Single-beidou reliable positioning method and system in complex environment based on residual consistency

Abstract

The application discloses a single-Beidou complex environment reliable positioning method and system based on residual consistency, and relates to the technical field of Beidou satellite navigation and positioning. In the application, the anchor node of the coordinate obtained through single-Beidou system positioning broadcasts its own position information to the network, and the network node calculates the minimum hop number to each anchor node through multi-hop communication. Secondly, each anchor node calculates the average hop distance according to the actual geometric distance between the known anchor nodes and the corresponding hop number, and the unknown node estimates the distance to each anchor node according to the average hop distance. In the application, the absolute coordinates of the anchor nodes are obtained through single-Beidou system positioning, and the wireless node network cooperative positioning mechanism is combined to introduce the anchor node geometric consistency modeling and adaptive screening mechanism in the DV-Hop positioning framework, so that the constraint conflict caused by the network topology distortion is reduced, and the positioning stability and reliability in the complex environment are improved.

Description

Technical Field

[0001] This invention relates to the field of BeiDou satellite navigation and positioning technology, and in particular to a reliable positioning method and system for single BeiDou satellites in complex environments based on residual consistency. Background Technology

[0002] With the continuous improvement of the BeiDou Navigation Satellite System, single BeiDou positioning technology has been widely used in power line inspection, transmission line monitoring, substation operation and maintenance, and industrial facility management. However, in actual engineering environments, especially in scenarios with building obstructions, metal structure reflections, multipath propagation, and complex spatial layouts, single BeiDou positioning signals are easily interfered with, significantly reducing their positioning accuracy and stability. To compensate for the shortcomings of satellite signals in complex environments, wireless node networks are often introduced in engineering practice for assisted positioning. Collaborative estimation is achieved through connectivity relationships or hop count information between nodes, thereby improving overall positioning reliability. Against this backdrop, ranging-free network positioning technology has become a cost-effective and scalable solution. In actual deployment, a small number of nodes capable of receiving BeiDou satellite signals are typically set up as anchor nodes in the network. Their absolute coordinates are obtained through BeiDou single-system positioning, while the remaining nodes, when BeiDou signals are limited or unavailable, collaborate with the anchor nodes through a wireless communication network for positioning, thus achieving reliable positioning in complex environments.

[0003] Among existing range-free positioning methods, the DV-Hop (Distance Vector-Hop) algorithm is the most widely used and typical example. This method does not rely on additional ranging hardware; instead, it indirectly estimates the geometric distance between nodes using hop count information from the network topology. Specifically, anchor nodes first broadcast their own location information to the network, and each node calculates the minimum hop count to each anchor node. Subsequently, anchor nodes calculate the average hop size (AHS) based on the actual Euclidean distances between known anchor nodes and the corresponding hop counts. Unknown nodes then estimate their distance using their own hop counts to each anchor node and the corresponding average hop size. Finally, the least squares method is used to solve for their own coordinates. This method is simple in structure, easy to implement, and suitable for large-scale network deployments, making it highly valuable in wireless sensor networks and BeiDou-assisted positioning systems.

[0004] However, the DV-Hop algorithm implicitly assumes that distance estimates generated by different anchor nodes are geometrically consistent, and that all distance values ​​derived from hop counts can be uniformly interpreted within the same Euclidean space and reasonably understood through global least squares optimization. This assumption holds to some extent when the network topology is relatively uniform. However, in complex real-world environments, such as those with irregular obstacles or local voids, the shortest hop path often exhibits significant direction dependence. Because communication paths must circumvent obstacles or propagate along specific channels, a non-uniform proportional relationship may arise between the hop counts corresponding to different anchor nodes and the actual geometric distances. This leads to spatial heterogeneity in the average hop distance, and the distance estimates derived from different anchor nodes may also exhibit systematic biases.

[0005] Under the above conditions, if the distance estimates of all anchor nodes are still uniformly incorporated into the global least squares optimization, a set of conflicting geometric constraints may be forcibly satisfied. Since these constraints do not originate from consistent geometric proportions, the least squares solution often has to compromise between multiple sets of incompatible constraints, thus introducing overall estimation bias, and even leading to the accumulation of errors as the number of anchor nodes increases. Practice shows that in some complex network structures, simply increasing the number of anchor nodes does not consistently improve positioning accuracy; on the contrary, it may lead to unstable positioning results.

[0006] To address the shortcomings of the DV-Hop algorithm in complex environments, existing technologies have proposed a series of improvements. One type of method improves the calculation of average hop distance, such as by introducing a weighting mechanism or topology compensation model, to reduce errors in the hop count to distance conversion process. Another type of method employs weighted least squares or intelligent optimization algorithms in the location estimation stage to enhance the ability to suppress abnormal distance estimates. In addition, some methods select some anchor nodes for local estimation to reduce the uncertainty caused by distant anchor nodes. However, most of the above methods still assume that the distance estimates of all anchor nodes are compatible overall, and do not explicitly analyze the geometric consistency between different anchor nodes.

[0007] Therefore, current technologies lack a positioning method that can filter and reconstruct anchor node distance estimates from a geometric consistency perspective without changing the basic framework of DV-Hop or adding additional ranging hardware or complex communication burdens. Especially in complex environments, how to identify and eliminate anchor node constraints that are geometrically incompatible with the current estimation results, and construct a relatively consistent subset of constraints to improve the stability and reliability of the positioning results, still requires further research and improvement. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a reliable positioning method and system for complex environments using a single BeiDou system based on residual consistency. Without altering the original hop count propagation and average hop distance calculation process, or adding additional ranging hardware and communication overhead, this invention utilizes anchor nodes whose absolute coordinates are obtained through BeiDou satellite single-system positioning as reference nodes. It performs residual consistency evaluation and adaptive screening on the anchor nodes participating in the positioning calculation, identifies and eliminates constraints incompatible with the current geometric solution, forming a relatively consistent subset of anchor nodes. Position estimation is then performed on this subset, thereby reducing systematic biases caused by topological distortion or spatial heterogeneity and improving the stability and reliability of positioning results under complex environmental conditions.

[0009] This invention is based on the traditional DV-Hop (Distance Vector-Hop) positioning algorithm framework. Without changing the original hop propagation and average hop distance calculation process, it improves the consistency of the position estimation stage.

[0010] In the positioning network, some nodes can receive BeiDou satellite signals and obtain their own absolute coordinates as anchor nodes through BeiDou single-system positioning; the remaining nodes are unknown nodes, which only exchange information with neighboring nodes through wireless communication networks, and their positions need to be estimated by the method of this invention.

[0011] The method includes the following steps: First, the anchor node that obtains its coordinates through BeiDou single-system positioning broadcasts its own location information to the network, and the network node calculates the minimum number of hops to each anchor node through multi-hop communication; Second, each anchor node calculates the average hop distance based on the actual geometric distance between known anchor nodes and the corresponding number of hops, and the unknown node estimates its distance to each anchor node accordingly.

[0012] Based on this, this invention constructs a residual consistency evaluation mechanism. For the current position estimate of an unknown node, the residual value between it and the distance estimates of each anchor node is calculated, and the residual statistic is used as the criterion for the geometric consistency of the anchor nodes. An iterative approach is used to adaptively select a subset of anchor nodes with high residual consistency, gradually eliminating anchor node constraints incompatible with the current geometric solution. The expansion terminates when adding new anchor nodes fails to significantly reduce the overall residual statistic, forming a final consistent anchor node set. Subsequently, the position of the unknown node is solved using least squares or weighted least squares methods on this subset of anchor nodes.

[0013] Compared with existing technologies, this invention utilizes BeiDou single-system positioning to obtain the absolute coordinates of anchor nodes, and combines a wireless node network collaborative positioning mechanism to introduce anchor node geometric consistency modeling and adaptive filtering mechanism in the DV-Hop positioning framework, thereby reducing constraint conflicts caused by network topology distortion and improving positioning stability and reliability in complex environments.

[0014] Furthermore, the residual statistics can be replaced by the median, mean, or other robust estimators, and the location estimation stage can be implemented using ordinary least squares, weighted least squares, or other numerical optimization algorithms, all of which are equivalent alternative technical solutions of this invention.

[0015] This invention is achieved through the following technical solution:

[0016] A reliable positioning method for single BeiDou navigation in complex environments based on residual consistency includes:

[0017] S1: Deploy a wireless communication network containing anchor nodes and unknown nodes in the area to be located. The anchor nodes obtain absolute coordinates through Beidou single system positioning and broadcast their own location information to the wireless communication network. The unknown nodes receive the broadcast messages from each anchor node and calculate the minimum hop count to each anchor node. At the same time, each anchor node obtains the minimum hop count information between each other.

[0018] S2: Each anchor node calculates its average hop distance based on the minimum hop count information between itself and other anchor nodes, and broadcasts it to the unknown node. The unknown node estimates the estimated distance to each anchor node based on the minimum hop count to each anchor node and the average hop distance of the corresponding anchor node.

[0019] S3: Based on the estimated distance from the unknown node to each anchor node, construct a residual consistency evaluation model. Sort all reachable anchor nodes of the unknown node according to the minimum number of hops and estimated distance. Select a preset number of anchor nodes at the top of the sort to form an initial anchor node subset. Calculate the initial estimated position and initial residual consistency score of the unknown node based on the initial anchor node subset and the residual consistency evaluation model.

[0020] S4: Using the initial estimated position of the unknown node as the current estimated position and the initial residual consistency score as the current residual consistency score, perform adaptive expansion update of the anchor node to obtain the updated final anchor node subset, the updated estimated position, and the updated residual consistency score.

[0021] S5: Using the final anchor node subset as the constraint set and the updated estimated position as the initial optimization value, the weighted least squares method is used for iterative optimization to obtain the final positioning result of the unknown node. The reliability level of the final positioning result is evaluated by combining the updated residual consistency score. The final positioning result, final anchor node subset information, residual consistency score and reliability level are output.

[0022] The specific details of step S1 are as follows:

[0023] Each anchor node broadcasts a message to the wireless communication network, carrying its own spatial coordinates and current hop count. Upon receiving the broadcast message, any intermediate or unknown node determines whether its hop count is better than the corresponding hop count stored locally. If it is better than the currently stored record, it updates the local storage record, increments the hop count by 1, and continues to broadcast. Otherwise, it discards the message. Through the above broadcast forwarding process, each unknown node obtains the minimum hop count of each reachable anchor node, and each anchor node also obtains the minimum hop count of each other.

[0024] During the broadcast forwarding process, forwarding is only allowed to continue when the minimum hop count in the node's local storage record is updated; duplicate messages from the same anchor node and the same broadcast round are deduplicated, and a maximum hop count limit is set to restrict the broadcast spread.

[0025] The specific details of step S2 are as follows:

[0026] Each anchor node calculates the average physical length, i.e., average jump distance, corresponding to each jump from its own perspective, based on the minimum number of hops between itself and other anchor nodes, combined with the actual Euclidean distance between itself and other anchor nodes. Then, it broadcasts the average jump distance and its own position information to unknown nodes in the network. The unknown nodes receive and record this information.

[0027] The average jump distance is the ratio of the sum of the actual Euclidean distances from the anchor node to all other known anchor nodes to the sum of the corresponding minimum jump numbers;

[0028] An unknown node calculates the distance to each anchor node by multiplying its minimum number of hops to each anchor node by the average hop distance of the corresponding anchor node. This is how an unknown node estimates the distance.

[0029] The specific details of step S3 are as follows:

[0030] The residual consistency evaluation model includes anchor node residuals and anchor node subset residual consistency scores. The anchor node residual is the difference between the geometric distance from the measured location to the anchor node and the estimated distance corresponding to the anchor node. The smaller the absolute value of the residual, the more the measured location conforms to the constraints of the anchor node; the larger the absolute value, the more obvious the inconsistency between the anchor node and the measured location. The anchor node subset residual consistency score is defined based on the anchor node residual, and is the median of the absolute values ​​of the anchor node residuals.

[0031] Sort all reachable anchor nodes of the unknown node in ascending order of minimum hop count. If the hop counts are the same, sort them in ascending order of estimated distance. Then select a preset number of anchor nodes that are at the top of the sorting to form an initial subset of anchor nodes.

[0032] Based on the initial anchor node subset, the linearized least squares method is used to solve for the initial estimated position of the unknown node. Specifically, a reference anchor node is selected in the initial anchor node subset, a system of linear equations about the coordinates of the unknown node is constructed and solved by the least squares method to obtain the initial estimated position. After obtaining the initial estimated position of the unknown node, the initial residual consistency score corresponding to the initial anchor node subset under the initial estimated position is calculated by combining the residual consistency evaluation model.

[0033] The specific details of step S4 are as follows:

[0034] Using the initial estimated position and initial residual consistency score as the iterative benchmark, the anchor node subset is updated in a stepwise expansion manner: For each candidate anchor node not yet selected into the initial anchor node subset, the absolute value of its residual at the current estimated position is calculated, and the anchor node with the smallest absolute residual value is selected as the trial anchor node, which is temporarily added to the current anchor node subset to form the trial subset. Based on the trial subset, the trial estimated position and the corresponding trial residual consistency score are recalculated; a dual improvement condition of relative and absolute is set, and the trial anchor node is accepted only when the trial residual consistency score simultaneously meets the dual improvement condition of relative and absolute. The trial subset is updated to the current anchor node subset, the trial estimated position is updated to the current estimated position, and the trial residual consistency score is updated to the current residual consistency score, and the next round of expansion continues; if the dual improvement condition of relative and absolute is not met, the expansion is terminated; the current anchor node subset and the current residual consistency score are used as the final anchor node subset and residual consistency score.

[0035] Set an upper limit on the number of anchor node subsets. Stop iteration when the anchor node subset reaches the upper limit, candidate anchor nodes are processed, or the trial residual consistency score does not meet the dual improvement conditions of relative and absolute.

[0036] The specific details of step S5 are as follows:

[0037] Based on the final anchor node subset and introducing a reciprocal weighting coefficient based on the estimated distance, the weighted least squares method is used to solve for the final location of the unknown node. After the solution is completed, the final positioning result of the unknown node is output, along with the final anchor node subset and the final residual consistency score. When the final residual consistency score is small and the size of the final anchor node subset is between the preset minimum number of anchor nodes and the preset maximum number of anchor nodes, it indicates that the positioning result has good geometric consistency and high reliability. Conversely, when the final consistency score is large, it indicates that the unknown node still has strong constraint conflicts under the current network conditions, and the positioning result is marked as a low reliability result, and further compensation measures are taken.

[0038] A reliable positioning system for complex environments using a single BeiDou system based on residual consistency includes:

[0039] Hop count information acquisition module: Deploy a wireless communication network containing anchor nodes and unknown nodes in the area to be located. Anchor nodes obtain absolute coordinates through Beidou single system positioning and broadcast their own location information to the wireless communication network. Unknown nodes receive the broadcast messages from each anchor node and calculate the minimum hop count to each anchor node. At the same time, each anchor node obtains the minimum hop count information between each other.

[0040] Distance estimation module: Each anchor node calculates its average hop distance based on the minimum hop count information between itself and other anchor nodes, and broadcasts it to unknown nodes. Unknown nodes estimate the estimated distance to each anchor node based on the minimum hop count to each anchor node and the average hop distance of the corresponding anchor node.

[0041] The residual consistency evaluation model construction module constructs a residual consistency evaluation model based on the estimated distance from the unknown node to each anchor node. All reachable anchor nodes of the unknown node are sorted by minimum number of hops and estimated distance. A preset number of anchor nodes at the top of the sorting are selected to form an initial anchor node subset. The initial estimated position and initial residual consistency score of the unknown node are calculated based on the initial anchor node subset and the residual consistency evaluation model.

[0042] Adaptive expansion update module: Using the initial estimated position of the unknown node as the current estimated position and the initial residual consistency score as the current residual consistency score, perform adaptive expansion update of the anchor node to obtain the updated final anchor node subset, the updated estimated position, and the updated residual consistency score;

[0043] The results output module uses the final anchor node subset as the constraint set and the updated estimated position as the initial optimization value. It then uses the weighted least squares method for iterative optimization to obtain the final positioning result of the unknown node. The reliability level of the final positioning result is evaluated by combining the updated residual consistency score. The module outputs the final positioning result, the final anchor node subset information, the residual consistency score, and the reliability level.

[0044] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the single BeiDou reliable positioning method for complex environments based on residual consistency.

[0045] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the single BeiDou reliable positioning method for complex environments based on residual consistency.

[0046] The advantages of this invention are: by introducing an anchor node residual consistency evaluation and adaptive selection mechanism, this invention improves the accuracy and stability of single BeiDou positioning in complex environments without adding additional ranging hardware or changing the original hop count propagation process. Simulation results show that in network environments with significant topological distortion, the method of this invention reduces the positioning error by an average of about 40% compared to the traditional DV-Hop algorithm, and by about 20% compared to the local weighted least squares method with a fixed number of anchor nodes. Simultaneously, the error fluctuation range is significantly reduced, and the positioning results are more stable. In near-uniform network environments, the method of this invention maintains comparable accuracy to existing improved algorithms, but the number of selected anchor nodes is reduced to about 5-6, reducing the computational scale and improving computational efficiency by about 15%-20%. Therefore, this invention effectively improves the positioning reliability in complex environments while maintaining the lightweight characteristics of the algorithm, and has good engineering application value. Attached Figure Description

[0047] Figure 1 The flowchart shows the overall process of a reliable positioning method for single BeiDou in complex environments based on residual consistency.

[0048] Figure 2 This is a flowchart of the adaptive filtering process for anchor nodes based on residual consistency. Detailed Implementation

[0049] To enable those skilled in the art to better understand the technical solution of the present invention, the following detailed description of a reliable positioning method for single BeiDou in complex environments based on residual consistency, in conjunction with preferred embodiments, is provided by the present invention.

[0050] This invention addresses the problems of inconsistent anchor node distance assumptions, large global aggregation errors, and insufficient stability of positioning results in single BeiDou-assisted positioning or DV-Hop-like hop-count positioning under complex environments. It proposes an anchor node selection and positioning solution method based on residual consistency. While retaining the traditional DV-Hop minimum hop-count propagation mechanism, this method constructs a residual consistency evaluation index to adaptively select reachable anchor nodes and uses a subset of anchor nodes with high geometric consistency to estimate the location of the node to be positioned, thereby improving the positioning reliability in complex environments.

[0051] like Figure 1 As shown, a reliable positioning method for single BeiDou navigation in complex environments based on residual consistency is characterized by comprising:

[0052] S1: Deploy a wireless communication network containing anchor nodes and unknown nodes within the area to be located. Anchor nodes obtain absolute coordinates through BeiDou single-system positioning and broadcast their own location information to the wireless communication network. Unknown nodes receive the broadcast messages from each anchor node and calculate the minimum hop count to each anchor node. Simultaneously, each anchor node obtains the minimum hop count information between itself and others. The specific details are as follows:

[0053] Each anchor node broadcasts a message to the wireless communication network, carrying its own spatial coordinates and current hop count. Upon receiving the broadcast message, any intermediate or unknown node determines whether its hop count is better than the corresponding hop count stored locally. If it is better than the currently stored record, it updates the local storage record, increments the hop count by 1, and continues to broadcast. Otherwise, it discards the message. Through the above broadcast forwarding process, each unknown node obtains the minimum hop count of each reachable anchor node, and each anchor node also obtains the minimum hop count of each other.

[0054] During the broadcast forwarding process, forwarding is only allowed to continue when the minimum hop count in the node's local storage record is updated; duplicate messages from the same anchor node and the same broadcast round are deduplicated, and a maximum hop count limit is set to restrict the broadcast spread.

[0055] In this embodiment, a wireless communication network is deployed within the target area. The wireless communication network includes several anchor nodes and several unknown nodes. Anchor nodes are nodes with known locations, whose coordinates are pre-obtained through BeiDou single-system positioning; unknown nodes are nodes to be located, and their locations need to be estimated using the method of this invention. For ease of explanation, this embodiment is assumed to be a two-dimensional positioning scenario. The positions of the anchor nodes are denoted as follows: in, and These represent the x-coordinate and y-coordinate of the anchor node in a two-dimensional coordinate system, respectively. Unknown node. The actual location is recorded as in, and These represent the true x-coordinate and true y-coordinate of the unknown node, respectively.

[0056] Unknown node The final estimated position is denoted as The final estimated position is a position estimate calculated using the method of this invention, which is used to determine the true position of the unknown node. The approximate representation has an estimation error compared to the true location.

[0057] For unknown nodes Its reachable anchor node set Recorded as

[0058]

[0059] in, This indicates the number of anchor nodes reachable from the unknown node. Unknown node With anchor node The minimum number of hops between them is denoted as Anchor node With anchor node The minimum number of hops between them is denoted as .

[0060] First, a wireless communication network is deployed within the area to be located. This network comprises multiple nodes, including several anchor nodes and several unknown nodes. Preferably, each node includes a processor, a memory, and a wireless communication module. The anchor node's memory stores at least its node identifier and spatial coordinate information obtained through BeiDou single-system positioning. The unknown nodes are used for position estimation; initially, they do not have position coordinates but possess wireless communication and data processing capabilities to receive broadcast information from the anchor nodes and complete subsequent solutions.

[0061] Preferably, the memory of the anchor node stores at least its node identifier and spatial coordinate information; the memory of the unknown node stores at least the minimum number of hops, average hop distance, estimated distance, candidate anchor node sequence, current selection subset, current estimated position, and residual consistency evaluation value corresponding to each anchor node. Through the above initialization, it is ensured that the unknown node can complete the selection and positioning calculation locally, or that the edge gateway or the main station server can centrally solve the problem.

[0062] After node initialization, the DV-Hop hop count propagation process is executed. Specifically, each anchor node broadcasts a message to the network carrying its own identifier and current hop count. Preferably, each anchor node initially sends a hop count of 0. When any intermediate node or unknown node receives a broadcast message from an anchor node, it determines whether the hop count in the message is better than the corresponding hop count already stored locally. If it is better, it updates its local record, increments the hop count by 1, and continues broadcasting; otherwise, it discards the message.

[0063] Through the above broadcast forwarding process, each unknown node in the network can obtain the minimum hop count to each reachable anchor node, denoted as . At the same time, the minimum number of hops between each anchor node can also be obtained, denoted as... It should be noted that this step only utilizes network connectivity and message propagation processes, without requiring an additional physical distance measurement module, thus maintaining the low cost and easy deployment characteristics of the traditional DV-Hop mechanism.

[0064] Optionally, to reduce broadcast redundancy and communication burden, the following control strategies can be set: forwarding is only allowed when the node's local minimum hop count is updated; duplicate messages from the same anchor node and the same broadcast round are deduplicated; and a maximum hop count limit is set when necessary to restrict the broadcast propagation range. All of the above strategies can be implemented without changing the basic principles of this invention.

[0065] S2: Each anchor node calculates its average hop distance based on the minimum hop count information between itself and other anchor nodes, and broadcasts this information to the unknown nodes. The unknown nodes then estimate the distance to each anchor node based on the minimum hop count to each anchor node and the average hop distance to the corresponding anchor node. Details are as follows:

[0066] Each anchor node calculates the average physical length, or average hop distance, corresponding to each hop from its own perspective, based on the minimum hop count obtained from other anchor nodes and the actual Euclidean distance from other anchor nodes. Then, it broadcasts the average hop distance along with its own position information to unknown nodes in the network. The unknown nodes receive and record this information. The average hop distance is the ratio of the sum of the actual Euclidean distances from the anchor node to all other known anchor nodes to the sum of the corresponding minimum hop counts. The unknown node uses the product of its minimum hop count to each anchor node and the average hop distance of the corresponding anchor node to calculate the hop count-to-distance conversion to each anchor node, i.e., the estimated distance.

[0067] After obtaining the minimum number of hops between anchor nodes, each anchor node calculates its own average hop distance. For any anchor node... Its average jump distance Defined as

[0068]

[0069] in, and Representing anchor nodes and anchor node Location coordinates, This represents the Euclidean distance between the two. This represents the minimum number of hops between the two. The physical meaning of the above formula is: with anchor nodes... For reference, the ratio of the total actual geometric distance from the anchor node to the other anchor nodes is calculated to the total minimum number of jumps, thus obtaining the "average physical length corresponding to each jump" from the perspective of the anchor node.

[0070] After obtaining the average jump distance After that, anchor node It is broadcast along with its own identifier to unknown nodes in the network. The unknown nodes receive and record the average hop distance from each reachable anchor node, which is used to subsequently calculate the estimated distance to each anchor node.

[0071] Unknown node Obtaining itself from the anchor node Minimum number of hops and anchor node average jump distance Then, calculate the estimated distance from the unknown node to the anchor node:

[0072]

[0073] In the formula, Indicates unknown nodes To anchor node The hop count is converted to distance. At this point, the unknown node has a set of distance estimates for all reachable anchor nodes. .

[0074] Unlike traditional DV-Hop, this invention does not directly perform global least squares localization based on all the estimated distances mentioned above, but further considers each anchor node... In fact, towards unknown nodes A geometric assumption is provided regarding its position, namely the first... The distance assumptions or geometric constraints corresponding to each anchor node are denoted as follows: It indicates that the position of the unknown node satisfies The constraint relationship. That is, the anchor node. Estimated distance provided Corresponding to anchor nodes With the center, and The geometric constraint is the radius. Ideally, the geometric constraints generated by different anchor nodes should intersect near the same location; however, in complex environments, due to factors such as communication link detours, spatial heterogeneity, and obstacle obstruction, the estimated distances corresponding to different anchor nodes may have significant anchor-point dependency errors. This error can be abstractly represented as... ,in, , indicating an unknown node With anchor node The true Euclidean distance between them This represents the distance estimate obtained by converting hop count. The distortion factor is related to the anchor node and the path. This is a random error term. When different anchor nodes... When the differences are significant, all geometric constraints may not be satisfactorily satisfied simultaneously at the same location. Therefore, directly including all anchor nodes in the global solution will introduce a large systematic bias. Based on this, the present invention further introduces a residual consistency analysis mechanism.

[0075] S3: Based on the estimated distances from the unknown node to each anchor node, construct a residual consistency evaluation model. Sort all reachable anchor nodes of the unknown node according to the minimum number of hops and estimated distance. Select a predetermined number of anchor nodes at the top of the sorting to form an initial anchor node subset. Calculate the initial estimated position and initial residual consistency score of the unknown node based on the initial anchor node subset and the residual consistency evaluation model. The specific content is as follows:

[0076] like Figure 2 As shown, the residual consistency evaluation model includes anchor node residuals and anchor node subset residual consistency scores. The anchor node residual is the difference between the geometric distance from the measured location to the anchor node and the estimated distance corresponding to the anchor node. The smaller the absolute value of the residual, the more the measured location conforms to the constraints of the anchor node; the larger the absolute value, the more obvious the inconsistency between the anchor node and the measured location. Then, the anchor node subset residual consistency score is defined based on the anchor node residual, which is the median of the absolute values ​​of the anchor node residuals.

[0077] Sort all reachable anchor nodes of the unknown node in ascending order of minimum hop count. If the hop counts are the same, sort them in ascending order of estimated distance. Then select a preset number of anchor nodes that are at the top of the sorting to form an initial subset of anchor nodes.

[0078] Based on the initial anchor node subset, the linearized least squares method is used to solve for the initial estimated position of the unknown node. Specifically, a reference anchor node is selected in the initial anchor node subset, a system of linear equations about the coordinates of the unknown node is constructed and solved by the least squares method to obtain the initial estimated position. After obtaining the initial estimated position of the unknown node, the initial residual consistency score corresponding to the initial anchor node subset under the initial estimated position is calculated by combining the residual consistency evaluation model.

[0079] To determine which anchor nodes have good geometric compatibility, this invention defines the location to be measured. anchor node residual for

[0080] In equation (5), Candidate positions To anchor node geometric distance, Unknown node Relative to anchor node The estimated distance. Therefore, the residual. Reflects location For anchor nodes The degree to which the provided distance assumption is satisfied. The smaller the absolute value, the more closely the candidate location matches the anchor node. The larger the absolute value of the constraint, the more obvious the inconsistency between the anchor node and the candidate position.

[0081] Furthermore, for any subset of anchor nodes This invention defines the subset at the candidate position. Residual consistency score for

[0082]

[0083] in, Represents a subset of anchor nodes The absolute values ​​of the residuals corresponding to each anchor node are statistically analyzed, and the median is taken as the consistency evaluation result.

[0084] This invention preferably uses the median of the absolute value of the residuals as the consistency evaluation index because the median is less sensitive to a few outlier anchor nodes than the mean, and can better reflect the overall mainstream consistency of a group of anchor nodes. When most anchor nodes in a subset are geometrically compatible, the calculated score is relatively small; when the subset contains many incompatible anchor nodes, the score will increase significantly. Therefore, the above scoring formula can effectively serve as the basis for subsequent anchor node selection and expansion.

[0085] To improve the stability of the subsequent screening process, this invention preferably first checks the unknown nodes. Sort all reachable anchor nodes. The preferred sorting method is: first sort by the minimum number of hops. Arrange from smallest to largest; if the minimum number of jumps is the same, then arrange according to the estimated distance. Arrange them in ascending order. The resulting sequence of candidate anchor nodes is obtained after sorting. ,in, Indicates the sorted order of the first... The index corresponding to each anchor node. Indicates the total number of reachable anchor nodes. This represents the sorted sequence of anchor node indices. The reason for using the above sorting method is that, generally, the smaller the minimum hop count, the shorter the propagation path and the fewer detours between the unknown node and its corresponding anchor node, and the more reliable the distance estimate obtained from the hop count is. Given the same hop count, anchor nodes with smaller estimated distances usually have better local geometric constraints. Therefore, prioritizing the construction of an initial subset from anchor nodes with low hop counts and close proximity is beneficial for forming a more stable initial position solution.

[0086] Let the initial minimum number of anchor nodes be Then the initial anchor node subset Defined as

[0087]

[0088] in, Indicates the first position in the sorted sequence Anchor node index. In a two-dimensional positioning scenario, theoretically at least three non-collinear anchor nodes are required to complete planar positioning. Preferably, to improve numerical stability, Choose 4. This way, even if some anchor nodes are nearly collinear, a more robust initial position estimate can still be obtained through redundancy constraints.

[0089] Obtaining the initial subset of anchor nodes Then, the initial estimated positions of the unknown nodes are calculated based on this subset. This solution process can be represented as the following nonlinear least squares problem:

[0090]

[0091] in, Indicates all candidate positions Select the optimal solution that minimizes the objective function. Represents a subset of initial anchor nodes The calculated initial position estimate of the unknown node. For ease of engineering implementation, this invention preferably uses a linearized least squares method to solve the above equation. Specifically, in the initial anchor node subset... Select a reference anchor node, for example, take As a reference anchor node, then for any other anchor node ,have

[0092]

[0093] in, Indicates the position coordinates of the selected reference anchor node. This represents the estimated distance between the unknown node and the reference anchor node. Expanding the above equation, we get...

[0094]

[0095] in, and These represent the x-coordinate and y-coordinate of the reference anchor node in a two-dimensional coordinate system, respectively. Further simplification involves considering the unknown coordinates. and The linear expression:

[0096]

[0097] By combining all the equations obtained from the above formula, a system of linear equations can be formed.

[0098]

[0099] in, Represents the position vector of the unknown node. This represents the coefficient matrix composed of the coordinate differences of each anchor node. This represents a constant vector consisting of distance estimates and coordinate terms. In this case, the initial position estimate can be obtained using the least squares method.

[0100]

[0101] in, Representation matrix transpose, This represents the inverse operation of a matrix. In practical applications, if... In cases of pathological or near-singular conditions, pseudo-inverse forms can be used.

[0102]

[0103] in, Representation matrix The pseudo-inverse. Or, in the form of adding regularization terms.

[0104]

[0105] in, For smaller positive numbers, It is the identity matrix, used to enhance numerical stability.

[0106] Obtaining the initial position estimate Then, the corresponding initial residual consistency score is further calculated. :

[0107]

[0108] S4: Using the initial estimated position of the unknown node as the current estimated position and the initial residual consistency score as the current residual consistency score, perform adaptive expansion update of the anchor node to obtain the updated final subset of anchor nodes, the updated estimated position, and the updated residual consistency score; the specific content is as follows:

[0109] Using the initial estimated position and initial residual consistency score as the iterative benchmark, the anchor node subset is updated in a stepwise expansion manner: For each candidate anchor node not yet selected into the initial anchor node subset, the absolute value of its residual at the current estimated position is calculated, and the anchor node with the smallest absolute residual value is selected as the trial anchor node, which is temporarily added to the current anchor node subset to form the trial subset. Based on the trial subset, the trial estimated position and the corresponding trial residual consistency score are recalculated; a dual improvement condition of relative and absolute is set, and the trial anchor node is accepted only when the trial residual consistency score simultaneously meets the dual improvement condition of relative and absolute. The trial subset is updated to the current anchor node subset, the trial estimated position is updated to the current estimated position, and the trial residual consistency score is updated to the current residual consistency score, and the next round of expansion continues; if the dual improvement condition of relative and absolute is not met, the expansion is terminated; the current anchor node subset and the current residual consistency score are used as the final anchor node subset and residual consistency score.

[0110] Set an upper limit on the number of anchor node subsets. Stop iteration when the anchor node subset reaches the upper limit, candidate anchor nodes are processed, or the trial residual consistency score does not meet the dual improvement conditions of relative and absolute.

[0111] Given the initial positions and initial scores, this invention employs a gradual expansion approach to adaptively update the subset of anchor nodes, rather than including all reachable anchor nodes at once. Let the current iteration number be... The current subset of anchor nodes is The current estimated position is The current consistency score is .

[0112] For each candidate anchor node that has not yet been selected into the current subset

[0113]

[0114] Calculate the absolute value of the residual at the current estimated location:

[0115]

[0116] in, This indicates the relationship between the unknown node and the anchor node at the current estimated location. The corresponding residuals, This represents the absolute value of the residual. The anchor node that best matches the current estimate is selected, i.e., the anchor node that satisfies the following formula:

[0117]

[0118] in, This represents the set of candidate anchor nodes that have not yet been selected into the current subset of anchor nodes. This represents the index of the anchor node with the smallest residual selected. This indicates selecting the index value that minimizes the objective function. Then, temporarily add it to the current anchor node subset to construct a trial subset.

[0119]

[0120] Subsequently, in the trial subset The least squares-based localization solution process is re-executed to obtain the trial location estimate. Then, calculate the consistency score of the trial subset at the trial position according to equation (6):

[0121]

[0122] To avoid a decrease in overall geometric consistency due to the addition of inappropriate anchor nodes, this invention sets up dual judgment conditions. An anchor node is accepted only if its addition improves the consistency score to meet the corresponding improvement judgment condition. The judgment conditions employ a segmented judgment mechanism:

[0123] When the current consistency score Greater than the preset threshold When this is the case, a relative improvement criterion is adopted, i.e., the condition is satisfied.

[0124]

[0125] When the current consistency score Less than or equal to the preset threshold When this is the case, the absolute improvement criterion is adopted, that is, if the condition is satisfied...

[0126]

[0127] in, The switching threshold for consistency scores is used to avoid the problem of relatively improving condition failure when the score is low. To relatively improve the threshold, it is used to constrain the score to decrease by at least a certain percentage; To ensure absolute improvement, a threshold is set to constrain the score to decrease by at least a certain absolute value. This dual-threshold mechanism effectively avoids incorrectly accepting anchor nodes due to minor numerical fluctuations. This enables adaptive decision-making at different consistency levels, improving the stability and robustness of the anchor node selection process.

[0128] When the decision condition formula is true, accept the trial anchor node and update it.

[0129]

[0130]

[0131]

[0132] Then continue to the next iteration.

[0133] When the decision condition formula is not met, it indicates that introducing new anchor nodes will not significantly improve the overall residual consistency, or that conflicting geometric constraints may have already begun to be introduced. In this case, the expansion process is terminated, and the current subset of anchor nodes is... This is the final selection result:

[0134]

[0135] Furthermore, the present invention can also set an upper limit for the subset of anchor nodes. Therefore, the expansion can be terminated when any of the following conditions are met: first, the size of the current anchor node subset reaches its upper limit; second, all candidate anchor nodes have been processed; third, the newly added anchor node no longer meets the acceptance conditions shown in the decision formula. Through the above method, this invention can adaptively select a subset of anchor nodes with high geometric consistency from all reachable anchor nodes for final positioning.

[0136] In a preferred embodiment, the initial number of anchor nodes is limited. A maximum of 4 anchor nodes can be selected. A value of 12 is acceptable, which relatively improves the threshold. A value of 0.03 is acceptable, which would significantly improve the threshold. Based on network communication radius Settings, for example The parameter settings above are for illustrative purposes only, and those skilled in the art can adjust them according to the actual network scale and deployment environment.

[0137] S5: Using the final anchor node subset as the constraint set and the updated estimated positions as the initial optimization values, iterative optimization is performed using the weighted least squares method to obtain the final location result of the unknown nodes. The reliability level of the final location result is evaluated by combining the updated residual consistency score. The output includes the final location result, final anchor node subset information, residual consistency score, and reliability level. Details are as follows:

[0138] Based on the final anchor node subset and introducing a reciprocal weighting coefficient based on the estimated distance, the weighted least squares method is used to solve for the final location of the unknown node. After the solution is completed, the final positioning result of the unknown node is output, along with the final anchor node subset and the final residual consistency score. When the final residual consistency score is small and the size of the final anchor node subset is within a reasonable range (between the preset minimum number of anchor nodes and the preset maximum number of anchor nodes), it indicates that the positioning result has good geometric consistency and high reliability. Conversely, when the final consistency score is large, it indicates that the unknown node still has strong constraint conflicts under the current network conditions, and the positioning result is marked as a low reliability result, and further compensation measures are taken.

[0139] Obtaining the final subset of anchor nodes Subsequently, the present invention further performs weighted least squares solving on this subset to improve the final positioning accuracy. Final position estimation It can be represented as

[0140]

[0141] in, Represents anchor node The weighting coefficients. Preferably, inverse distance-based weights are used:

[0142]

[0143] in, As a weighted index, Indicates estimated distance of The result of exponentiation. To avoid small positive constants with a denominator of zero, the above formula is used to enhance the role of closer anchor nodes in the final solution. This is because, compared to farther anchor nodes, closer anchor nodes typically have smaller hop propagation distortion and stronger local geometric constraints.

[0144] For final location estimation The formula can also be used to construct a weighted system of equations using the linearization of squared differences. Let the weighting matrix be... Then the final position estimate can be expressed as

[0145]

[0146] in, This represents the final position estimate of the unknown node; This represents the coefficient matrix constructed from the coordinate differences of the anchor nodes; This represents a constant vector formed by combining the distance estimate and the corresponding coordinate terms; This represents the weighted matrix, which is a diagonal matrix where the diagonal elements are the weight coefficients corresponding to each anchor node. ; Representation matrix transpose, Representation matrix The result of the inverse operation. If If numerical instability exists, pseudo-inverse or regularization methods can also be used to solve the problem. After solving, the unknown nodes are obtained. Final position estimation results .

[0147] In practical applications, when the number of reachable anchor nodes is insufficient or the localization equation matrix exhibits singular or ill-conditioned conditions, methods such as pseudo-inverse solving, adding regularization terms, or reselecting a subset of initial anchor nodes can be used to improve numerical stability. For example, when the matrix... or When irreversibility is not possible, a pseudo-inverse solution can be used; when the number of reachable anchor nodes is less than three, it can be determined that the unknown node does not yet meet the positioning conditions. Those skilled in the art can use other equivalent numerical stabilization methods according to specific implementation requirements.

[0148] After completing the final solution, this invention outputs the location results of the unknown nodes. Optionally, auxiliary indicators related to positioning reliability can also be output simultaneously for further judgment and application by the upper-level system. These auxiliary indicators include, but are not limited to, the final anchor node subset. Final subset size

[0149]

[0150] and final consistency score

[0151]

[0152] Among them, when Smaller and When within a reasonable range, it usually indicates that the obtained positioning results have good geometric consistency and high reliability; conversely, when... A larger value indicates that the unknown node still faces strong constraint conflicts under the current network conditions. In this case, the location result can be marked as a low-reliability result, allowing the system to take further compensatory measures, such as delayed relocation, introducing supplementary anchor nodes, increasing the number of observation rounds, or triggering manual verification.

Claims

1. A reliable positioning method for single BeiDou navigation in complex environments based on residual consistency, characterized in that, include: S1: Deploy a wireless communication network containing anchor nodes and unknown nodes in the area to be located. The anchor nodes obtain absolute coordinates through Beidou single system positioning and broadcast their own location information to the wireless communication network. The unknown nodes receive the broadcast messages from each anchor node and calculate the minimum hop count to each anchor node. At the same time, each anchor node obtains the minimum hop count information between each other. S2: Each anchor node calculates its average hop distance based on the minimum hop count information between itself and other anchor nodes, and broadcasts it to the unknown node. The unknown node estimates the estimated distance to each anchor node based on the minimum hop count to each anchor node and the average hop distance of the corresponding anchor node. S3: Based on the estimated distance from the unknown node to each anchor node, construct a residual consistency evaluation model. Sort all reachable anchor nodes of the unknown node according to the minimum number of hops and estimated distance. Select a preset number of anchor nodes at the top of the sort to form an initial anchor node subset. Calculate the initial estimated position and initial residual consistency score of the unknown node based on the initial anchor node subset and the residual consistency evaluation model. S4: Using the initial estimated position of the unknown node as the current estimated position and the initial residual consistency score as the current residual consistency score, perform adaptive expansion update of the anchor node to obtain the updated final anchor node subset, the updated estimated position, and the updated residual consistency score. S5: Using the final anchor node subset as the constraint set and the updated estimated position as the initial value for optimization, the weighted least squares method is used for iterative optimization to obtain the final positioning result of the unknown node. The reliability level of the final positioning result is evaluated by combining the updated residual consistency score. Output the final positioning result, final anchor node subset information, residual consistency score, and reliability level.

2. The reliable positioning method for single BeiDou navigation in complex environments based on residual consistency according to claim 1, characterized in that, The specific details of step S1 are as follows: Each anchor node broadcasts a message to the wireless communication network, carrying its own spatial coordinates and current hop value. Upon receiving the broadcast message, any intermediate node or unknown node determines whether the hop value is better than the corresponding hop value already stored locally. If it is better than the currently stored record, the local storage record is updated, the hop value is incremented by 1, and the message is broadcast again. Otherwise, the message is discarded. Through the above broadcast forwarding process, each unknown node obtains the minimum hop count of each reachable anchor node, and each anchor node also obtains the minimum hop count of each other.

3. The reliable positioning method for single BeiDou in complex environments based on residual consistency according to claim 2, characterized in that, During the broadcast forwarding process, forwarding is only allowed to continue when the minimum hop count in the node's local storage record is updated; duplicate messages from the same anchor node and the same broadcast round are deduplicated, and a maximum hop count limit is set to restrict the broadcast spread.

4. The reliable positioning method for single BeiDou navigation in complex environments based on residual consistency according to claim 1, characterized in that, The specific details of step S2 are as follows: Each anchor node calculates the average physical length, i.e., average jump distance, corresponding to each jump from its own perspective, based on the minimum number of hops between itself and other anchor nodes, combined with the actual Euclidean distance between itself and other anchor nodes. Then, it broadcasts the average jump distance and its own position information to unknown nodes in the network. The unknown nodes receive and record this information. The average jump distance is the ratio of the sum of the actual Euclidean distances from the anchor node to all other known anchor nodes to the sum of the corresponding minimum jump numbers; An unknown node calculates the distance to each anchor node by multiplying its minimum number of hops to each anchor node by the average hop distance of the corresponding anchor node. This is how an unknown node estimates the distance.

5. The reliable positioning method for single BeiDou navigation in complex environments based on residual consistency according to claim 1, characterized in that, The specific details of step S3 are as follows: The residual consistency evaluation model includes anchor node residuals and anchor node subset residual consistency scores. The anchor node residual is the difference between the geometric distance from the measured location to the anchor node and the estimated distance corresponding to the anchor node. The smaller the absolute value of the residual, the more the measured location conforms to the constraints of the anchor node. The larger the absolute value, the more obvious the inconsistency between the anchor node and the measured location. Then, based on the anchor node residuals, define the anchor node subset residual consistency score, which is the median of the absolute values ​​of the anchor node residuals. Sort all reachable anchor nodes of the unknown node in ascending order of minimum hop count. If the hop counts are the same, sort them in ascending order of estimated distance. Then select a preset number of anchor nodes that are at the top of the sorting to form an initial subset of anchor nodes. Based on the initial anchor node subset, the linearized least squares method is used to solve for the initial estimated position of the unknown node. Specifically, a reference anchor node is selected in the initial anchor node subset, a system of linear equations about the coordinates of the unknown node is constructed and solved by the least squares method to obtain the initial estimated position. After obtaining the initial estimated position of the unknown node, the initial residual consistency score corresponding to the initial anchor node subset under the initial estimated position is calculated by combining the residual consistency evaluation model.

6. The reliable positioning method for single BeiDou navigation in complex environments based on residual consistency according to claim 1, characterized in that, The specific details of step S4 are as follows: Using the initial estimated position and the initial residual consistency score as the iterative benchmark, the anchor node subset is updated in a stepwise expansion manner: for each candidate anchor node that has not yet been selected into the initial anchor node subset, the absolute value of its residual at the current estimated position is calculated, the anchor node with the smallest absolute residual value is selected as the trial anchor node, and it is temporarily added to the current anchor node subset to form the trial subset. Based on the trial subset, the trial estimated position and the corresponding trial residual consistency score are recalculated. Set both relative and absolute improvement conditions. Only accept the trial anchor node if the trial residual consistency score meets both relative and absolute improvement conditions. Update the trial subset to the current anchor node subset, update the trial estimated position to the current estimated position, update the trial residual consistency score to the current residual consistency score, and continue to the next round of expansion. If both relative and absolute improvement conditions are not met, the expansion is terminated. The current anchor node subset and the current residual consistency score are used as the final anchor node subset and residual consistency score. Set an upper limit on the number of anchor node subsets. Stop iteration when the anchor node subset reaches the upper limit, candidate anchor nodes are processed, or the trial residual consistency score does not meet the dual improvement conditions of relative and absolute.

7. The reliable positioning method for single BeiDou navigation in complex environments based on residual consistency according to claim 1, characterized in that, The specific details of step S5 are as follows: Based on the final anchor node subset, and by introducing a reciprocal weighting coefficient based on the estimated distance, the weighted least squares method is used to solve for the final position of the unknown node. After the solution is completed, the final positioning result of the unknown node is output, along with the final anchor node subset and the final residual consistency score. When the final residual consistency score is less than the preset consistency threshold, and the size of the final anchor node subset is between the preset minimum number of anchor nodes and the preset maximum number of anchor nodes, it indicates that the positioning result has good geometric consistency and high reliability. Conversely, when the final consistency score is large, it indicates that the unknown node still has strong constraint conflicts under the current network conditions. The location result is marked as a low reliability result, and further compensation measures are taken.

8. A reliable positioning system for complex environments using a single BeiDou system based on residual consistency, characterized in that: include: Hop count information acquisition module: Deploy a wireless communication network containing anchor nodes and unknown nodes in the area to be located. Anchor nodes obtain absolute coordinates through Beidou single system positioning and broadcast their own location information to the wireless communication network. Unknown nodes receive the broadcast messages from each anchor node and calculate the minimum hop count to each anchor node. At the same time, each anchor node obtains the minimum hop count information between each other. Distance estimation module: Each anchor node calculates its average hop distance based on the minimum hop count information between itself and other anchor nodes, and broadcasts it to unknown nodes. Unknown nodes estimate the estimated distance to each anchor node based on the minimum hop count to each anchor node and the average hop distance of the corresponding anchor node. The residual consistency evaluation model construction module constructs a residual consistency evaluation model based on the estimated distance from the unknown node to each anchor node. All reachable anchor nodes of the unknown node are sorted by minimum number of hops and estimated distance. A preset number of anchor nodes at the top of the sorting are selected to form an initial anchor node subset. The initial estimated position and initial residual consistency score of the unknown node are calculated based on the initial anchor node subset and the residual consistency evaluation model. Adaptive expansion update module: Using the initial estimated position of the unknown node as the current estimated position and the initial residual consistency score as the current residual consistency score, perform adaptive expansion update of the anchor node to obtain the updated final anchor node subset, the updated estimated position, and the updated residual consistency score; The output module uses the final anchor node subset as the constraint set and the updated estimated position as the initial value for optimization. It uses the weighted least squares method for iterative optimization to obtain the final positioning result of the unknown node. The reliability level of the final positioning result is evaluated by combining the updated residual consistency score. Output the final positioning result, final anchor node subset information, residual consistency score, and reliability level.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the single BeiDou reliable positioning method for complex environments based on residual consistency as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the single BeiDou reliable positioning method for complex environments based on residual consistency as described in any one of claims 1-7.

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