is used to structurally complete and decompose the sparse observation tensor, thus recovering the complete likelihood structure. This eliminates the need to traverse and calculate all candidate target states, significantly reducing computational complexity in high-dimensional state spaces. It effectively addresses the core pain points of traditional techniques, such as high computational overhead and poor real-time performance. This allows the application to flexibly adapt to various engineering scenarios with high real-time requirements and limited computational resources, providing lightweight support for the engineering implementation of direct localization technology. Furthermore, this application explicitly models the peak structure of the target localization likelihood, directly corresponding the target state estimate to the peak position of the rank-one factor vector. This fully preserves the inherent physical structure characteristics of direct localization technology. Compared to existing completion methods that rely solely on overall reconstruction errors, this approach offers stronger interpretability, clearly tracing the physical logic of target state estimation and facilitating subsequent technical optimization and engineering debugging. In terms of positioning performance, this application achieves accurate separation of the target's main peak structure from the environmental background interference structure through a dual-branch decoding structure of a deep structured tensor completion network. Simultaneously, the introduction of single-peak regularization constraints effectively avoids the main peak shift problem caused by overall reconstruction errors in existing acceleration methods, significantly improving target positioning accuracy and enhancing positioning robustness in complex interference environments, thus adapting to positioning needs in different scenarios. Furthermore, the structured modeling approach adopted in this application has excellent scalability, easily extending to high-dimensional state spaces containing more parameters such as position, velocity, and clock deviation without significant modifications to the core architecture, adapting to the needs of multi-parameter joint positioning and broadening its applicability. In summary, this application, while fully retaining the advantages of physical modeling in direct positioning technology, effectively solves the computational bottleneck problem caused by high-dimensional grid search, balancing computational efficiency, positioning accuracy, and scalability, providing an efficient, reliable, and scalable solution for the practical application of direct positioning technology in complex environments and multiple scenarios.

[0160] Specific limitations regarding the fast direct localization device based on deep structured tensor completion can be found in the limitations of the fast direct localization method based on deep structured tensor completion described above, and will not be repeated here. Each module in the aforementioned fast direct localization device based on deep structured tensor completion can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the operations corresponding to each module.

[0161] In one embodiment, a computer device is provided, which may be a terminal device, and its internal structure diagram may be as follows: Figure 4As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computational and control capabilities. The memory includes a readable storage medium storing computer-readable instructions. The network interface communicates with external terminals via a network connection. When executed by the processor, the computer-readable instructions implement a fast direct localization method based on deep structured tensor completion. The readable storage medium provided in this embodiment includes both non-volatile and volatile readable storage media.

[0162] In this application embodiment, a computer device is provided, including a memory, a processor, and computer-readable instructions stored in the memory and executable on the processor. When the processor executes the computer-readable instructions, it implements the steps of the fast direct positioning method based on deep structured tensor completion as described above.

[0163] In this embodiment of the application, a readable storage medium is provided, which stores computer-readable instructions. When the computer-readable instructions are executed by a processor, they implement the steps of the fast direct positioning method based on deep structured tensor completion described above.

[0164] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by instructing related hardware with computer-readable instructions. These computer-readable instructions can be stored in a non-volatile readable storage medium or a volatile readable storage medium. When executed, these computer-readable instructions can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0165] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions 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.

[0166] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A fast and direct localization method based on deep structured tensor completion, characterized in that, The method includes: The target state space of the target to be located is discretized, and a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor is constructed. Sparse sampling is performed on the high-dimensional discrete grid framework to obtain the sparse observation tensor; The sparse observation tensor is structurally decomposed using a pre-defined deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental interference. This includes: recovering the structured decomposition result from the sparse observation tensor using the pre-defined deep structured tensor completion network. The structured decomposition result is a superposition of a rank-one peak tensor and a low-rank background tensor. The rank-one peak tensor is used to characterize the main peak structure corresponding to the true state of the target, and each modality factor vector has a single-peak characteristic. The low-rank background tensor is used to characterize background changes and interference structures. Based on the maximum value index of the factor vector of the main peak structure, the target state estimate of the target to be located is determined; The training process of the deep structured tensor completion network includes: Construct a total loss function consisting of a weighted sum of a reconstruction error term and a unimodal regularization term; Based on the total loss function, the parameters of the deep structured tensor completion network are iteratively updated through backpropagation; The reconstruction error term is used to measure the deviation between the reconstructed high-order target localization likelihood tensor and the true high-order target localization likelihood tensor. The single-peak regularization term is used to constrain the modal factor vectors of the rank-one peak tensor so that they exhibit a monotonically increasing trend before the peak position corresponding to the true state of the target in the corresponding dimension and a monotonically decreasing trend after the peak position.

2. The fast direct localization method based on deep structured tensor completion as described in claim 1, characterized in that, The process of discretizing the target state space of the target to be located and constructing a high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor includes: Based on the number of parameter dimensions corresponding to the target state, each dimension of the state parameter is uniformly or non-uniformly divided into several discrete grid points to form a high-dimensional discrete state grid covering the range of target candidate states. In this context, the grid dimension of the high-dimensional discrete state grid corresponds one-to-one with the dimension of the high-order target localization likelihood tensor, the grid point combination corresponds one-to-one with the candidate target state, and each element of the high-order target localization likelihood tensor corresponds to the target localization likelihood value under a candidate target state.

3. The fast direct localization method based on deep structured tensor completion as described in claim 1, characterized in that, The step of sparsely sampling the high-dimensional discrete grid framework to obtain the sparse observation tensor includes: According to the preset sampling rules, grid points with a preset sampling ratio are selected from all grid points of the high-dimensional discrete grid framework as observation grid points; Calculate the location likelihood value corresponding to the observed grid point, and mark the likelihood value of the non-observed grid point as missing or set to zero; The sparse observation tensor is obtained by combining the likelihood values ​​of the observed grid points with the corresponding grid dimension index information.

4. The fast direct localization method based on deep structured tensor completion as described in claim 1, characterized in that, The step of recovering the structured decomposition result from the sparse observation tensor using the preset deep structured tensor completion network includes: The sparse observation tensor and auxiliary sensor information are subjected to feature fusion and global attention aggregation to obtain a global feature representation; The global feature representation is decoded in multiple branches, and the set of rank factors of the rank-one peak tensor and the set of low-rank factors of the low-rank background tensor are output respectively.

5. The fast direct localization method based on deep structured tensor completion as described in claim 4, characterized in that, The step of performing feature fusion and global attention aggregation on the sparse observation tensor and auxiliary sensor information to obtain a global feature representation includes: The sparse observation tensor is decomposed into grid dimension index, grid position index and observation value, and then encoded to obtain dimension feature, position feature and observation value feature. The dimensional features, location features, and observation features are aggregated to obtain the observation features; The auxiliary sensor information is encoded to obtain sensor features; The observed features and the sensor features are concatenated and fused, and then processed by global attention aggregation to obtain the global feature representation.

6. The fast direct localization method based on deep structured tensor completion as described in any one of claims 1 to 5, characterized in that, The deep structured tensor completion network includes an encoding module, a peak branch decoding module, and a background branch decoding module; the encoding module is used to fuse sparse observation tensors and auxiliary sensor information to output a global feature representation; The peak branch decoding module is used to generate factor vectors corresponding to the main peak structure based on the global feature representation; the background branch decoding module is used to generate factor vectors corresponding to the background interference structure based on the global feature representation.

7. A fast direct positioning device based on deep structured tensor completion, characterized in that, The device includes: High-dimensional discrete grid building units are used to discretize the target state space of the target to be located, and to construct the high-dimensional discrete grid framework corresponding to the high-order target localization likelihood tensor. A sparse observation tensor generation unit is used to perform sparse sampling on the high-dimensional discrete grid framework to obtain a sparse observation tensor. The sparse observation tensor decomposition unit is used to perform structured decomposition on the sparse observation tensor through a preset deep structured tensor completion network to obtain the main peak structure representing the true state of the target and the background structure representing environmental interference. This includes: recovering the structured decomposition result from the sparse observation tensor through the preset deep structured tensor completion network; the structured decomposition result is a superposition of a rank-one peak tensor and a low-rank background tensor; wherein the rank-one peak tensor is used to characterize the main peak structure corresponding to the true state of the target, and each modality factor vector has unimodal characteristics; the low-rank background tensor is used to characterize background changes and interference structures. The target state estimation value generation unit is used to determine the target state estimation value of the target to be located based on the maximum value index of the factor vector of the main peak structure. The device further includes a network training unit, used for: Construct a total loss function consisting of a weighted sum of a reconstruction error term and a unimodal regularization term; Based on the total loss function, the parameters of the deep structured tensor completion network are iteratively updated through backpropagation; The reconstruction error term is used to measure the deviation between the reconstructed high-order target localization likelihood tensor and the true high-order target localization likelihood tensor. The single-peak regularization term is used to constrain the modal factor vectors of the rank-one peak tensor so that they exhibit a monotonically increasing trend before the peak position corresponding to the true state of the target in the corresponding dimension and a monotonically decreasing trend after the peak position.

8. A computer-readable storage medium storing computer-readable instructions, characterized in that, When the computer-readable instructions are executed by the processor, they implement the steps of the fast direct localization method based on deep structured tensor completion as described in any one of claims 1 to 6.

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