CN113453149A - RSSI ranging-based water quality monitoring network positioning method - Google Patents

RSSI ranging-based water quality monitoring network positioning method Download PDF

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CN113453149A
CN113453149A CN202110715054.6A CN202110715054A CN113453149A CN 113453149 A CN113453149 A CN 113453149A CN 202110715054 A CN202110715054 A CN 202110715054A CN 113453149 A CN113453149 A CN 113453149A
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常波
张新荣
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Huaiyin Institute of Technology
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    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/025—Services making use of location information using location based information parameters
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Abstract

A water quality monitoring network positioning method based on RSSI ranging establishes RF communication modeling; obtaining the reference distance d of the wireless signal0Rear path loss PL(d0) (ii) a Periodically measuring the received signal strength RSSI between a node to be positioned and a neighbor reference node thereof, and then calculating a path loss index n in the current monitoring area by using an RF wireless signal propagation model; comparing the measured distance between the reference nodes with the actual distance according to the known reference node coordinates to obtain the relative ranging error of the RSSI; and establishing a distance equation of the monitoring node, performing Taylor series expansion, processing by adopting a weighted least square algorithm WLS, and updating the parameter vector. The method can effectively reduce the ranging error, can make the positioning method based on RSSI ranging suitable for water quality monitoring systems in various different environments, and can meet the positioning requirements of the water quality on-line monitoring system with complicated and severe network environment and limited positioning cost.

Description

RSSI ranging-based water quality monitoring network positioning method
Technical Field
The invention belongs to the technical field of water quality monitoring, and particularly relates to a water quality monitoring network positioning method based on RSSI ranging.
Background
The Wireless Sensor Networks (WSNs) can be self-organized and rapidly deployed, environmental monitoring information is cooperatively sensed and acquired through a plurality of sensor nodes in the WSNs, and data processing results are sent to terminal equipment by utilizing the advantages of distributed processing and multi-hop transmission of the environmental monitoring information. The wireless sensor network has the characteristics of strong fault tolerance, long service life and the like, so that the wireless sensor network has wide application prospect in the field of lake and river environment water quality monitoring. The water quality on-line monitoring system integrating data acquisition, data transmission, predictive analysis and information display can enable the wireless sensor network to comprehensively and accurately acquire data information, and further can provide effective basis for evaluating and improving the environmental water quality condition. The positioning problem is a key problem which is basically and indispensable in the water quality monitoring wireless network.
In the prior art, a direct method for obtaining node position information is to use a Global Positioning System (GPS) to perform positioning, but is limited by the cost of a water quality monitoring system, the deployment environment and other fields, and the implementation process is extremely difficult, so research on a monitoring point positioning technology is necessary. In general, a more reasonable solution is to provide some monitoring nodes with GPS coordinates as anchor nodes, beacon nodes or reference nodes, and other nodes are called unknown nodes, common nodes or blind nodes, and the coordinates of the nodes can be estimated by using a corresponding positioning algorithm through wireless communication based on the known position of the anchor node. Currently, the positioning algorithms are generally classified into two categories, namely range-based (range-based) positioning algorithms and range-free (range-free) positioning algorithms. The Range-free ranging algorithm has small communication overhead but poor accuracy. Time of arrival (TOA) and angle of arrival (AOA) ranging algorithms achieve higher positioning accuracy through distance or angle measurement, but are more costly, computationally intensive, and communication overhead.
The RSSI (received signal strength indicator) distance measurement algorithm measures the strength of a received signal and utilizes an RF wireless propagation model to obtain the estimation of the distance between monitoring nodes, so that the power consumption and the cost are lower. However, RF signal propagation modeling is affected by environmental factors and appropriate measures need to be taken to reduce ranging errors. In the existing positioning method, the distance measurement error cannot be effectively reduced, so that the positioning method based on RSSI (received signal strength indicator) distance measurement cannot be applied to water quality monitoring systems in various different environments, and the positioning requirements of the water quality online monitoring system with complicated and severe network environment and limited positioning cost cannot be met.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides the RSSI ranging-based water quality monitoring network positioning method, which can effectively reduce ranging errors, can enable the RSSI ranging-based positioning method to be suitable for water quality monitoring systems in different environments, and can meet the positioning requirements of the water quality on-line monitoring systems with complicated and severe network environments and limited positioning cost.
The invention provides a water quality monitoring network positioning method based on RSSI ranging, which comprises the following steps:
the method comprises the following steps: establishing an RF communication model according to formula (1);
Figure BDA0003134273900000021
wherein n is a path loss exponent; d0A reference distance for signal propagation; pR(d0) Is d after signal transmission0Received signal strength of (X)σThe mean value is 0, and the standard deviation range is 4-10 Gaussian random variables;
step two: obtaining the reference distance d of the wireless signal according to the formula (2)0Rear path loss PL(d0)；
Figure BDA0003134273900000022
In the formula, GtIs the node transmit antenna gain, in units dBi; grIs the receive antenna gain, in units dBi; l is the system loss coefficient; λ is the RF signal wavelength, in m;
step three: the method comprises the following steps of periodically measuring the received signal strength RSSI between a node to be positioned and a neighbor reference node thereof, and then calculating a path loss index n in a current monitoring area by using an RF wireless signal propagation model, wherein the specific steps are as follows:
s11, making PX equal to PR(d0)+XσThe formula (3) can be obtained by substituting the formula (2) with the formula (3);
Figure BDA0003134273900000023
s12, calculating the reference node R according to the formula (4)3And a reference node R1Inter RSSI value PR(d1) (ii) a Calculating a reference node R according to equation (5)3And a reference node R2Inter RSSI value PR(d2)；
Figure BDA0003134273900000024
Figure BDA0003134273900000025
In the formula (d)1As a reference node is R3To a further reference node R in the vicinity1Actual distance between, d2As a reference node is R3To a further reference node R in the vicinity2The actual distance between;
s13, let d01m, simultaneously obtaining formula (6) by formula (4) and formula (5);
Figure BDA0003134273900000031
s14, substituting the RSSI value obtained by the wireless communication between the reference nodes into a formula (6) to obtain a path loss index n which accords with the environmental characteristics of the actual monitoring area;
step four: according to the known reference node coordinates, comparing the measured distance between the reference nodes with the actual distance to obtain the relative ranging error of the RSSI, and the method specifically comprises the following steps:
s21, setting the reference node as Ri(xi，yi) The actual distance to other reference nodes is rikK is 1, 2, …, n, k is not equal to i, wherein n is the number of reference nodes participating in the correction calculation; reference node RiThe measured distances to other reference nodes are recorded as dik， k＝1，2，…，n，k≠i；
S22, obtaining the reference node R according to the formula (7)iDistance average relative error mu between actual distance and measured distanceiAnd as a reference node RiRelative error coefficients of the RSSI-based distance measurements;
Figure BDA0003134273900000032
s23, setting a threshold tau and adjusting the network positioning performance by controlling the tau; when | muiWhen | ≧ τ, the reference node position is abnormal and can not participate in positioning of the monitoring node, otherwise, the reference node position can participate in positioning calculation;
s24, when the monitoring node receives the broadcast message of the reference node, the monitoring node sends Pr(d) Calculating and obtaining the measurement distance between the monitoring node and the reference node in the communication range of the monitoring node through the model of the formula (1), and then correcting the measurement distance through a formula (8) according to the relative error coefficient of each reference node;
Figure BDA0003134273900000033
in the formula (d)uiIs a monitoring node and a reference node RiThe measured distance therebetween, in m;
Figure BDA0003134273900000034
is a monitoring node and a reference node RiCorrected distance therebetween, in m;
step five: positioning the monitoring node, which comprises the following steps:
s31, setting the unknown node in the network as U (x)1，y1) The reference node is Ri(xi，yi) To unknown node is U (x)1，y1) Measured distance of diI ═ 1, 2, …, N; establishing a distance equation of monitoring nodes in the water quality monitoring wireless network according to a formula (9);
Figure BDA0003134273900000035
s32, setting the initial coordinate as (x)0，y0) And make
Figure BDA0003134273900000041
Then (x)0，y0) Is aligned with
Figure BDA0003134273900000042
Performing Taylor series expansion, and neglecting components of second order and above to obtain a formula (10);
f(x，y)＝f(x0，y0)+fx(x0，y0)Δx+fy(x0，y0)Δy (10)；
s33, sorting the formula (10) to obtain a formula (11);
Figure BDA0003134273900000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003134273900000044
ax＝fx(x0，y0)；ay＝fy(x0，y0)；
s34, sorting the formula (11) to obtain a formula (12);
h＝GΔ+ε(d2) (12)；
in the formula (I), the compound is shown in the specification,
Figure BDA0003134273900000045
Δ＝[Δx Δy]T；
Figure BDA0003134273900000046
s35, processing the formula (12) by adopting a weighted least square algorithm WLS to obtain a formula (13);
Δ＝(GTWG)-1GTWh (13)；
in the formula, W is a covariance matrix of a measurement error epsilon;
s36, making W cov-1(ε), deriving equation (14) to update the parameter vector;
θ(k+1)＝θ(k)+Δ (14)。
in the second step, the path loss index value n is between 2 and 4, and the more the number of obstacles and the more the shielding are, the larger the n value is.
The method mainly comprises three parts of RSSI ranging, measurement distance correction, monitoring node positioning and the like. Firstly, ranging is carried out by acquiring a dynamic path loss index; then, by comparing the difference between the measured distance of the reference nodes and the actual distance, the relative error coefficient of each reference node is obtained so as to correct the measured distance; and finally, estimating the coordinates of the monitoring nodes by using a Taylor series expansion weighted least square positioning (WLS) algorithm. And obtaining the path loss factor in the current monitoring area by periodically measuring the RSSI value between the monitoring nodes in the wireless network and utilizing an RF wireless signal propagation model. The adaptability of the water quality monitoring system to different monitoring area environments is improved, and the distance measurement error is reduced. And then, the difference value is obtained between the measured distance and the actual distance between the reference nodes to obtain the relative distance measurement error of the RSSI, so that the error correction can be carried out on the measured distance between the node to be positioned and the reference nodes, the adverse effect of inaccurate signal propagation modeling on distance calculation is greatly reduced, and the method is suitable for water quality monitoring systems under various different environments. And in the positioning calculation stage, the position coordinates of the monitoring nodes are solved by adopting a Taylor series least square iterative algorithm. The method is used for linearizing the nonlinear observation equation by using the Taylor series expansion method for the isotropic WSN, so that the linear mode is adopted for processing, the calculation complexity of the node coordinates is reduced, and the prior information of the observation data is fully considered, so that the network positioning precision is improved. The method is beneficial to realizing automatic monitoring and positioning of the environmental water quality, so that the monitoring node can process the collected data of pH value, dissolved oxygen, conductivity, turbidity and the like and then wirelessly transmit the processed data to the monitoring center, and an operator can realize real-time monitoring of the water environment parameters by using the terminal information.
Detailed Description
The present invention will be further described with reference to the following examples.
The invention provides a water quality monitoring network positioning method based on RSSI ranging, which comprises the following steps:
the method comprises the following steps: in the lake and river environment where the water quality monitoring system is placed, various kinds and sizes of biological fishes and other facilities inside the lake and river environment are dense and have uneven distribution conditions, so that an RF signal propagation model becomes complicated due to the influence of factors such as multipath, diffraction and barrier shielding. In order to adapt to the lake and river environment of the water quality monitoring system, a simplified lognormal distribution model is adopted for ranging, and RF communication modeling is established according to a formula (1);
Figure BDA0003134273900000051
in the formula, n is a path loss index, the value is 2-4, and the more the number of obstacles and the more the shielding are, the larger the n value is; d0A reference distance for signal propagation; pR(d0) Is d after signal transmission0Received signal strength of (X)σIs a Gaussian random variable with a mean value of 0 and a standard deviation range of 4-10;
of course, the received signal strength can also be through PR(d)＝P+G-PL(d) Calculating, wherein P is the transmitting signal intensity of the monitoring node, dBm; g represents node transmitting antenna gain, dBi; pL(d) The signal strength loss at communication distance d, dB. The greater the measured RSSI, the closer the distance between nodes, and the smaller the ranging error due to the RSSI offset.
In addition, PR(d0) Is d0The received signal strength of (A) can be through PR(d0)＝P+G-PL(d0) To be determined.
Step two: obtaining the reference distance d of the wireless signal according to the formula (2)0Rear path loss PL(d0)；
Figure BDA0003134273900000052
In the formula, GtIs the node transmit antenna gain, in units dBi; grIs the receive antenna gain, in units dBi; l is the system loss coefficient; λ is the RF signal wavelength, in m;
step three: the method comprises the following steps of dynamically obtaining a path loss index, periodically measuring the received signal strength RSSI between a node to be positioned and a neighbor reference node thereof, and then calculating the path loss index n in a current monitoring area by using an RF wireless signal propagation model, wherein the specific steps are as follows:
s11, making PX equal to PR(d0)+XσThe formula (3) can be obtained by substituting the formula (2) with the formula (3);
Figure BDA0003134273900000061
s12, calculating the reference node R according to the formula (4)3And a reference node R1Inter RSSI value PR(d1) (ii) a Calculating a reference node R according to equation (5)3And a reference node R2Inter RSSI value PR(d2)；
Figure BDA0003134273900000062
Figure BDA0003134273900000063
In the formula (d)1As a reference node is R3To a further reference node R in the vicinity1Actual distance between, d2As a reference node is R3To a further reference node R in the vicinity2The actual distance between;
s13, let d01m, simultaneously obtaining formula (6) by formula (4) and formula (5);
Figure BDA0003134273900000064
s14, substituting the RSSI value obtained by the wireless communication between the reference nodes into a formula (6) to obtain a path loss index n which accords with the environmental characteristics of the actual monitoring area;
as can be seen from equation (6), the path loss exponent n depends on PR(d1)，PR(d2) And d1，d2And P isR(d0) The value is irrelevant. And calculating the actual distance between the nodes by utilizing the coordinates of each reference node, substituting the RSSI value obtained by the wireless communication between the reference nodes into the formula (6), thereby obtaining the path loss index n which accords with the environmental characteristics of the actual monitoring area, and obtaining better positioning precision by ranging and positioning. The method not only enhances the adaptability of the RSSI ranging algorithm to the monitoring environment, but also improves the positioning accuracy of the network monitoring node. In order to reduce the increase of communication overhead caused by dynamically acquiring the path loss exponent n, it is reasonable to select a data acquisition frequency according to the actual monitoring requirement of the system, and periodically collect RSSI values obtained by wireless communication between reference nodes, thereby dynamically acquiring the path loss exponent n at any time.
Step four: the measurement distance between the water quality monitoring node and each reference node directly influences the positioning accuracy of the network node, so that in actual positioning, the distance calculated by the formula (1) is not accurate due to the error of the RSSI measurement value, and finally the positioning accuracy of the node is limited inevitably. One of the solutions is that, because the coordinates of the reference nodes are known, the measured distance between the reference nodes can be compared with the actual distance to obtain the relative ranging error of the RSSI, so that the measured distance between the monitoring node and the reference node can be subjected to error correction when the monitoring node is positioned, and the ranging accuracy is improved.
According to the known reference node coordinates, comparing the measured distance between the reference nodes with the actual distance to obtain the relative ranging error of the RSSI, and the method specifically comprises the following steps:
s21, setting the reference node as Ri(xi，yi) Implementation to other reference nodesThe distance between the two electrodes is rikK is 1, 2, …, n, k is not equal to i, wherein n is the number of reference nodes participating in the correction calculation; reference node RiThe measured distances to other reference nodes are recorded as dik， k＝1，2，…，n，k≠i；
S22, obtaining the reference node R according to the formula (7)iDistance average relative error mu between actual distance and measured distanceiAnd as a reference node RiRelative error coefficients of the RSSI-based distance measurements;
Figure BDA0003134273900000071
i.e. the reference node RiThe RSSI-based distance measurement of (a) relative error coefficient(s). Wherein n is the number of all reference nodes in the region; mu.siReflecting the reference node RiThe accuracy of the measured distance is called the relative error coefficient.
S23, setting a threshold tau and adjusting the network positioning performance by controlling the tau; when | muiWhen | ≧ τ, the reference node position is abnormal and can not participate in positioning of the monitoring node, otherwise, the reference node position can participate in positioning calculation;
the performance of network positioning is adjusted by controlling the value of tau so as to make a trade-off between the amount of computation and the positioning accuracy.
S24, when the monitoring node receives the broadcast message of the reference node, the monitoring node sends Pr(d) Calculating and obtaining the measurement distance between the monitoring node and the reference node in the communication range of the monitoring node through the model of the formula (1), and then correcting the measurement distance through a formula (8) according to the relative error coefficient of each reference node;
Figure BDA0003134273900000072
in the formula (d)uiIs a monitoring node and a reference node RiThe measured distance therebetween, in m;
Figure BDA0003134273900000073
is a monitoring node and a reference node RiCorrected distance therebetween, in m;
step five: positioning the monitoring node, which comprises the following steps:
s31, setting the unknown node in the network as U (x)1，y1) The reference node is Ri(xi，yi) To unknown node is U (x)1，y1) Measured distance of diI ═ 1, 2, …, N; establishing a distance equation of monitoring nodes in the water quality monitoring wireless network according to a formula (9);
Figure BDA0003134273900000074
s32, setting the initial coordinate as (x)0，y0) And make
Figure BDA0003134273900000075
Then (x)0，y0) Is aligned with
Figure BDA0003134273900000076
Performing Taylor series expansion, and neglecting components of second order and above to obtain a formula (10);
f(x，y)＝f(x0，y0)+fx(x0，y0)Δx+fy(x0，y0)Δy (10)；
s33, sorting the formula (10) to obtain a formula (11);
Figure BDA0003134273900000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003134273900000082
ax＝fx(x0，y0)；ay＝fy(x0，y0)；
s34, obtaining a formula (12) by arranging the formula (11) due to the existence of the error;
h＝GΔ+ε(d2) (12)；
in the formula (I), the compound is shown in the specification,
Figure BDA0003134273900000083
Δ＝[Δx Ay]T；
Figure BDA0003134273900000084
s35, processing the formula (12) by adopting a weighted least square algorithm WLS to obtain a formula (13);
Δ＝(GTWG)-1GTWh (13)；
in the formula, W is a covariance matrix of a measurement error epsilon;
s36, making W equal to Cov-1(ε), deriving equation (14) to update the parameter vector;
θ(k+1)＝θ(k)+Δ (14)。
the technical scheme is verified through simulation experiments and analysis in the following process:
1. simulation model and test data
In the experimental research and analysis process, in order to reflect the influence of the number, density and communication radius of the anchor nodes of the sensor nodes on the positioning error, the average positioning error of the nodes is used as a main evaluation standard in the execution process of the positioning algorithm. In order to reduce errors caused by random distribution of network nodes, the average value of results obtained by 100 times of simulation is taken as a final positioning result under the condition of the same parameters. Defining the positioning error of the node i in the network as E according to the formula (15)aiI.e. by
Figure BDA0003134273900000085
Wherein R is a communication radius, pi＝[xci yci]TFor the final estimated position of node i, zi＝[xi yi]TIs true of node iA true position;
obtaining the average positioning error of the nodes in the network as E according to the formula (16)aI.e. by
Figure BDA0003134273900000091
Where i is 1, 2, …, N is the number of unknown nodes in the network, and the average positioning error EaThe smaller the positioning accuracy is;
matlab is selected as a simulation test platform. The simulation environment is set to be a rectangular area of 100m × 100m, and network parameters such as the network scale, that is, the number of monitoring nodes, the number of reference nodes, the communication distance of the monitoring nodes and the like are different according to simulation conditions.
The method adopts RF wireless propagation ranging modeling, the expression of which is shown in the formula (1), wherein the input of the model is the RSSI value, and the output of the model is the d value. In an actual environment, the RSSI value has certain errors due to the interference of the environmental factors around the monitored node, so that the ranging errors are caused. The method comprises the steps of calculating an RSSI value according to the actual distance between the monitoring nodes, and adding sigma of a standard deviationfThe result of the gaussian noise is used as the RSSI input value of the distance observation model. Standard deviation sigma of gaussian measurement noisefThe expression is shown in formula (17):
Figure BDA0003134273900000092
wherein R represents the maximum communication radius of the node, RiRepresents the node communication distance, muiThe distance measurement error is represented, and different distance measurement errors can be simulated by adjusting the parameter.
In the simulation result, an algorithm A represents the algorithm of the application, an algorithm B represents a Taylor series expansion algorithm based on real coordinates, and an algorithm C represents a (common LS) basic algorithm. And the positioning accuracy of the 3 algorithms under different ranging errors, anchor node density and node communication radiuses is simulated and analyzed in a comparison manner.
And (3) testing the influence of different ranging errors on the positioning precision, and setting the number of reference nodes as n-20 and the number of nodes as 400. The simulation results are shown in the following table.
Figure BDA0003134273900000093
As can be seen from the above table, the C algorithm is very sensitive to the distance measurement error, and when the variance of the distance measurement error is large, the positioning accuracy of the method is obviously reduced. The algorithm B relatively reduces the adverse effect of the ranging error on the positioning precision, but the effect is not obvious. The algorithm A provided by the application can greatly reduce the adverse effect of the ranging error, so that the method has higher positioning precision.
When the variance of the range error is
Figure BDA0003134273900000094
Then, the positioning accuracy of the algorithm B is about 0.20, and the positioning accuracy of the algorithm C is about 0.22; when the variance of the range error
Figure BDA0003134273900000095
As the positioning accuracy increases, the positioning accuracy of all three algorithms starts to gradually decrease, but the positioning accuracy of the a algorithm is always higher than that of the B and C algorithms. The reason is mainly when the range error is small, i.e. when
Figure BDA0003134273900000096
In time, the positioning error mainly comes from the unknown node positioning calculation error caused by the distance ranging error. Because the algorithm A adopts the measurement distance correction, the positioning precision is obviously improved, and when the distance measurement error is gradually increased, the influence of the distance measurement error on the positioning precision of the monitoring node is increased. The algorithm A reduces random errors caused by ranging, and the ranging value after error correction improves the positioning precision.
Testing the relation between the number of anchor nodes and the positioning precision, and setting a simulation experiment environment: 100 nodes are randomly distributed in an area of 100m multiplied by 100m, and the communication radius of the nodes is 40 m. The simulation gave the results shown in the following table.
Figure BDA0003134273900000101
As can be seen from the above table, the positioning errors of algorithm B and algorithm C are larger when the number of reference nodes is small. The reason is that when the ratio of the reference node is low, the information used for calculating the distance and the position in the network is reduced, and the distance error between the unknown node and the anchor node becomes large. The A algorithm effectively corrects the measurement distance by using the correction coefficients of a plurality of reference nodes, so that the positioning error caused by fewer reference nodes can be obviously reduced.
Testing the influence of the node communication radius on the positioning precision, and setting a simulation experiment environment: 100 nodes are randomly distributed in a 100m multiplied by 100m area, and the number of reference nodes is 15. The simulation gave the results shown in the following table.
Figure BDA0003134273900000102
As can be seen from the above table, the increase of the node communication radius also has an important influence on the positioning accuracy. When the node communication distance is increased, the information quantity between the monitoring node and the reference node is increased, the reference nodes in the communication periphery of the monitoring node are increased step by step, and therefore the positioning of the monitoring node is achieved, and the positioning accuracy is improved as more reference node distances are utilized to correct the distance from the monitoring node to the anchor node. As can be seen from the table, under the same conditions, the positioning accuracy of the algorithm a is higher than that of the algorithms B and C.
2. Experiments and analyses
In order to actually check the positioning characteristics of the algorithm, a small wireless sensor network experimental test system is built in a 15m multiplied by 15m area of a laboratory in a teaching building by using a CC2530 node. The system is provided with 6 anchor nodes which are uniformly deployed in a test area, in addition, 10 unknown nodes and 1 sink node are deployed at manually selected positions, and the whole system further comprises 1 control background. The node communication distance is 15m, the height of the node from the ground is about 0.5m, data is transmitted every 20s, and the average value of 50 measurements in an experiment is taken as an experiment result.
After the specific position of the node to be positioned is set, the node is assumed to be an unknown node, and measurement and positioning are carried out. Based on the experimental data, the experimental results are shown in table 1.
Table 1 measurement positioning results of the experiment
Numbering of nodes to be positioned Actual position of node Post measurement positioning Distance between two positions Positioning error Eai
01 (3.0，3.0) (4.2，3.5) 1.30 0.09
02 (3.0，9.0) (3.4，7.1) 1.96 0.13
03 (6.0，6.0) (5.3，8.1) 2.21 0.15
04 (6.0，12.0) (6.6，10.7) 1.43 0.10
05 (9.0，3.0) (7.4，3.2) 1.61 0.11
06 (9.0，6.0) (8.5，7.6) 1.68 0.11
07 (12.0，3.0) (10.4，4.1) 1.94 0.13
08 (12.0，6.0) (11.1，7.9) 2.10 0.14
09 (12.0，9.0) (10.8，9.3) 1.24 0.08
10 (15.0，6.0) (12.7，5.2) 2.44 0.16
As can be seen from table 1, the positioning error of the a algorithm in the actual testing environment is 0.16, the minimum positioning error is 0.08, and the average value is 0.120. Through experimental research and analysis, under the same conditions, the mean value of the positioning errors obtained by simulation experiments is 0.113, and the positioning precision of the algorithm A under the actual test condition is slightly lower than the simulation precision. The analysis reason is mainly that in an actual test environment, the RF signals among the test nodes are influenced by factors such as wall bodies, equipment and barriers, so that the error of the RSSI measured value is increased, and the positioning accuracy is damaged. In the actual test, the accuracy of the RSSI measurement value is also reduced due to human body shielding caused by personnel movement, and the factor is not considered in the simulation experiment. The results show that the experimental and simulation data of algorithm a are slightly different, which can illustrate the feasibility of the method positioning.
The positioning algorithm provided by the application is utilized to analyze 16 groups of test data, and Gaussian random variable is set to be Xσ(0, 10), 100 nodes are randomly distributed in a 100m × 100m area, the communication radius of the nodes is 40m, and the number n of the anchor nodes is 20. In order to reduce errors caused by network random distribution, the positioning results obtained by experiments are all mean values of results obtained by simulating 50 times under the same parameter condition, and the positioning errors of the test data are shown in the following table.
Figure BDA0003134273900000111
And (3) analysis: the maximum value of the positioning error in the table is 0.35, the minimum value is 0.18, and the average value is. Because 6 anchor nodes are uniformly deployed in a laboratory test area, the positioning error of the edge of the area is large, and the overall positioning effect is good. If some reference nodes are more deployed at the edge of the test area, the positioning effect can be further improved.
Conclusion
The application provides a water quality monitoring wireless sensor network Taylor series least square iterative positioning algorithm based on RSSI ranging and distance correction, on the basis of deep research of an RSSI positioning principle and application requirements of a water quality monitoring positioning system, an RF wireless signal propagation model is applied to obtain a path loss factor in a current monitoring area, the ranging is corrected based on RSSI ranging relative errors of reference nodes, and in the positioning stage, the position coordinates of monitoring nodes are solved by adopting a linearization processing method of the Taylor series least square iterative algorithm.
Simulation tests and positioning experiments show that the method fully considers the influence of factors such as ranging errors and the number of reference nodes on positioning precision, obtains a good positioning effect, and can meet the positioning requirements of industrial and agricultural water environment monitoring systems with complex and severe network environments and limited positioning cost. Comparing the method with the LS positioning algorithm, the positioning error mean values of the two algorithms are 2.1425m and 2.9251m respectively, and the average running time of the positioning algorithm is 0.2372s and 1.9163s respectively, which shows that the method has higher positioning accuracy and lower calculation complexity.

Claims (2)

1. A water quality monitoring network positioning method based on RSSI ranging is characterized by comprising the following steps:
the method comprises the following steps: establishing an RF communication model according to formula (1);
Figure FDA0003134273890000011
wherein n is a path loss exponent; d0A reference distance for signal propagation; pR(d0) Is d after signal transmission0Received signal strength of (X)σIs the mean valueA Gaussian random variable with the standard deviation of 0 and the range of 4-10;
step two: obtaining the reference distance d of the wireless signal according to the formula (2)0Rear path loss PL(d0)；
Figure FDA0003134273890000012
In the formula, GtIs the node transmit antenna gain, in units dBi; grIs the receive antenna gain, in units dBi; l is the system loss coefficient; λ is the RF signal wavelength, in m;
step three: the method comprises the following steps of periodically measuring the received signal strength RSSI between a node to be positioned and a neighbor reference node thereof, and then calculating a path loss index n in a current monitoring area by using an RF wireless signal propagation model, wherein the specific steps are as follows:
s11, making PX equal to PR(d0)+XσThe formula (3) can be obtained by substituting the formula (2) with the formula (3);
Figure FDA0003134273890000013
s12, calculating the reference node R according to the formula (4)3And a reference node R1Inter RSSI value PR(d1) (ii) a Calculating a reference node R according to equation (5)3And a reference node R2Inter RSSI value PR(d2)；
Figure FDA0003134273890000014
Figure FDA0003134273890000015
In the formula (d)1As a reference node is R3To a further reference node R in the vicinity1In betweenActual distance, d2As a reference node is R3To a further reference node R in the vicinity2The actual distance between;
s13, let d01m, simultaneously obtaining formula (6) by formula (4) and formula (5);
Figure FDA0003134273890000016
s14, substituting the RSSI value obtained by the wireless communication between the reference nodes into a formula (6) to obtain a path loss index n which accords with the environmental characteristics of the actual monitoring area;
step four: according to the known reference node coordinates, comparing the measured distance between the reference nodes with the actual distance to obtain the relative ranging error of the RSSI, and the method specifically comprises the following steps:
s21, setting the reference node as Ri(xi，yi) The actual distance to other reference nodes is rikK is 1, 2, …, n, k is not equal to i, wherein n is the number of reference nodes participating in the correction calculation; reference node RiThe measured distances to other reference nodes are recorded as dik，k＝1，2，…，n，k≠i；
S22, obtaining the reference node R according to the formula (7)iDistance average relative error mu between actual distance and measured distanceiAnd as a reference node RiRelative error coefficients of the RSSI-based distance measurements;
Figure FDA0003134273890000021
s23, setting a threshold tau and adjusting the network positioning performance by controlling the tau; when | muiWhen | ≧ τ, the reference node position is abnormal and can not participate in positioning of the monitoring node, otherwise, the reference node position can participate in positioning calculation;
s24, when the monitoring node receives the broadcast message of the reference node, the monitoring node sends Pr(d) Calculating and obtaining the communication range of the monitoring node and the monitoring node through the model of the formula (1)Measuring distances among the internal reference nodes, and then correcting the measuring distances by a formula (8) according to the relative error coefficients of all the reference nodes;
Figure FDA0003134273890000022
in the formula (d)uiIs a monitoring node and a reference node RiThe measured distance therebetween, in m;
Figure FDA0003134273890000023
is a monitoring node and a reference node RiCorrected distance therebetween, in m;
step five: positioning the monitoring node, which comprises the following steps:
s31, setting the unknown node in the network as U (x)1，y1) The reference node is Ri(xi，yi) To unknown node is U (x)1，y1) Measured distance of diI ═ 1, 2, …, N; establishing a distance equation of monitoring nodes in the water quality monitoring wireless network according to a formula (9);
Figure FDA0003134273890000024
s32, setting the initial coordinate as (x)0，y0) And make
Figure FDA0003134273890000025
Then (x)0，y0) Is aligned with
Figure FDA0003134273890000026
Performing Taylor series expansion, and neglecting components of second order and above to obtain a formula (10);
f(x，y)＝f(x0，y0)+fx(x0，y0)Δx+fy(x0，y0)Δy (10)；
s33, sorting the formula (10) to obtain a formula (11);
Figure FDA0003134273890000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003134273890000032
ax＝fx(x0，y0)；ay＝fy(x0，y0)；
s34, sorting the formula (11) to obtain a formula (12);
h＝GΔ+ε(d2) (12)；
in the formula (I), the compound is shown in the specification,
Figure FDA0003134273890000033
Δ＝[Δx Δy]T；
Figure FDA0003134273890000034
s35, processing the formula (12) by adopting a weighted least square algorithm WLS to obtain a formula (13);
Δ＝(GTWG)-1GTWh (13)；
in the formula, W is a covariance matrix of a measurement error epsilon;
s36, making W cov-1(ε), deriving equation (14) to update the parameter vector;
θ(k+1)＝θ(k)+Δ (14)。
2. the RSSI ranging-based water quality monitoring network positioning method according to claim 1, wherein in the second step, a path loss index value n is between 2 and 4, and the more the number of obstacles and the more the shielding are, the larger the n value is.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116033441A (en) * 2023-03-30 2023-04-28 江西农业大学 Environment geographic information monitoring network and updating method thereof
WO2023221656A1 (en) * 2022-05-17 2023-11-23 上海船舶运输科学研究所有限公司 Information fusion-based wireless sensor network positioning method for marine search and rescue

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023221656A1 (en) * 2022-05-17 2023-11-23 上海船舶运输科学研究所有限公司 Information fusion-based wireless sensor network positioning method for marine search and rescue
CN116033441A (en) * 2023-03-30 2023-04-28 江西农业大学 Environment geographic information monitoring network and updating method thereof
CN116033441B (en) * 2023-03-30 2023-06-20 江西农业大学 Environment geographic information monitoring network and updating method thereof

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