CN107144810B - Wireless multi-hop non-ranging positioning method based on structure risk minimization - Google Patents

Wireless multi-hop non-ranging positioning method based on structure risk minimization Download PDF

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CN107144810B
CN107144810B CN201611189753.7A CN201611189753A CN107144810B CN 107144810 B CN107144810 B CN 107144810B CN 201611189753 A CN201611189753 A CN 201611189753A CN 107144810 B CN107144810 B CN 107144810B
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hop count
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CN107144810A (en
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刘钰
严家佳
程炳华
郑玮
严筱永
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Jinling Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention provides a wireless multi-hop non-ranging positioning method based on structure risk minimization, which comprises an initialization stage, a hop count-distance optimal mapping model construction stage and a position estimation stage, wherein a distance vector routing exchange protocol is used, after nodes communicate for a period of time, all nodes in a network obtain the shortest hop count and the physical distance between the nodes and a reference node, the hop count-distance optimal mapping model is constructed, and the hop count from an unknown node to the reference node is utilized to obtain the corresponding physical distance under the guidance of the mapping model; and finally, obtaining the estimated position of the unknown node by a trilateration method. The invention adopts the risk structure minimization to construct the hop count-distance mapping model, the confidence range of the structure risk minimization is utilized to constrain the experience risk, and the calculation process has no zero result, thereby avoiding the problem of collinearity existing in the position relation among reference nodes in a small partition or neighborhood.

Description

Wireless multi-hop non-ranging positioning method based on structure risk minimization
Technical Field
The invention relates to a wireless multi-hop non-ranging positioning method based on structure risk minimization.
Background
As mobile devices become more popular, wireless network-based applications grow in number, and in many wireless applications, location information for nodes is often a prerequisite for other wireless network-based applications. For example: in the wireless monitoring of sewage discharge and the wireless monitoring of city gas pipeline, when the incident takes place, the first problem that monitoring personnel cared about is exactly where the emergent incident that takes place suddenly takes place, and only exact know the concrete position that takes place suddenly, and such monitoring just has actual meaning, just can solve proruption problem rapidly. For the relationship between the information of wireless monitoring and the position, there is literature statistics that about 80% of the information of wireless monitoring is related to the position.
In most wireless monitoring applications, wireless network nodes are deployed randomly by machine into a monitored area. The position information of the node can acquire the position information of the event by a method that the equipment carries a GPS or is calibrated manually. Because of the limitations of deployment environment, cost and the like, it is often infeasible for all nodes to be additionally provided with a GPS chip or manually set, so in a monitoring area, only a few nodes know the positions of the nodes, and most nodes do not know the specific position information of the nodes in advance. In order to enable an unknown node to acquire global position information under the condition of only a small number of known position nodes, position estimation needs to be performed through a certain method and algorithm. Through development for many years, scientific research personnel provide a plurality of wireless node position estimation strategies and methods, and wireless network positioning technologies can be roughly divided into the following steps according to whether a measurement technology is used in the positioning process: wireless positioning based on ranging technology and wireless positioning based on non-ranging technology. Distance (angle) information between wireless nodes is obtained through physical electromagnetic signal measurement based on ranging positioning. After obtaining distance (angle) learning, the unknown node may estimate its position using trilateration, triangulation, or maximum likelihood estimation. Generally, the accuracy of a wireless positioning method based on ranging is relatively high, but the positioning performance depends heavily on the accuracy of physical measurement.
In order to ensure the distance measurement accuracy, the measurement hardware is often required to be harsh, so that the cost becomes high and even unacceptable, and the positioning based on the distance measurement mode is not suitable for large-scale wireless application. In order to reduce the overhead of hardware cost, a method irrelevant to ranging is mostly adopted to estimate the node position in large-scale wireless network positioning. The non-ranging positioning method utilizes the self-organization characteristic of the wireless network, namely, the wireless network data is transmitted in a multi-hop transmission mode, so that the physical distance between the wireless network nodes can be described or approximately represented by the hop count under the condition of no ranging hardware. However, the performance of non-ranging positioning technology in practical applications still suffers from a number of technical difficulties, among which the most fatal non-ranging positioning technology can only achieve ideal positioning results in an isotropic network with high node density and uniform distribution, and the positioning effect is very poor even the positioning results are not available in an anisotropic network with non-uniform node distribution and irregular deployment.
Most of non-ranging-based positioning methods obtain the hop count between nodes through the connection relationship between the nodes, and then estimate the positions of the nodes. Therefore, the non-ranging method does not require distance and direction information between nodes, making it suitable for large-scale wireless network applications. There are many ways to convert the hop count to approximate physical distance, the most notable of which are at present: DV-hop method, Amorphous method and PDM method.
The DV-hop method and the Amorphous method are based on hop algorithm, and the accurate position estimation obtained by the DV-hop method and the Amorphous method is that the topology of network nodes is assumed to be isotropic, namely, the deployment area is regular, the visual distance between the nodes is spread, and the distribution is uniform. Unfortunately, the actual network often has irregular deployment area and uneven node distribution due to random scattering, obstruction of obstacles, and the like. As shown in fig. 1, in fig. 1a, the physical distances from node a to nodes B, C, D are the same, and the hop counts between them are 5, 4, 3; as in fig. 1B, the physical distance of the straight line from node a to node B is very short, and the number of hops from node a to node B is very long due to the deployment irregularity caused by the obstruction. Both of these problems cause a deviation between the minimum number of hops and the true physical distance.
The invention provides a multi-hop non-ranging distributed wireless positioning method based on structure risk minimization based on the advantages of other non-ranging positioning methods by surrounding the three characteristics of multi-hop, non-ranging and distributed, namely: multi-hop Localization through structured Risk Minimization, MLSRM. The MLSRM method adopts the structure risk minimization to construct the hop count-distance mapping relation between reference nodes, each unknown node estimates the distance between each unknown node and the connected reference node by adopting the relation model in a distributed mode, and finally estimates the position of the unknown node.
Disclosure of Invention
The invention aims to provide a wireless multi-hop non-ranging positioning method based on structural risk minimization, which is characterized in that the optimal relation between node hop count and distance is found by adopting a structural risk minimization learning theory, the generalization capability of structural risk minimization is exerted to improve the hop count-distance conversion capability, and finally, each unknown node adopts a distributed calculation mode to estimate the position of the unknown node.
The technical solution of the invention is as follows:
a wireless multi-hop non-ranging positioning method based on structure risk minimization comprises an initialization stage, a hop count-distance optimal mapping model building stage and a position estimation stage,
in the initialization stage, a distance vector routing exchange protocol is used, and after nodes communicate for a period of time, all nodes in a network obtain the shortest hop count and the physical distance between the nodes and a reference node;
constructing a hop count-distance optimal mapping model, and obtaining a distance prediction formula after obtaining the shortest hop count and the physical distance between reference nodes:
Figure BDA0001185645230000031
wherein I is a unit diagonal matrix, gamma is a proportional parameter of two risks of an empirical risk and a confidence range,
Figure BDA0001185645230000032
is htThe vector after the centralization processing is carried out,
Figure BDA0001185645230000033
is the column mean value of H, and the hop count matrix H and the distance matrix D are subjected to centralized operation in the operation process to obtain corresponding matrices
Figure BDA0001185645230000034
And
Figure BDA0001185645230000035
Figure BDA0001185645230000036
is composed of
Figure BDA0001185645230000037
A stack of n rows of (a);
in the position estimation stage, the hop count from an unknown node to a reference node is utilized to obtain a corresponding physical distance under the guidance of a mapping model; and finally, obtaining the estimated position of the unknown node by a trilateration method.
Further, in the initialization stage, all nodes in the network obtain the shortest hop count with the reference node, and the specific process is as follows: in the monitoring area, the reference node sends a broadcast information packet with self position information to other nodes in the communication radius, after each node in the monitoring area receives the packet information, the node records the minimum Hop count of the connected reference node, and simultaneously adds 1 to the Hop count field Hop _ counts value in the packet, but when the node receives the packet from the same reference node and the Hop count field value is not the minimum value, the program automatically ignores the packet.
Further, the broadcast information packet at least includes a reference node representation field ID, coordinate location information and a Hop count field Hop _ counts, wherein the coordinate location information includes X and Y, and the packet format is as follows:
Figure BDA0001185645230000038
further, in the position estimation stage, in the monitoring area, an unknown node t is connected with more than k reference node signals, k is more than or equal to 3, and a coordinate-distance relation equation exists between the reference node and the unknown node, namely:
Figure BDA0001185645230000039
wherein (x, y) is the coordinate of the unknown node, (x)1,y1),(x2,y2),…,(xk,yk) Is composed ofReferring to the node coordinates, if the 1 st to k-1 st equations are subtracted from the k-th equation, respectively, the following results are obtained:
Figure BDA0001185645230000041
order to
Figure BDA0001185645230000042
Figure BDA0001185645230000043
Figure BDA0001185645230000044
The equation set of equation (18) is converted into the form Ax ═ b, and due to the presence of measurement errors, the equation set behaves correctly in the form: ax ═ b +. To obtain an optimal solution for the unknown node position, the sum of the squares of the errors is used as a criterion, i.e.:
Figure BDA0001185645230000045
the gradient of equation (19) is found to be 0, resulting in:
Figure BDA0001185645230000046
if the references are not on a straight line, the square matrix ATWhen A is reversible, the estimated coordinates of the unknown nodes are easily obtained:
Figure BDA0001185645230000047
the invention has the beneficial effects that: according to the wireless multi-hop non-ranging positioning method based on the structure risk minimization, a risk structure minimization is adopted to construct a hop count-distance mapping model, the confidence range of the structure risk minimization is utilized to constrain the experience risk, and a zero result does not exist in the calculation process, so that the problem of co-linearity of the position relation among reference nodes in a small partition or a neighborhood is avoided. In addition, the hop count and distance data are centralized in the calculation and operation processes, so that the problem of conversion of the dimension of the hop count and the distance is solved. In the aspect of selecting the regularization parameters, the MLSRM method provided by the invention adopts an empirical optimal value, so that an unnecessary optimization process is avoided. Experiments on different deployments and node distribution further verify that the method provided by the invention is superior to a classical multi-hop non-ranging positioning method.
Drawings
FIG. 1 is a schematic illustration of an anisotropic network.
Fig. 2 is a flow chart of the wireless multi-hop non-ranging positioning method based on structure risk minimization according to the present invention.
Fig. 3 is a schematic diagram of four node distribution cases, in which (a) there is no-occlusion deployment and nodes are randomly distributed, (b) there is no-occlusion deployment and nodes are regularly distributed, (c) there is occlusion deployment and nodes are randomly distributed, and (d) there is occlusion deployment and nodes are regularly distributed.
FIG. 4 is a C-shaped region, regularly distributed four algorithm error profiles, wherein (a) the DV-hop error profile, (b) the Amorphous error profile, (C) the PDM error profile, and (d) the MLSRM error profile.
FIG. 5 is a schematic diagram of positioning results of four algorithms of C-shaped deployment and regular distribution.
FIG. 6 is a diagram of four algorithm error distribution diagrams under a regular distribution in a line-of-sight environment.
FIG. 7 is a schematic diagram of four algorithm positioning results in a line-of-sight environment and in a regular distribution.
FIG. 8 is a diagram of four algorithm error distribution diagrams under random distribution in a line-of-sight environment.
FIG. 9 is a schematic diagram of the positioning results of four algorithms of C-shaped deployment and random distribution.
FIG. 10 is a graph of four algorithm error distributions in a random distribution in a line-of-sight environment.
FIG. 11 is a diagram illustrating the positioning results of four algorithms randomly distributed in a line-of-sight environment.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Examples
The positioning parameters of the embodiments are described below without loss of generality assuming that there are n wireless network nodes in a two-dimensional plane
Figure BDA0001185645230000051
Wherein, the first m, m < n, and reference nodes equipped with GPS/BDS or manually set positions in advance. In the initial stage, the method adopts Dijkstra algorithm or Floyd algorithm to obtain the shortest hop count vector between nodes, adopts H to represent the shortest hop count vector between reference nodes, and the corresponding shortest hop count matrix is H; the physical distance matrix between the corresponding reference nodes is D. Let the shortest hop count vector from the ith reference node to other reference nodes in the area be: h isi＝[hi,1,…,hi,m]T(ii) a The corresponding physical distance between reference nodes is expressed as: di＝[di,1,…,di,m]T. The shortest hop count from the ith unknown node to the reference node is expressed as:
Figure BDA0001185645230000061
corresponding matrix is
Figure BDA0001185645230000062
In artificial intelligence, machine learning based positioning mechanisms, the positioning process is generally divided into two phases [7,11,12], namely: an offset phase and a localization phase. In the training stage, a hop-to-distance mapping model is trained by learning the measured distance (hop count) and the physical distance between known nodes; in the positioning stage, the unknown node estimates the distance from the unknown node to the reference node by the hop count from the unknown node to the reference node and by using the mapping model obtained in the training stage.
The multi-hop non-ranging node positioning method based on the structure risk minimization of the embodiment repartitions the positioning process, as shown in fig. 2, the method is divided into: the method comprises an initialization stage, a hop count-distance optimal mapping model building stage and a position estimation stage.
The first stage is as follows: an initialization stage: by using the DV-hop method, a distance vector routing exchange protocol is used, and after nodes communicate for a period of time, all nodes in the network obtain the shortest hop count between the nodes and a reference node. The specific process is as follows: in the monitoring area, the reference node sends a broadcast information packet with self position information to other nodes in the communication radius, the packet at least comprises a reference node representation field ID, coordinate position information (X and Y) and a Hop count field (Hop _ counts, the initialization value is 1), and the packet format is as follows:
ID X Y Hop_counts
after each node in the monitoring area receives the grouping information, the node records the minimum Hop count of the connected reference node, and adds 1 to the Hop count field value Hop _ counts in the grouping, but when the node receives the information from the same reference node, the program automatically ignores the grouping when the Hop count field value is not the minimum value. Using the above method, eventually all nodes within the whole monitored area record the minimum number of hops to the reference node to which they are connected.
The distance between the reference nodes is obtained by adopting a physical distance formula according to the self coordinates, namely:
Figure BDA0001185645230000063
wherein d isijDenotes the Euclidean distance from the ith node to the jth node, (x)i,yi)、(xj,yj) Is the coordinate of the reference node i, j
And a second stage: and constructing a hop count-distance optimal mapping model. After the shortest hop count and the physical distance between the reference nodes are obtained, since a mapping relationship exists between the shortest hop count and the actual distance between the reference nodes, the relationship between the hop count and the actual distance is expressed as follows: d is HT + V, where D is the physical distance between reference nodes, H is the shortest hop count matrix between reference nodes, V is the error matrix, and T is the mapping relationship between the smallest hop count and the actual distance. The per-column vector of T can be obtained by minimizing the mean square error of the error, i.e.:
Figure BDA0001185645230000071
easy to obtain, column vector tiLeast squares solution of (c):
ti＝(HTH)-1HTdi(6)
the Risk functional is usually minimized by equation (5) as a loss function, and such a Minimization function is also referred to as Empirical Risk Minimization (ERM). Then, the empirical risk minimization for the hop count-distance optimal linear transformation is expressed as:
Figure BDA0001185645230000072
the hop count-distance mapping model is constructed by adopting experience risk minimization, and the problem that the number of reference nodes is seriously depended exists. The problem of overfitting is easily caused when the number of nodes is too large, the problem of under-fitting is easily caused when the number of nodes is too small, and in short, the problem of weak generalization capability exists when the mapping model is constructed by adopting empirical risk minimization. In order to improve the popularization capability of the hop count-distance model, the embodiment starts from the VC dimension concept based on the statistical learning theory, and adopts the Structure Risk Minimization (SRM) principle to construct the hop count-distance mapping model. And a mapping model with minimized structural risk is adopted, and the actual risk of the mapping model consists of two parts, namely an empirical risk and a confidence range, which are related to the VC dimension of the learning machine and the training sample number of the VC dimension. Under the condition of limited reference node number, the experience risk is minimized, the confidence range is narrowed, so that the smaller actual risk can be obtained, and the better popularization of the prediction of the distance between the unknown node and the reference node is kept. Therefore, a structural risk minimization principle is further adopted in the neighborhood to obtain a relation coefficient between the hop count and the distance, namely:
Figure BDA0001185645230000073
wherein R isemp(ti) For empirical risk, φ (h/n) is the confidence range, h is the VC dimension, and n is the number of samples. In connection with equation (7), it can be seen that equation (8) and equation (6) differ in that the confidence range φ (h/n) constrains the empirical risk of equation (7) so that it is non-zero, thereby avoiding the problem of correlation of positional relationships among reference nodes in a smaller partition or neighborhood.
Let, choose a penalty term with a contraction variable for the confidence range in the minimization of structural risk, namely:
φ(h/n)＝γ||β||2,0≤γ≤1 (9)
where γ is a proportionality parameter for both risks, equation (8) becomes:
Figure BDA0001185645230000081
it is easy to know that equation (10) is a conditional extremum problem, which can be solved by converting it into an unconditional extremum problem with the lagrange equation:
Figure BDA0001185645230000082
wherein α ═ α1,α2,…,αn]；αi∈Rn(i ═ 1,2, …, n) represents the lagrange multiplier.
By calculating the gradient of equation (11) to be 0, the hop count-distance relationship between reference nodes can be obtained:
Figure BDA0001185645230000083
the matrix form of equation (12) is:
Figure BDA0001185645230000084
at this time, it can be seen that the matrix
Figure BDA0001185645230000085
Element ti injIndicating the effect of the number of hops from the jth reference node on the physical distance from the ith reference node.
Figure BDA0001185645230000086
Middle main diagonal element tiiIt is considered to be a scaling factor that converts the number of hops to distance. The physical distance of an unknown node from a reference node can thus be defined as the weighted sum of the hop counts to all reference nodes. This is because
Figure BDA0001185645230000087
In which distance characteristics to all reference nodes in all directions are stored, so
Figure BDA0001185645230000088
The anisotropic relationship between the node adjacency distance and the physical distance can be accurately described. Whereas I γ facilitates scaling without many reference nodes
Figure BDA0001185645230000089
The generalization ability of the method enables the hop count-distance relationship to be accurate not only near the reference node but also far away from the reference node
Figure BDA0001185645230000091
The mapping accuracy of (2) is still maintained.
When an unknown node t in the monitoring area obtains the hop count vector h thereoftAfter, pass type(14) The physical distances to the respective reference nodes are obtained, and equation (14) is specifically expressed as follows:
f(ht)＝(Iγ+HTH)-1HTDht(14)
the hop count and the distance have different dimension levels, and the hop count matrix H and the distance matrix D are subjected to centralized operation in the operation process by considering dimension difference in the conversion process of the hop count-distance relation to obtain corresponding matrices
Figure BDA0001185645230000092
And
Figure BDA0001185645230000093
therefore, the prediction equation (14) of the distance becomes:
Figure BDA0001185645230000094
in the formula (I), the compound is shown in the specification,
Figure BDA0001185645230000095
is htThe vector after the centralization processing is carried out,
Figure BDA0001185645230000096
is the column average of H and,
Figure BDA0001185645230000097
is composed of
Figure BDA0001185645230000098
Of n rows.
And a third stage: and a position estimation stage. In a monitoring area, an unknown node t is connected with more than k (k is more than or equal to 3) reference node signals, and a coordinate-distance relation equation exists between the reference node and the unknown node, namely:
Figure BDA0001185645230000099
wherein (x, y) is the coordinate of the unknown node, (x)1,y1),(x2,y2),…,(xk,yk) Are reference node coordinates. If the 1 st to k-1 st equations are subtracted from the k-th equation, respectively, it can be obtained:
Figure BDA00011856452300000910
order to
Figure BDA0001185645230000101
Figure BDA0001185645230000102
Figure BDA0001185645230000103
The equation set of equation (18) can be converted to the form Ax ═ b. Due to the presence of measurement errors, the system of equations behaves correctly in the form: ax ═ b +. To obtain an optimal solution for the unknown node position, the sum of the squares of the errors is used as a criterion, i.e.:
Figure BDA0001185645230000104
the gradient of equation (19) is found to be 0, resulting in:
Figure BDA0001185645230000105
if the references are not on a straight line, the square matrix ATWhen A is reversible, the estimated coordinates of the unknown nodes are easily obtained:
Figure BDA0001185645230000106
the MLSRM method transmits the coordinate of the reference node and the hop count information by a flooding method, so that the broadcasting cost of O (m) is required; the adoption of the structure risk minimization method to construct the hop count-distance mapping relation needs O (m)3) Calculating the cost; each unknown node can estimate the distance from each unknown node to the reference node by using the hop count-distance mapping relation, so that the distributed estimation process can be calculated; therefore, the time complexity of the MLSRM method can only consider the broadcast cost and the calculation cost of the mapping model construction, i.e. O (m) + O (m)3)。
Performance evaluation
The multi-hop non-ranging positioning method is very suitable for application in a large-scale scene, and the large-scale application has the characteristics of numerous wireless nodes. Therefore, verifying that positioning applications in large-scale scenarios may require thousands of wireless nodes to be impractical under current experimental conditions and under insufficient expenditure; in addition, the performance evaluation of the positioning algorithm needs to be verified in different scenarios, and sometimes parameters related to the algorithm need to be adjusted in the same scenario, which results in huge workload. For these reasons, in large-scale wireless network positioning research, simulation software MATLAB is usually adopted to verify the performance of the wireless network positioning algorithm.
The experiment was also compared with the same type of Amorphous, PDM algorithm. For the sake of fairness, the PDM method sets a discard characteristic value threshold for the TSVD, and sets a corresponding characteristic vector with the discard characteristic value less than or equal to 3; the performance of the MLSRM method is also related to the scaling parameter γ, which can be obtained by cross-checking or L-curve methods, but which is computationally expensive considering that in general | | | aTA | < 0.01 is an ill-defined matrix, and thus γ is experimentally set to 0.01.
Experimental scene setting and parameter setting
The multi-hop non-ranging positioning performance evaluation experiment based on the structure risk minimization sets two deployments and two distributions, and four experiment scenes are total. Two deployments are: the non-occluded deployment is (a) and (b) in fig. 3 and the occluded deployment is (C) and (d) in fig. 3, wherein the occluded deployment is due to the presence of a large obstacle so that the distribution area takes a C-shape. Non-line-of-sight propagation can result when there are large obstacles in the deployment area. The two distributions are: regular distribution and random distribution. The size of all four scenes is 1000m × 1000m, and 500 nodes exist in randomly distributed scenes as shown in the graph (2a, 2 c); 441 nodes are deployed in a regularly distributed and sight distance spread scene, and the distance between the nodes is 50 m; 285 nodes are deployed in a regularly distributed and non-line-of-sight spread scene, and the distance between the nodes is 40 m.
In order to reduce the problem that the result of a single experiment cannot represent the general performance of the algorithm, the experiment is arranged in the same scene, the experiment is repeated for multiple times, and the result value is finally obtained for 50 times. In the experiment, the accuracy of the final positioning result of the unknown node is inspected by increasing the number of reference nodes, and the effective communication radius of the node is assumed to be 100m in the experiment. The experiments were divided into two groups according to the distribution, namely: random distribution and regular distribution.
Regular distribution
In this set of experiments, node deployment is divided into two categories: (1) deploying inter-regional node line-of-sight communication; (2) the presence of obstacles between nodes in the deployment area results in non-line-of-sight communications.
Fig. 4 is a diagram showing an error range of multiple positioning in a non-occlusion regular distribution, and an error diagram of multiple operations in multiple operations and different reference node environments by the algorithm proposed in the embodiment and four classical non-ranging multi-hop positioning methods. To compare the advantages of the methods mentioned in the examples, the examples are described using a box plot function (boxplot) in MATLAB, which can show the error range of the algorithm run multiple times, and the magnitude of the error concentration, thus showing the stability of the algorithm from the side. The abscissa of the error map shows the number of reference nodes and the ordinate shows the RMS error, which is expressed in detail as follows:
Figure BDA0001185645230000121
wherein n is the number of unknown nodes in the region, (x)i,yi) For the real coordinates of the unknown node,
Figure BDA0001185645230000122
coordinates are estimated for the unknown nodes.
From fig. 4, it is easy to find that the two methods DV-hop and Amorphous are affected by network topology anisotropy, not only the positioning accuracy is low, but also the problems of collinearity among reference nodes, the directionality of the position and the like cannot be considered in the positioning calculation process, so that the position estimation result is very unstable. The PDM and the MLSRM method mentioned in the embodiment directly adopt a hop count-distance mapping relation to construct a conversion model, the directionality of the position is considered, and meanwhile, a regularization method is adopted in the calculation process, so that the collinear problem is avoided. The method provided by the embodiment optimizes the selection of risk structure parameters on the basis of previous research, and eliminates the dimension problem in the hop count-distance mapping by adopting a centralization method, so that the deployment area presents an anisotropic network, and the algorithm provided by the embodiment is one of four multi-hop non-ranging methods with the optimal performance.
Fig. 5 shows the estimation results of four non-ranging multi-hop positioning methods with reference node number of 35 and a certain operation in a C-shaped deployment area. Wherein the circle represents an unknown node, the square represents a reference node, and the straight line connects the real coordinate of the unknown node and its estimated coordinate, the longer the straight line, the larger the positioning error. The RMS value of DV-hop is; the RMS value of Amorphous is; the RMS value of PDM is;
fig. 5a shows the node distribution plot for this experiment. The positioning result of the DV-hop method shown in fig. 5b under the deployment condition easily finds that the network topology structure exhibits various dissimilarities due to occlusion, and further distorts the hop count during the distance conversion, which causes a particularly large estimation error of an unknown node at the C-shaped port of the DV-hop method. The Amorphous algorithm (figure 5c) developed on the basis of the DV-hop method also has the problem of abnormal matching when the hop count is converted into the distance in an anisotropic environment. Fig. 5d shows the positioning result of the PDM method. The PDM method performs optimal conversion on the hop count-distance relation by using a regularization method under the guidance of a least square method, the method considers the problem of node directivity in the conversion, and generalizes a hop count-distance relation model by using the regularization method, but dimension conversion problems and optimization rejection characteristic value threshold are caused by the fact that operation parameters cannot be centralized in the PDM operation process. Fig. 5e is a positioning result of the algorithm MLSRM provided in the embodiment, in which the algorithm considers the problem of dimension conversion of the hop count-distance relationship model, and the operation result is obviously superior to the first 4 classical algorithms by referring to the previous parameter selection.
Fig. 6 is a diagram showing error ranges of multiple deployments and different reference node numbers under the condition that nodes are regularly distributed in a line-of-sight environment. The problem of deployment anisotropy does not exist in a line-of-sight propagation environment, but the positioning results of the DV-hop algorithm and the Amorphous algorithm are still unstable, and the positioning error sometimes becomes larger when the number of reference nodes is large. This is because the degree of co-linearity between reference nodes is more severe than for a random deployment when the nodes are regularly distributed. The PDM method and the MLSRM method provided by the embodiment make full use of the reference nodes in the deployment area, and a regularization method is adopted to avoid the problem of collinearity among the reference nodes. The MLSRM method has stable positioning performance and is superior to the PDM method.
Fig. 7 shows a certain operation result of 4 positioning methods regularly distributed in a line-of-sight scene when the number of reference nodes is 45 in a line-of-sight environment. FIG. 6b shows the DV-hop localization result with RMS error of 31.1906; FIG. 6c is a graph of the alignment results of the Amorphous method with an RMS error of 33.2699; FIG. 6d is a graph of the positioning results of the PDM method with an RMS error of 20.0773; FIG. 6e is a diagram of the positioning result of the proposed MLSRM, whose RMS error is 17.7796. Due to the co-linearity problem, the DV-hop and Amorphous methods have significantly lower localization performance than in a random deployment environment. The PDM method and the MLSRM method can still maintain excellent performance due to the adoption of the regularization method.
Random distribution
The most common node in the real environment is randomly distributed, and fig. 8 shows that in an area of 1000m × 1000m, in an occlusion environment, the nodes randomly deploy multiple positioning results of four multi-hop non-ranging positioning methods.
It is easy to find that the PDM method and the MLSRM method proposed in the examples still have higher positioning accuracy than the DV-hop and Amorphous methods. Although the Amorphous method is theoretically more accurate in distance estimation than the DV-hop method, in practical experiments it was found that the Amorphous method is more sensitive to anisotropy, and therefore its localization performance in anisotropic networks is significantly weaker than the DV-hop method. In addition, the Amorphous method does not consider the collinear problem among the nodes compared with the DV-hop method, so that the positioning precision of the DV-hop and Amorphous algorithms is not reduced along with the increase of the nodes, even the positioning precision is reduced under the condition of more nodes, for example, when the number of reference nodes is 40, the positioning precision range of the two algorithms is almost not much different from the number of reference nodes of 20, and the precision median is very close. The MLSRM method is considered to be more comprehensive than the PDM method in the calculation process, so the positioning performance is obviously higher than that of the PDM method.
Fig. 9 shows the result of one run of the four-pass algorithm with a C-shaped random deployment and a 35 number of reference nodes. In the anisotropic network, the unknown node at the C-shaped port has an abnormally large mismatching degree due to hop count-distance, so that the estimation error of the DV-hop method at the unknown node at the C-shaped port is also the largest. The Amorphous positioning method is an improved method of the DV-hop method, but the connectivity of adjacent areas is required to be known in advance, the connectivity is easy to predict in uniform and regular areas, and the prediction is more error in an anisotropic network, so that the position estimation of the Amorphous positioning in the anisotropic network is very poor. The PDM method and the MLSRM method both adopt a hop number matrix and a distance matrix of reference nodes to construct a mapping model, and estimate respective directivities of all the reference nodes in a deployment area, so that positioning results of the PDM method and the MLSRM method are obviously superior to those of the DV-hop and Amorphous methods. The RMS value of the DV-hop method in the figure is; the RMS value of the Amorphous method is; the PDM method and MLSRM method values are:
since there is no problem of anisotropy in the line-of-sight region, this set of experiments mainly verifies whether the MLSRM method proposed in the example can still achieve higher performance.
Fig. 10 shows an estimation error range diagram of multiple redeployments of four methods, and in a multiple deployment test, the influence of the number of reference nodes on a final positioning result is also evaluated by setting different numbers of reference nodes. Compared with an anisotropic network environment, the positioning performance of the DV-hop and Amorphous algorithms in a line-of-sight propagation environment is obviously improved as can be easily seen from the graph, and the Amorphous method gives full play to the advantage of distance estimation, so that the positioning performance is obviously superior to that of the DV-hop. However, the relative positions of the reference nodes are not considered by the DV-hop algorithm and the Amorphous algorithm, so that the positioning performance is not obviously improved along with the increase of the number of the reference nodes. From the figure, it can be seen that the positioning performance of PDM and the MLSRM method proposed in the example is stable and superior to both DV-hop and Amorphous, but the advantage of PDM is relatively weak.
Fig. 11 is a positioning result of nodes randomly deploying four methods in a line-of-sight environment, where the number of reference nodes in fig. 11 is 45. FIG. 11b shows the DV-hop localization result with RMS error of 26.6835; FIG. 11c shows the results of the Amorphosus method with an RMS error of 19.8791; FIG. 11d shows the positioning result of the PDM method, which has an RMS error of 14.4452; FIG. 11e shows the positioning result of the MLSRM proposed in the example, whose RMS error is 12.3378. As is clear from the figure, the MLSRM method proposed in the examples has the best positioning performance, and the PDM method is inferior, and the Amorphous positioning performance is lower than that of the MLSRM and PDM methods but better than that of the DV-hop method.

Claims (4)

1. A wireless multi-hop non-ranging positioning method based on structure risk minimization is characterized in that: comprises an initialization stage, a hop count-distance optimal mapping model building stage and a position estimation stage,
in the initialization stage, a distance vector routing exchange protocol is used, and after nodes communicate for a period of time, all nodes in a network obtain the shortest hop count and the physical distance between the nodes and a reference node;
adopting a structure risk minimization principle to construct a hop count-distance optimal mapping model, and obtaining a distance prediction formula after obtaining the shortest hop count and the physical distance between reference nodes:
Figure FDA0002312203070000011
wherein I is a unit diagonal matrix, gamma is a proportional parameter of two risks of an empirical risk and a confidence range,
Figure FDA0002312203070000012
is htThe vector after the centralization processing is carried out,
Figure FDA0002312203070000013
is the column mean value of H, and the hop count matrix H and the distance matrix D are subjected to centralized operation in the operation process to obtain corresponding matrices
Figure FDA0002312203070000014
And
Figure FDA0002312203070000015
Figure FDA0002312203070000016
is composed of
Figure FDA0002312203070000017
A stack of n rows of (a);
in the position estimation stage, the hop count from an unknown node to a reference node is utilized to obtain a corresponding physical distance under the guidance of a mapping model; and finally, obtaining the estimated position of the unknown node by a trilateration method.
2. The wireless multi-hop non-ranging positioning method based on structure risk minimization as claimed in claim 1 wherein: in the initialization stage, all nodes in the network obtain the shortest hop count with the reference node, and the specific process is as follows: in the monitoring area, the reference node sends a broadcast information packet with self position information to other nodes in the communication radius, after each node in the monitoring area receives the packet information, the node records the minimum Hop count of the connected reference node, and simultaneously adds 1 to the Hop count field Hop _ counts value in the packet, but when the node receives the packet from the same reference node and the Hop count field value is not the minimum value, the program automatically ignores the packet.
3. The wireless multi-hop non-ranging positioning method based on structure risk minimization according to claim 1 or 2, characterized in that: the broadcast information packet at least comprises a reference node representation field ID, coordinate position information and Hop count field Hop _ counts, wherein the coordinate position information comprises X and Y, and the packet format is as follows:
ID X Y Hop_counts
。
4. the wireless multi-hop non-ranging positioning method based on structure risk minimization according to claim 1 or 2, characterized in that: in the position estimation stage, in a monitoring area, an unknown node t is connected with more than k reference node signals, k is more than or equal to 3, and a coordinate-distance relation equation exists between the reference node and the unknown node, namely:
Figure FDA0002312203070000021
wherein (x, y) is the coordinate of the unknown node, (x)1,y1),(x2,y2),…,(xk,yk) If the 1 st to k-1 st equations are subtracted from the kth equation, respectively, to obtain the reference node coordinates:
Figure FDA0002312203070000022
order to
Figure FDA0002312203070000023
Figure FDA0002312203070000024
Figure FDA0002312203070000025
The equation set of equation (18) is converted into the form Ax ═ b, and due to the presence of measurement errors, the equation set behaves correctly in the form: ax ═ b +. To obtain an optimal solution for the unknown node position, the sum of the squares of the errors is used as a criterion, i.e.:
Figure FDA0002312203070000026
the gradient of equation (19) is found to be 0, resulting in:
Figure FDA0002312203070000027
if the references are not on a straight line, the square matrix ATWhen A is reversible, the estimated coordinates of the unknown nodes are easily obtained:
Figure FDA0002312203070000031
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