CN113115205B - Distributed cooperative positioning method based on angle measurement - Google Patents

Distributed cooperative positioning method based on angle measurement Download PDF

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CN113115205B
CN113115205B CN202110354737.3A CN202110354737A CN113115205B CN 113115205 B CN113115205 B CN 113115205B CN 202110354737 A CN202110354737 A CN 202110354737A CN 113115205 B CN113115205 B CN 113115205B
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CN113115205A (en
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武楠
杨吕骁
李彬
杨碧珩
崔姬石
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Beijing Institute of Technology BIT
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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
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a distributed cooperative positioning method based on angle measurement, wherein in a cooperative positioning scene, each user node realizes distributed updating of position estimation of each user by utilizing self-based position prior information, observing the arrival azimuth angle between each node in the communication range of each user node and using a factor graph model and a generalized approximate message transfer algorithm, and finally enabling each node to simultaneously obtain a high-precision positioning result through multiple rounds of iteration, thereby realizing high-precision position estimation with low complexity.

Description

Distributed cooperative positioning method based on angle measurement
Technical Field
The invention belongs to the technical field of cooperative positioning, and particularly relates to a distributed cooperative positioning method based on angle measurement.
Background
In recent years, with the rapid development of wireless networks and communication technologies, the demand of users for precise positioning has sharply risen. Common positioning methods mainly include a distance measurement based method, an angle measurement based method, and other measurement based methods according to a specific mechanism of positioning. In the location based on ranging, the distance or the distance Difference between nodes is obtained by acquiring the Time of Arrival (TOA) or the Time Difference of Arrival (TDOA) of a signal, so that the location solution is implemented by using a method such as trilateral location or multilateral location. However, it is not easy to obtain a highly accurate distance measurement. Ultra Wide Band (UWB) wireless communication technology uses extremely narrow pulse signals with strong multipath resolution to realize centimeter-level positioning, but the technology is usually used in specific areas such as factories and the like, and the deployment cost is very high. The high-frequency or millimeter wave communication used in the fifth generation mobile communication (5G) can realize higher-precision time difference of arrival measurement, however, a high-precision crystal oscillator is required to be adopted to further reduce the clock error, so that higher cost is faced.
With the development of wireless communication technologies such as 5G, a large-scale antenna (Massive MIMO) technology is widely applied to various communication nodes, and provides a beam with higher resolution for a user, so that high-precision positioning based on angle measurement becomes possible. The antenna array is used for measuring the Angle of Arrival (AOA) of the transmitted signal, including the information of the azimuth Angle and the pitch Angle between the nodes, and the position estimation of the user node can be calculated.
However, the conventional positioning method requires that each node with unknown position needs to establish communication with a sufficient number of anchor nodes (such as base stations), and it is difficult to simultaneously satisfy the requirements of anchor node coverage area, communication stability and positioning accuracy. Therefore, the cooperative localization has been receiving attention from researchers. In cooperative positioning, the user node can not only communicate with the anchor node, but also communicate with other user nodes to obtain more observation information to assist positioning, thereby reducing the requirement on the arrangement density of the anchor node; or on the premise of prior position information, the high-precision position estimation can be realized only through the cooperation between user nodes without depending on anchor nodes. In addition, compared with a centralized cooperation scheme, the distributed cooperation scheme can effectively reduce the communication cost and energy consumption of the user node, and further improves the practicability of cooperative positioning.
Disclosure of Invention
In view of this, the present invention provides a distributed cooperative positioning method based on angle measurement, which can achieve high-precision position estimation with low complexity.
The technical scheme for realizing the invention is as follows:
a distributed cooperative positioning method based on angle measurement comprises the following steps:
step one, constructing a wireless cooperative positioning network;
and step two, utilizing a generalized approximate message transfer algorithm to realize position estimation.
Further, the first step is specifically as follows:
1.1, define a group of NThe distributed wireless cooperative positioning network composed of nodes aims to estimate two-dimensional position coordinates x of each nodeiI is 1,2, …, N; in the cooperative positioning network, the prior mean value of the positions of all nodes is known
Figure BDA0003000778740000021
And variance
Figure BDA0003000778740000022
(the covariance between variables is ignored in the invention) and each node can receive the KiSignals of adjacent nodes, and measuring the arrival angle theta of the signals on a two-dimensional planei,k,k＝1,2,…,Ki；
1.2, in order to reduce the calculation complexity of position estimation, the invention adopts a linearization mode to construct the relationship between angle observation and position coordinates; for node i, a linear observation of the system is defined
Figure BDA0003000778740000023
Figure BDA0003000778740000024
Where ρ isi,k＝[cosθi,k,sinθi,k]T(ii) a Therefore, for the node i, the model for constructing the wireless cooperative positioning network is rhoi＝Aizi+diWherein the position coordinate variable
Figure BDA0003000778740000031
By K adjacent to node iiPosition coordinates of each node and node i itself, AiAs a linear transformation matrix which varies dynamically with the node position estimate, diTo observe noise;
1.3, solving the edge probability distribution of each coordinate variable by adopting a factor graph method; in the distributed network, for each node i, the position coordinates of adjacent nodes and the position coordinates of the adjacent nodes are expressed as variable nodes, each factor obtained after the decomposition of the combined posterior probability density function is expressed as a factor node, and the variable nodes with the corresponding relation are connected with the factor nodes to form edges, so that a factor graph of the node i is formed, and the estimated value of the coordinate variable of the node i is obtained.
Further, the second step is specifically as follows:
2.1, initializing the message on the factor graph by using the mean value and the variance of the prior observation of each node position; through mutual communication, each node obtains prior information of adjacent nodes, measures the arrival angle of signals and calculates linear observation rho; considering the factor graph formed at the ith node; initializing the mean z of the probability distribution of each variable node using the position priors of the neighboring nodes and the node itself(0)And variance
Figure BDA0003000778740000032
Wherein the superscript (t) of each variable represents the iteration round t; for simplicity of expression, the subscript i representing the node sequence number in each variable will be ignored in step 2.2;
2.2, for the linear model rho, Az + d, using a generalized approximate message transfer algorithm to realize message updating on the factor graph; on the initialized factor graph, message transmission is realized through iterative computation;
2.3, the iterative process in step 2.2 is stopped after reaching the convergence condition, at which point
Figure BDA0003000778740000033
The position estimation result is the final position estimation result of the ith node; at this time, each user node obtains a position estimation result with higher accuracy.
Further, the iterative process in step 2.2 is as follows:
in the t-th iteration:
a. for node i, based on the estimated value of the position coordinate in the initialization or the previous iteration
Figure BDA0003000778740000034
Calculating the estimated value of the distance between each adjacent node and the node i
Figure BDA0003000778740000041
Based on the estimated value of the distance,dynamic computation of linear transformation matrices
Figure BDA0003000778740000042
Wherein
Figure BDA0003000778740000043
diag (f) denotes a diagonal matrix composed of a column vector f as the main diagonal element, InWhich represents an identity matrix of order n,
Figure BDA0003000778740000044
represents the kronecker product;
b. for each observed value ρ of the linear observations ρjBased on initialisation or obtained in a previous iteration
Figure BDA0003000778740000045
And linear transformation matrix A obtained in the iteration of the current round(t)Computing the second moment of the pseudo-priors for their respective noise-free observations
Figure BDA0003000778740000046
And first moment
Figure BDA0003000778740000047
c. For each observed value ρ of the linear observations ρjBased on initialisation or obtained in a previous iteration
Figure BDA0003000778740000048
Obtained in the iteration of the current round
Figure BDA0003000778740000049
Calculating the second moment of the message transmitted to the adjacent variable node
Figure BDA00030007787400000410
And first moment
Figure BDA00030007787400000411
d. Based onObtained in an initialisation or previous iteration
Figure BDA00030007787400000412
Obtained in the iteration of the current round
Figure BDA00030007787400000413
Calculating the second moment of the product of all linear observations transmitted to the node i message
Figure BDA00030007787400000414
And a first moment r(t)；
e. Based on results from the iteration
Figure BDA00030007787400000415
Calculating the mean value of the estimated values of the i-position distribution of the nodes as
Figure BDA00030007787400000416
Variance of
Figure BDA00030007787400000417
f. The estimation result of the variable distribution obtained by the iteration of the current round
Figure BDA00030007787400000418
Broadcasting to adjacent nodes, and receiving the estimation result of the position distribution obtained by the adjacent nodes after the iteration, thereby constructing the mean value and the variance of the probability distribution of the variable nodes after the iteration
Figure BDA00030007787400000419
Has the advantages that:
(1) the invention provides a linearization model based on angle observation under a cooperative positioning scene. Based on the model, the minimum mean square error estimation of the position variable is realized by Gaussian approximation of the position and angle observation of each node and using a generalized approximate message transfer algorithm, so that the position estimation precision is ensured, and meanwhile, the calculation complexity is effectively reduced.
(2) The invention realizes the message transmission algorithm and the position estimation in a distributed mode, effectively reduces the communication cost and the energy consumption of the user node and improves the practicability of the system.
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Fig. 1 is a schematic view of a cooperative positioning network topology.
FIG. 2 is a diagram illustrating the relationship between angle-of-arrival observation and linear observation.
Fig. 3 is a flow chart of a two-dimensional distributed cooperative positioning algorithm based on angle measurement.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
In the existing positioning method based on angle measurement, a plurality of anchor nodes with known positions are generally required to be arranged, and a plurality of angle measurements are obtained to realize the calculation of the user position. However, if the angle measurement between user nodes can be introduced into the model and inaccurate position coordinates of each node are broadcast to other user nodes within the communication range, the constraint on the arrangement of the anchor nodes can be reduced or the positioning accuracy can be improved when the arrangement of the anchor nodes is fixed. On the basis, the invention provides a distributed cooperative positioning method based on angle measurement, and a robust positioning system is constructed. Under a cooperative positioning scene, each user node observes the arrival azimuth angle among all nodes in the communication range based on the position prior information of the user node, realizes distributed updating of the position estimation of each user by using a factor graph model and a generalized approximate message transfer algorithm, and finally enables all nodes to obtain high-precision positioning results at the same time through multiple rounds of iteration.
The method comprises the following specific steps:
description and modeling of a wireless cooperative positioning network;
in a distributed wireless cooperative positioning network composed of N nodes, a signal is assumed to be spread in a free space at a line of sight, and a schematic diagram of a network topology is shown in fig. 1. The goal of cooperative positioning is to estimate the two-dimensional position coordinates x of each nodei＝[xi,yi]T,i＝1,2,…,N。
For each node i, the mean of its location priors is known
Figure BDA0003000778740000061
And variance
Figure BDA0003000778740000062
Figure BDA0003000778740000063
In order to reduce the computational complexity, the invention assumes mutual independence between the position variables and ignores the covariance between the variables. In particular, the variance of the anchor node location coordinates should be considered zero. The cooperative positioning network does not limit the existence of the anchor nodes and the quantity and distribution of the anchor nodes.
In the cooperative positioning process, each node can receive signals of a plurality of nodes in the communication range of the node, and measure the arrival angle of the signals on a two-dimensional plane. Let node i be able to receive a message from KiSignals of adjacent nodes, the node numbers being m respectivelyi,k,k＝1,2,…,Ki. As shown in FIG. 2, node m is showni,kThe observed value of the arrival angle of the transmitted signal is
Figure BDA00030007787400000611
Where atan2(y, x) is an element (-pi, pi)]Four-quadrant arctangent, e, representing two-dimensional coordinates (x, y)i,kTo observe the noise.
The invention provides a two-dimensional cooperative positioning method based on angle measurement, namely, an observation theta is constructedi,kAnd position coordinate xiThe high-precision estimation of the position coordinates is realized with low complexity by the relationship between the two.
Secondly, in order to reduce the calculation complexity of position estimation, the invention adopts a linearization mode to construct the relationship between angle observation and position coordinates. For node i, a linear observation of the system is defined
Figure BDA0003000778740000064
Figure BDA0003000778740000065
Where ρ isi,k＝[cosθi,k,sinθi,k]TAs shown in fig. 2. Therefore, for the node i, the model for constructing the wireless cooperative positioning network is rhoi＝Aizi+diWherein the position coordinate variable
Figure BDA0003000778740000066
Figure BDA0003000778740000067
As a linear transformation matrix which varies dynamically with the node position estimate, diTo observe the noise. For convenient expression, for variable ziIs blocked and relabeled as
Figure BDA0003000778740000068
Figure BDA0003000778740000069
Namely, it is
Figure BDA00030007787400000610
Thirdly, in order to describe the joint posterior probability density function of the position coordinates of each node in the whole network and solve the edge probability distribution of each coordinate variable, the invention adopts a Factor Graph (Factor Graph) method. For the wireless cooperative positioning network provided by the invention, for the node i, the position coordinates of the adjacent nodes and the node i are expressed as variable nodes, each factor obtained after the decomposition of the combined posterior probability density function is expressed as a factor node, and the variable nodes and the factor nodes with the corresponding relation are connected into edges, so that a factor graph of the node i is formed. The factor graph can represent the factorization of a complex global function with multiple variables, and the solution of the edge probability distribution of all the variables is realized through algorithms such as belief propagation and generalized approximate message transfer. In the distributed network, each node forms a factor graph, and the estimated value of the coordinate variable of the node i is calculated from the factor graph of the node i.
Step two, using generalized approximate message transfer algorithm to realize position estimation
Initializing the message on the factor graph by using the mean and variance of the prior observation of the position of each node aiming at the model in the step one. Through mutual communication, each node obtains prior information of adjacent nodes, measures the arrival angle of signals and calculates linear observation rho. Consider the factor graph formed at the ith node. Initializing mean values of variable node probability distributions using position priors of neighboring nodes and nodes themselves
Figure BDA0003000778740000071
Figure BDA0003000778740000072
And variance
Figure BDA0003000778740000073
Figure BDA0003000778740000074
Where the superscript (t) of each variable represents the iteration round t. For simplicity of expression, the subscript i representing the node serial number in each variable is ignored in the second step and used
Figure BDA0003000778740000075
An estimated value representing an unknown variable fjRepresenting the jth element of the vector f.
And secondly, for the linear model rho being Ax + d, using a Generalized Approximate Message Passing (GAMP) algorithm to realize Message updating on the factor graph. And (c) iteratively executing the following steps a-f on the initialized factor graph to realize message passing. In the t-th iteration:
a. for node i, based on the estimated value of the position coordinate in the initialization or the previous iteration
Figure BDA0003000778740000076
Calculating the estimated value of the distance between each adjacent node and the node i
Figure BDA0003000778740000077
Where |) represents the 2-norm of the vector. Dynamically calculating a linear transformation matrix based on the distance estimates
Figure BDA0003000778740000078
Figure BDA0003000778740000079
Wherein
Figure BDA00030007787400000710
diag (f) denotes a diagonal matrix composed of a column vector f as the main diagonal element, InWhich represents an identity matrix of order n,
Figure BDA00030007787400000711
representing the kronecker product.
b. For each observed value ρ of the linear observations ρjBased on initialisation or obtained in a previous iteration
Figure BDA0003000778740000081
And linear transformation matrix A obtained in the iteration of the current round(t)Calculating the pseudo-prior second moment of its corresponding noiseless observation as
Figure BDA0003000778740000082
First moment of
Figure BDA0003000778740000083
Figure BDA0003000778740000084
Wherein DEG represents the Hadamard product, sjInitial value of (2)
Figure BDA0003000778740000085
Is represented by a matrix A(t)The j-th row element of (1).
c. For each observed value ρ of the linear observations ρjBased on initialisation or obtained in a previous iteration
Figure BDA0003000778740000086
Obtained in the iteration of the current round
Figure BDA0003000778740000087
Calculating the second moment of the message transmitted to the adjacent variable node as
Figure BDA0003000778740000088
First moment of
Figure BDA0003000778740000089
d. Based on initialization or obtained in the previous iteration
Figure BDA00030007787400000810
Obtained in the iteration of the current round
Figure BDA00030007787400000811
Calculating all linear observation position coordinate variables transmitted to node i
Figure BDA00030007787400000812
Product of messages with a second moment of
Figure BDA00030007787400000813
First moment of
Figure BDA00030007787400000814
Figure BDA00030007787400000815
e. Based on results from the iteration
Figure BDA00030007787400000816
Calculating the mean value of the estimated values of the i-position distribution of the nodes as
Figure BDA00030007787400000817
Variance of
Figure BDA00030007787400000818
Figure BDA00030007787400000819
Wherein
Figure BDA00030007787400000820
Representing the division of the corresponding elements of the matrix.
f. The estimation result of the variable distribution obtained by the iteration of the current round
Figure BDA00030007787400000821
Broadcast to adjacent nodes and receive the position estimation result of the local iteration of the adjacent nodes to update
Figure BDA00030007787400000822
Figure BDA00030007787400000823
Thereby constructing the mean value and the variance of the probability distribution of the variable nodes after the iteration
Figure BDA00030007787400000824
The iterative process in the step II is stopped after reaching the convergence condition, and the iterative process in the step II is stopped at the moment
Figure BDA00030007787400000825
Namely the final position estimation result of the ith node. At this time, each user node obtains a position estimation result with higher accuracy.
The complete algorithm flow chart of the invention is shown in fig. 3.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. A distributed cooperative positioning method based on angle measurement is characterized by comprising the following steps:
step one, constructing a wireless cooperative positioning network;
secondly, position estimation is achieved by utilizing a generalized approximate message transfer algorithm;
the first step is specifically as follows:
1.1 defining a distributed wireless cooperative positioning network consisting of N nodes, the aim of which is to estimate the two-dimensional position coordinates x of each nodeiI ═ 1,2, …, N; in the cooperative positioning network, the prior mean value of the positions of all nodes is known
Figure FDA0003534135890000011
And variance
Figure FDA0003534135890000012
And each node can receive the data from KiSignals of adjacent nodes, and measuring the arrival angle theta of the signals on a two-dimensional planei,k,k＝1,2,…,Ki；
1.2, constructing a relation between angle observation and position coordinates by adopting a linearization mode; for node i, a linear observation of the system is defined
Figure FDA0003534135890000013
Where ρ isi,k＝[cosθi,k,sinθi,k]T(ii) a Therefore, for the node i, the model for constructing the wireless cooperative positioning network is rhoi＝Aizi+diWherein the position coordinate variable
Figure FDA0003534135890000014
By K adjacent to node iiPosition coordinates of each node and node i itself, AiAs a linear transformation matrix which varies dynamically with the node position estimate, diTo observe noise;
1.3, in the distributed network, for each node i, expressing the position coordinates of adjacent nodes and the position coordinates of the adjacent nodes and the node i as variable nodes, expressing each factor obtained after decomposing the combined posterior probability density function as factor nodes, and connecting the variable nodes with corresponding relations with the factor nodes to form edges, thereby forming a factor graph of the node i to obtain the estimated value of the coordinate variables of the node i;
the second step is specifically as follows:
2.1, initializing the message on the factor graph by using the mean value and the variance of the prior observation of each node position; through mutual communication, each node obtains prior information of adjacent nodes, measures the arrival angle of signals and calculates linear observation rho; considering the factor graph formed at the ith node; initializing the mean z of the probability distribution of each variable node using the position priors of the neighboring nodes and the node itself(0)And variance
Figure FDA0003534135890000015
Wherein the superscript (t) of each variable represents the iteration round t;
2.2, for the linear model rho (Az + d), using a generalized approximate message transfer algorithm to realize message updating on the factor graph; on the initialized factor graph, message transmission is realized through iterative computation;
2.3, the iterative process in step 2.2 is stopped after reaching the convergence condition, at which point
Figure FDA0003534135890000021
The position estimation result is the final position estimation result of the ith node; at this time, each user node obtains a position estimation result with higher accuracy.
2. A distributed cooperative positioning method based on angular measurement according to claim 1, characterized in that the iteration process in step 2.2 is as follows:
in the t-th iteration:
a. for node i, based on the estimated value of the position coordinate in the initialization or the previous iteration
Figure FDA0003534135890000022
Calculating the estimated value of the distance between each adjacent node and the node i
Figure FDA0003534135890000023
Dynamically calculating a linear transformation matrix based on the distance estimates
Figure FDA0003534135890000024
Wherein
Figure FDA0003534135890000025
Figure FDA0003534135890000026
diag (f) denotes a diagonal matrix composed of a column vector f as the main diagonal element, InWhich represents an identity matrix of order n,
Figure FDA0003534135890000027
represents the kronecker product;
b. for each observed value ρ of the linear observations ρjBased on initialisation or obtained in a previous iteration
Figure FDA0003534135890000028
And linear transformation matrix A obtained in the iteration of the current round(t)Computing the second moment of the pseudo-priors for their respective noise-free observations
Figure FDA0003534135890000029
And first moment
Figure FDA00035341358900000210
c. For each observed value ρ of the linear observations ρjBased on initialisation or obtained in a previous iteration
Figure FDA00035341358900000211
Obtained in the iteration of the current round
Figure FDA00035341358900000212
Calculating the second moment of the message transmitted to the adjacent variable node
Figure FDA00035341358900000213
And first moment
Figure FDA00035341358900000214
d. Based on initialization or obtained in the previous iteration
Figure FDA00035341358900000215
With A obtained in the iteration of the current round(t),
Figure FDA00035341358900000216
Calculating the second moment of the product of all linear observations transmitted to the node i message
Figure FDA00035341358900000217
And a first moment r(t)；
e. Based on results from the iteration
Figure FDA0003534135890000031
Calculating the mean value of the estimated values of the i-position distribution of the nodes as
Figure FDA0003534135890000032
Variance of
Figure FDA0003534135890000033
f. The estimation result of the variable distribution obtained by the iteration of the current round
Figure FDA0003534135890000034
Broadcasting to adjacent nodes, and receiving the estimation result of the position distribution obtained by the adjacent nodes after the iteration, thereby constructing the mean value and the variance of the probability distribution of the variable nodes after the iteration
Figure FDA0003534135890000035
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