CN108761384B - Target positioning method for robust sensor network - Google Patents

Target positioning method for robust sensor network Download PDF

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CN108761384B
CN108761384B CN201810399511.3A CN201810399511A CN108761384B CN 108761384 B CN108761384 B CN 108761384B CN 201810399511 A CN201810399511 A CN 201810399511A CN 108761384 B CN108761384 B CN 108761384B
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CN108761384A (en
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申晓红
柳溪
王海燕
贾天一
姚海洋
常娟
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Northwestern Polytechnical University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
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    • G01S5/0252—Radio frequency fingerprinting
    • 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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Abstract

The invention provides a robust sensor network target positioning method, which is characterized in that a weighted integral least square method is used for positioning a TDOA sensor network target, the influence of a TDOA measurement error and a sensor node position error on positioning performance is considered, and the weighted integral least square method is used for solving. The invention fully utilizes the prior information of the sensor position error variance and the TDOA measurement error variance, and when a target is positioned outside the sensor network, the method has the minimum deviation and good positioning performance under the conditions of high-power sensor node position error and high-power time measurement error.

Description

Target positioning method for robust sensor network
Technical Field
The invention relates to the field of wireless sensor networks, in particular to a target positioning method under the condition of simultaneously considering the position error of a sensor node in a network and the measurement error of TDOA.
Background
The wireless sensor network technology is an important technology widely applied in recent years, and the target positioning function of the wireless sensor network technology is crucial to civil application such as environment monitoring and military application such as enemy target detection. The target positioning function is to obtain the position of the target by processing and calculating the information by using the information about the target collected by the sensor nodes in the network. The existing sensor network target positioning algorithm is mainly divided into a target positioning algorithm based on ranging and a non-ranging target positioning algorithm. In the ranging-based target location algorithm, the methods mainly used include a Time Difference of Arrival (TDOA) method based on a signal Arrival angle, a signal reception strength, a signal Arrival Time, and a signal Arrival Time Difference. The TDOA target positioning method is a method mainly used in modern target positioning due to the advantages of high positioning precision, good real-time performance and the like. The invention selects a target positioning method based on TDOA.
However, when the sensor network is used to perform target positioning, the error factor has a large influence on the positioning accuracy. On the one hand, there is measurement error of TDOA measurements; on the other hand, the sensor node may have a position error. For example, in an underwater acoustic sensor network, a sensor node moves with ocean current to cause a large position error; for another example, sensor nodes installed on an airplane or a drone may cause position errors as the position of the aircraft changes. When the TDOA target location method is used for location, generally, a nonlinear relation between a measured quantity and an unknown target position is firstly converted into a linear relation for calculation by introducing an intermediate variable, and only additive noise exists in a linear equation at the moment. However, due to the influence of errors on the positioning accuracy, when the TDOA measurement errors and the sensor node position errors are considered, the nonlinear relationship is converted into the linear relationship, and then not only additive noise but also multiplicative noise exists. However, if the pseudo linear equation is still solved by using a conventional algorithm, the positioning accuracy is inevitably reduced.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a target positioning method based on a weighted integral least square method, which is used for positioning a TDOA sensor network target by using the weighted integral least square method, simultaneously considers the influence of TDOA measurement errors and sensor node position errors on the positioning performance, solves the problem by using the weighted integral least square method, and improves the estimation precision of the target position.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
first, for M sensorsSensor network of device nodes, sensor node skMeasured position [ x ]k，yk]TTwo-dimensional coordinates representing the kth sensor node in the sensor network, k being 1, 2 …, M; one sensor node is arbitrarily selected as a reference node s1(ii) a Observing the difference of distance measurement rt1Representing the distance from the target transmitting signal to the t-th sensor node and the distance from the target transmitting signal to the reference node s1 T 2, 3, M; x is the number oft1For the t-th sensor node and the reference node s1Difference between x coordinates, yt1For the t-th sensor node and the reference node s1The difference between the y coordinates; computing pseudowire observation matrices
Figure GDA0003502629090000021
And pseudo linear measurement vector
Figure GDA0003502629090000022
Second step, knowing Δ xkAnd Δ ykRespectively as the true position coordinates of the sensor nodes
Figure GDA0003502629090000023
And
Figure GDA0003502629090000024
and all satisfy mean 0 and variance σ2Normal distribution of (2); n iskThe measurement error of the observation distance of the kth sensor node is represented, the mean value is 0, and the variance is
Figure GDA0003502629090000025
Normal distribution of (2); Δ GaAnd Δ h are respectively a multiplicative error matrix and an additive error matrix, and the pseudo-linear equation is (G)a+ΔGa)zaCalculating covariance matrix of Δ h
Figure GDA0003502629090000026
Wherein, the elements of the t-th row and the j-th column
Figure GDA0003502629090000027
It is known that
Figure GDA0003502629090000028
Figure GDA0003502629090000029
Are respectively covariance matrices
Figure GDA00035026290900000210
The block matrixes of (M-1) x (M-1) are all matrixes, then the covariance matrix
Figure GDA00035026290900000211
Thirdly, the covariance matrix is processed
Figure GDA00035026290900000212
Decomposed into a 3 x 3 matrix Q0And a matrix Q of (M-1) × (M-1)x，
Figure GDA00035026290900000213
Fourth, construct the pseudo-linear equation (G)a+ΔGa)zaH + Δ h, wherein the unknown quantity z is to be determineda＝[ux uy r1]TAnd multiplicative error matrix deltagaThe additive error matrix Δ h is also unknown; selecting an error threshold epsilon, and solving the position [ u ] of the target u by using a weighted integral least square methodx uy]T。
The error threshold epsilon is less than 10-3Is constant.
The fourth step of solving the position of the target u by using a weighted integral least square method comprises the following specific steps:
step 1, firstly, an unknown quantity z to be solved is givenaInitial value of (2)
Figure GDA0003502629090000031
Step 2, obtaining the unknown quantity z substituted into the iterative processaInitial value of
Figure GDA0003502629090000032
Step 3, two iteration quantities v of the solution required in the iteration process are given(i)And za (i)Where i represents the number of iterations,
Figure GDA0003502629090000033
Figure GDA0003502629090000034
step 4, repeating step 3 when
Figure GDA0003502629090000035
When the calculation is finished, or when the number of iterations is more than 200,
Figure GDA0003502629090000036
the invention has the beneficial effects that: taking into account the TDOA measurement noise and the sensor node position error, the method is compared with a conventional Least square method (LS), a Weighted Least square method (WLS), and a Total Least square method (TLS). The model solved by the LS method and the WLS method is a linear equation G only containing additive noise delta hazaWhen the sensor node position error and the TDOA measurement error are considered at the same time, the model is constructed to contain not only additive noise Δ h but also multiplicative noise Δ GaTherefore, the LS method and the WLS method are not well suited for solving the model. However, the TLS algorithm is applicable to solving the model, but does not consider the correlation between error components in an amplification matrix constructed by additive noise and multiplicative noise, and thus cannot obtain good positioning accuracy. The inventionThe target positioning method combined with the WTLS fully utilizes the prior information of the sensor position error variance and the TDOA measurement error variance, and when a target is positioned outside a sensor network, the method has the minimum deviation and has good positioning performance under the conditions of high-power sensor node position error and high-power time measurement error.
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FIG. 1 is a flow chart of a computing method of the present invention.
Fig. 2 is a schematic diagram of the real location geometry of the sensor network for target location in accordance with the present invention.
FIG. 3 is a comparison graph of target positioning deviation under different measurement noise variances and the variance of the fixed network node position error of the present invention.
FIG. 4 is a comparison graph of the target positioning deviation under the conditions of fixed measurement noise variance and different network node position error variances.
FIG. 5 is a comparison graph of the mean square error of target positioning under the conditions of the variance of the position error of the fixed network node and the variance of the measured noise.
FIG. 6 is a comparison graph of the target position mean square error under the conditions of fixed measurement noise variance and different network node position error variances according to the present invention.
In the figure, LS represents a least square method, WLS represents a weighted least square method, TLS represents a total least square method, and WTLS represents a weighted total least square method.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
There are M sensor nodes in the known sensor network, where the sensor node is skWhich measures the position [ x ]k，yk]TAnd the two-dimensional coordinates of the kth sensor node in the sensor network are shown, wherein k is 1, 2 … and M. s1And the reference node is one of the sensor nodes selected randomly. Unknown target position u ═ ux uy]T。
tkIndicating the observed kth passTime when the sensor node receives the target transmission signal, tk＝to+τk-ξkIn which τ iskRepresenting the true propagation time, t, of the target transmit signal to the kth sensor nodeoRepresenting the moment, ξ, of the target emitted signalkRepresenting the TDOA measurement error for the kth sensor node. Time delay difference measurement ti1Representing the observed propagation time of the target transmission signal to the t-th sensor node and the propagation time of the target transmission signal to the reference node s1Is 2, 3, M, then t is tt1＝τt-τ1-(ξt-ξ1) Observed distance difference measurement rt1Representing the distance from the target transmitting signal to the t-th sensor node and the distance from the target transmitting signal to the reference node s1Is measured. The observed distance difference r can be obtained from equation (14)t1Where c denotes the propagation speed of the signal, nk＝cξkMeasurement error, n, representing the observed distance of the kth sensor nodetA measurement error indicating an observed distance of the t-th sensor node other than the reference node,
Figure GDA0003502629090000041
true value representing the distance difference:
Figure GDA0003502629090000042
known as Δ xkAnd Δ ykRespectively as the true position coordinates of the sensor nodes
Figure GDA0003502629090000043
And
Figure GDA0003502629090000044
an error of (2) is
Figure GDA0003502629090000045
Figure GDA0003502629090000046
Representing sensor node measurement location skIs measured.
The invention derives from an observed quantity s having noisekAnd ri1Estimate an unknown target u with a position of [ ux uy]T。rk 0The distance from the target transmitting signal to the kth sensor node is represented, and the relationship between the real value and the target position can be obtained by the formula (15):
Figure GDA0003502629090000051
because the relation between the real value and the target position is nonlinear, an intermediate variable r is added1Representing the distance from the reference node to the unknown target, a linear relationship between the observed quantity and the target position can be obtained. Since the relation between the observed quantity and the real value can be expressed as
Figure GDA0003502629090000052
Unknown quantity to be found is za＝[uxuy r1]TThen the linear relationship is expressed as shown in equation (16):
(Ga+ΔGa)za＝h+Δh (16)
wherein G isaIs a pseudo-linear observation matrix, h is a pseudo-linear measurement vector, Δ GaAnd Δ h are the multiplicative error matrix and the additive error matrix, respectively. x is the number oft1For the t-th sensor node and the reference node s1Difference between the measured quantities of the x-coordinate, yt1For the t-th sensor node and the reference node s1The multiplicative error matrix deltaG can be calculated from the difference between the measured quantities of the y coordinate according to equation (17) and equation (18)aAnd additive error matrix Δ h:
Figure GDA0003502629090000053
Figure GDA0003502629090000054
for the pseudo-linear equation constructed in equation (16), the solution can be performed using the overall least squares method, and the general calculation method is to pair the augmented matrix [ Ga|h]Singular value decomposition is performed. However, the method is directly applied to the problem of poor TDOA target location, correlation between error components in an amplification matrix constructed by additive noise and multiplicative noise is not considered, and the obtained location accuracy is not ideal and is not suitable for the problem of target location. To solve the problem of robust TDOA target location, the present invention proposes solving the pseudolinear equation in equation (16) using a weighted integral least squares approach.
The method of the present invention is further described below, and is implemented on the premise of the technical scheme of the present invention, and a detailed implementation mode and a specific operation process are given.
The first step is as follows: computing pseudowire observation matrix GaAnd a pseudo linear measurement vector h
The known sensor network has M sensor nodes, wherein the sensor node is skWhich measures the position [ x ]k，yk]TAnd the two-dimensional coordinates of the kth sensor node in the sensor network are shown, wherein k is 1, 2 … and M. s1And the reference node is one of the sensor nodes selected randomly. Observing the difference of distance measurement rt1Representing the distance from the target transmitting signal to the t-th sensor node and the distance from the target transmitting signal to the reference node s1 T 2, 3, M. x is the number oft1For the t-th sensor node and the reference node s1Difference between x coordinates, yt1For the t-th sensor node and the reference node s1Calculating the pseudo-linear observation matrix G according to the formula (1) and the formula (2) by using the difference value of the y coordinatesaAnd a pseudo-linearity measurement vector h:
Figure GDA0003502629090000061
Figure GDA0003502629090000062
the second step is that: calculating a multiplicative error matrix Δ GaCovariance matrix of additive error matrix Δ h
Figure GDA0003502629090000063
Sum Σh
Known as Δ xkAnd Δ ykRespectively as the true position coordinates of the sensor nodes
Figure GDA0003502629090000064
And
Figure GDA0003502629090000065
and all satisfy mean 0 and variance σ2Normal distribution of (1), nkThe measurement error of the observation distance of the kth sensor node is represented, the mean value is 0, and the variance is
Figure GDA0003502629090000066
Is normally distributed. Δ GaAnd Δ h are respectively a multiplicative error matrix and an additive error matrix, and the pseudo-linear equation is (G)a+ΔGa)zaThe covariance matrix Σ of the additive error matrix Δ h is calculated from equation (3) as h + Δ hh：
Figure GDA0003502629090000067
Therein, sigmatjThe elements representing the t-th row and the j-th column can be calculated by formula (4):
Figure GDA0003502629090000068
it is known that
Figure GDA0003502629090000069
Are respectively covariance matrices
Figure GDA00035026290900000610
The three block matrixes of (M-1) x (M-1) are all the matrixes, and then the multiplicative error matrix delta G can be calculated by the formula (5), the formula (6) and the formula (7)aCovariance matrix of
Figure GDA00035026290900000611
：
Figure GDA00035026290900000612
Figure GDA00035026290900000613
Figure GDA0003502629090000071
The third step: factorized multiplicative error matrix Δ GaCovariance matrix of
Figure GDA0003502629090000072
Is two matrices Q0And QxCovariance matrix
Figure GDA0003502629090000073
Can be decomposed into the form of equation (8), and Q can be calculated from equations (9) and (10)0And Qx，Q0Is a 3 x 3 matrix, QxIs a matrix of (M-1) × (M-1):
Figure GDA0003502629090000074
Figure GDA0003502629090000075
Figure GDA0003502629090000076
the fourth step: solving a target u with a position [ u ] by using a weighted integral least square methodx uy]T
Due to the simultaneous TDOA measurement error Δ ri1，Having a size of nk-n1And the sensor node position error DeltaxkAnd Δ ykAnd in order to convert the non-linear equation into a linear equation, an intermediate unknown r is added1Representing the distance of the reference node to the unknown target, the pseudowire equation thus constructed is (G)a+ΔGa)zaH + Δ h, where the unknown to be solved is za＝[ux uyr1]TAnd multiplicative error matrix deltagaThe sum additive error matrix Δ h is also unknown. Selecting an error threshold epsilon, wherein epsilon is less than 10-3For the pseudo linear equation, a weighted integral least squares method can be used to solve the target u.
The specific implementation steps of solving by using the weighted integral least square method are as follows:
initialization: firstly, giving the unknown quantity to be solved as zaInitial value of (2)
Figure GDA0003502629090000077
Step 1: the unknowns z substituted into the iterative process are obtained by equation (11)aInitial value of (d):
Figure GDA0003502629090000078
step 2: equations (12) and (13) give the two iteration quantities v to be solved in the iterative process(i)And za (i)Where i represents the number of iterations:
Figure GDA0003502629090000079
Figure GDA0003502629090000081
Figure GDA0003502629090000082
Figure GDA0003502629090000083
and step 3: repeating the step 2 when the I Z isa (i+1)-za (i)When | < epsilon, the calculation ends, or when the number of iterations is greater than 200,
Figure GDA0003502629090000084
and 4, step 4: the output u, u is the result zaThe first two items uxAnd uy。
The sensor network geometry shown in FIG. 2, knowing the real position of the target as u0＝[0 1000]TThe real coordinate positions of the nine sensor nodes are respectively s1＝[0，0]，s2＝[200，0]，
Figure GDA0003502629090000085
s4＝[0，200]，
Figure GDA0003502629090000086
s6＝[-200，0]，
Figure GDA0003502629090000087
s8＝[0，-200]，
Figure GDA0003502629090000088
Known sensor node position error Δ xkAnd Δ ykAll satisfyMean 0 and variance σ2Normal distribution of (1), nkThe measurement error of the observation distance of the kth sensor node is represented, the mean value is 0, and the variance is
Figure GDA0003502629090000089
Is normally distributed. As shown in FIGS. 3 and 5, σ in the experiment was taken2＝3，
Figure GDA00035026290900000810
11 different values are taken, starting from 0.5 and starting from 0.5 to 5.5. The error threshold epsilon of the algorithm is less than 10-3The constants of (2) were subjected to 11 simulation experiments. As shown in FIGS. 4 and 6, in the test, the specimen was taken
Figure GDA00035026290900000811
σ211 different values are taken, starting from 0.5 and starting from 0.5 to 5.5. The error threshold epsilon of the algorithm is less than 10-3The constants of (2) were subjected to 11 simulation experiments.
The target localization performance of the contrast Least Squares (LS), Weighted Least Squares (WLS), Total Least Squares (TLS), and Weighted Total Least Squares (WTLS) methods in FIGS. 3-6. The performance index is measured by the mean square error (RMSE) and the deviation (bias) of the estimated target position from the true target position, and equations (19) and (20) define the two indices:
Figure GDA00035026290900000812
Figure GDA00035026290900000813
in the formula ukThe target estimated position of the k-th trial is indicated, and L50000 indicates the total number of trials.
Through the simulation experiments of fig. 3 to 6, it can be obtained that when the target is outside the sensor node network, and when the high-power sensor node position error and the high-power measurement error occur, under the index of bias, the results with better positioning effect than the other three methods can be obtained by combining the WTLS method, that is, the deviation between the target position estimation value and the true value is small as a whole.

Claims (3)

1. A target positioning method of a robust sensor network is characterized by comprising the following steps:
first, for a sensor network with M sensor nodes, sensor node skMeasured position [ x ]k，yk]TTwo-dimensional coordinates representing the kth sensor node in the sensor network, k being 1, 2 …, M; one sensor node is arbitrarily selected as a reference node s1(ii) a Observing the difference of distance measurement rt1Representing the distance from the target transmitting signal to the t-th sensor node and the distance from the target transmitting signal to the reference node s1T 2, 3, M; x is the number oft1For the t-th sensor node and the reference node s1Difference between x coordinates, yt1For the t-th sensor node and the reference node s1The difference between the y coordinates; computing pseudowire observation matrices
Figure FDA0003502629080000011
And pseudo linear measurement vector
Figure FDA0003502629080000012
Second step, knowing Δ xkAnd Δ ykRespectively as the true position coordinates of the sensor nodes
Figure FDA0003502629080000013
And
Figure FDA0003502629080000014
and all satisfy mean 0 and variance σ2Normal distribution of (2); n iskDenotes the kth sensorThe measurement error of the observation distance of the node satisfies that the mean value is 0 and the variance is
Figure FDA00035026290800000115
Normal distribution of (2); Δ GaAnd Δ h are respectively a multiplicative error matrix and an additive error matrix, and the pseudo-linear equation is (G)a+ΔGa)zaCalculating covariance matrix of Δ h
Figure FDA0003502629080000015
Wherein, the elements of the t-th row and the j-th column
Figure FDA0003502629080000016
It is known that
Figure FDA0003502629080000017
Figure FDA0003502629080000018
Are respectively covariance matrices
Figure FDA0003502629080000019
The block matrixes of (M-1) x (M-1) are all matrixes, then the covariance matrix
Figure FDA00035026290800000110
Thirdly, the covariance matrix is processed
Figure FDA00035026290800000111
Decomposed into a 3 x 3 matrix Q0And a matrix Q of (M-1) × (M-1)x，
Figure FDA00035026290800000112
The fourth step, construct the pseudo-linear equation
Figure FDA00035026290800000113
Wherein the unknown quantity z is to be determineda＝[ux uy r1]TAnd multiplicative error matrix
Figure FDA00035026290800000114
The additive error matrix Δ h is also unknown; selecting an error threshold epsilon, and solving the position [ u ] of the target u by using a weighted integral least square methodx uy]T。
2. The robust sensor network object locating method of claim 1, wherein: the error threshold epsilon is less than 10-3Is constant.
3. The robust sensor network target positioning method of claim 1, wherein the fourth step of solving the position of the target u using a weighted integral least squares method comprises the following specific steps:
step 1, firstly, giving unknown quantity to be solved
Figure FDA0003502629080000021
Step 2, obtaining the unknown quantity z substituted into the iterative processaInitial value of
Figure FDA0003502629080000022
Step 3, two iteration quantities v of the solution required in the iteration process are given(i)And za (i)Where i represents the number of iterations,
Figure FDA0003502629080000023
Figure FDA0003502629080000024
step 4, repeating step 3 when
Figure FDA0003502629080000025
When the calculation is finished, or when the number of iterations is more than 200,
Figure FDA0003502629080000026
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