CN113286257B - Novel distributed non-ranging positioning method - Google Patents

Novel distributed non-ranging positioning method Download PDF

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CN113286257B
CN113286257B CN202110553237.2A CN202110553237A CN113286257B CN 113286257 B CN113286257 B CN 113286257B CN 202110553237 A CN202110553237 A CN 202110553237A CN 113286257 B CN113286257 B CN 113286257B
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CN113286257A (en
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严筱永
周剑
王帅
叶晶
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Nanjing University of Posts and Telecommunications
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    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
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Abstract

The invention provides a novel distributed non-ranging positioning method, which is characterized in that distance estimation between adjacent nodes is finished according to the number of potential neighbor relay nodes, and then the estimated distance between multi-hop nodes is obtained in an accumulation mode; then, detecting the distance estimation residual between anchor nodes, and deducing the threshold value of the maximum hop range of the network; secondly, positioning unknown nodes with enough anchor nodes within the maximum hop range; judging whether the obtained estimated position is abnormal or not according to the relation between the distance from the estimated position to the anchor node and the corresponding estimated distance, and if the obtained estimated position is abnormal, correcting by adopting a weighted Bounding-Box algorithm; and finally, upgrading the positioning node to a new anchor node, and still judging and correcting by using the maximum hop count and the abnormity to assist the unfinished positioning node to position until all the nodes realize positioning. The invention has low requirement on equipment, low energy consumption and high position estimation precision.

Description

Novel distributed non-ranging positioning method
Technical Field
The invention relates to the technical field of computer network application, in particular to a novel distributed non-ranging positioning method.
Background
Wireless location technology is not only one of the key technologies of wireless networks, but also provides support for other wireless applications, such as routing, topology control, and the like. Wireless data without location information is often meaningless. Non-ranging positioning is a positioning method for indirectly acquiring the distance between nodes by adopting information such as hop count between nodes, area density or neighbor node count and the like. The non-ranging multi-hop positioning has the advantages of low requirement on equipment and high cost performance, and therefore is widely concerned.
Most of the conventional non-ranging positioning methods collect positioning information among anchor nodes in the whole network, estimate a distance estimation model, push the distance estimation model to each unknown node, and finally realize position estimation with the help of a multilateration method. The frequent collection of the positioning information and the pushing of the distance estimation model cause the communication congestion among the nodes of the whole network, and more seriously, a large amount of energy of the nodes is consumed, so that the network nodes can not work normally due to the rapid loss of energy.
The literature [ Simic S N, science S.distributed localization in wireless ad hoc networks [ R ]. Technical Report UCB/ERL,2002,2: by derivation, the unknown node should be located in the overlapped cells of the communication areas of all the anchor nodes, but the method is only suitable for one-hop positioning, only the anchor nodes adjacent to the unknown node are used, and the center of the overlapped area is used as the estimated position of the unknown node. Therefore, the Bounding-Box algorithm is often unable to be applied to a multi-hop network, and the problem of influence of the distance from the anchor node to the unknown node is also ignored.
Disclosure of Invention
In order to solve the technical problems, the invention provides a novel distributed non-ranging positioning method, which not only inherits the advantages of the conventional non-ranging positioning method, but also has the advantages of low energy consumption, high communication efficiency and high positioning precision, and is very suitable for node positioning in a complex environment.
The novel distributed non-ranging positioning method comprises the following steps:
step 1, when a network is initialized, when information is transmitted along a transmission path, a node on the path completes the distance between every two nodes in the network in a distributed mode according to the number of potential neighbor relay nodes through a Muller method, and then the distance between any node pair is obtained in an accumulation mode;
step 2, obtaining a distance estimation residual error by subtracting the estimation distance between the anchor nodes obtained in the step 1 from the corresponding real distance, detecting the residual error between the anchor nodes hop by adopting a Modified Thompson Tau detection method, and determining the maximum hop range in the network;
step 3, under the limitation of the maximum hop range obtained in the step 2, performing position estimation on an unknown node with enough anchor nodes by adopting a multilateral ranging method, judging the relation between the distance from the estimated position to the anchor nodes and the corresponding estimated distance, judging whether the distance is greater than the distance of the anchor nodes, if so, performing abnormal estimation, and correcting the abnormal estimated position by adopting a weighted Bounding-Box;
and 4, upgrading the positioning node to a new anchor node, combining the maximum hop range obtained in the step 2, repeating the step 3, and assisting the unfinished positioning node to iteratively finish positioning until all the nodes in the network realize positioning.
Further, when the network is initialized, when information is transmitted along a transmission path, nodes on the path rapidly complete the distance between every two nodes in the network in a distributed manner with the help of a Muller method according to the number of potential neighbor relay nodes, and then obtain the distance between any pair of nodes in an accumulation manner, wherein the process can be divided into the following steps:
step 1-1, initializing a network, connecting nodes into a network, and acquiring a shortest path among multi-hop nodes by adopting a Dijkstra or Floyd algorithm;
step 1-2, in the step 1-1, while executing Dijkstra or Floyd algorithm, the nodes in the network can naturally know the number of the directly interconnected neighbor nodes, in the information propagation direction, the potential relay node distribution range of any node occupies 1/3 of the communication range of any node, if the number of the neighbor nodes of any node is k, k/3-1 nodes in the k neighbor nodes of any node are potential relay nodes, wherein 1 in k/3-1 represents the any node;
1-3, obtaining the expected advancing distance of every two adjacent nodes on an information transmission path in a distributed mode; starting from a starting node, calculating the distance between two adjacent nodes on an information transmission path in a distributed manner hop by hop, wherein k/3-1 edges exist between any node and k/3-1 potential relay nodes on the information transmission path, each potential relay node edge has an arch region, and the ratio of the coverage area of the arch region to the coverage area of the node is assumed to be X i I =1, \ 8230;, k/3-1, and the shortest path is obtained by Dijkstra or Floyd algorithm, so that the most likely relay node should be the one of the potential relay nodes farthest from the information sending node, and the ratio of the arch area adjacent to the corresponding relay node to the whole coverage area is the smallest; suppose X i In accordance with a uniform distribution, i.e. X i U (0, 0.5), that is, when the relay node approaches the information sending node indefinitely, X i The trend was 0.5; when a relay node approaches an edge of coverage where information is sent out indefinitely, X i And tends to be 0, thereby obtaining a cumulative distribution function,
Figure GDA0003877977930000031
then obtain the corresponding probability density function f X (x)，
Figure GDA0003877977930000032
The desired value of the ratio of the area of the arch to the area of the total coverage area is thus obtained,
Figure GDA0003877977930000033
the arcuate area corresponding to the expected distance of travel of the information emitting node is,
Figure GDA0003877977930000034
wherein R is the node communication radius, pi R 2 Is the coverage area of the communication of the node,
the arcuate area corresponding to the desired advance distance is obtained, and thus a function including the desired advance distance is obtained, i.e.
Figure GDA0003877977930000035
Where a is the desired relay node, o is the information sending node, d o→a Is the desired advance distance;
the function containing the desired advance distance is a non-linear function, and a solution equation is first constructed,
Figure GDA0003877977930000036
then, a quick convergence Muller method is adopted for iteration to solve, the solution formula is as follows,
Figure GDA0003877977930000041
where, κ is the number of iterations,
Figure GDA0003877977930000042
in addition, selection
Figure GDA0003877977930000043
And
Figure GDA0003877977930000044
as 3 initial values for Muller method iteration;
step 1-4: calculating the estimated distance between the multi-hop nodes; respectively calculating the estimated distance between two adjacent nodes from the starting node to the target node along the information propagation path, and then obtaining the estimated distance from the starting node to the target node in an accumulation way, namely
Figure GDA0003877977930000045
Where S is the start node, D is the destination node, and p points to a node on the S to D path.
Further, in step 2, the estimated distance between the anchor nodes obtained in step 1 is subtracted from the corresponding real distance to obtain a distance estimated residual, a Modified Thompson Tau detection method is used to detect the residual between the anchor nodes hop by hop, and the maximum hop count range in the network is determined, which includes the following steps:
step 2-1: sequentially collecting estimated residual errors among anchor nodes according to hop counts; obtaining and recording the estimated distance between the anchor nodes in the steps 1-4, calculating the real distance between every two anchor nodes according to the coordinates between the anchor nodes, subtracting the corresponding real distance from the estimated distance between the anchor nodes to obtain the residual errors between the corresponding anchor nodes, and sorting, clustering and recording the residual errors according to the hop count between the nodes;
step 2-2: detecting residual errors hop by hop and obtaining the maximum hop range of the network; testing the residual error between anchor nodes clustered according to the hop number by using Modified Thompson Tau hop by hop from the 2 nd hop; suppose that there are l residuals r in the h-th hop h，i I =1, \ 8230;, l, taking this residueMedian of difference med h That is to say that,
Figure GDA0003877977930000046
in the h-hop, in med h For the centre, the absolute deviation of each residual is recorded, i.e.
δ h，i ＝|r h，i -med h |，i＝1，…，l
Wherein r is h，i Represents the ith residual in the h-th hop,
while the offset of the h-th hop corrects for the quarter-bit distance, i.e.
Figure GDA0003877977930000051
Wherein the content of the first and second substances,
Figure GDA0003877977930000052
and
Figure GDA0003877977930000053
respectively representing the 75% quantile and the 25% quantile of the h-th jump residual,
at this time, when delta h，i ≥τIQR h When is, r corresponds to h，i And if the value is an abnormal value, an improper estimation distance appears in the h hop, the h-1 hop is the maximum hop count range threshold value of the network, otherwise, the detection process is repeatedly executed for the next hop until the maximum hop count between the anchor nodes is reached.
Further, in step 3, under the limitation of the maximum hop count range obtained in step 2, performing position estimation on an unknown node having enough anchor nodes by using a multilateral ranging method, determining a relationship between a distance from an estimated position to an anchor node and a corresponding estimated distance, determining whether the former is greater than the latter, if so, performing abnormal estimation, and correcting the abnormal estimated position by using a weighted Bounding-Box, which includes the steps of:
step 3-1: after the steps 1 and 2 are carried out, an unknown node in the network can be connected with enough anchor nodes (the number of two-dimensional plane anchor nodes is more than or equal to 3, and the number of three-dimensional space anchor nodes is more than or equal to 4) within the maximum hop number range, and the node initially carries out position estimation by adopting a multilateral measurement method;
step 3-2: step 3-1, after obtaining the preliminary estimated position, respectively calculating the real distance from the position to the neighbor anchor node within the maximum hop number range, then comparing the real distance with the corresponding estimated distance obtained in step 1, and if the former is smaller than the latter, outputting the estimated position as the final estimated position; otherwise, the estimated position is an abnormal estimated position;
step 3-3: correcting the abnormal estimated position by adopting a weighted Bounding-Box algorithm; after finding that the estimated position is not a usable result through the step 3-2, correcting the position by adopting a weighted Bounding-Box algorithm, wherein the corrected position is,
Figure GDA0003877977930000054
wherein the content of the first and second substances,
Figure GDA0003877977930000055
corrected position for unknown node, (x) v ，y v ) The coordinates of four corners of the rectangular area are obtained by adopting a common Bounding-Box algorithm, and omega (v) is a weighting function (x) v ，y v ) The following formula is adopted for the acquisition of (c),
Figure GDA0003877977930000061
Figure GDA0003877977930000062
Figure GDA0003877977930000063
Figure GDA0003877977930000064
Figure GDA0003877977930000065
wherein (x) i ，y i ) Is the coordinates of the anchor node within the k maximum hop count,
Figure GDA0003877977930000066
estimating the distance from the unknown node u to the anchor node obtained in the step 1;
the expression of ω (v) is,
Figure GDA0003877977930000067
wherein v is the four corners obtained by the ordinary Bounding-Box algorithm,
Figure GDA0003877977930000068
is the Chebyshev distance of k anchor nodes in the range from four corners to the maximum hop count, and the expression is as follows,
Figure GDA0003877977930000069
wherein abs (. Circle.) represents an absolute value.
Further, in step 4, the positioning node is upgraded to a new anchor node, and the positioning is completed by assisting the uncompleted positioning node in iteration according to the maximum hop range in step 2 and the checking and correcting process in step 3 until all nodes in the network are positioned, which comprises the following steps:
due to the limitation of the maximum hop range obtained in the step 2, after the step 3 is executed, the number of the anchor nodes around the unknown node may not meet the minimum requirement of the multilateral ranging method (namely, at least 3 anchor nodes on a two-dimensional plane and at least 4 anchor nodes in a three-dimensional space), so that part of the unknown nodes cannot be positioned, and after the unknown nodes with enough neighbor anchor nodes in the maximum hop range obtain estimated positions by adopting the step 3, the unknown nodes are immediately upgraded into new anchor nodes, the anchor nodes are combined to assist the unknown nodes which are not positioned, and the steps 2 and 3 are repeated until all the unknown nodes are gradually positioned, so that the unknown nodes of the whole network are positioned.
The invention has the beneficial effects that: the method provided by the invention estimates the distance between the nodes in a distributed manner while initializing the network, thereby avoiding excessive communication energy consumption; according to the invention, the maximum hop range of the whole network is obtained by utilizing a small amount of distance estimation residual errors among anchor nodes, so that unknown node positioning only relates to local information (nodes in the maximum hop range), and the influence of abnormal distance estimation on positioning is reduced; under the assistance of a weighted Bounding-Box algorithm, the abnormal estimation result caused in a complex environment is corrected, so that the method is suitable for the complex environment; the invention upgrades the positioned node as the new anchor node, the new anchor node cooperates with the anchor node to position the non-positioned node, and the local node is utilized to complete the node positioning step by step, thereby improving the communication efficiency.
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In order that the present invention may be more readily and clearly understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings.
FIG. 1 is a flow chart of a novel distributed non-ranging positioning method;
fig. 2 is a schematic diagram illustrating distance estimation between adjacent nodes according to the present invention, wherein (a) in fig. 2 is a distribution of potential relay nodes of an information sending node o, and (b) in fig. 2 is a corresponding arc area of the potential relay nodes;
FIG. 3 is a node distribution diagram for simulating a complex environment according to the present invention, wherein (a) in FIG. 3 is a C-shaped network and (b) in FIG. 3 is a Z-shaped network;
fig. 4 is a diagram illustrating the positioning effect of the present invention by using only step 1 to perform positioning, wherein (a) in fig. 4 is the positioning result of C-shaped network, and (b) in fig. 4 is the positioning result of Z-shaped network;
FIG. 5 is a residual graph of the distribution of nodes of FIG. 3 according to the present invention, wherein (a) in FIG. 5 is a C-shaped network residual test result and (b) in FIG. 5 is a Z-shaped network residual test result;
fig. 6 is a diagram illustrating a positioning effect after obtaining a maximum hop count range for the node distribution of fig. 3 according to the present invention, wherein (a) in fig. 6 is a diagram illustrating a positioning result of a C-shaped network, and (b) in fig. 6 is a diagram illustrating a positioning result of a Z-shaped network;
FIG. 7 is a diagram illustrating the positioning effect of the embodiment of the present invention after correcting the abnormal estimated position in FIG. 6, wherein (a) in FIG. 7 is a diagram illustrating the positioning result after C-network correction, and (b) in FIG. 7 is a diagram illustrating the positioning result after Z-network correction;
fig. 8 is a final positioning effect diagram of the present invention, in which (a) in fig. 8 is a final positioning result diagram of a C-shaped network, and (b) in fig. 8 is a final positioning result diagram of a Z-shaped network.
Detailed Description
As shown in fig. 1, the novel distributed non-ranging positioning method of the present invention includes the following steps:
step 1, when a network is initialized, when information is transmitted along a transmission path, a node on the path completes the distance between every two nodes in the network in a distributed mode according to the number of potential neighbor relay nodes through a Muller method, and then the distance between any node pair is obtained in an accumulation mode;
step 2, obtaining a distance estimation residual error by subtracting the estimation distance between the anchor nodes obtained in the step 1 from the corresponding real distance, detecting the residual error between the anchor nodes hop by adopting a Modified Thompson Tau detection method, and determining the maximum hop range in the network;
step 3, under the limitation of the maximum hop range obtained in the step 2, performing position estimation on an unknown node with enough anchor nodes by adopting a multilateral ranging method, judging the relation between the distance from the estimated position to the anchor nodes and the corresponding estimated distance, judging whether the distance is greater than the distance of the anchor nodes, if so, judging whether abnormal estimation occurs, and correcting the abnormal estimation position by adopting a weighted Bounding-Box;
and 4, upgrading the positioning node to a new anchor node, combining the maximum hop range obtained in the step 2, repeating the step 3, and assisting the unfinished positioning node to iteratively finish positioning until all the nodes in the network realize positioning.
The process of the step 1 comprises the following specific steps:
step 1-1, initializing a network, and connecting nodes into a network; considering that the energy carried by the nodes is limited, when the initial node of information transmission is far away from the destination node of information reception, the information exchange between the initial node and the destination node is carried out in a multi-hop mode; in the process of starting initialization of the network, in consideration of the efficiency of information propagation, algorithms such as Dijkstra, floyd and the like are adopted to obtain a path from an initial node to a destination node, wherein the path is the shortest path;
step 1-2, acquiring the number of potential information transfer relay nodes; neighbor nodes of nodes on the information transfer path can be obtained by adopting Dijkstra or Floyd algorithm. In the information propagation direction of any node, the potential relay nodes occupy 1/3 of the coverage area of the node; assuming that k nodes exist in the coverage range of any node, considering that the nodes are uniformly distributed in the local range, k/3-1 nodes are potential relay nodes, wherein 1 is the node per se;
1-3, obtaining the expected advancing distance of every two adjacent nodes on an information transmission path in a distributed mode; as shown in fig. 2 (wherein, (a) in fig. 2 is the distribution of potential relay nodes of the information issuing node o, and (b) in fig. 2 is the corresponding arc-shaped areas of the potential relay nodes, which are sorted according to size), the information issuing node o has k/3-1 potential relay points, i.e., (a) shaded portions in fig. 2, which correspond to k/3-1 arc-shaped areas, i.e., (b) in fig. 2; considering the arcuate area SA 1 ，…，SA (k/3-1) The area ratio of a communication coverage area C (o) with a node o is X i ，i＝1，…，(k/3-1)，X i A uniform distribution of 0 to 0.5 is met; considering that Dijkstra or Floyd, etc. obtains the shortest path between nodes, the finally selected relay node should be the one along the information propagation direction (o → D in fig. 2 (a)) and closest to the edge of C (o); correspondingly, the area ratio X of the arch area corresponding to the finally selected relay node to the coverage area i Should be the smallest one. Thus, the cumulative distribution function F can be obtained by the min distribution of the multidimensional random variable X (x)＝1-(1-2x) k/3-1 Then X i Is 3/2 (3 + k), then the desired area of the arcuate region adjacent to the finally selected relay node is 3 π R 2 /2 (3 + k). Combining an arch area formula to obtain:
Figure GDA0003877977930000091
with the help of the quick convergence root-finding method of Muller, the distance d between every two adjacent nodes on the information propagation path is quickly obtained o→i ；
Step 1-4, at the same time of network initialization, adopting step 1-3 to calculate two adjacent distances on the data transmission path, then accumulating the distances along the information transmission path, and finally obtaining the estimated distance between any two pairs of communicated nodes in the network, namely
Figure GDA0003877977930000092
Where S is the start node, D is the destination node, and p points to a node on the S to D path.
In the step 2, the estimated distance between the anchor nodes obtained by the method in the step 1 is subtracted from the corresponding real distance to obtain a distance estimated residual error, the Modified Thompson Tau is adopted to detect the residual error between the anchor nodes hop by hop, and the maximum hop count range in the network is determined; the process can be divided into the following steps:
step 2-1: after the estimated distance between the anchor nodes is obtained according to the steps 1-4, subtracting the real distance between the anchor nodes to obtain an estimated residual error between the anchor nodes;
step 2-2: clustering the obtained residual errors among the anchor nodes according to hop counts; then, starting from the second jump, the residual error of each jump is detected by using Modified Thompson Tau, and when delta is obtained h，i ≥τIQR h The ith residual r in the corresponding h hop h,i The value is an abnormal value, so that an improper estimation distance occurs in the h hop, and the h-1 hop is the maximum hop count range threshold value of the network; if there are l h jump residuals, the median of the jump residuals is med h ，δ h,i Is the absolute deviation value of the h-th hop, i.e. delta h，i ＝|r h，i -med h I =0, ·, l; and the offset of the jump corrects the quartileDistance IQR h Comprises the following steps:
Figure GDA0003877977930000093
wherein
Figure GDA0003877977930000094
And
Figure GDA0003877977930000095
respectively representing 75% quantiles and 25% quantiles of the jump residual;
in step 3, under the limitation of the maximum hop range obtained in step 2, position estimation is performed on an unknown node with enough anchor nodes by using a multilateral ranging method, and the relationship between the distance from the estimated position to the anchor node and the corresponding estimated distance is judged to determine whether the distance is greater than the distance, if the distance is greater than the distance, abnormal estimation occurs, and the abnormal estimation position is corrected by using a weighted Bounding-Box, which includes the following steps:
step 3-1: after the steps 1 and 2 are carried out, an unknown node in the network can be connected with enough anchor nodes (the number of two-dimensional plane anchor nodes is more than or equal to 3, and the number of three-dimensional space anchor nodes is more than or equal to 4) within the maximum hop number range, and the node initially carries out position estimation by adopting a multilateral measurement method;
step 3-2: step 3-1, after obtaining the preliminary estimated position, respectively calculating the real distance from the position to the neighbor anchor node within the maximum hop number range, then comparing the real distance with the corresponding estimated distance obtained in step 1, and if the former is smaller than the latter, outputting the estimated position as the final estimated position; otherwise, the estimated position is an abnormal estimated position;
step 3-3: and 3-2, immediately correcting by adopting a weighted Bounding-Box algorithm after finding that the estimated position is not a usable result, wherein the corrected position is,
Figure GDA0003877977930000101
wherein the content of the first and second substances,
Figure GDA0003877977930000102
for the corrected position of the unknown node, (x) v ,y v ) The coordinates of the four corners of the rectangular area are obtained by using the Bounding-Box algorithm, and ω (v) is a weighting function. (x) v ,y v ) The following formula is adopted for the acquisition of (c),
Figure GDA0003877977930000103
Figure GDA0003877977930000104
Figure GDA0003877977930000105
Figure GDA0003877977930000106
Figure GDA0003877977930000107
wherein (x) i ,y i ) Is the coordinates of the anchor node within the k maximum hop count,
Figure GDA0003877977930000108
and (4) adopting the unknown node u obtained in the step (1) to estimate the distance from the anchor node.
The expression of ω (v) is,
Figure GDA0003877977930000109
wherein v is the four corners obtained by the ordinary Bounding-Box algorithm,
Figure GDA00038779779300001010
is the tangent ratio of k anchor nodes in the range from four corners to maximum hop countThe length of the snowfall distance, expressed as,
Figure GDA0003877977930000111
wherein abs (. Circle.) represents an absolute value.
In step 4, the positioning node is upgraded to a new anchor node, and the incomplete positioning node is assisted to complete positioning iteratively according to the maximum hop range in step 2 and the checking and correcting process in step 3 until all nodes in the network are positioned, wherein the process is as follows:
due to the limitation of the maximum hop range obtained in the step 2, after the step 3 is executed, the number of the anchor nodes around the unknown node may not meet the minimum requirement of the multilateration ranging method (namely, at least 3 anchor nodes on a two-dimensional plane and at least 4 anchor nodes in a three-dimensional space), so that part of the unknown nodes cannot be positioned, and after the unknown nodes with enough neighbor anchor nodes in the maximum hop range are subjected to the estimation position obtained in the step 3, the unknown nodes are immediately upgraded into new anchor nodes, the unknown nodes which are not positioned are assisted by the anchor nodes, and the steps 2 and 3 are repeated until all the unknown nodes are gradually positioned, so that the unknown node positioning of the whole network is realized.
The invention randomly deploys network nodes in a network area, and divides the network nodes into unknown nodes and anchor nodes according to whether the positions of the network nodes are known or not, wherein the positions of the anchor nodes are known in advance, and the unknown nodes are nodes waiting for obtaining estimated positions.
In consideration of the present example, the network nodes are randomly deployed in a complex network environment, and due to obstacles or power loss of the nodes, the topology of the network appears irregular. The present invention employs an easily distinguishable C-shaped as in fig. 3 (a) and Z-shaped topology as in fig. 3 (b). In this scenario, there are 400 nodes, which contain 25 anchor nodes (e.g., squares in fig. 3), and the remaining 375 nodes are unknown nodes, i.e., solid circles in fig. 3 (a) and fig. 3 (b). All nodes have the same communication radius, the communication radius is 40, and if the distance between adjacent nodes is less than 40, direct paths, namely straight lines in fig. 3 (a) and 3 (b), exist between the adjacent nodes.
For the node distribution cases in fig. 3 (a) and fig. 3 (b), after the method shown in step 1 is adopted to obtain the network nodes, the multilateration estimation method is directly adopted to perform position estimation, and the obtained estimation results are shown in fig. 4 (a) and fig. 4 (b) (fig. 4 (a) is a C-shaped network, RMS =232.99; fig. 4 (b) is a Z-shaped network, RMS = 246.75). In the figure, the diamonds mean the estimated positions, the connecting lines between them and the solid circles mean the estimated errors, the longer the lines the greater the errors, and vice versa the smaller the errors.
For more scientific evaluation of the positioning accuracy, the Root Mean Square error (RMS) is used in the embodiment of the present invention, and the RMS formula is as follows:
Figure GDA0003877977930000112
wherein (x) u ,y u ) And
Figure GDA0003877977930000121
the real position and the estimated position of the unknown node are respectively, and n is the number of the unknown nodes.
By adopting the step 2, the estimated residual errors between the anchor nodes are checked hop by using the Modified Thompson Tau, as shown in fig. 5, in the C-shaped network and the Z-shaped network according to the embodiment of the present invention, it is found that an abnormal value occurs in the residual error of the 6 th hop in the C-shaped network in (a) in fig. 5, and the maximum hop count range is 5, and an abnormal value occurs in the residual error of the 5 th hop in the Z-shaped network in (b) in fig. 5, and the maximum hop count range is 4.
After setting the maximum number of hops (5 for the C-shaped network and 4 for the Z-shaped network in this example), the unknown node performs position estimation only using the anchor nodes within the maximum number of hops, and fig. 6 (a) and 6 (b) are the positioning results of the C-shaped network and the Z-shaped network in this example, respectively. Due to the limitation of the maximum hop range, there may be some areas where the unknown nodes cannot obtain enough anchor nodes, and thus cannot implement multilateration. Positioning results of the C-shaped network of fig. 6 (a), where 37 unknown nodes cannot be positioned, RMS =28.67; the positioning result of the zigzag network in fig. 6 (b), in which 11 unknown nodes cannot be positioned, RMS =39.11, which is represented by a plus sign in fig. 6 (a) and fig. 6 (b).
After the maximum hop range set in the step 2 is adopted, the estimation error between the nodes still exists; in a complex environment, particularly when the anchor nodes are distributed in a narrow area due to the obstruction, the distribution of the anchor nodes is easy to approach to the vicinity of a straight line. The error plus the approximately collinear distribution of anchor nodes results in an anomaly in the estimated position of the unknown node, causing the estimated position to deviate far from the true position. The example corrects the estimation of the anomaly by using the weighted Bounding-Box method of the invention, wherein (a) in fig. 7 is the result of correcting the estimation of the anomaly occurring in the C-shaped network in (a) in fig. 6, and RMS =29.3; fig. 7 (b) is a result of correcting the estimation of the abnormality of the zigzag network in fig. 6 (b), and RMS =24.52.
After the steps 1-3 are adopted, a positioning result with higher precision can be obtained, but the problem that part of unknown nodes cannot be positioned due to the maximum hop range is still solved. The method comprises the steps of firstly positioning unknown nodes with enough anchor nodes around, upgrading the unknown nodes into new anchor nodes after the estimated positions are obtained, and assisting in subsequently positioning other unknown nodes. The process is repeatedly and iteratively executed until the whole network node realizes positioning. The positioning node without positioning realization in fig. 7 gradually realizes positioning through step 4, and the positioning result is shown in fig. 8, wherein (a) in fig. 8 is the final positioning result of the C-shaped network, and RMS =35.14; in fig. 8, (b) is the final positioning result of the zigzag network, RMS =30.04.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all equivalent variations made by using the contents of the present specification and the drawings are within the protection scope of the present invention.

Claims (3)

1. The novel distributed non-ranging positioning method is characterized by comprising the following steps:
step 1, when a network is initialized, when information is transmitted along a transmission path, a node on the path completes the distance between every two nodes in the network in a distributed mode according to the number of potential neighbor relay nodes through a Muller method, and then the distance between any node pair is obtained in an accumulation mode; the method comprises the following steps:
step 1-1, initializing a network, connecting nodes into a network, and acquiring a shortest path among multi-hop nodes by adopting a Dijkstra or Floyd algorithm;
step 1-2, in the step 1-1, while executing Dijkstra or Floyd algorithm, the nodes in the network can naturally know the number of the directly interconnected neighbor nodes, and the potential relay node distribution range of any node occupies 1/3 of the communication range of the any node in the information propagation direction; if the number of the neighbor nodes of the arbitrary node is k, k/3-1 nodes in the k neighbor nodes of the arbitrary node are potential relay nodes, wherein 1 in k/3-1 represents the arbitrary node;
step 1-3, after the step 1-2 is executed, any node can know k/3-1 potential relay nodes, so that k/3-1 edges exist between the any node and the k/3-1 potential relay nodes, and an arch area exists on each potential relay node edge; assuming that the ratio of the coverage area of the arcuate region to the node is X i (i =1, \8230;, k/3-1), and the shortest path is obtained by using Dijkstra or Floyd algorithm, so that the most likely relay node is the node farthest from the information sending node among the potential relay nodes, and the ratio of the arch area adjacent to the corresponding relay node to the whole coverage area should be the smallest; suppose X i In accordance with a uniform distribution, i.e. X i U (0, 0.5), that is, when the relay node approaches the information sending node indefinitely, X i The trend was 0.5; when a relay node approaches an edge of coverage where information is sent out indefinitely, X i Tending towards 0, whereby a cumulative distribution function is obtained,
Figure QLYQS_1
further obtain the corresponding probability density function f X (x)，
Figure QLYQS_2
The desired value of the ratio of the area of the arch to the area of the total coverage area is thus obtained,
Figure QLYQS_3
the arcuate area corresponding to the expected distance of advancement of the information emitting node is,
Figure QLYQS_4
wherein R is the node communication radius, pi R 2 Is the coverage area of the communication of the node,
the expected distance of advance, i.e. the arcuate area corresponding to the estimated distance between adjacent nodes on the information propagation path, is obtained, and thus a function containing the expected distance of advance, i.e. the
Figure QLYQS_5
Where a is the desired relay node, o is the information sending node, d o→a Is the desired advance distance;
the function containing the desired advance is a non-linear one, first constructing a solution equation that,
Figure QLYQS_6
then, a rapidly convergent Muller method is adopted to carry out iteration to solve, the solution formula is as follows,
Figure QLYQS_7
where κ is the number of iterations，
Figure QLYQS_8
In addition, selection
Figure QLYQS_9
And
Figure QLYQS_10
as 3 initial values for Muller method iteration;
step 1-4: the estimated distance between any two connected nodes on the information transmission path can be obtained through the steps 1-3; thus, the estimated distance between the multi-hop nodes can be obtained in an additive manner, i.e. in such a way that
Figure QLYQS_11
Wherein S is a starting node, D is a destination node, and p points to a node on a path from S to D;
step 2, obtaining a distance estimation residual error by subtracting the estimation distance between the anchor nodes obtained in the step 1 from the corresponding real distance, detecting the residual error between the anchor nodes hop by adopting a Modified Thompson Tau detection method, and determining the maximum hop range in the network; the method comprises the following steps:
step 2-1: sequentially collecting estimated residual errors among anchor nodes according to hop counts; obtaining and recording the estimated distances among the anchor nodes in the steps 1-4, calculating the real distance between every two anchor nodes according to the coordinates among the anchor nodes, subtracting the corresponding real distance from the estimated distance among the anchor nodes to obtain the residual errors among the corresponding anchor nodes, and sorting, clustering and recording the residual errors according to the hop count among the nodes;
step 2-2: detecting residual errors hop by hop and obtaining the maximum hop range of the network; testing the residual errors between anchor nodes clustered according to the hop number by using Modified Thompson Tau hop by hop from the 2 nd hop; suppose that the h-th hop exists
Figure QLYQS_12
A residual error
Figure QLYQS_13
Get this
Figure QLYQS_14
Median of individual residuals med h That is, the amount of the oxygen present in the gas,
Figure QLYQS_15
in the h-hop, in med h To centre, the absolute deviation of each residual is recorded, i.e.
Figure QLYQS_16
Wherein r is h，i Represents the ith residual in the h hop,
while the offset of the h-th hop corrects for the quarter-bit distance, i.e.
Figure QLYQS_17
Wherein the content of the first and second substances,
Figure QLYQS_18
and
Figure QLYQS_19
respectively representing the 75% quantile and the 25% quantile of the h-th jump residual,
at this time, when delta h,i ≥τIQR h R is corresponding to h,i If the value is an abnormal value, an improper estimation distance occurs in the h hop, the h-1 hop is the maximum hop count range threshold value of the network, otherwise, the detection process is repeatedly executed for the next hop until the maximum hop count between anchor nodes is reached;
step 3, under the limitation of the maximum hop range obtained in the step 2, performing position estimation on an unknown node with enough anchor nodes by adopting a multilateral ranging method, judging the relation between the distance from the estimated position to the anchor nodes and the corresponding estimated distance, judging whether the distance is greater than the distance of the anchor nodes, if so, judging whether abnormal estimation occurs, and correcting the abnormal estimation position by adopting a weighted Bounding-Box;
and 4, upgrading the positioning nodes to new anchor nodes, combining the maximum hop range obtained in the step 2, repeating the step 3, and assisting the unfinished positioning nodes to iterate to finish positioning until all the nodes in the network realize positioning.
2. The novel distributed non-ranging positioning method according to claim 1, wherein in step 3, under the limitation of the maximum hop count range obtained in step 2, position estimation is performed on an unknown node having enough anchor nodes by using a multilateral ranging method, and a relationship between a distance from an estimated position to an anchor node and a corresponding estimated distance is determined, whether the unknown node is greater than the anchor node is determined, if the distance is greater than the anchor node, abnormal estimation occurs, and a weighted Bounding-Box is used to correct the abnormal estimated position, which includes the following steps:
step 3-1: after the steps 1 and 2, an unknown node in the network can be connected with enough anchor nodes within the maximum hop range, and the unknown node initially carries out position estimation by adopting a multilateration method; the sufficient anchor nodes mean that the number of two-dimensional plane anchor nodes is more than or equal to 3, and the number of three-dimensional space anchor nodes is more than or equal to 4;
step 3-2: step 3-1, after obtaining the preliminary estimated position, respectively calculating the actual distance from the position to the neighbor anchor node within the maximum hop-count range, then comparing the actual distance with the corresponding estimated distance obtained in step 1, and if the actual distance is smaller than the corresponding estimated distance, outputting the estimated position as the final estimated position; otherwise, the estimated position is an abnormal estimated position;
step 3-3: and 3-2, immediately correcting by adopting a weighted Bounding-Box algorithm after finding that the estimated position is not a usable result, wherein the corrected position is,
Figure QLYQS_20
wherein, the first and the second end of the pipe are connected with each other,
Figure QLYQS_21
for the corrected position of the unknown node, (x) v ,y v ) The coordinates of four corners of a rectangular area are obtained by adopting a common Bounding-Box algorithm, and omega (v) is a weighting function (x) v ,y v ) The following formula is adopted for the acquisition of (c),
Figure QLYQS_22
Figure QLYQS_23
Figure QLYQS_24
Figure QLYQS_25
Figure QLYQS_26
wherein (x) i ,y i ) Is the coordinates of the anchor node within the k maximum hop count,
Figure QLYQS_27
estimating the distance from the unknown node u to the anchor node obtained in the step 1;
the expression of ω (v) is,
Figure QLYQS_28
where v is the four corners obtained by the ordinary Bounding-Box algorithm,
Figure QLYQS_29
is the Chebyshev distance of k anchor nodes in the range from four corners to the maximum hop count, and the expression is,
Figure QLYQS_30
wherein abs (. Circle.) represents an absolute value.
3. The novel distributed non-ranging positioning method according to claim 1, wherein in the step 4, the positioning node that has been completed is upgraded to a new anchor node, the maximum hop count range obtained in the step 2 is combined, the step 3 is repeated, and the positioning is completed by assisting the positioning node that has not been completed to iterate until all nodes in the network are positioned, and the method comprises the steps of:
due to the limitation of the maximum hop range obtained in the step 2, after the step 3 is executed, the number of anchor nodes around an unknown node may not meet the minimum requirement of the multilateral ranging method, enough anchor nodes refer to at least 3 anchor nodes on a two-dimensional plane, and at least 4 anchor nodes in a three-dimensional space, so that part of the unknown nodes cannot be positioned, and after the unknown nodes with enough neighbor anchor nodes in the maximum hop range are estimated and unknown by the step 3, the unknown nodes are immediately upgraded into new anchor nodes, the anchor nodes are combined with the auxiliary unknown nodes which are not positioned, the step 2 and the step 3 are repeated, the nodes which are not positioned are positioned until all the unknown nodes are gradually positioned, and the positioning of the unknown nodes of the whole network is realized.
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