CN111405514A - Cooperative positioning method and system for wireless sensor network under hollow terrain - Google Patents
Cooperative positioning method and system for wireless sensor network under hollow terrain Download PDFInfo
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Abstract
The invention relates to a method and a system for cooperative positioning of a wireless sensor network under a hollow terrain. The cooperative positioning method and the system for the wireless sensor network under the cavity terrain construct a cooperative positioning model after acquiring application data of the wireless sensor network under the cavity terrain, determine an optimal auxiliary node in the cooperative positioning model according to an optimal selection strategy or a suboptimal selection strategy, determine an iteration parameter in the cooperative positioning model by adopting an update rule transmitted by variation messages according to the optimal auxiliary node, and finally realize accurate positioning on the wireless sensor network under the cavity terrain according to the iteration parameter. Moreover, the construction of the cooperative positioning model provided by the invention can further solve the problem of sparsity in the positioning process.
Description
Technical Field
The invention relates to the technical field of system engineering, in particular to a method and a system for cooperative positioning of a wireless sensor network under a hollow terrain.
Background
Wireless Sensor Networks (WSNs) are composed of a large number of sensor nodes randomly deployed in a monitoring area, and a multi-hop ad hoc network system is formed in a wireless communication manner, wherein the sensor nodes can acquire monitoring information and upload the monitoring information to a central management system, but the monitoring information has practical application value only on the premise of knowing a monitoring position, so that the research on the wireless sensor network positioning technology has very important significance.
At present, wireless sensor network positioning research is focused on homogeneous network positioning technology, homogeneous network positioning methods are mature and widely applied in various fields, but wireless sensor networks often face complex distribution environments, and in actual network deployment and application, due to the deployment mode (random distribution of aircrafts), physical space limitations (natural environmental factors such as buildings, lakes, mountains or basins) and some non-predictable factors (node faults) and the like, positioning accuracy is reduced or even positioning fails under special conditions, and the wireless sensor networks are prevented from executing predetermined functions. The heterogeneous network caused by the complex environment is not suitable for a general positioning method, and the positioning precision can not meet the actual engineering requirement.
In part of researches, a heterogeneous network is taken as a research object, the influence of the heterogeneous network on the ranging precision is considered, the positioning problem of the heterogeneous network is researched from the distance estimation direction, and a selective multi-lateralization (SM) method is provided to realize positioning after the screening of anchor nodes is combined. Partial research also provides a DV-maxHop method, and an interactive extended Pymote simulation framework is adopted for deep statistics and visual analysis. In addition, the influence of network topological structures, particularly cavity networks, on node positioning results under various non-ranging models is explored, the characteristic of cavity terrain is explored, the ranging accuracy of the nodes under the cavity terrain is improved by creating virtual nodes, and positioning achieved by adopting a heuristic multi-dimensional scaling method is also an important direction in heterogeneous network positioning research. However, most of the research on the problem of the holes in the heterogeneous network is focused on the non-cooperative positioning method, when the number of anchor nodes and unknown nodes is small, the positioning failure is easily caused, and the positioning accuracy of the non-cooperative positioning method is still to be improved compared with the actual engineering requirement.
Disclosure of Invention
The cooperative positioning method and system for the wireless sensor network under the hollow terrain can solve the problem of node sparsity in the positioning process of the heterogeneous sensor network, and further improve the positioning accuracy of the wireless sensor network under the hollow terrain.
In order to achieve the purpose, the invention provides the following scheme:
a method for cooperative positioning of a wireless sensor network under a hollow terrain comprises the following steps:
acquiring application data of a wireless sensor network under a hollow terrain; the application data includes: the method comprises the following steps that the distance between an unknown node in a wireless sensor network and other unknown nodes in the communication radius of the unknown node under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network are determined;
constructing a co-location model according to the application data;
determining an optimal auxiliary node in the co-location model according to an optimal selection strategy or a suboptimal selection strategy;
determining iteration parameters in the cooperative positioning model by adopting an updating rule transmitted by variation messages according to the optimal auxiliary node;
and finishing the positioning of the wireless sensor network under the hollow terrain according to the iteration parameters.
Optionally, the constructing a co-location model according to the application data specifically includes:
constructing a maximum likelihood probability model of the collaborative position of the unknown node according to the distance between the unknown node and other unknown nodes in the communication radius of the unknown node in the wireless sensor network under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network;
determining maximum likelihood probability models of the collaborative positions of all nodes in the wireless sensor network under the hollow terrain according to the maximum likelihood probability models of the collaborative positions of the unknown nodes;
determining a position maximum likelihood probability model of all nodes in the wireless sensor network under the hollow terrain according to the initial position of the unknown node;
and constructing the cooperative positioning model according to the maximum likelihood probability model of the cooperative positions of all the nodes in the wireless sensor network under the hollow terrain.
Optionally, the determining an optimal auxiliary node in the co-location model according to the optimal selection strategy or the sub-optimal selection strategy specifically includes:
determining a node corresponding to the minimum folding angle on the shortest path tree in the co-location model as an optimal auxiliary node;
and if a plurality of nodes corresponding to the minimum folding angles on the shortest path tree in the cooperative positioning model are determined, constructing a selection triangle, and determining the vertex corresponding to the two adjacent sides with the minimum difference in the selection triangle as the optimal auxiliary node.
Optionally, the determining, according to the optimal auxiliary node, an iteration parameter in the co-location model by using an update rule transmitted by a variation message specifically includes:
get factor node gmn；
According to the update rule of the variation message transmission, passing through a formula
Determining from the factor node gmnMessages to variable node z
Wherein,
as an initial value of the path tree break angle, θmFor the actual position of the unknown node m, θnThe actual location of unknown node n within communication range of any anchor node or m,
is known as
Expectation of lower variable node z, p (—) is occurrence probability;
by the formula
Determining the position parameter of the unknown node m after l iterations
Wherein,
for the initial position of the unknown node m,
as the initial position of unknown node m
N is any anchor node or unknown node within communication range of m,
s is a set of anchor nodes, dmnFor unknown measured distances between node m and node n,
is dmnThe variance of (a) is determined,
for the location parameters of the unknown node after l-1 iterations,
for a revised distance between the unknown node m and any anchor node or unknown node n within communication range of m at i-1 iterations,
to learn the calculated distance of the estimated location of node m from node n at l-1 iterations,
for the location parameter of the unknown node m after l-1 iterations,
is a set of other unknown nodes within the communication radius of the unknown node m.
By the formula
Determining variance parameter of unknown node m after l iterations
By the formula
Determining variance of shortest path tree of nodes m and n after l iterations
By the formula
Determining the break angle of the shortest path tree of the nodes m and n after l iterations
Wherein,
is node mN, variance of the shortest path tree after l iterations,
is the initial value of the shortest path tree break angle,
is composed of
The initial variance of the measured time period of the time period,
and
are all intermediate variables of l-1 iterations,
is an estimate of the dog-ear after l-1 iterations.
A co-location system of a wireless sensor network under hollow terrain, comprising:
the application data acquisition module is used for acquiring application data of the wireless sensor network under the hollow terrain; the application data includes: the method comprises the following steps that the distance between an unknown node in a wireless sensor network and other unknown nodes in the communication radius of the unknown node under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network are determined;
the cooperative positioning model building module is used for building a cooperative positioning model according to the application data;
the optimal auxiliary node determining module is used for determining the optimal auxiliary node in the cooperative positioning model according to the optimal selection strategy or the suboptimal selection strategy;
the iteration parameter determining module is used for determining iteration parameters in the cooperative positioning model by adopting an updating rule transmitted by variation messages according to the optimal auxiliary node;
and the positioning module is used for finishing the positioning of the wireless sensor network under the hollow terrain according to the iteration parameters.
Optionally, the co-location model building module specifically includes:
the first maximum likelihood probability model building unit is used for building a maximum likelihood probability model of the collaborative position of an unknown node according to the distance between the unknown node and other unknown nodes in the communication radius of the unknown node in the wireless sensor network under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network;
the second maximum likelihood probability model building unit is used for determining maximum likelihood probability models of the collaborative positions of all the nodes in the wireless sensor network under the hollow terrain according to the maximum likelihood probability models of the collaborative positions of the unknown nodes;
the position maximum likelihood probability model building unit is used for determining position maximum likelihood probability models of all nodes in the wireless sensor network under the hollow terrain according to the initial position of the unknown node;
and the cooperative positioning model building unit is used for building the cooperative positioning model according to the maximum likelihood probability models of the cooperative positions of all the nodes in the wireless sensor network under the hollow terrain and the position maximum likelihood probability model.
Optionally, the optimal auxiliary node determining module specifically includes:
the optimal auxiliary node determining unit is used for determining one node corresponding to the minimum folding angle on the shortest path tree in the cooperative positioning model as an optimal auxiliary node;
and if a plurality of nodes corresponding to the minimum folding angles on the shortest path tree in the cooperative positioning model are determined, constructing a selection triangle, and determining the vertex corresponding to the two adjacent sides with the minimum difference in the selection triangle as the optimal auxiliary node.
Optionally, the iteration parameter determining module specifically includes:
a factor node acquisition unit for acquiring a factor node gmn；
A message determining unit for determining the update rule of the variation message transmission according to the formula
Determining from the factor node gmnMessages to variable node z
Wherein,
as an initial value of the path tree break angle, θmFor the actual position of the unknown node m, θnThe actual location of unknown node n within communication range of any anchor node or m,
is known as
Expectation of lower variable node z, p (—) is occurrence probability;
a position parameter determination unit for determining the position of the object by formula
Determining the position parameter of the unknown node m after l iterations
Wherein,
for the initial position of the unknown node m,
as the initial position of unknown node m
N is any anchor node or m-channelAn unknown node within the range of the signal,
s is a set of anchor nodes, dmnThe distance between node m and node n is unknown,
is dmnThe variance of (a) is determined,
for the location parameters of the unknown node after l-1 iterations,
the corrected distance between the unknown node m and any anchor node or unknown node n in the communication range of the unknown node m,
to learn the calculated distance of the estimated location of node m from node n at l-1 iterations,
for the location parameter of the unknown node m after l-1 iterations,
is a set of other unknown nodes within the communication radius of the unknown node m.
A variance parameter determination unit for determining variance of the received signal by formula
Determining variance parameter of unknown node m after l iterations
A variance determining unit for determining variance by formula
Determining the shortest-path tree of nodes m, n after l iterationsVariance (variance)
A break angle determining unit for determining a break angle by a formula
Determining the break angle of the shortest path tree of the nodes m and n after l iterations
Wherein,
is the variance of the shortest path tree of the nodes m and n after l iterations,
is the initial value of the shortest path tree break angle,
is composed of
The initial variance of the measured time period of the time period,
and
are all intermediate variables of l-1 iterations,
is an estimate of the dog-ear after l-1 iterations.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the cooperative positioning method and the system for the wireless sensor network under the hollow terrain, the cooperative positioning model is constructed after application data of the wireless sensor network under the hollow terrain are obtained, the optimal auxiliary node in the cooperative positioning model is determined according to the optimal selection strategy or the suboptimal selection strategy, then the iteration parameter in the cooperative positioning model is determined according to the optimal auxiliary node by adopting the update rule of variation message transmission, and finally the accurate positioning of the wireless sensor network under the hollow terrain is realized according to the iteration parameter. In addition, the construction of the cooperative positioning model provided by the invention can further solve the problem of node sparsity in the positioning process.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of a co-location method for a wireless sensor network under a hollow terrain according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating a relationship between node distance measurement and a cavity location according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of an optimal selection strategy according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a sub-optimal selection strategy according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a cooperative positioning system of a wireless sensor network under a hollow terrain according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The cooperative positioning method and the system for the wireless sensor network under the hollow terrain can solve the problem of sparsity in the positioning process, so that the wireless sensor network under the hollow terrain can be accurately positioned.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a co-location method for a wireless sensor network under a hollow terrain according to an embodiment of the present invention, and as shown in fig. 1, the co-location method for the wireless sensor network under the hollow terrain includes:
s1, acquiring application data of the wireless sensor network under the hollow terrain; the application data includes: the method comprises the following steps that the distance between an unknown node in a wireless sensor network and other unknown nodes in the communication radius of the unknown node under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network are determined;
s2, constructing a co-location model according to the application data;
s3, determining the optimal auxiliary node in the co-location model according to the optimal selection strategy or the suboptimal selection strategy;
s4, determining iteration parameters in the co-location model by adopting an update rule transmitted by variation messages according to the optimal auxiliary node;
and S5, positioning the wireless sensor network under the hollow terrain according to the iteration parameters.
Wherein the step of constructing the co-location model according to the application data in S2 includes:
constructing a maximum likelihood probability model of the collaborative position of an unknown node according to the distance between the unknown node and other unknown nodes in the communication radius of the unknown node, the distance between the unknown node and anchor nodes in the communication radius of the unknown node and the actual positions of all the anchor nodes in the wireless sensor network under the hollow terrain;
determining maximum likelihood probability models of the collaborative positions of all nodes in the wireless sensor network under the hollow terrain according to the maximum likelihood probability models of the collaborative positions of the unknown nodes;
determining a position maximum likelihood probability model of all nodes in the wireless sensor network under the hollow terrain according to the initial position of the unknown node;
and constructing the cooperative positioning model according to the maximum likelihood probability model of the cooperative positions of all the nodes in the wireless sensor network under the hollow terrain.
The specific implementation process for constructing the co-location model comprises the following steps:
suppose there is M-N in a wireless sensor networkA+NaA node, wherein NAIndicating the number of anchor nodes, NaIndicating the number of unknown nodes, the position of the mth node is
Wherein
A set of unknown nodes is represented as,
representing a set of anchor nodes, with an actual distance between nodes m, n of
Where | · | | represents the 2 norm of the vector.
The unknown nodes are assumed to be randomly distributed in a certain area, a direct communication mode is adopted for the unknown nodes in the communication radius, the distance between the unknown nodes in the communication radius is calculated through Received Signal Strength (RSS), in the positioning process of the nodes, only the unknown nodes in the communication radius generate a synergistic effect, and the unknown nodes outside the communication radius do not consider positioning synergy temporarily. The distance between the unknown node and the anchor node is estimated by adopting a multi-hop mode, namely the shortest distance between the node m and the node n, which is calculated by the shortest path tree, represents the distance d between the unknown node and the anchor nodemnBut due to the presence of holesAs shown in fig. 2, a rectangle H in the graph represents a void, m represents an unknown node, n represents an unknown node in any anchor node or m communication range, a connecting line between m, o, and n represents a shortest path tree spanning the void between the nodes m and n, wherein a node o represents a node on a boundary of the void, also called an auxiliary node, for a path not passing through the void, no auxiliary node exists, r represents a communication radius, a distance between nodes is represented by a shortest path tree, and a distance d between nodes is represented by a shortest path treeso≈d1,dot≈d2,dgo≈d3,dgs≈d4,dgt≈d5The node g is any node of the communication radius inner points of the node o and is called a virtual node. Therefore, the distance d between the nodes is determined according to the formula (1)mnIs modified into
As shown in equation (1).
Wherein the node o is the node m, the node located at the void boundary on the shortest path of n, dmo,donThe shortest paths between nodes m, o and between nodes o, n,
for the break angle ∠ sot on the shortest path tree of the node m and n, the modified node distance follows normal distribution
For the unknown nodes and the unknown nodes within the communication radius, the observation distance does not relate to the hole problem, so that
In summary, the maximum likelihood model of cooperative location compliance of a single unknown node is
Wherein,
represents the distance set of the unknown node m and the unknown node and the anchor node i in all communication radiuses, j represents any node in the wireless sensor network,
for other unknown node sets within the communication radius of node m, p (×) represents the probability of an event occurring.
The maximum likelihood model to which all nodes in the network are subjected is
Wherein,
represents the set of the modified distances between all unknown nodes and the anchor nodes in all communication radiuses,
representing the set of all unknown node locations.
Accordingly, the objective function of the co-location model is
Wherein,
initial positions obtained for all unknown nodes by external measurement or other methods, assuming variance of
The location obeys a Gaussian distribution of
The probability density function related to the maximum likelihood function comprises Gaussian distribution of node distance and Gaussian distribution of break angle on shortest path, wherein the Gaussian distribution of the node distance is
Wherein,
representing the variance of the distance estimate between nodes m, n.
The distribution may be expressed as when the inter-node distance degenerates to an unknown inter-node distance within the communication radius
Furthermore, the break angle compliance parameter on the shortest path tree is
The probability density function of the normal distribution of (1) is as follows:
s3, determining the optimal auxiliary node in the co-location model according to the optimal selection policy or the sub-optimal selection policy includes:
determining a node corresponding to the minimum folding angle on the shortest path tree in the co-location model as an optimal auxiliary node;
and if a plurality of nodes corresponding to the minimum folding angles on the shortest path tree in the cooperative positioning model are determined, constructing a selection triangle, and determining the vertex corresponding to the two adjacent sides with the minimum difference in the selection triangle as the optimal auxiliary node.
The specific implementation process of S3 is as follows:
in the process, the connection line between the shortest path and the actual distance is simplified into a triangular model, but the nodes passing through the shortest path tree may pass through the boundary nodes of a plurality of holes, different hole boundary nodes are different as the vertices of the triangle to influence the positioning result, and the hole boundary nodes serving as the vertices of the triangle are selected to be called as auxiliary nodes.
The Cramer-Rao lower bound is the minimum achievable variance of unbiased estimation, so that the optimal achievable estimation performance is established by setting the lower bound of an estimator, and the Cramer-Rao method can depict the robustness of the estimation method, the Cramer-Rao lower bound (CR L B) of position estimation under a special configuration is given, CR L B has progressive compactness and can be regarded as a measurement standard in wireless sensor network positioning, however, the solution of CR L B needs to derive a closed-loop solution of a marginal probability density function, and is difficult to realize in mathematical derivation, and in addition, CR L B cannot give the mean square error of a random variable, namely a hidden variable, in a mixed estimation problem.
Therefore, the invention adopts a Hybrid Cram é -Rao lower bound (HCR L B) to represent the positioning limit of the algorithm, and the HCR L B can be obtained by combining probability densities and can represent the bound of any generalized unbiased estimation.
Compared with the non-cooperative HCR L B, the cooperative HCR L B increases the influence of unknown nodes in the communication radius on the positioning result, and the node ranging in the communication radius is not influenced by the hole terrain, so that the derivation is carried out by the HCR L B in the non-cooperative mode when the hole auxiliary node is selected, the derivation process and the conclusion can be simplified, and the selection result is not influenced.
HCR L B for node positioning under hollow terrain and relation thereof with lower error bound are
Wherein,
as an estimate of position and angle, phim＝[Θm,Ψm]The true values of position and angle. ΨmThe true value of the dog-ear on the shortest path tree is represented.
For the expectation operator, it means that the variable in parentheses is expected, and if the subscript exists, it means that the variable indicated by the subscript is expected, as
Presentation pair
In the expectation that the position of the target is not changed,
represents a pair dmIn the expectation that the position of the target is not changed,
is shown to be known
Under the condition of dmThe expectation is that.
Is a Hybrid Information Matrix (HIM), defined as:
after derivation, HIM is converted to
In the derivation of the above formula, there is a non-linear term
And processing in a second-order Taylor expansion mode. Meanwhile, in the process of solving the expectation of the equation, the product of adjacent edges is processed by means of a trilateral relation formula of a triangle, wherein the trilateral relation formula is as follows
Wherein, a triangle formed by the sensor nodes m, n and the middle point o defines an angle amn＝∠onm,bmn＝∠omn。
Further derivation can obtain
Final positioning model with respect to thetamAnd
submatrix of HIM
Can be expressed as
Wherein diag (×) represents a diagonal matrix, i represents any anchor node from 1 to n,
oirepresenting an auxiliary node in the shortest path tree between nodes m, i, the derivative variable y in the equationi,G'mi,G”mnAre respectively defined as
Wherein,
αmnrepresents the angle theta between the connecting line of the nodes m and n and the abscissa axis of the distribution areai＝(xiYi) represents the coordinates of any anchor node,
is the initial estimation value of the folding angle on the shortest path tree of the node m, i.
In a positioning model with holes, a better positioning effect can be achieved when the estimated CR L B of the determined parameters is equal to HCR L B, and the importance of the CR L0B of the determined parameters is proved to be stronger than that of HCR L1B under the normal condition, the CR L2B related to the position of an unknown node is larger than that of HCR L B, under the premise that the position of the node and the measurement variance are known, the HCR L B of the unknown node is constant, but the CR L B cannot be obtained due to the reason that the integral term closed-loop solution cannot be obtained, therefore, one way of reducing the CR L B of the unknown node is obtained by analyzing the essential condition of the asymptotic importance of the HCR L B, because the HCR L B is known and fixed, when the essential condition is met, the CR L B can approach the HCR L B infinitely, and the essential condition is that
Substituting each expression into the sufficient condition to obtain
The above conditions indicate the tightness of HCR L B with variable (a)mi-bmi) And
in this regard, when the network topology is fixed, the other variables in the equation are constants, but since there is more than one hole boundary node on the shortest path tree between nodes, when selecting different hole boundary nodes to form a triangle (where the node is defined as an auxiliary node), the essential condition of importance is dependent on the variable (a)mi-bmi) And
a change is made. However, most of the auxiliary nodes cannot satisfy the essential conditions in the equation, so that the asymptotic tightness cannot be achieved, but the optimal auxiliary node can be found to be more approximate to the conditions in the equation. Therefore, the present invention defines a tightness function according to the above equation, and analyzes the tightness achieved by different auxiliary nodes, as shown below
It can be shown that when the variables satisfy the conditions
|ami-bmi|∈[0,π/3]Tightness function with respect to break angle
Monotonically decreasing. When in use
It can be shown that the tightness function is less than 0. Following the angle of the corner
Increasing from 1/2 π to π, the tightness function decreases monotonically. The process shows that when the folding angle is satisfied
When the condition (2) is satisfied, the tightness function is closer to 0, and when the tightness function is 0, the lower error bound of the estimator can be effectively reduced. Therefore, the smaller the angle of the break angle on the shortest path tree is, the closer the compactness function is to 0, and the better the positioning effect of the node is. In the hole network of the present invention, the break angle of the auxiliary node is usually between 1/2 pi and pi, and the difference between the other two angles of the triangle is usually between 0 and 1/3 pi.
According to the above-mentioned deduction the optimum selection strategy can be obtained, i.e. the break angle correspondent to auxiliary node on the shortest path tree
The smaller the lower bound of positioning error. FIG. 3 is a schematic diagram of an optimal selection strategy, in which
All unknown nodes, S1Being anchor nodes, all nodes and their dotted lines constitute a shortest path tree between nodes,
and the two nodes can form a triangle with the node to be positioned and the anchor node on the inner boundary of the cavity, but the corresponding break angles of the two nodes are different in size. If a node is selected
Constructing a triangular model with a smaller corresponding angle,therefore, the influence of the holes on node ranging can be reflected better, and the trilateral estimation of the formed triangle is more accurate by taking the node as an auxiliary node. If a node is selected
Then the node
Inaccurate estimation of the distance caused by the connection line will seriously affect the positioning result. The above analysis is consistent with the expression of the optimal selection strategy.
In the same manner, the variable cos (a) is analyzedmi-bmi) The effect on the fitness function is seen as the variable cos (a)mi-bmi) Derivative of (a) is by break angle
Determine relative angle of break
Influence on the tightness function, variable cos (a)mi-bmi) Has a negligible effect, so that the selection of the auxiliary node should first take into account the break angle
Only when the shortest path tree has a special condition that the folding angles are equal or close, the cosine values of the analysis angle difference select the auxiliary nodes, although the probability of the special condition is smaller, the invention still provides a corresponding analysis and selection mode.
Can prove when
|ami-bmi|∈[0,π/3]When the condition is satisfied, the tightness function is related to the variable cos (a)mi-bmi) Monotonically increasing. The compactness function is close to 0 when the cosine of the angle difference is around 1, and is far from 0 when the cosine of the angle difference is around 0.5. According to the method, a sub-optimal selection strategy can be obtained, namely, the auxiliary node firstly selects the most according to the selection strategyAnd selecting the optimal selection strategy, and when the optimal selection strategy cannot provide enough judgment basis, selecting the auxiliary node with smaller length difference between two adjacent sides of the auxiliary node in the triangle, so that the lower limit of the positioning error is smaller.
The above problem can be explained by geometric means, and fig. 4 shows a schematic diagram of a suboptimal selection strategy, in a shortest path tree between nodes, if the shortest path is more tortuous, the linear distance between nodes depends on the angle of the path bending, otherwise, the linear distance between nodes has a smaller relationship with the degree of the path bending. In this case, the auxiliary node located in the middle of the shortest path tree can obtain better positioning results. As shown in FIG. 4, the two break angles on the shortest path tree are similar in size, i.e.
Then the node
Is greater than the node
Of the distance between them, thus
The above equation shows that when the auxiliary node is located near the midpoint of the shortest path, a better positioning effect can be obtained.
At S4, according to the optimal auxiliary node, the specific implementation process of determining the iteration parameters in the co-location model by using the update rule of variation message delivery includes:
the cooperative positioning model under the known hole terrain can be abstracted to solve the maximum value of the joint likelihood estimation objective function, in order to solve the maximum value of the target, the invention adopts a cooperative method of message transmission to realize optimized solution, and the following parameters of cooperative positioning are deduced.
Based on a network structure of local factorization in a joint likelihood function, the wireless sensor network containing the holes can carry out derivation under a factor graph framework, and variable nodes and factor nodes realize association inference by a message transfer algorithm. Among various message passing algorithms, the variation message passing updating rule is used for deducing the cooperative positioning parameter in the invention due to the excellent characteristic in distributed calculation.
Definition of
The rule slave factor node g is updated based on the VMP messagemnMessages to the relevant variable node z can be represented as
Wherein,
as an initial value of the path tree break angle, θmFor the actual position of the unknown node m, θnThe actual location of unknown node n within communication range of any anchor node or m,
is known as thetam、θn 
The expectation of the lower variable node Z, p (×) is the probability of occurrence.
The probability distribution of the estimated values in the expectation operator is from the trial distribution of the previous iteration, and correspondingly, the posterior distribution of the variable nodes is
The logarithm of the likelihood function for the anchor node and the unknown node in the above equation is known as
According to the variable node posterior distribution formula, the result is from the factor node gmnMessages to related variable nodes may be represented in the following form
Slave factor node gmnThe variables to node location can be expressed as anchor nodes and unknown node factor variable distinctions respectively
Wherein,
respectively the coordinates of the nodes m, n and the distance d after the previous iterationmnThe measured distance between the unknown node and the unknown node in the communication radius is the estimated distance after the previous iteration
Can be respectively expressed as
Slave factor node gmnThe calculation of the folding angle variable on the shortest path to the node is due to the non-linear item
And
therefore, nonlinear terms in the equation are derived in the form of Taylor expansion, and the derived result can be expressed as
Wherein the intermediate variable
Intermediate variables
Intermediate variables
Intermediate variables
Further derivation of the Slave factor node gmnAngle of tree to shortest path
Is expressed as
In order to ensure that the message transmission information is in a closed loop form, the node position and the back of the shortest path break angle are assumedIf the probability of experience is still Gaussian distribution, the position variable and the shortest path break angle variable of the unknown node m, any anchor node or unknown node n in the communication range of m are transmitted to the factor node g after each message updatemnRespectively is
In the derivation, the position parameter of the unknown node m after l iterations
And variance parameter
Are respectively as
Wherein,
is the initial position of the unknown node m, follows the prior distribution of the positions of the unknown node m,
for unknown node m initial position
N is any anchor node or unknown node within m communication rangeThe point(s) is (are) such that,
s is a set of anchor nodes, dmnThe distance between node m and node n is unknown,
is dmnThe variance of (a) is determined,
for the location parameters of the unknown node after l-1 iterations,
the corrected distance between node m and node n is unknown,
to learn the calculated distance of the estimated location of node m from node n at l-1 iterations,
for the location parameter of the unknown node m after l-1 iterations,
is a set of other unknown nodes within the communication radius of the unknown node m.
Break angle of shortest path tree of node m, n after l iterations
And its variance
Are respectively as
Wherein,
is the variance of the shortest path tree of the nodes m and n after l iterations,
is the initial value of the shortest path tree break angle,
is composed of
The initial variance of the measured time period of the time period,
is an intermediate variable of l-1 iterations and
is an intermediate variable of l-1 iterations and
is an intermediate variable of l-1 iterations
Is an intermediate variable of l-1 iterations and
is an estimate of the dog-ear after l-1 iterations.
Compared with the prior art, the cooperative positioning method of the wireless sensor network under the hollow terrain has the following advantages that:
1. the invention solves the positioning problem of the heterogeneous network, particularly the situation that the distribution terrain of the wireless sensor network contains holes, provides a positioning method and improves the positioning precision;
2. aiming at the situations of low node density and limited communication radius in the cavity network, a cooperative positioning model is established, and the problem of sparse network in the positioning process is solved;
3. the method adjusts the estimated position of the unknown node by means of the information of other unknown nodes in the communication range, provides iterative parameters and a process of the cooperative positioning method, and effectively improves the positioning accuracy of the sparse network.
4. The invention further provides a method for selecting the auxiliary node in the cavity boundary node by means of the tightness analysis of the Clarmero boundary, further improves the positioning process and improves the positioning precision.
In addition, aiming at the provided method for the cooperative positioning system of the wireless sensor network under the hollow terrain, the invention also correspondingly provides a cooperative positioning system of the wireless sensor network under the hollow terrain. As shown in fig. 5, the system includes: the system comprises an application data acquisition module 1, a cooperative positioning model construction module 2, an optimal auxiliary node determination module 3, an iteration parameter determination module 4 and a positioning module 5.
The application data acquisition module 1 is used for acquiring application data of the wireless sensor network under the hollow terrain; the application data includes: the method comprises the following steps that the distance between an unknown node in a wireless sensor network and other unknown nodes in the communication radius of the unknown node under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network are determined; the cooperative positioning model building module 2 is used for building a cooperative positioning model according to the application data; the optimal auxiliary node determining module 3 is used for determining an optimal auxiliary node in the co-location model according to an optimal selection strategy or a suboptimal selection strategy; the iteration parameter determining module 4 is configured to determine an iteration parameter in the co-location model by using an update rule transmitted by a variation message according to the optimal auxiliary node; and the positioning module 5 is used for positioning the wireless sensor network under the hollow terrain according to the iteration parameters.
The cooperative localization model building module 2 specifically includes: the device comprises a first maximum likelihood probability model building unit, a second maximum likelihood probability model building unit, a position maximum likelihood probability model building unit and a co-location model building unit.
The first maximum likelihood probability model building unit is used for building a maximum likelihood probability model of the collaborative position of an unknown node according to the distance between the unknown node and other unknown nodes in the communication radius of the unknown node in the wireless sensor network under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node and the actual positions of all anchor nodes in the network; the second maximum likelihood probability model building unit is used for determining maximum likelihood probability models of the collaborative positions of all the nodes in the wireless sensor network under the hollow terrain according to the maximum likelihood probability models of the collaborative positions of the unknown nodes; the position maximum likelihood probability model building unit is used for determining position maximum likelihood probability models of all nodes in the wireless sensor network under the hollow terrain according to the initial position of the unknown node; and the cooperative positioning model building unit is used for building the cooperative positioning model according to the maximum likelihood probability models of the cooperative positions of all the nodes in the wireless sensor network under the hollow terrain and the position maximum likelihood probability model.
The optimal auxiliary node determining module 3 specifically includes: and an optimal auxiliary node determining unit.
The optimal auxiliary node determining unit is used for determining one node corresponding to the minimum folding angle on the shortest path tree in the cooperative positioning model as an optimal auxiliary node; and if a plurality of nodes corresponding to the minimum folding angles on the shortest path tree in the cooperative positioning model are determined, constructing a selection triangle, and determining the vertexes corresponding to the two adjacent sides with the minimum difference in the selection triangle as the optimal auxiliary nodes.
The iteration parameter determining module 4 specifically includes: the device comprises a factor node acquisition unit, a message determination unit, a position parameter determination unit, a variance determination unit and a folding angle determination unit.
Wherein, the factor node obtaining unit is used for obtaining a factor node gmn；
The message determining unit is used for passing a formula according to the update rule of the variation message transmission
Determining from the factor node gmnMessages to variable node Z
Wherein,
as an initial value of the path tree break angle, θmFor the actual position of the unknown node m, θnThe actual location of unknown node n within communication range of any anchor node or m,
is known as thetam、θn、
Expectation of lower variable node Z, p (—) is occurrence probability;
the position parameter determining unit is used for passing the formula
Determining the position parameter of the unknown node m after l iterations
Wherein,
for the initial position of the unknown node m,
as the initial position of unknown node m
N is any anchor node or unknown node within communication range of m,
s is a set of anchor nodes, dmnThe distance between the unknown node m and any anchor node or unknown node n in the communication range of the unknown node m,
is dmnThe variance of (a) is determined,
for the location parameters of the unknown node after l-1 iterations,
to do so for the revised distance between the unknown node m and the anchor node n at l-1 iterations,
to iterate over l-1 times the computed distance of the estimated location of unknown node m from any anchor node or unknown node n within communication range of m,
for the location parameter of the unknown node m after l-1 iterations,
is a set of other unknown nodes within the communication radius of the unknown node m.
The variance parameter determination unit is used for passing the formula
Determining variance parameter of unknown node m after l iterations
The variance determining unit is used for passing the formula
Determining variance of shortest path tree of nodes m and n after l iterations
The bevel angle determining unit is used for passing the formula
Determining the break angle of the shortest path tree of the nodes m and n after l iterations
Wherein,
is the variance of the shortest path tree of the nodes m and n after l iterations,
is the initial value of the shortest path tree break angle,
is composed of
The initial variance of the measured time period of the time period,
is an intermediate variable of l-1 iterations and
is an intermediate variable of l-1 iterations and
is an intermediate variable of l-1 iterations
Is an intermediate variable of l-1 iterations and
is an estimate of the dog-ear after l-1 iterations.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A method for cooperative positioning of a wireless sensor network under a hollow terrain is characterized by comprising the following steps:
acquiring application data of a wireless sensor network under a hollow terrain; the application data includes: the method comprises the following steps that the distance between an unknown node in a wireless sensor network and other unknown nodes in the communication radius of the unknown node under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network are determined;
constructing a co-location model according to the application data;
determining an optimal auxiliary node in the co-location model according to an optimal selection strategy or a suboptimal selection strategy;
determining iteration parameters in the cooperative positioning model by adopting an updating rule transmitted by variation messages according to the optimal auxiliary node;
and finishing the positioning of the wireless sensor network under the hollow terrain according to the iteration parameters.
2. The method according to claim 1, wherein the constructing a co-location model according to the application data specifically includes:
constructing a maximum likelihood probability model of the collaborative position of an unknown node according to the distance between the unknown node and other unknown nodes in the communication radius of the unknown node, the distance between the unknown node and anchor nodes in the communication radius of the unknown node and the actual positions of all the anchor nodes in the wireless sensor network under the hollow terrain;
determining maximum likelihood probability models of the collaborative positions of all nodes in the wireless sensor network under the hollow terrain according to the maximum likelihood probability models of the collaborative positions of the unknown nodes;
determining a position maximum likelihood probability model of all nodes in the wireless sensor network under the hollow terrain according to the initial position of the unknown node and the actual position of the unknown node;
and constructing the cooperative positioning model according to the maximum likelihood probability model of the cooperative positions of all the nodes in the wireless sensor network under the hollow terrain.
3. The method according to claim 1, wherein the determining an optimal auxiliary node in the co-location model according to an optimal selection strategy or a sub-optimal selection strategy specifically comprises:
determining a node corresponding to the minimum folding angle on the shortest path tree in the co-location model as an optimal auxiliary node;
and if a plurality of nodes corresponding to the minimum folding angles on the shortest path tree in the cooperative positioning model are determined, constructing a selection triangle, and determining the vertexes corresponding to the two adjacent sides with the minimum difference in the selection triangle as the optimal auxiliary nodes.
4. The method according to claim 1, wherein the determining, according to the optimal auxiliary node, the iteration parameter in the co-location model by using an update rule of variational message transfer specifically comprises:
get factor node gmn；
According to the update rule of the variation message transmission, passing through a formula
Determining from the factor node gmnTo variable node
Of a message
Wherein,
as an initial value of the path tree break angle, θmFor the actual position of the unknown node m, θnThe actual location of unknown node n within communication range of any anchor node or m,
is known as thetam、θn、
Lower variable node
P () is the probability of occurrence;
by the formula
Determining the position parameter of the unknown node m after l iterations
Wherein,
for the initial position of the unknown node m,
as the initial position of unknown node m
N is any anchor node or unknown node within communication range of m,
is a set of anchor nodes, dmnThe distance between the unknown node m and the anchor node n,
is dmnThe variance of (a) is determined,
the position parameter of the unknown node after l-1 iterations is l-1Iterating the corrected distance between the unknown node m and the node n,
to learn the calculated distance of the estimated location of node m from node n at l-1 iterations,
for the location parameter of the unknown node m after l-1 iterations,
is a set of other unknown nodes within the communication radius of the unknown node m.
By the formula
Determining variance parameter of unknown node m after l iterations
By the formula
Determining variance of shortest path tree of nodes m and n after l iterations
By the formula
Determining the break angle of the shortest path tree of the nodes m and n after l iterations
Wherein,
is the most node m, nThe variance of the short-path tree after l iterations,
is the initial value of the shortest path tree break angle,
is composed of
The initial variance of the measured time period of the time period,
and
are all intermediate variables of l-1 iterations,
is an estimate of the dog-ear after l-1 iterations.
5. A cooperative positioning system of a wireless sensor network under a hollow terrain comprises:
the application data acquisition module is used for acquiring application data of the wireless sensor network under the hollow terrain; the application data includes: the method comprises the following steps that the distance between an unknown node in a wireless sensor network and other unknown nodes in the communication radius of the unknown node under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node, the initial position of the unknown node and the actual positions of all anchor nodes in the network are determined;
the cooperative positioning model building module is used for building a cooperative positioning model according to the application data;
the optimal auxiliary node determining module is used for determining the optimal auxiliary node in the cooperative positioning model according to the optimal selection strategy or the suboptimal selection strategy;
the iteration parameter determining module is used for determining iteration parameters in the cooperative positioning model by adopting an updating rule transmitted by variation messages according to the optimal auxiliary node;
and the positioning module is used for finishing the positioning of the wireless sensor network under the hollow terrain according to the iteration parameters.
6. The system of claim 5, wherein the co-location model building module specifically comprises:
the first maximum likelihood probability model building unit is used for building a maximum likelihood probability model of the collaborative position of the unknown node according to the distance between the unknown node and other unknown nodes in the communication radius of the unknown node in the wireless sensor network under the hollow terrain, the distance between the unknown node and anchor nodes in the communication radius of the unknown node and the actual positions of all anchor nodes in the network;
the second maximum likelihood probability model building unit is used for determining maximum likelihood probability models of the collaborative positions of all the nodes in the wireless sensor network under the hollow terrain according to the maximum likelihood probability models of the collaborative positions of the unknown nodes;
the position maximum likelihood probability model building unit is used for determining position maximum likelihood probability models of all nodes in the wireless sensor network under the hollow terrain according to the initial position of the unknown node;
and the cooperative positioning model building unit is used for building the cooperative positioning model according to the maximum likelihood probability models of the cooperative positions of all the nodes in the wireless sensor network under the hollow terrain and the position maximum likelihood probability model.
7. The system of claim 5, wherein the optimal auxiliary node determination module specifically comprises:
the optimal auxiliary node determining unit is used for determining one node corresponding to the minimum folding angle on the shortest path tree in the cooperative positioning model as an optimal auxiliary node;
and if a plurality of nodes corresponding to the minimum folding angles on the shortest path tree in the cooperative positioning model are determined, constructing a selection triangle, and determining the vertexes corresponding to the two adjacent sides with the minimum difference in the selection triangle as the optimal auxiliary nodes.
8. The system of claim 5, wherein the iterative parameter determination module specifically comprises:
a factor node acquisition unit for acquiring a factor node gmn；
A message determining unit for determining the update rule of the variation message transmission according to the formula
Determining from the factor node gmnTo variable node
Of a message
Wherein,
as an initial value of the path tree break angle, θmFor the actual position of the unknown node m, θnThe actual location of unknown node n within communication range of any anchor node or m,
is known as thetam、θn、
Lower variable node
Expectation of (1), p (.)) Is the probability of occurrence;
a position parameter determination unit for determining the position of the object by formula
Determining the position parameter of the unknown node m after l iterations
Wherein,
for the initial position of the unknown node m,
as the initial position of unknown node m
N is any anchor node or unknown node within communication range of m,
is a set of anchor nodes, dmnThe distance between the unknown node m and the anchor node n,
is dmnThe variance of (a) is determined,
for the location parameters of the unknown node after l-1 iterations,
to do so for the revised distance between the unknown node m and the anchor node n at l-1 iterations,
to learn the calculated distance of the estimated location of node m from node n at l-1 iterations,
for the location parameter of the unknown node m after l-1 iterations,
is a set of other unknown nodes within the communication radius of the unknown node m.
A variance parameter determination unit for determining variance of the received signal by formula
Determining variance parameter of unknown node m after l iterations
A variance determining unit for determining variance by formula
Determining variance of shortest path tree of nodes m and n after l iterations
A break angle determining unit for determining a break angle by a formula
Determining the break angle of the shortest path tree of the nodes m and n after l iterations
Wherein,
is the variance of the shortest path tree of the nodes m and n after l iterations,
is the initial value of the shortest path tree break angle,
is composed of
The initial variance of the measured time period of the time period,
and
are all intermediate variables of l-1 iterations,
is an estimate of the dog-ear after l-1 iterations.
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