A micro-positioning method applied to an arrow and a device thereof

Abstract

The application relates to the technical field of position positioning, and particularly discloses a micro positioning algorithm applied to an arrow and a device thereof. The algorithm comprises the following steps: collecting original observation distances of arrow nodes and constructing a three-element verification subnetwork; performing geometric rigidity analysis on the original ranging distances, screening a topological distortion subnetwork, identifying coherent reflection links through judgment logic, and establishing a pseudo-anchor point sequence; performing blocking pruning based on the pseudo-anchor point sequence, combining with relaxation optimization of a minimum tension spanning tree, constructing a quasi-static rigid topology, and taking the topology as a benchmark to solve lagging geometric coordinates and output positioning coordinates through time delay compensation. The device comprises a subnetwork verification module, a deformation quantization module, a distortion identification module, a network optimization module and a coordinate determination module. Through topology optimization and time delay compensation, the application is favorable for eliminating reflection interference and improving the positioning reliability of the arrow.

Description

Technical Field

[0001] This invention relates to the field of location positioning technology, and more specifically to a miniature positioning method and apparatus for arrows. Background Technology

[0002] In scenarios such as hunting competitions and outdoor training, arrows use miniaturized positioning devices to achieve real-time position tracking of high-speed flying arrows.

[0003] Arrows are small, only able to carry miniature radio modules and antennas, limiting their hardware physical specifications and inherently restricting their maximum communication radius and signal reception sensitivity. Furthermore, the high flight speed of arrows, influenced by aerodynamics, results in high relative motion rates between nodes. Traditional positioning algorithms do not incorporate this characteristic for link selection, easily misclassifying multipath noise with large delays in non-line-of-sight environments as valid links. In complex environments such as forests and mountains, radio signals are easily reflected by rocks, trees, and other objects, forming coherent reflection links. When these false links are mixed with valid links, it leads to topology distortion, further exacerbating the distortion of ranging data.

[0004] Therefore, the present invention provides a method and apparatus for miniature positioning of arrows. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for miniature positioning of arrows to solve the aforementioned background problems.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for miniature positioning of arrows includes the following steps:

[0008] The original ranging matrix is ​​obtained and geometric stiffness analysis is performed to obtain the geometric closure residual of the three-element verification subnet; the degree of subnet deformation is quantified based on the geometric closure residual to obtain the geometric tension index;

[0009] Topologically distorted subnets are screened based on the geometric tension index; ranging links of the topologically distorted subnets are extracted and cross-validated to identify coherent reflection links with coherent reflection characteristics, and a pseudo-anchor point sequence is established based on the coherent reflection links.

[0010] Based on the pseudo-anchor sequence, the topology network is subjected to blocking pruning to obtain the remaining topology structure. Then, the minimum tension spanning tree is relaxed and optimized to construct a quasi-static rigid topology that removes reflection interference and has converged geometric potential energy.

[0011] Using the quasi-static rigid topology as a spatial reference and performing coordinate calculations, the hysteresis geometric coordinates are obtained; the relative motion rate of the arrow is acquired, and the computational delay compensation is performed on the hysteresis geometric coordinates to output the positioning coordinates of the arrow node.

[0012] Furthermore, the original ranging matrix is ​​obtained as follows:

[0013] Collect the original observation distance of the arrow node and perform physical constraint verification to obtain the verified usable link;

[0014] Obtain all available verification links and perform full permutations and combinations according to the minimum geometric closed loop principle to construct a ternary verification subnet and the original ranging matrix.

[0015] Furthermore, the physical constraint verification is performed as follows:

[0016] Read the hardware physical parameters of the arrow node micro-antenna and the aerodynamic limits of arrow flight;

[0017] Based on hardware physical indicators, the original observation distance is spatially limit-checked, and a single-level verification link that meets the spatial limit is selected.

[0018] By combining aerodynamic limits, the rate limit of the primary verification link is verified, and the primary verification link with phase jump is eliminated to obtain the verifiable link.

[0019] Furthermore, the process of quantifying the degree of subnet deformation is as follows:

[0020] Obtain the geometric closure residuals of all ternary verification subnets and perform normalization mapping on the subnet deformation degree to obtain the geometric tension index of each group of ternary verification subnets.

[0021] Furthermore, the method for identifying the coherent reflection link is as follows:

[0022] Extract all verifiable links in the topologically distorted subnet and construct a set of risky links;

[0023] Cross-validation of multi-dimensional attributes is performed on the risk link set to identify coherent reflection links with coherent reflection characteristics, thus obtaining the coherent reflection links.

[0024] Furthermore, the method for performing cross-validation is as follows:

[0025] Perform entropy analysis on the distance drift within a time window on the risk link set to obtain the distance drift entropy;

[0026] Construct a physical consistency verification logic for ranging-path loss and calculate the power prediction residual;

[0027] By combining distance drift entropy and power prediction residual, a mutual exclusion logic for entropy value and residual is established to identify hidden coherent reflection links.

[0028] Furthermore, the mutual exclusion determination logic is established as follows:

[0029] Using distance drift entropy as the horizontal axis and power prediction residual as the vertical axis, a mutually exclusive decision space containing distance drift entropy and power prediction residual is established.

[0030] Map the verifiable links in the risk link set to the mutual exclusion decision space, and extract the links that fall into the low-entropy-high residual region within the mutual exclusion decision space as coherent reflection links.

[0031] Furthermore, the quasi-static rigid topology is constructed as follows:

[0032] The geometric tension index is defined as the potential energy weight of each edge in the topological network.

[0033] Obtain all nodes in the remaining topology, run a weighted graph theory spanning tree algorithm, and iteratively optimize the algorithm with the objective function of minimizing the cumulative potential energy weight of the path.

[0034] Based on iterative optimization, a set of links that can connect all arrow nodes and have the minimum sum of total geometric tension exponents is searched, which serves as the minimum tension spanning tree;

[0035] Force-guided relaxation optimization is performed on the minimum tension spanning tree to obtain the elastic stiffness coefficient;

[0036] The geometric potential energy equation of the system is constructed based on the elastic stiffness coefficient and the original observation distance. The minimum value of the geometric potential energy equation is solved under quasi-static conditions until the total stress deviation of the entire system no longer decreases and the energy balance state is reached.

[0037] Lock the node connections and spatial geometric constraints under energy equilibrium conditions, and output a quasi-static rigid topology.

[0038] Furthermore, the force-directed relaxation optimization is performed as follows:

[0039] Each arrow node in the minimum tension generating tree is treated as a virtual mass, and the ranging link between nodes is treated as a virtual spring.

[0040] The reciprocal of the geometric tension exponent of the link is used to set the elastic stiffness coefficient of the virtual spring.

[0041] A miniature positioning device for arrows includes the following modules:

[0042] Subnet verification module: used to collect the original observation distance of arrow nodes and perform physical constraint verification to obtain the verification available links; obtain all the verification available links and perform full permutation and combination according to the minimum geometric closed loop principle to construct the ternary verification subnet and the original ranging matrix;

[0043] Deformation Quantification Module: Used to perform geometric stiffness analysis on the original ranging matrix to obtain the geometric closure residual of the ternary verification subnet; based on the geometric closure residual, the deformation degree of the subnet is quantified to obtain the geometric tension index;

[0044] Distortion identification module: Screening of topologically distorted subnets based on geometric tension index; extraction of ranging links from the topologically distorted subnets and cross-validation; identification of coherent reflection links with coherent reflection characteristics; and establishment of pseudo-anchor point sequences based on coherent reflection links.

[0045] Network optimization module: Based on the pseudo-anchor sequence, the topology network is subjected to blocking pruning to obtain the remaining topology structure and relaxation optimization of the minimum tension spanning tree is performed to construct a quasi-static rigid topology that removes reflection interference and has converged geometric potential energy.

[0046] Coordinate determination module: used to take the quasi-static rigid topology as a spatial reference and perform coordinate calculation to obtain the hysteresis geometric coordinates; to obtain the relative motion rate of the arrow and perform calculation delay compensation on the hysteresis geometric coordinates, and output the positioning coordinates of the arrow node.

[0047] The beneficial effects of this invention are as follows:

[0048] 1. Broadcast handshakes and two-way ranging are initiated through the miniature radio modules built into the arrow nodes. Rate limit verification eliminates links with phase jumps, effectively improving the targeting of link selection. A ternary verification subnet is constructed according to the minimum geometric closed-loop principle, regularizing available links into basic units connected by three nodes, providing a structurally regular and highly reliable set of links for subsequent topology analysis. Geometric stiffness analysis of the ternary verification subnet yields geometric closure residuals, which help reflect the physical connectivity and adaptation status of the subnet topology. Furthermore, a geometric tension index is obtained through topology perimeter normalization mapping, transforming the degree of subnet deformation into a quantifiable indicator, making the structural stability of different ternary subnets comparable.

[0049] 2. Based on the geometric tension index, subnets with excessive topological distortion are screened, and corresponding high-risk links are extracted for multi-dimensional attribute cross-validation. Power prediction residuals are used to identify signal strength anomalies in reflection paths through the free space distance-power attenuation law; then, through the entropy-residual mutual exclusion decision space, coherent reflection links with low entropy and high residuals are identified and locked. The constructed pseudo-anchor sequence clearly marks false paths, improving the accuracy of link screening.

[0050] 3. Using the geometric tension index as the potential energy weight, a minimum tension spanning tree is constructed to select structurally stable skeleton links. Then, through force-directed relaxation optimization of a multi-mass system, a virtual spring model is used to simulate node constraints. This helps the topology approach energy equilibrium under the influence of the geometric potential energy equation, forming a geometrically stable quasi-static rigid topology and reducing the impact of reflection interference on the topology. Nodes with high connectivity and low geometric tension index are selected as origin anchors to establish a local Cartesian coordinate system. Based on the effective links in the quasi-static rigid topology, the lag geometric coordinates are calculated. The computational delay is obtained by converting the number of clock cycles of the statistical system operation. A compensation equation is constructed based on the relative motion rate to extrapolate and correct the lag geometric coordinates along the motion vector direction. This helps reduce the positional deviation caused by computation time, making the output positioning coordinates more closely match the actual flight trajectory of the arrow and improving the consistency between the coordinates and the true position. Attached Figure Description

[0051] The invention will now be further described with reference to the accompanying drawings.

[0052] Figure 1 This is a flowchart of a micro-positioning method for arrows according to the present invention;

[0053] Figure 2 This is a flowchart of the process for identifying topologically distorted subnets in this invention;

[0054] Figure 3 This is a flowchart illustrating the method for multi-dimensional attribute cross-validation in this invention;

[0055] Figure 4 This is a functional block diagram of a miniature positioning device for arrows in this invention. Detailed Implementation

[0056] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with specific embodiments.

[0057] Example 1:

[0058] like Figure 1 As shown, a miniature positioning method for arrows includes the following steps:

[0059] S10. Collect the original observation distance of the arrow node and perform physical constraint verification to obtain the verification available links; obtain all the verification available links and perform full permutation and combination according to the minimum geometric closed loop principle to construct the ternary verification subnet and the original ranging matrix.

[0060] The method for obtaining the verifiable usable link by collecting the original observation distance of the arrow node and performing physical constraint verification is as follows:

[0061] Preferably, the arrowhead in silent listening state is acquired and used as the arrow node; the arrow node triggers a short-cycle broadcast handshake through the built-in micro radio module, receives the response frames from other arrow nodes within the effective communication range, and defines all nodes that successfully send back response frames as candidate neighbor nodes to be verified.

[0062] Obtain all candidate neighbor nodes and construct a candidate neighbor set;

[0063] Based on each candidate neighbor node in the candidate neighbor set, the payload data in the response frame is parsed, and the instantaneous state information of the candidate neighbor node is extracted from the node's local cache based on the payload data.

[0064] It should be noted that the instantaneous state information includes: the unique device identifier (ID) of the neighboring node, the hardware timestamp when the acknowledgment frame arrived, and the received signal strength indication (RSSI) of the radio signal.

[0065] Based on the hardware timestamp in the instantaneous state information, the arrow node initiates a two-way ranging process at the current moment to obtain the original observation distance between the current node and each candidate neighbor node.

[0066] Read the hardware physical parameters of the arrow node's micro-antenna and the aerodynamic limits of the arrow's flight, perform physical constraint verification on the original observation distance, and screen the verifiable links between the arrow node and candidate neighbor nodes.

[0067] The method for performing physical constraint verification is as follows:

[0068] S101. Based on hardware physical indicators, perform spatial limit verification on the original observation distance and select a verification link that meets the spatial limit.

[0069] Preferably, the method for performing spatial limit verification is to read the maximum received sensitivity threshold from the hardware physical specifications of the arrow node micro-antenna;

[0070] Based on the sensitivity threshold, the maximum theoretical communication radius is calculated by back-calculating using existing free space path loss algorithms.

[0071] The original observation distance is compared with the theoretical communication radius. If the original observation distance is higher than or equal to the theoretical communication radius, the current ranging of the arrow node is determined to be multipath large delay noise under non-line-of-sight conditions.

[0072] If the original observation distance is lower than the theoretical communication radius, the communication link formed by the arrow node and the candidate neighbor node is used as a verification link.

[0073] S102. Combine aerodynamic limits to perform rate limit verification on the first-level verification link, eliminate the first-level verification link with phase jump, and obtain the verification usable link.

[0074] The preferred method for performing rate limit verification is as follows:

[0075] For a single-verification link, obtain the original observation distance of the corresponding candidate neighbor node in the previous time step, and combine it with the original observation distance at the current time step to calculate the distance change at the current time step relative to the original observation distance at the previous time step.

[0076] Obtain the time difference between the current moment and the previous moment, and calculate the equivalent relative motion rate of the first-level verification link by combining the distance change.

[0077] Set a monitoring period, acquire N relative motion velocities within the monitoring period, and perform phase jump judgment and screening against aerodynamic limits, and remove the verification link with phase jump;

[0078] Preferably, the method for determining and screening phase jumps is as follows: if there are two consecutive relative motion rates that are higher than or equal to twice the aerodynamic limit speed within the monitoring period, it is determined that there is a sudden phase jump in the original observation distance of the current link; otherwise, it is considered that the relative motion rate is within the expected range, and the first-level verification link is marked as a verification usable link.

[0079] The method for constructing a ternary verification subnet by acquiring all available verification links and performing full permutations and combinations according to the minimum geometric closed-loop principle is as follows:

[0080] Obtain all available verification links, perform full permutations and combinations according to the minimum geometric closed loop principle, and construct multiple ternary verification subnets consisting of three interconnected nodes;

[0081] The node ID sequences and their valid observation distances corresponding to the verification links in all three-element verification subnets are structurally encapsulated to generate the original ranging matrix.

[0082] Understandably, the purpose of constructing a ternary verification subnet is: firstly, to establish minimum rigid constraints. Unlike binary links, which cannot prove their authenticity due to instability, the ternary structure is the smallest unit in Euclidean space that can lock the geometric shape through the side length closure condition. The axiom of the triangle inequality can be used to quickly identify the path virtual growth caused by non-line-of-sight.

[0083] Objective 2: To balance computing power and coverage, compared to fully connected high-order subnets (such as quaternions or quintuples), ternary subnets have the lowest combinatorial complexity, which meets the real-time processing requirements of Micro Arrow under the constraints of battery capacity and chip computing power, that is, to obtain the most basic topology verification capability with the least computing power cost.

[0084] S20. Perform geometric stiffness analysis on the original ranging matrix to obtain the geometric closure residual of the ternary verification subnet; quantify the degree of subnet deformation based on the geometric closure residual to obtain the geometric tension index;

[0085] The method for performing geometric rigidity analysis on the original ranging matrix to obtain the geometric closure residual of the ternary verification subnet is as follows:

[0086] Preferably, all three-element verification subnets in the original ranging matrix are traversed, and three independent effective observation distances are extracted from each three-element verification subnet;

[0087] Identify the longest, middle, and shortest distances among three independent effective observation distances, and label them as the longest distance measurement side, the middle distance measurement side, and the shortest distance measurement side, respectively;

[0088] A rigid judgment rule based on the triangle inequality axiom is constructed. The longest measuring side, the middle measuring side, and the shortest measuring side are substituted into the rigid judgment rule. If the condition is met, no action is taken.

[0089] If the conditions are not met, Euclidean space closure calculations are performed to obtain the geometric closure residuals of the ternary verification subnet.

[0090] Preferably, the method for performing closure calculations in Euclidean space is to obtain the value of the longest measuring edge and the sum of the values ​​of the middle measuring edge and the shortest measuring edge.

[0091] Subtract the sum of the values ​​of the middle and shortest measuring sides from the value of the longest measuring side to obtain the difference result;

[0092] If the difference result is positive, it is defined as a geometrically closed residual, which indicates that the subnet has path virtual growth caused by non-line-of-sight reflections; if the difference result is negative, it is set to zero or the absolute value is taken to indicate geometric compression.

[0093] The method for obtaining the geometric tension index based on the deformation degree of the subnet quantized by the geometrically closed residual is as follows:

[0094] Obtain the geometric closure residuals of all ternary verification subnets and perform normalization mapping on the degree of subnet deformation to obtain the geometric tension index of each group of ternary verification subnets.

[0095] Preferably, the normalization mapping process is performed as follows: the sum of the longest ranging edge, the middle ranging edge, and the shortest ranging edge is calculated to obtain the topological perimeter of the ternary verification subnet; the topological perimeter is used to perform a division ratio operation on the geometric closure residual to obtain the normalized ratio result, which is used as the geometric tension index.

[0096] Example 2:

[0097] Please see Figure 1As shown, a miniature positioning method for arrows includes the following steps:

[0098] S30. Screening of topologically distorted subnets based on geometric tension index; extraction of ranging links from the topologically distorted subnets and cross-validation, identification of coherent reflection links with coherent reflection characteristics, and establishment of pseudo-anchor point sequences based on coherent reflection links;

[0099] The method for selecting topologically distorted subnets based on the geometric tension index is as follows:

[0100] Preferably, a deformation tolerance threshold corresponding to the geometric tension index is set, and the geometric tension index of all ternary verification subnets is obtained and compared with the deformation tolerance threshold:

[0101] like Figure 2 As shown, if the geometric tension index of the ternary verification subnet is higher than or equal to the preset deformation tolerance threshold, the ternary verification subnet is marked as a topologically distorted subnet.

[0102] Conversely, if the geometric tension index of the ternary verification subnet is lower than the preset deformation tolerance threshold, the change in the geometric tension index will be continuously monitored.

[0103] The method for extracting ranging links from the topology-distorted subnet and performing cross-validation is as follows:

[0104] Extract all verifiable links in the topologically distorted subnet and construct a set of risky links;

[0105] Cross-validation of multi-dimensional attributes is performed on the risk link set to identify coherent reflection links with coherent reflection characteristics, thus obtaining the coherent reflection links.

[0106] Preferred, such as Figure 3 As shown, the method for performing multi-dimensional attribute cross-validation is as follows:

[0107] S301. Perform entropy analysis of distance drift within the time window on the risk link set to obtain the distance drift entropy;

[0108] Preferably, the entropy analysis of distance drift within the time window is performed as follows: obtain N original ranging values ​​of the risk link within a preset sliding time window, set the distance quantization step size (e.g., 1cm), map the original ranging values ​​to multiple discrete distance intervals, count the frequency of the ranging values ​​falling in each distance interval, calculate the probability of occurrence of each distance interval, and obtain a ranging probability distribution histogram.

[0109] Based on the histogram of the ranging probability distribution, the Shannon entropy formula is used to perform cumulative calculations to obtain the original distance entropy value that characterizes the disorder of the ranging sequence.

[0110] Obtain the average signal-to-noise ratio of the link within the sliding time window, and construct the noise penalty coefficient using an inverse proportional function;

[0111] For example, the noise penalty coefficient can be constructed as follows: ;

[0112] in, The noise penalty coefficient is SNR, which is the average signal-to-noise ratio of the link.

[0113] It should be noted that the lower the SNR, the noisier the signal, and the more noise the original distance entropy value contains. Therefore, amplitude compression is required using a smaller coefficient. The higher the SNR, the cleaner the signal, and the original distance entropy value is preserved.

[0114] Multiply the original distance entropy value by the noise penalty coefficient to obtain the effective entropy value after channel quality correction.

[0115] Obtain the maximum allowable flight speed of the arrow within the sliding time window, obtain the maximum possible range of the theoretically possible distribution of the distance measurement values ​​through historical monitoring data, and calculate the theoretical maximum entropy value under this state if the distance measurement values ​​are uniformly distributed within the maximum range.

[0116] Divide the effective entropy value by the theoretical maximum entropy value to obtain the dimensionless normalized distance drift entropy.

[0117] It should be noted that normalized distance drift entropy is used to characterize the dynamic richness of link data. In a high-speed arrow network, the distance value of a real direct link will necessarily contain reasonable dynamic changes due to relative motion (corresponding to high distance drift entropy). However, strong reflection links formed by stationary objects (such as rocks) often exhibit unnatural numerical locking characteristics, i.e., information stagnation (corresponding to extremely low distance drift entropy).

[0118] S302. Construct the physical consistency verification logic for ranging-path loss and calculate the power prediction residual.

[0119] Preferably, the method for calculating the power prediction residual is as follows:

[0120] Based on the current ranging values ​​of available links in the risk link set, the theoretical received power that should theoretically be available at this distance is inferred by using the existing log-normal shadowing fading model.

[0121] The real-time received signal strength (RSSI) of the link is collected, and the absolute value of the difference between the real-time received signal strength and the theoretical received power value is calculated to obtain the power prediction residual.

[0122] It should be noted that the reflection path usually involves long-distance transmission that is not straight. However, due to the focusing effect of the reflecting surface, the signal strength is abnormally high or abnormally low due to medium absorption, which seriously violates the distance-power attenuation law in free space and produces power prediction residuals.

[0123] S303. Combine distance drift entropy and power prediction residual to establish a mutually exclusive judgment logic of entropy value and residual to identify hidden coherent reflection links.

[0124] Preferably, the method for establishing the mutual exclusion decision logic of entropy value-residual is as follows:

[0125] Using distance drift entropy as the horizontal axis and power prediction residual as the vertical axis, a mutually exclusive decision space containing distance drift entropy and power prediction residual is established.

[0126] Map the verifiable links in the risk link set to the mutual exclusion decision space, and extract the links that fall into the low-entropy-high residual region in the mutual exclusion decision space as coherent reflection links.

[0127] Extract the link IDs of all links marked as coherent reflection links and their associated node IDs;

[0128] The link ID and node ID are indexed and associated to construct a sequence of false path anchor points to be removed, which serves as the pseudo anchor point sequence.

[0129] It is understandable that the purpose of establishing the entropy-residual mutual exclusion judgment logic is:

[0130] Objective 1: Rocks or thick tree trunks in forests often reflect extremely stable signals (low entropy), which traditional algorithms are prone to misidentifying as target links. By introducing power prediction residuals (high residuals), errors with stable distances but abnormal energy decay can be identified from the physical dimension of energy conservation.

[0131] Objective 2: To construct an orthogonal anti-spoofing system: Entropy represents the temporal dimension, while residuals represent the spatial dimension. Utilizing these two uncorrelated orthogonal dimensions for joint detection helps reduce the false alarm rate caused by relying on a single indicator and identifies highly concealed coherent reflection links.

[0132] S40. Based on the pseudo-anchor sequence, perform blocking pruning of the topology network to obtain the remaining topology structure and perform relaxation optimization of the minimum tension spanning tree to construct a quasi-static rigid topology that removes reflection interference and has converged geometric potential energy.

[0133] The method for obtaining the remaining topology structure by performing blocking pruning of the topology network based on the pseudo-anchor sequence is as follows:

[0134] The preferred method for implementing blocking pruning in the topology network is:

[0135] Establish the original ranging matrix, initialize the fully connected mask matrix with the same dimensions as the original ranging matrix, and set the connectivity state of all links to valid by default (i.e., the connectivity state of the fully connected mask matrix is ​​1).

[0136] Traverse the pseudo-anchor sequence and extract the link index of each coherent reflection link;

[0137] In the fully connected mask matrix, the connected state corresponding to the coherent reflection link is forcibly flipped to block (0) to obtain a sparsed availability mask matrix;

[0138] Perform a Hadamard product operation on the original ranging matrix and the availability mask matrix, that is, multiply corresponding elements to filter out all reflection paths marked as deceptive, and obtain the remaining topology structure containing only physically trusted links.

[0139] It should be noted that non-linear logical blocking replaces physical deletion with soft blocking at the logical level, preserving the network's underlying addressing capabilities and preventing the network from splitting into unlocatable information islands due to excessive deletion.

[0140] The method for constructing a quasi-static rigid topology that removes reflection interference and has convergent geometric potential energy through relaxation optimization of the minimum tension spanning tree is as follows:

[0141] Preferably, the method for constructing the minimum tension spanning tree is to redefine the geometric tension index as the potential energy weight of each edge in the topological network formed by the remaining topological structure.

[0142] It should be noted that the lower the geometric tension index, the better the closure of the subnet where the link is located, that is, the higher the physical confidence of the edge (the lower the potential energy).

[0143] Based on all nodes in the remaining topology, run a weighted graph spanning tree algorithm, using the minimum cumulative potential energy weight of the path as the objective function for iterative optimization;

[0144] The preferred graph-based tree-spanning algorithm is Prim's algorithm.

[0145] Based on iterative optimization, a set of links that can connect all arrow nodes and have the minimum sum of total geometric tension exponents is searched, which serves as the minimum tension spanning tree;

[0146] It should be noted that the purpose of iterative optimization is to forcibly remove high-tension redundant connections in forest multipath environments, and retain only the geometrically stable skeleton links as positioning references.

[0147] Force-directed relaxation optimization of multi-mass systems is performed on the minimum tension spanning tree to achieve global convergence of geometric potential energy;

[0148] Preferably, the execution-oriented relaxation optimization method is as follows: each arrow node in the minimum tension generation tree is regarded as a virtual mass point, and the ranging link between nodes is regarded as a virtual spring;

[0149] The reciprocal of the geometric tension exponent of the link is used to set the elastic stiffness coefficient of the virtual spring.

[0150] It should be noted that the smaller the tension in a link (the more reliable it is), the larger its reciprocal, meaning the stiffer the virtual spring and the stronger the constraint on the node; the larger the tension in a link, the softer its virtual spring, allowing the node to be fine-tuned within a certain range.

[0151] Construct the geometric potential energy equation of the system, which characterizes the total stress deviation between all ranging observations and calculated coordinates in the entire network;

[0152] Preferably, the method for constructing the geometric potential energy equation of the system is as follows: define each arrow node to be solved. The coordinate variables in three-dimensional space are Traverse each ranging link in the minimum tension spanning tree. Obtain the original observation distance corresponding to this link. and the virtual spring elastic stiffness coefficient Based on coordinate variables and using the distance formula between two points, the theoretical Euclidean distance of the link is constructed.

[0153] in, For the corresponding other arrow node;

[0154] The deformation residual between the theoretical Euclidean distance and the original observed distance is calculated, and the deformation residual is squared to obtain the elastic potential energy term. The elastic potential energy terms of all links are multiplied by their corresponding virtual spring stiffness coefficients and then summed to construct the geometric potential energy equation of the system.

[0155] ;

[0156] in, The set of links for the minimum tension spanning tree;

[0157] For theoretical Euclidean distance; This is the sum of the geometric potential energy of the system, used to characterize the total stress deviation between coordinates;

[0158] It should be noted that the physical meaning of the geometric potential energy equation is: by finding an optimal set of coordinates... This minimizes the sum of the deformation energies of all connections in the entire network; introducing... Using the reciprocal of the geometric tension exponent as a weight, the algorithm prioritizes the link length with low geometric tension (i.e., the most reliable), while squeezing the measurement error into the soft link with high geometric tension (i.e., low reliability), thus achieving the global optimal allocation.

[0159] Under quasi-static conditions, the geometric potential energy equation is solved for a minimum value, which drives the virtual particles at each arrow node to make tiny positional migrations in the coordinate system until the total stress deviation of the entire system no longer decreases and energy equilibrium is reached.

[0160] Lock the node connections under energy equilibrium state with spatial geometric constraints, and output a quasi-static rigid topology;

[0161] It is understandable that the purpose of constructing a minimum tension spanning tree and performing force-directed relaxation optimization is:

[0162] Function 1: In forest environments, multipath effects cannot be completely eliminated but can only be suppressed. Through a virtual spring model, the system will automatically squeeze unavoidable measurement errors into soft links with low stiffness coefficients (i.e., high tension and low reliability), thereby protecting the geometric accuracy of the backbone hard links.

[0163] Function 2: Achieving adaptive convergence of nonlinear topologies: Arrow networks are highly dynamic systems. The force-directed model does not rely on complex matrix inversion but simulates the energy dissipation process in the physical world. It can drive the topology to spontaneously slide from a chaotic state to the quasi-static equilibrium point with the lowest geometric potential energy, thereby obtaining the probabilistically optimal topological solution under the current conditions.

[0164] S50. Using the quasi-static rigid topology as a spatial reference and performing coordinate calculations, the hysteresis geometric coordinates are obtained; the relative motion rate of the arrow is obtained, and the computational delay compensation is performed on the hysteresis geometric coordinates to output the positioning coordinates of the arrow node.

[0165] The method for obtaining instantaneous relative coordinates by using the quasi-static rigid topology as a spatial reference and performing coordinate calculations is as follows:

[0166] From the quasi-static rigid topology output by S40, the arrow node with the highest connectivity and the lowest geometric tension exponent is selected as the origin anchor point.

[0167] The node connected to the origin and having the second lowest geometric tension exponent is selected as the axial auxiliary point. The direction from the origin to the axial auxiliary point is defined as the positive X-axis. The XOY plane is established by combining the third non-collinear node, thus constructing a unique local Cartesian coordinate system.

[0168] Based on the effective ranging links retained in the quasi-static rigid topology, the spatial position of each arrow node in the local Cartesian coordinate system is analyzed using the least squares method to obtain the hysteresis geometric coordinates.

[0169] It should be noted that since it takes time for the system to collect data from S10 to complete the topology reconstruction from S40, this spatial location represents the lagging geometric coordinates (i.e., the past real location) at the moment when the system starts to operate.

[0170] The method for obtaining the relative motion rate of the arrow, performing computational delay compensation on the lag geometric coordinates, and outputting the positioning coordinates of the arrow node is as follows:

[0171] Preferably, the method for performing computational latency compensation is as follows:

[0172] The total number of clock cycles consumed by the microcontroller of the acquisition system to execute steps S10 to S40 is converted into physical time units to obtain the computational delay.

[0173] The equivalent relative motion rate of the first-level verification link calculated in step S10 is used to perform position deduction of the lag geometric coordinates along the motion vector direction in combination with the calculation delay, and the corrected coordinates are output as the positioning coordinates of the arrow node.

[0174] Example 3:

[0175] Please see Figure 4 As shown, a miniature positioning device for arrows includes the following modules:

[0176] Subnet verification module: used to collect the original observation distance of arrow nodes and perform physical constraint verification to obtain the verification available links; obtain all the verification available links and perform full permutation and combination according to the minimum geometric closed loop principle to construct the ternary verification subnet and the original ranging matrix;

[0177] Deformation Quantification Module: Used to perform geometric stiffness analysis on the original ranging matrix to obtain the geometric closure residual of the ternary verification subnet; based on the geometric closure residual, the deformation degree of the subnet is quantified to obtain the geometric tension index;

[0178] Distortion identification module: Screening of topologically distorted subnets based on geometric tension index; extracting ranging links from the topologically distorted subnets and performing cross-validation; identifying coherent reflection links with coherent reflection characteristics; and establishing a pseudo-anchor point sequence based on the coherent reflection links.

[0179] Network optimization module: Based on the pseudo-anchor sequence, the topology network is subjected to blocking pruning to obtain the remaining topology structure and relaxation optimization of the minimum tension spanning tree is performed to construct a quasi-static rigid topology that removes reflection interference and has converged geometric potential energy.

[0180] Coordinate determination module: used to use quasi-static rigid topology as spatial reference and perform coordinate calculation to obtain hysteresis geometric coordinates; obtain the relative motion rate of the arrow to perform calculation delay compensation on the hysteresis geometric coordinates, and output the positioning coordinates of the arrow node.

[0181] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A miniature positioning method for arrowheads, characterized in that, Includes the following steps: The original ranging matrix is ​​obtained and geometric stiffness analysis is performed to obtain the geometric closure residual of the three-element verification subnet; the degree of subnet deformation is quantified based on the geometric closure residual to obtain the geometric tension index; The method for obtaining the original ranging matrix is ​​as follows: Collect the original observation distance of the arrow node and perform physical constraint verification to obtain the verified usable link; Obtain all available verification links and perform full permutations and combinations according to the minimum geometric closed loop principle to construct a ternary verification subnet and the original ranging matrix; The method for performing the physical constraint verification is as follows: Read the hardware physical parameters of the arrow node micro-antenna and the aerodynamic limits of arrow flight; Based on hardware physical indicators, the original observation distance is spatially limit-checked, and a single-level verification link that meets the spatial limit is selected. By combining aerodynamic limits, the rate limit verification of the first-level verification link is performed, and the first-level verification link with phase jump is eliminated to obtain the verification usable link. Topologically distorted subnets are screened based on the geometric tension index; ranging links of the topologically distorted subnets are extracted and cross-validated to identify coherent reflection links with coherent reflection characteristics, and a pseudo-anchor point sequence is established based on the coherent reflection links. The method for cross-validation is as follows: Perform entropy analysis on the distance drift within a time window on the risk link set to obtain the distance drift entropy; Construct a physical consistency verification logic for ranging-path loss and calculate the power prediction residual; By combining distance drift entropy and power prediction residual, a mutual exclusion logic of entropy value and residual is established to identify hidden coherent reflection links. The method for establishing the mutual exclusion determination logic is as follows: Using distance drift entropy as the horizontal axis and power prediction residual as the vertical axis, a mutually exclusive decision space containing distance drift entropy and power prediction residual is established. Map the verifiable links in the risk link set to the mutual exclusion decision space, and extract the links that fall into the low-entropy-high residual region in the mutual exclusion decision space as coherent reflection links. Based on the pseudo-anchor sequence, the topology network is subjected to blocking pruning to obtain the remaining topology structure. Then, the minimum tension spanning tree is relaxed and optimized to construct a quasi-static rigid topology that removes reflection interference and has converged geometric potential energy. The method for constructing the quasi-static rigid topology is as follows: The geometric tension index is defined as the potential energy weight of each edge in the topological network. Obtain all nodes in the remaining topology, run a weighted graph theory spanning tree algorithm, and iteratively optimize the algorithm with the objective function of minimizing the cumulative potential energy weight of the path. Based on iterative optimization, a set of links that can connect all arrow nodes and have the minimum sum of total geometric tension exponents is searched, which serves as the minimum tension spanning tree; Force-guided relaxation optimization is performed on the minimum tension spanning tree to obtain the elastic stiffness coefficient; The geometric potential energy equation of the system is constructed based on the elastic stiffness coefficient and the original observation distance. The minimum value of the geometric potential energy equation is solved under quasi-static conditions until the total stress deviation of the entire system no longer decreases and the energy balance state is reached. Lock the node connectivity and spatial geometric constraints under energy equilibrium, and output a quasi-static rigid topology; The method for performing the force-directed relaxation optimization is as follows: Each arrow node in the minimum tension generating tree is treated as a virtual mass, and the ranging link between nodes is treated as a virtual spring. The reciprocal of the geometric tension exponent of the link is used to set the elastic stiffness coefficient of the virtual spring. Using the quasi-static rigid topology as a spatial reference and performing coordinate calculations, the lag geometric coordinates are obtained. The relative motion rate of the arrow is obtained, and the operation delay compensation is performed on the lag geometric coordinates. The position of the lag geometric coordinates along the motion vector direction is deduced, and the positioning coordinates of the arrow node are output.

2. The miniature positioning method for arrows according to claim 1, characterized in that: The process of quantifying the degree of subnet deformation is as follows: Obtain the geometric closure residuals of all ternary verification subnets and perform normalization mapping on the subnet deformation degree to obtain the geometric tension index of each group of ternary verification subnets.

3. The miniature positioning method for arrows according to claim 1, characterized in that: The method for identifying the coherent reflection link is as follows: Extract all verifiable links in the topologically distorted subnet and construct a set of risky links; Cross-validation of multi-dimensional attributes is performed on the risk link set to identify coherent reflection links with coherent reflection characteristics, thus obtaining the coherent reflection links.

4. A miniature positioning device for arrowheads, used to implement the miniature positioning method for arrowheads as described in any one of claims 1-3, characterized in that, Includes the following modules: Subnet verification module: used to collect the original observation distance of arrow nodes and perform physical constraint verification to obtain the verification available links; obtain all the verification available links and perform full permutation and combination according to the minimum geometric closed loop principle to construct the ternary verification subnet and the original ranging matrix; Deformation module: used to perform geometric rigidity analysis on the original ranging matrix to obtain the geometric closure residuals of the ternary verification subnet; The geometric tension index is obtained by quantifying the deformation degree of the subnet based on the geometric closed residual. Distortion identification module: Screening of topologically distorted subnets based on geometric tension index; Extract ranging links from the topologically distorted subnet and perform cross-validation to identify coherent reflection links with coherent reflection characteristics, and establish a pseudo-anchor sequence based on the coherent reflection links; Network optimization module: Based on the pseudo-anchor sequence, the topology network is subjected to blocking pruning to obtain the remaining topology structure and relaxation optimization of the minimum tension spanning tree is performed to construct a quasi-static rigid topology that removes reflection interference and has converged geometric potential energy. Coordinate determination module: Used to take the quasi-static rigid topology as a spatial reference and perform coordinate calculation to obtain the lag geometric coordinates; obtain the relative motion rate of the arrow to perform calculation delay compensation on the lag geometric coordinates, perform position deduction along the motion vector direction on the lag geometric coordinates, and output the positioning coordinates of the arrow node.

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