CN113938826A - Distributed wireless cooperative positioning method - Google Patents

Distributed wireless cooperative positioning method Download PDF

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CN113938826A
CN113938826A CN202111204592.5A CN202111204592A CN113938826A CN 113938826 A CN113938826 A CN 113938826A CN 202111204592 A CN202111204592 A CN 202111204592A CN 113938826 A CN113938826 A CN 113938826A
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node
target node
cooperative positioning
nodes
time
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杨少石
曹越
冯志勇
张涛
王丽华
杨春雷
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Beijing University of Posts and Telecommunications
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Beijing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/025—Services making use of location information using location based information parameters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/029—Location-based management or tracking services

Abstract

The invention discloses a distributed wireless cooperative positioning method, which relates to the technical field of communication and network, and specifically comprises the following steps: firstly, building a distributed wireless cooperative positioning device; and randomly selecting a target node, wherein the rest nodes are collectively called cooperative positioning nodes. The target node broadcasts and sends a cooperative positioning request to obtain a response message of each cooperative positioning node; meanwhile, the target node sends a ranging request, and each cooperative positioning node returns prior information of the position of the cooperative positioning node; the target node establishes a local factor graph of message transmission; calculating posterior probabilities of random vectors of all nodes to be positioned in the local factor graph by using prior information, performing factor decomposition, and calculating local factor nodes; and finally, solving the position of the target node by using the prior probability of the random vector of the target node and the message transmitted with the factor node to realize final positioning. The invention reduces the computational complexity of the parameterized message transfer algorithm and has important significance for wireless cooperative positioning of network equipment.

Description

Distributed wireless cooperative positioning method
Technical Field
The invention relates to the technical field of communication and network, in particular to a distributed wireless cooperative positioning method.
Background
The position sensing capability has become one of the basic capabilities required by the wireless network, and the wireless positioning technology has been widely applied to military affairs, commercial and public services and the like.
The wireless positioning technology mainly comprises two types, namely a space satellite system and a ground wireless network. The positioning technology based on the space satellite system is suitable for outdoor open environment; in environments with weak or even no GPS signals, such as indoors, urban canyons, forest lands, etc., a ground-based wireless network is needed for positioning. However, in the positioning technology based on the terrestrial wireless network, the fuzzy location and insufficient number of anchor nodes may cause a large positioning error, or even no positioning.
The traditional ground wireless network positioning technology improves the positioning error by arranging anchor nodes with high density or high transmitting power; the novel wireless cooperative positioning technology improves positioning precision by establishing peer-to-peer communication and signal measurement among nodes to be positioned, and improves availability and reliability of positioning service. In addition, the centralized cooperative positioning method has the problems of large communication overhead of the central node, sensitivity to the fault of the central node, poor expansibility and robustness of the network and the like in a large network; the distributed cooperative positioning method has better expandability and robustness and is more attractive in the cooperative positioning technology.
The message transmission algorithm based on the factor graph has an important application prospect in the distributed cooperative positioning technology. The current research on cooperative positioning for the message transfer algorithm based on the factor graph mainly includes two directions: firstly, the core idea is that based on the transfer process of parameterized messages, a node to be positioned searches a certain probability distribution through a specific similarity measurement index to approximate the posterior probability distribution of the node position, then the parameter of the approximate distribution is used for replacing the parameter of the original distribution, and finally the position of each node to be positioned in the network is solved through message transfer among random variables on a factor graph; secondly, the core idea is a message transmission process based on particlized messages, the node to be positioned samples the posterior probability distribution of the node position according to a specific sampling rule, so that the parameter of the probability distribution reconstructed based on the sampling point (namely the particles) is equal to the parameter of the original posterior probability distribution, and finally, the position of each node to be positioned in the network is solved through message transmission among random variables on a factor graph.
For the message passing cooperative positioning algorithm based on the parameterized message representation, the optimal parameters of the approximate distribution of the original posterior probability distribution need to be solved by optimizing a specific similarity metric index, the computation complexity of which is high and a plurality of local optimal solutions may exist.
For the message transmission cooperative positioning algorithm based on the particlized message representation, a large number of particles need to be extracted from the posterior probability distribution of the position of the node to be positioned through a specific sampling method to represent the posterior probability distribution. Since the performance of the algorithm is directly related to the number of particles, a large number of particles are generally required to represent the original distribution. In addition, the computation complexity of the algorithm is proportional to the square of the number of particles, and the communication overhead is proportional to the number of particles, so that the computation complexity and the communication overhead of the algorithm are high.
Disclosure of Invention
The invention provides a distributed wireless cooperative positioning method, which aims to solve the problem of high computational complexity in the existing research of a message transmission cooperative positioning technology, reduce the computation amount, communication overhead and cooperative positioning time consumption of nodes in a network and better provide a rapid positioning guarantee for the nodes in the network.
The distributed wireless cooperative positioning method comprises the following specific steps:
step one, a distributed wireless cooperative positioning device comprising a target node, a plurality of nodes to be positioned and a plurality of anchor nodes is built;
the method specifically comprises the following steps: the nodes are distributed in a spatial area according to any topology to form an ad hoc network, one node to be positioned is randomly selected as a target node, and the other nodes to be positioned and anchor nodes which are communicated with the target node are collectively called cooperative positioning nodes of the target node.
Wherein, every node of awaiting positioning all includes: the device comprises a first control unit, a first wireless communication unit, a first storage unit and a first calculation unit; the first control unit controls the motion trail of each node to be positioned;
a first wireless communication unit in a target node acquires all cooperative positioning nodes in a communication range of the target node and stores the cooperative positioning nodes in a cooperative positioning node list; and receiving the cooperative positioning response signal, the arrival time of the ranging signal, the response time of the ranging signal and the position information of the cooperative positioning node.
The first storage unit is used for storing a cooperative positioning node list, ranging information between a target node and all cooperative positioning nodes, an estimation value of position information of the target node and the position information of the cooperative positioning nodes.
The first calculating unit completes the calculation of the distance between the target node and each cooperative positioning node, the calculation of the position of the target node and the position updating of the target node, and stores the distance, the position calculation and the position updating of the target node in the first storage unit.
The anchor node includes: a second control unit, a second wireless communication unit and a second storage unit; the second control unit realizes the motion trail control of each anchor node;
the second wireless communication unit acquires all nodes to be positioned which are communicated with the anchor node, stores the nodes to be positioned in a node list to be positioned and stores the nodes to be positioned in the second storage unit; meanwhile, a cooperative positioning request and a ranging request are received, and self position information is sent to a node to be positioned, which is communicated with the anchor node.
The second storage unit is used for storing the position of the anchor node and transmitting the position to the second wireless communication unit.
And the second wireless communication unit senses the connection state of the anchor node and each node in the list, and if the anchor node is disconnected from the node to be positioned in the list, the disconnected node is deleted from the list, and the list is updated.
Step two, the target node sends a cooperative positioning request through the first wireless communication unit in a broadcasting way to obtain the response message of each cooperative positioning node in the communication range of the target node, obtain a cooperative positioning node set directly communicated with the target node, store the cooperative positioning node set in a cooperative positioning node list and store the cooperative positioning node set in a first storage unit of the target node;
the cooperative positioning node set comprises an anchor node with a known actual position and a node to be positioned with an unknown actual position;
step three, the target node sends a ranging request to each node in the cooperative positioning node set, and each cooperative positioning node respectively sends the prior information of the position of the cooperative positioning node, the time of receiving the ranging request and the time of sending a ranging response message to the target node through a respective first wireless communication unit and stores the prior information, the time of receiving the ranging request and the time of sending the ranging response message in a first storage unit of the target node;
step four, the first computing unit of the target node establishes a local factor graph describing the message transmission process between the target node and the cooperative positioning node thereof according to the cooperative positioning node list;
in the local factor graph, the position of each node in the list is respectively used as a random variable and is represented by an edge; for each factor, represented by a node; if a random variable appears in the factor, the edge corresponding to the random variable is connected to the node corresponding to the factor. Constructing an equal-sign node for random variables appearing in more than two factors, wherein the random variables on each edge connecting the equal-sign node are the same;
calculating posterior probabilities of random vectors of all nodes to be positioned in the local factor graph by using prior information of all the cooperative positioning nodes, performing factorization and calculating local factor nodes;
the specific process is as follows:
501, calculating Euclidean distances between a target node and each cooperative positioning node;
the euclidean distance between the target node i and the cooperative positioning node j is expressed as:
Figure BDA0003306372340000031
wherein c is electromagneticThe velocity of the wave propagating in air; t is t4Receiving the local time of the ranging response for the target node i; t is t1Sending a local time of a ranging request to a cooperative positioning node j for a target node i; t is t3Sending the local time of the ranging response to the target node i for the cooperative positioning node j; t is t2Receiving a local time of the ranging request for the cooperative positioning node j;
step 502, calculating an observation model of a target node by using the Euclidean distance;
target node i is at time t to Euclidean distance dijIs observed in a model of
Figure BDA0003306372340000032
Figure BDA0003306372340000033
Wherein
Figure BDA0003306372340000034
And (4) measuring the distance between the target node i and the cooperative positioning node j at the time t.
Step 503, carrying out linearization processing on the observation model, and processing the observation equation of each node into a linear model;
the linearized formula is:
Figure BDA0003306372340000035
Figure BDA0003306372340000036
representing the estimation value of the target node i to the position of the target node i at the moment t based on the random vector quantity at the moment t-1;
Figure BDA0003306372340000037
representing the estimation value of the cooperative positioning node j to the position of the cooperative positioning node j at the moment t based on the random vector quantity at the moment t-1,
Figure BDA0003306372340000038
is a constant term and is a constant number,
Figure BDA0003306372340000039
the euclidean distance between the target node i and the cooperative positioning node j at the time t is estimated, that is:
Figure BDA0003306372340000041
in the linearization processing process, respectively calculating a state transition equation and a state observation equation of a random vector of the position of the target node i at the moment t;
the state transition equation is expressed as:
Figure BDA0003306372340000042
wherein the content of the first and second substances,
Figure BDA0003306372340000043
representing a random vector of a target node i at a time T, and Δ T representing a time interval;
Figure BDA0003306372340000044
representing the velocity vector over a time interval deltat,
Figure BDA0003306372340000045
representing the state transition noise vector, obeying a mean of zero vector and a covariance matrix of Fi (t)(ii) a gaussian distribution of;
the observation equation of state is expressed as:
Figure BDA0003306372340000046
wherein the content of the first and second substances,
Figure BDA0003306372340000047
views of a random vector representing target node i at time tMeasuring value, | | · | |, which represents the euclidean distance,
Figure BDA0003306372340000048
a random vector representing a cooperative positioning node of the target node i at time t,
Figure BDA0003306372340000049
representing the observed noise vector, obeying a mean of zero vector and a covariance matrix of
Figure BDA00033063723400000410
The distribution of the gaussian component of (a) is,
Figure BDA00033063723400000411
and (3) a set of random vectors representing the cooperative positioning nodes of the target node i at the time t.
Step 504, aiming at the time from 0 to T, the posterior probability P (X) of all the random vectors of the positions of the nodes to be positioned is calculated(0:T)|Z(1:T))；
Satisfies the following conditions:
Figure BDA00033063723400000412
wherein ". varies" means "proportional to", X(0:T)Representing a matrix of random vectors of the positions of all nodes in the environment between time 0 and time T, Z(1:T)Representing a matrix formed by observations of random vectors of the positions of all nodes of the node pair itself and of the nodes connected thereto, Z, in an environment between time 1 and time T(1:T)By
Figure BDA00033063723400000413
And
Figure BDA00033063723400000414
is composed of (a) wherein
Figure BDA00033063723400000415
Representing a matrix formed by observed values of random vectors of self positions of all nodes in the environment from time 1 to time T,
Figure BDA00033063723400000416
representing a matrix formed by observations of random vectors of the positions of connected nodes of all pairs of nodes in an environment between time 1 and time T, X(·)Representing a matrix of random vectors of the positions of all nodes in the environment at a particular time.
Step 505, for the posterior probability P (X)(0:T)|Z(1:T)) The local factor node of the message transmission process from the time 0 to the time T between the target node and the cooperative positioning node is calculated;
the factor node represents the transition of the position state of the target node i, and the calculation formula is as follows:
Figure BDA00033063723400000417
Figure BDA00033063723400000418
representing the state transition probability of the random vector of the position of the target node i at the adjacent time,
Figure BDA00033063723400000419
and the likelihood function represents the observed value of the target node i to the self position random vector when the sample value of the position random vector of the target node i at the adjacent moment is known.
Step six, utilizing the prior probability of the random vector of the target node i at the moment t and the random vector of the target node i
Figure BDA00033063723400000420
Connected factor node direction
Figure BDA00033063723400000421
Message passed, calculated from
Figure BDA00033063723400000422
To all of
Figure BDA00033063723400000423
The messages transmitted by the connected factor nodes are further used for solving the posterior probability distribution of the random vector of the position of the target node i at the moment t
Figure BDA00033063723400000424
Namely the position of the target node i, and the distributed wireless cooperative positioning is realized.
Specifically, the method comprises the following steps:
first, at time t, through the factor node fi (tt-1)And the random vector posterior probability of the position of the target node i at the time t-1
Figure BDA0003306372340000051
Calculating a position random vector of a target node i at time t-1
Figure BDA0003306372340000052
Flow direction factor node fi (tt-1)Of a message
Figure BDA0003306372340000053
Figure BDA0003306372340000054
Then, calculating all position random vectors of the target node i
Figure BDA0003306372340000055
Connected factor nodes are in the direction of time t
Figure BDA0003306372340000056
Delivered messages, i.e. messages delivered to the target node i by the anchor node (i) connected to the target node i
Figure BDA0003306372340000057
And the node agent (i) to be positioned connected with the target node i transfers the message to the target node i
Figure BDA0003306372340000058
At the same time, calculate from
Figure BDA0003306372340000059
To all of
Figure BDA00033063723400000510
Messages transmitted by connected factor nodes, i.e. messages passed by the target node i to the anchor node (i) connected thereto
Figure BDA00033063723400000511
And the message transferred by the target node i to the node anchor (i) to be positioned connected with the target node i
Figure BDA00033063723400000512
Secondly, the posterior probability distribution of the target node i is updated according to all messages transmitted to the target node i, namely:
Figure BDA00033063723400000513
wherein the content of the first and second substances,
Figure BDA00033063723400000514
representing the set of all anchor nodes connected to the target node i at time t,
Figure BDA00033063723400000515
represents the set of all nodes to be positioned connected with the target node i at the time t,
Figure BDA00033063723400000516
representing the mean vector of the random vectors of the target node i at the time t;
Figure BDA00033063723400000517
indicating the position of the target node i at the time tA covariance matrix of the random vector;
finally, the target node i estimates the random vector at the time t
Figure BDA00033063723400000518
Expressed as:
Figure BDA00033063723400000519
to this end, an estimate of the random vector
Figure BDA00033063723400000520
As the final position of the target node i at time t.
The invention has the advantages that:
the invention adopts a message transmission cooperative positioning method based on a linearization state space model, designs a distributed wireless cooperative positioning method among network equipment through linearization of the model, and comprises acquisition of a cooperative positioning node list, a distance measurement strategy without time synchronization among nodes, a set of node positioning process and a set of corresponding devices, thereby reducing the computational complexity of a parameterized message transmission algorithm and having important significance for wireless cooperative positioning of the network equipment.
Drawings
FIG. 1 is a schematic diagram of a distributed wireless cooperative positioning method of the present invention;
FIG. 2 is a flow chart of a distributed wireless cooperative positioning method of the present invention;
FIG. 3 is a schematic diagram of a node device to be positioned according to the present invention;
FIG. 4 is a schematic view of an anchor node apparatus according to the present invention;
FIG. 5 is a factor graph of a classic plus factor node according to the present invention;
FIG. 6 is a factor graph of a classical multiplier node according to the present invention;
FIG. 7 is a factor graph of a classical equal-sign factor node according to the present invention;
FIG. 8 is a local factor graph of the message passing process from time 0 to time t between the target node and its cooperative positioning node according to the present invention;
FIG. 9 is a state transition equation representation of a random vector for a target node i at time t in accordance with the present invention;
FIG. 10 is a partial factorization form of the message passing process between the target node and its cooperating positioning nodes of the present invention;
FIG. 11 is a factor graph of ranging information of a target node to a cooperative positioning node at a given time according to the present invention;
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention provides a distributed wireless cooperative positioning method, which is used for formulating a node positioning strategy as shown in figure 1 aiming at a system and an application scene formed by randomly arranged distributed sensors or mobile nodes;
the method comprises the following specific steps: firstly, a target node broadcasts and sends a cooperative positioning request through a wireless communication unit; the nodes which can participate in cooperative positioning return to a target node cooperative positioning response message; the target node generates a cooperative positioning node list according to the cooperative positioning response message; then, the target node sends a ranging request to the cooperative positioning node; the cooperative positioning node sends the self position information, the local time of receiving the ranging request and the local time of sending the ranging response message to the target node; the target node stores the information to a data storage unit;
a calculation unit of the target node describes a change process of the position state of each node in the network along with time by using a state space model to obtain a state transfer equation and an observation equation of a random vector of the position of each node in the network; further generating a local factor graph of the target node according to the cooperative positioning node list; estimating posterior probability distribution of each node to be positioned at each moment position random vector through joint prior distribution of all node position random vectors at the initial moment, state transition probability of all node position random vectors and a joint likelihood function; predicting the prior probability of the random vector of the position of the target node at a given moment based on the linearization of the observation model and the factor graph representation of the observation model; calculating all messages transmitted to the position random vector by factor nodes connected with the position random vector of the target node; calculating messages transmitted from the position random vector to all factor nodes connected with the position random vector; solving the posterior probability distribution of the position random vector of the target node at a given moment; and finally, updating the position coordinates of the target node.
As shown in fig. 2, the specific steps are as follows:
step one, a distributed wireless cooperative positioning device comprising a target node, a plurality of nodes to be positioned and a plurality of anchor nodes is built;
specifically, the method comprises a specific number of nodes to be positioned with wireless communication capability and a specific number of anchor nodes with wireless communication capability. The nodes are distributed in a spatial area according to any topology to form an ad hoc network, one node to be positioned is randomly selected as a target node, and the other nodes to be positioned and anchor nodes which are communicated with the target node are collectively called cooperative positioning nodes of the target node.
Each node to be positioned is shown in fig. 3, and includes: the device comprises a first control unit, a first wireless communication unit, a first storage unit and a first calculation unit; the first control unit controls the motion trail of each node to be positioned;
a first wireless communication unit in a target node acquires all cooperative positioning nodes in a communication range of the target node and stores the cooperative positioning nodes in a cooperative positioning node list; the target node sends the prior position information of the target node at a specific time to each node to be positioned in the list through the first wireless communication unit of the target node, and receives a cooperative positioning response signal, a ranging signal arrival time, a ranging signal response time and position information of the cooperative positioning node of the target node.
The first storage unit is used for storing a cooperative positioning node list, ranging information between a target node and all cooperative positioning nodes, an estimation value of position information of the target node and the position information of the cooperative positioning nodes. The target node senses the connection state between the target node and each cooperative positioning node through the first wireless communication unit, if the target node and the cooperative positioning node are disconnected from communication, the disconnected node in the cooperative positioning node list is deleted, and the cooperative positioning node list in the first storage unit is updated.
The first calculating unit completes the calculation of the distance between the target node and each cooperative positioning node, the calculation of the position of the target node and the position updating of the target node, and stores the distance, the position calculation and the position updating of the target node in the first storage unit.
As shown in fig. 4, the anchor node includes: a second control unit, a second wireless communication unit and a second storage unit; the second control unit realizes the motion trail control of each anchor node;
the second wireless communication unit acquires all nodes to be positioned which are communicated with the anchor node, stores the nodes to be positioned in a node list to be positioned and stores the nodes to be positioned in the second storage unit; meanwhile, a cooperative positioning request and a ranging request are received, and self position information is sent to a node to be positioned, which is communicated with the anchor node.
The second storage unit is used for storing the position of the anchor node and transmitting the position to the second wireless communication unit.
And the second wireless communication unit senses the connection state of the anchor node and each node in the list, and if the anchor node is disconnected from the node to be positioned in the list, the disconnected node is deleted from the list, and the list is updated.
Step two, the target node sends a cooperative positioning request to all nodes in the communication range of the target node through the broadcast of the first wireless communication unit of the target node, obtains a response message of each cooperative positioning node in the communication range of the target node, obtains a cooperative positioning node set directly communicated with the target node, stores the cooperative positioning node set in a cooperative positioning node list and stores the cooperative positioning node set in a first storage unit of the target node;
the cooperative positioning node set comprises an anchor node with a known actual position and a node to be positioned with an unknown actual position;
step three, the target node sends a ranging request to each node in the cooperative positioning node set, and each cooperative positioning node respectively sends the prior information of the position of the cooperative positioning node, the time of receiving the ranging request and the time of sending a ranging response message to the target node through a respective first wireless communication unit and stores the prior information, the time of receiving the ranging request and the time of sending the ranging response message in a first storage unit of the target node;
step four, the first computing unit of the target node establishes a local factor graph describing the message transmission process between the target node and the cooperative positioning node thereof according to the cooperative positioning node list;
in the local factor graph, the position of each node in the list is respectively used as a random variable and is represented by an edge; for each factor, represented by a node; if a random variable appears in the factor, the edge corresponding to the random variable is connected to the node corresponding to the factor. Constructing an equal-sign node for random variables appearing in more than two factors, wherein the random variables on each edge connecting the equal-sign node are the same;
calculating posterior probabilities of random vectors of all nodes to be positioned in the local factor graph by using prior information of all the cooperative positioning nodes, performing factorization and calculating local factor nodes;
the specific process is as follows:
step 501, a first calculating unit of a target node reads the time when each cooperative positioning node receives a ranging request and the time when each cooperative positioning node sends a ranging response message from a first storage unit of the first calculating unit, and calculates the Euclidean distance between the target node and each cooperative positioning node;
the euclidean distance between the target node i and the cooperative positioning node j is expressed as:
Figure BDA0003306372340000081
wherein c is the speed of electromagnetic wave propagation in air; t is t4Receiving the local time of the ranging response for the target node i; t is t1Sending a local time of a ranging request to a cooperative positioning node j for a target node i; t is t3Sending the local time of the ranging response to the target node i for the cooperative positioning node j; t is t2Receiving a local time of the ranging request for the cooperative positioning node j;
step 502, calculating an observation model of a target node by using the Euclidean distance;
target node i is at time t to Euclidean distance dijIs observed in a model of
Figure BDA0003306372340000082
Figure BDA0003306372340000083
Wherein
Figure BDA0003306372340000084
And (4) measuring the distance between the target node i and the cooperative positioning node j at the time t.
Step 503, carrying out linearization processing on the observation model, and processing the observation equation of each node into a linear model;
the linearized formula is:
Figure BDA0003306372340000085
Figure BDA0003306372340000086
representing the estimation value of the target node i to the position of the target node i at the moment t based on the random vector quantity at the moment t-1;
Figure BDA0003306372340000087
representing the estimation value of the cooperative positioning node j to the position of the cooperative positioning node j at the moment t based on the random vector quantity at the moment t-1,
Figure BDA0003306372340000088
is a constant term and satisfies:
Figure BDA0003306372340000089
Figure BDA00033063723400000810
the euclidean distance between the target node i and the cooperative positioning node j at the time t is estimated, that is:
Figure BDA00033063723400000811
to this end, the observation equations for the individual nodes have been treated as linear models.
In the linearization processing process, a first calculation unit of a target node uses a state space model to describe the process that the position state of the target node changes along with time to obtain a state transition equation and a state observation equation of a target node i at a moment t;
based on the above linearization process, the ranging information of the target node i to the node j at the time t can be obtained
Figure BDA00033063723400000812
The factor graph representation of (a) is further expanded into the form as shown in fig. 11.
For node i, the state transition equation of its location random vector at time t can be expressed as:
Figure BDA00033063723400000813
wherein
Figure BDA00033063723400000814
A random vector representing the position of the target node i at time t,
Figure BDA00033063723400000815
the state-transfer function is represented by a function,
Figure BDA00033063723400000816
representing the state transition noise vector, obeying a mean of zero vector and a covariance matrix of Fi (t)(ii) a gaussian distribution of;
for node i, the observation equation of its location random vector at time t can be expressed as:
Figure BDA0003306372340000091
wherein
Figure BDA0003306372340000092
An observed value representing a random vector of the position of the target node i at the time t;
Figure BDA0003306372340000093
the representation of the observation function is shown,
Figure BDA0003306372340000094
a random vector representing the position of a certain cooperative positioning node of the target node i at time t,
Figure BDA0003306372340000095
representing the observed noise vector, obeying a mean of zero vector and a covariance matrix of
Figure BDA0003306372340000096
The distribution of the gaussian component of (a) is,
Figure BDA0003306372340000097
and (3) a set of random vectors representing the cooperative positioning nodes of the target node i at the time t.
Considering the motion model further, as shown in fig. 9, the state transition equation of the random vector of the position of the target node i at the time t is expressed as:
Figure BDA0003306372340000098
wherein Δ T represents a time interval;
Figure BDA0003306372340000099
representing the direction of speed within a time interval Δ TAn amount;
in this case, the state observation equation of the position random vector of the node i can be expressed as:
Figure BDA00033063723400000910
step 504, aiming at the factor graphs of all nodes from time 0 to time T, the posterior probability P (X) of the random vector of the positions of all the nodes to be positioned(0:T)|Z(1:T)) Satisfies the following conditions:
Figure BDA00033063723400000911
wherein ". varies" means "proportional to", X(0:T)Representing a matrix of random vectors of the positions of all nodes in the environment between time 0 and time T, Z(1:T)Representing a matrix formed by observations of random vectors of the positions of all nodes of the node pair itself and of the nodes connected thereto, Z, in an environment between time 1 and time T(1:T)By
Figure BDA00033063723400000912
And
Figure BDA00033063723400000913
is composed of (a) wherein
Figure BDA00033063723400000914
Representing a matrix formed by observed values of random vectors of self positions of all nodes in the environment from time 1 to time T,
Figure BDA00033063723400000915
representing a matrix formed by observations of random vectors of the positions of connected nodes of all pairs of nodes in an environment between time 1 and time T, X(·)Representing a matrix of random vectors of the positions of all nodes in the environment at a particular time.
By joint prior distribution P (X) of random vectors of all node positions at initial time(0)) State transition probability P (X) of random vector of all node positions(T)|X(T-1)) And a joint likelihood function p (Z) of observed values of the random vectors of the positions of the nodes when the sample values of the random vectors of the positions of all the nodes at the time T are known(T)|X(T)) Estimating the posterior probability distribution P (X) of the random vectors of the positions of all nodes from time 0 to t(0:t)|Z(1:t))：
Figure BDA00033063723400000916
Specifically, the method comprises the following steps:
the joint prior distribution of the random vectors of all node positions at time 0 is:
Figure BDA00033063723400000917
wherein A represents the set of all anchor nodes, and u represents the set of all nodes to be positioned;
the state transition probability of the random vector at all node positions at time t is:
Figure BDA00033063723400000918
the joint likelihood function of all node position random vectors at time t is:
Figure BDA00033063723400000919
step 505, for the posterior probability P (X)(0:T)|Z(1:T)) The local factor node of the message transmission process from the time 0 to the time T between the target node and the cooperative positioning node is calculated;
three typical factor nodes are defined: plus factor nodes (as shown in fig. 5), multiply factor nodes (as shown in fig. 6), and equal factor nodes (as shown in fig. 7).
The message computation update rule for the plus factor node is mathematically expressed as follows:
m+→Z＝mX→++mY→+
V+→Z＝VX→++VY→+
wherein m is a mean vector of the corresponding probability distribution, and V is a covariance matrix of the corresponding probability distribution; m is+→ZMean vector, V, representing the probability distribution corresponding to messages flowing from the plus factor node "+" to the random variable Z+→ZA covariance matrix representing a probability distribution corresponding to a message flowing from the plus factor node "+" to the random variable Z;
the message computation update rule for the multiplier factor node is mathematically expressed as follows:
mA→Y＝AmX→A
VA→Y＝AVX→AAH
wherein A represents a matrix or vector, mA→YA mean vector, V, representing the probability distribution corresponding to messages flowing from the multiplier factor node "A" to the random variable YA→YA covariance matrix representing the probability distribution of messages flowing from the multiplier node "A" to the random variable Y, AHRepresents the conjugate transpose of a;
the message calculation update rule for the equal sign factor node is defined as follows:
Figure BDA0003306372340000101
Figure BDA0003306372340000102
wherein m is＝→ZMeans vector, V, representing the probability distribution corresponding to a message flowing from equal-sign factor node ═ to random variable Z＝→ZA covariance matrix representing the probability distribution corresponding to a message flowing from an equal-sign factor node to the random variable Z,
Figure BDA0003306372340000103
Moore-Penrose Pseudo-Inverse operation.
Posterior probability P (X) of random vector according to positions of all nodes to be positioned(0:T)|Z(1:T)) The local factor graph of the message transmission process from the time 0 to the time t between the target node and the cooperative positioning node thereof as shown in fig. 8 can be constructed;
the factor node represents the transition of the position state of the target node i, and the calculation formula is as follows:
Figure BDA0003306372340000104
Figure BDA0003306372340000105
representing the state transition probability of the random vector of the position of the target node i at the adjacent time,
Figure BDA0003306372340000106
and the likelihood function represents the observed value of the target node i to the self position random vector when the sample value of the position random vector of the target node i at the adjacent moment is known.
Step six, utilizing the prior probability of the random vector of the target node i at the moment t and the random vector of the target node i
Figure BDA0003306372340000107
Connected factor node direction
Figure BDA0003306372340000108
Message passed, calculated from
Figure BDA0003306372340000109
To all of
Figure BDA00033063723400001010
The messages transmitted by the connected factor nodes are further used for solving the posterior probability distribution of the random vector of the position of the target node i at the moment t
Figure BDA00033063723400001011
Namely the position of the target node i, and the distributed wireless cooperative positioning is realized.
Predicting the prior probability of the random vector of the position of the target node i at the time t based on the linearization of the observation model and the factor graph representation; calculating all position random vectors of the target node i
Figure BDA00033063723400001012
Connected factor node direction
Figure BDA00033063723400001013
A message to be delivered; is calculated from
Figure BDA00033063723400001014
To all of
Figure BDA00033063723400001015
Message transmitted by connected factor nodes; solving the posterior probability distribution of the random vector of the position of the target node i at the moment t
Figure BDA00033063723400001016
(i.e. messages)
Figure BDA00033063723400001017
)。
Specifically, the method comprises the following steps:
first, at time t, through the factor node fi (tt-1)And the random vector posterior probability of the position of the target node i at the time t-1
Figure BDA0003306372340000111
Calculating a position random vector of a target node i at time t-1
Figure BDA0003306372340000112
Flow direction factor node fi (tt-1)Of a message
Figure BDA0003306372340000113
Figure BDA0003306372340000114
Then, calculating all position random vectors of the target node i
Figure BDA0003306372340000115
Connected factor nodes are in the direction of time t
Figure BDA0003306372340000116
Delivered messages, i.e. messages delivered to the target node i by the anchor node (i) connected to the target node i
Figure BDA0003306372340000117
And the node agent (i) to be positioned connected with the target node i transfers the message to the target node i
Figure BDA0003306372340000118
At the same time, calculate from
Figure BDA0003306372340000119
To all of
Figure BDA00033063723400001110
Messages transmitted by connected factor nodes, i.e. messages passed by the target node i to the anchor node (i) connected thereto
Figure BDA00033063723400001111
And the message transferred by the target node i to the node anchor (i) to be positioned connected with the target node i
Figure BDA00033063723400001112
The process of exchanging ranging information between nodes at time t for the local factor graph of the message passing process between the target node i and its cooperative positioning node is further decomposed into the form shown in fig. 10, which includes the target node iThe target node i at the time t compares the ranging information of the node agent (i) to be positioned connected with the target node i
Figure BDA00033063723400001113
Node agent (i) to be located measures the ranging information of target node i at time t
Figure BDA00033063723400001114
Ranging information of anchor node anchor (i) to which target node i is connected at time t
Figure BDA00033063723400001115
Secondly, the posterior probability distribution of the target node i is updated according to all messages transmitted to the target node i, namely:
Figure BDA00033063723400001116
wherein the content of the first and second substances,
Figure BDA00033063723400001117
representing the set of all anchor nodes connected to the target node i at time t,
Figure BDA00033063723400001118
represents the set of all nodes to be positioned connected with the target node i at the time t,
Figure BDA00033063723400001119
representing the mean vector of the random vectors of the target node i at the time t;
Figure BDA00033063723400001120
a covariance matrix representing a random vector of a target node i at a time t;
Figure BDA00033063723400001121
can be expressed as:
Figure BDA00033063723400001122
covariance matrix of random vector of target node i at time t
Figure BDA00033063723400001123
Can be expressed as:
Figure BDA00033063723400001124
finally, the target node i estimates the random vector at the time t
Figure BDA00033063723400001125
Expressed as:
Figure BDA00033063723400001126
to this end, an estimate of the random vector
Figure BDA00033063723400001127
As the final position of the target node i at time t.

Claims (6)

1. A distributed wireless cooperative positioning method is characterized by comprising the following specific steps;
firstly, a distributed wireless cooperative positioning device comprising a target node, a plurality of nodes to be positioned and a plurality of anchor nodes is built;
the method specifically comprises the following steps: the nodes are distributed in a spatial area according to any topology to form an ad hoc network, one node to be positioned is randomly selected as a target node, and the other nodes to be positioned and anchor nodes which are communicated with the target node are collectively called cooperative positioning nodes of the target node;
then, the target node sends a cooperative positioning request through the first wireless communication unit to obtain a response message of each cooperative positioning node in the communication range of the target node, and the target node generates a cooperative positioning node list according to the cooperative positioning response message;
then, the target node sends a ranging request to each cooperative positioning node in the list, and the cooperative positioning nodes send the prior information of the self position, the time of locally receiving the ranging request and the time of locally sending a ranging response message to the target node; the first computing unit of the target node establishes a local factor graph describing the message transmission process between the target node and the cooperative positioning node thereof according to the cooperative positioning node list;
finally, calculating posterior probability distribution of the positions of all nodes to be positioned in the local factor graph at each moment by using the prior information of each cooperative positioning node, performing factorization, and calculating local factor nodes; and further predicting the prior probability of the position of the target node at a given moment, calculating messages transmitted to the position by all factor nodes connected with the position of the target node and messages transmitted to all factor nodes connected with the position from the position, and further solving the posterior probability distribution of the position of the target node at the given moment, namely the position of the target node, so as to realize the distributed wireless cooperative positioning.
2. The distributed wireless cooperative positioning method according to claim 1, wherein in said distributed wireless cooperative positioning apparatus, each node to be positioned comprises: the device comprises a first control unit, a first wireless communication unit, a first storage unit and a first calculation unit; the first control unit controls the motion trail of each node to be positioned;
a first wireless communication unit in a target node acquires all cooperative positioning nodes in a communication range of the target node and stores the cooperative positioning nodes in a cooperative positioning node list; receiving a cooperative positioning response signal, a ranging signal arrival time, a ranging signal response time and position information of a cooperative positioning node;
the first storage unit is used for storing a cooperative positioning node list, ranging information between a target node and all cooperative positioning nodes, an estimation value of position information of the target node and the position information of the cooperative positioning nodes;
the first calculation unit completes the calculation of the distance between the target node and each cooperative positioning node, the position calculation of the target node and the position update of the target node, and stores the distance, the position calculation of the target node and the position update of the target node in the first storage unit;
the anchor node includes: a second control unit, a second wireless communication unit and a second storage unit; the second control unit realizes the motion trail control of each anchor node;
the second wireless communication unit acquires all nodes to be positioned which are communicated with the anchor node, stores the nodes to be positioned in a node list to be positioned and stores the nodes to be positioned in the second storage unit; meanwhile, receiving a cooperative positioning request and a ranging request, and sending self position information to a node to be positioned, which is communicated with the anchor node;
the second storage unit is used for storing the position of the anchor node and transmitting the position to the second wireless communication unit;
and the second wireless communication unit senses the connection state of the anchor node and each node in the list, and if the anchor node is disconnected from the node to be positioned in the list, the disconnected node is deleted from the list, and the list is updated.
3. The distributed wireless cooperative positioning method according to claim 1, wherein the cooperative positioning node set includes an anchor node with a known actual position and a node to be positioned with an unknown actual position.
4. A distributed wireless cooperative positioning method according to claim 1, wherein in the local factor graph, the position of each node in the list is respectively used as a random variable and represented by an edge; for each factor, represented by a node; if the random variable appears in the factor, connecting the edge corresponding to the random variable with the node corresponding to the factor; for random variables that occur in more than two factors, a equal-sign node is constructed, with the random variables on each edge connecting the equal-sign nodes being the same.
5. The distributed wireless cooperative positioning method according to claim 1, wherein the specific process of calculating the posterior probability of the random vector of all nodes to be positioned in the local factor graph and the local factor nodes is as follows:
501, calculating Euclidean distances between a target node and each cooperative positioning node;
the euclidean distance between the target node i and the cooperative positioning node j is expressed as:
Figure FDA0003306372330000021
wherein c is the speed of electromagnetic wave propagation in air; t is t4Receiving the local time of the ranging response for the target node i; t is t1Sending a local time of a ranging request to a cooperative positioning node j for a target node i; t is t3Sending the local time of the ranging response to the target node i for the cooperative positioning node j; t is t2Receiving a local time of the ranging request for the cooperative positioning node j;
step 502, calculating an observation model of a target node by using the Euclidean distance;
target node i is at time t to Euclidean distance dijIs observed in a model of
Figure FDA0003306372330000022
Figure FDA0003306372330000023
Wherein
Figure FDA0003306372330000024
Measuring the distance between the target node i and the cooperative positioning node j at the moment t;
step 503, carrying out linearization processing on the observation model, and processing the observation equation of each node into a linear model;
the linearized formula is:
Figure FDA0003306372330000025
Figure FDA0003306372330000026
representing the estimation value of the target node i to the position of the target node i at the moment t based on the random vector quantity at the moment t-1;
Figure FDA0003306372330000027
representing the estimation value of the cooperative positioning node j to the position of the cooperative positioning node j at the moment t based on the random vector quantity at the moment t-1,
Figure FDA0003306372330000028
is a constant term and is a constant number,
Figure FDA0003306372330000029
the euclidean distance between the target node i and the cooperative positioning node j at the time t is estimated, that is:
Figure FDA00033063723300000210
in the linearization processing process, respectively calculating a state transition equation and a state observation equation of a random vector of the position of the target node i at the moment t;
the state transition equation is expressed as:
Figure FDA0003306372330000031
wherein the content of the first and second substances,
Figure FDA0003306372330000032
representing a random vector of a target node i at a time T, and Δ T representing a time interval;
Figure FDA0003306372330000033
representing the velocity vector over a time interval deltat,
Figure FDA0003306372330000034
representing the state transition noise vector, obeying a mean of zero vector and a covariance matrix of Fi (t)(ii) a gaussian distribution of;
the observation equation of state is expressed as:
Figure FDA0003306372330000035
wherein the content of the first and second substances,
Figure FDA0003306372330000036
represents the observed value of the random vector of the target node i at the moment t, | | · | | represents the euclidean distance,
Figure FDA0003306372330000037
a random vector representing a cooperative positioning node of the target node i at time t,
Figure FDA0003306372330000038
representing the observed noise vector, obeying a mean of zero vector and a covariance matrix of
Figure FDA0003306372330000039
The distribution of the gaussian component of (a) is,
Figure FDA00033063723300000310
representing a set consisting of random vectors of cooperative positioning nodes of a target node i at a time t;
step 504, aiming at the time from 0 to T, the posterior probability P (X) of all the random vectors of the positions of the nodes to be positioned is calculated(0:T)|Z(1:T))；
Satisfies the following conditions:
Figure FDA00033063723300000311
wherein ". varies" means "proportional to", X(0:T)Representing a matrix of random vectors of the positions of all nodes in the environment between time 0 and time T, Z(1:T)Representing a matrix formed by observations of random vectors of the positions of all nodes of the node pair itself and of the nodes connected thereto, Z, in an environment between time 1 and time T(1:T)By
Figure FDA00033063723300000312
And
Figure FDA00033063723300000313
is composed of (a) wherein
Figure FDA00033063723300000314
Representing a matrix formed by observed values of random vectors of self positions of all nodes in the environment from time 1 to time T,
Figure FDA00033063723300000315
representing a matrix formed by observations of random vectors of the positions of connected nodes of all pairs of nodes in an environment between time 1 and time T, X(·)Representing a matrix formed by random vectors of positions of all nodes in the environment at a specific moment;
step 505, for the posterior probability P (X)(0:T)|Z(1:T)) The local factor node of the message transmission process from the time 0 to the time T between the target node and the cooperative positioning node is calculated;
the factor node represents the transition of the position state of the target node i, and the calculation formula is as follows:
Figure FDA00033063723300000316
Figure FDA00033063723300000317
representing a target nodeThe position of i is randomized to the state transition probability of the vector at the adjacent time,
Figure FDA00033063723300000325
) And the likelihood function represents the observed value of the target node i to the self position random vector when the sample value of the position random vector of the target node i at the adjacent moment is known.
6. The distributed wireless cooperative positioning method according to claim 1, wherein the step of calculating the position of the target node at a given time includes the following steps:
firstly, a factor node f at a time t is passed through a target node ii (t|t-1)And the random vector posterior probability of the position of the target node i at the time t-1
Figure FDA00033063723300000319
Calculating the position random vector of the target node i at the moment t-1
Figure FDA00033063723300000320
Flow direction factor node fi (t|t-1)Of a message
Figure FDA00033063723300000321
Figure FDA00033063723300000322
Then, calculating all position random vectors of the target node i
Figure FDA00033063723300000323
Connected factor nodes are in the direction of time t
Figure FDA00033063723300000324
Delivered messages, i.e. delivered to target node i by anchor node (i) connected to target node iMessage
Figure FDA0003306372330000041
And the node agent (i) to be positioned connected with the target node i transfers the message to the target node i
Figure FDA0003306372330000042
At the same time, calculate from
Figure FDA0003306372330000043
To all of
Figure FDA0003306372330000044
Messages transmitted by connected factor nodes, i.e. messages passed by the target node i to the anchor node (i) connected thereto
Figure FDA0003306372330000045
And the message transferred by the target node i to the node anchor (i) to be positioned connected with the target node i
Figure FDA0003306372330000046
Secondly, updating the posterior probability distribution of the target node i according to all messages transmitted to the target node i to obtain the position of the target node i, namely:
Figure FDA0003306372330000047
wherein the content of the first and second substances,
Figure FDA0003306372330000048
representing the set of all anchor nodes connected to the target node i at time t,
Figure FDA0003306372330000049
indicating all connections to target node i to be positioned at time tA set of nodes is provided, wherein,
Figure FDA00033063723300000410
representing the mean vector of the random vectors of the target node i at the time t;
Figure FDA00033063723300000411
a covariance matrix representing a random vector of a target node i at a time t;
finally, the target node i estimates the random vector at the time t
Figure FDA00033063723300000412
Expressed as:
Figure FDA00033063723300000413
to this end, an estimate of the random vector
Figure FDA00033063723300000414
As the final position of the target node i at time t.
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