CN111083632A - Ultra-wideband indoor positioning method based on support vector machine - Google Patents

Ultra-wideband indoor positioning method based on support vector machine Download PDF

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CN111083632A
CN111083632A CN201911255480.5A CN201911255480A CN111083632A CN 111083632 A CN111083632 A CN 111083632A CN 201911255480 A CN201911255480 A CN 201911255480A CN 111083632 A CN111083632 A CN 111083632A
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符强
董兴波
孙希延
纪元法
任风华
严素清
付文涛
黄建华
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Guilin University of Electronic Technology
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Abstract

The invention discloses an ultra-wideband indoor positioning method based on a support vector machine, which comprises the steps of firstly collecting a certain number of TDOA values of an area to be positioned and user positions corresponding to the TDOA values, then dividing the collected data set into a training set and a testing set according to the ratio of 4:1, then inputting the training set into the support vector machine after normalization processing, continuously carrying out cross validation to select optimal parameters c and g, sorting according to the average accuracy of the cross validation, selecting a parameter combination with the highest classification accuracy as the optimal parameters of a model, inputting the obtained optimal parameters and the training set into the support vector machine to obtain a support vector machine model, and after the support vector machine model is trained, inputting the collected TDOA values into the trained support vector machine in the process of resolving coordinates to solve real-time coordinates, wherein the results show that the real-time performance and the positioning accuracy of the algorithm are better than those of the traditional positioning algorithm in a high-density positioning environment A conventional algorithm.

Description

Ultra-wideband indoor positioning method based on support vector machine
Technical Field
The invention relates to the field of indoor positioning, in particular to an ultra-wideband indoor positioning method based on a support vector machine.
Background
At present, Ultra Wide Band (UWB) transmits data through nanosecond-microsecond-level non-sine wave narrow pulses, and one of the remarkable characteristics of the UWB is high data transmission rate, and the UWB also has the characteristics of strong anti-interference capability, high transmission rate, large system memory, good penetrating performance, small sending power and the like, so that the UWB technology can realize high precision of indoor positioning and positioning;
because the TOA is mainly based on the time measurement of signal transmission arrival between nodes, the requirement of the TOA on the aspect of time synchronization of each node is stricter, in addition, because the TOA positioning algorithm needs to have at least three useful back-and-forth communications between the base station and the mobile station when performing distance measurement, which is also the main reason that the power LOSs of the base station and the mobile station is greatly increased, because the time synchronization of the TDOA is consistent with the time synchronization between the known base stations, compared with the known base stations, the time between the known base stations is obviously simpler than the synchronization of the target to be measured, therefore, the TDOA is more widely applied, the traditional TDOA positioning algorithms include Chan algorithm, Fang algorithm, Taylor algorithm and the like, and the Chan algorithm has high positioning accuracy under the condition of LOS or under the condition that the TDOA measurement error is small; under the condition of NLOS or poor channel performance, the positioning accuracy is greatly reduced, so that one of important factors influencing the positioning accuracy is a non-line-of-sight error, the Taylor series expansion method is one of recursive calculation methods, the method needs to estimate an initial position, the calculation complexity is high, the estimated value of the initial position has a large influence on the positioning accuracy, the Fang algorithm can only use three base stations for positioning, TDOA measured values given by other base stations are not fully utilized, Jiankan, and Yanfan simulation results show that in actual UWB positioning, Chan and Taylor algorithms are two algorithms with high positioning accuracy;
the support vector machine is commonly used in the aspects of voice recognition, biomedicine, noise processing and the like, can solve the problem of high dimension, solves the problem of machine learning under a small sample, can process the interaction of nonlinear characteristics, does not have the problem of local minimum value, does not need to rely on whole data, and has stronger generalization capability.
Disclosure of Invention
The invention aims to provide an ultra-wideband indoor positioning method based on a support vector machine, which solves the technical problem that the positioning of the existing algorithm in a high-density environment is difficult to meet the requirement.
In order to achieve the above object, the present invention provides an ultra-wideband indoor positioning method based on a support vector machine, including:
obtaining TDOA data of an area to be positioned, and receiving absolute time difference of arrival of two signals through a base station to obtain data;
acquiring user position data, and obtaining a user position corresponding to the TDOA data by inputting the TDOA data;
preprocessing the collected TDOA data and the user position data, and dividing the data into a first part and a second part;
and inputting the first part and the second part into a vector machine to obtain coordinate data.
The invention relates to an ultra-wideband indoor positioning method based on a support vector machine, which comprises the steps of firstly collecting a certain number of TDOA values of an area to be positioned and user positions corresponding to the TDOA values, then dividing the collected data set into a training set and a testing set according to the ratio of 4:1, then carrying out normalization processing, inputting the training set into the support vector machine, continuously carrying out cross validation to select optimal parameters c and g, sorting according to the average accuracy of the cross validation, selecting the parameter combination with the highest classification accuracy as the optimal parameters of a model, inputting the obtained optimal parameters and the training set into the support vector machine to obtain a support vector machine model, and after the support vector machine model is trained, inputting the collected TDOA values into the trained support vector machine in the process of resolving coordinates to solve real-time coordinates, the result shows that compared with the traditional positioning algorithm, the real-time performance and the positioning accuracy of the algorithm are superior to those of the traditional algorithm in a high-density positioning environment.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without any creative effort.
Fig. 1 is an overall flow chart of the indoor positioning of the present invention.
Fig. 2 is a detailed flowchart of step 102.
Fig. 3 is a detailed flowchart of step 103.
Fig. 4 is an overall flow chart of the indoor positioning of the present invention.
FIG. 5 is a diagram of support vector machine parameters of the present invention.
FIG. 6 is a kernel function implementation non-linear mapping of the present invention.
FIG. 7 is a comparison graph of decision coefficients and root mean square error of different training data samples according to the present invention.
FIG. 8 is a comparison graph of the root mean square error of three algorithms of the present invention under different TDOA differences.
FIG. 9 is a comparison graph of positioning time for different positioning quantities for the three algorithms of the present invention.
Fig. 10 is a diagram of the results of a 3D positioning simulation of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and are intended to be illustrative of the invention and should not be construed as limiting the invention.
In the description of the present invention, it is to be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like, indicate orientations or positional relationships that are based on the orientations or positional relationships illustrated in the drawings, are used for convenience in describing the invention and to simplify the description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated, and thus are not to be construed as limiting the invention. Further, in the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
Example 1:
referring to fig. 1, the present invention provides an ultra-wideband indoor positioning method based on a support vector machine, including:
s101, TDOA data of an area to be positioned is obtained, and data are obtained by receiving the absolute time difference of arrival of two signals through a base station;
s102, acquiring user position data, and obtaining a user position corresponding to TDOA data by inputting the TDOA data;
s103, preprocessing the acquired TDOA data and the user position data, and dividing the data into a first part and a second part;
s104, the data sets of the first part and the second part are linear inseparable, the data sets are mapped to a high-dimensional space through a proper kernel function, and a linear discriminant function is constructed in the high-dimensional space;
s105, normalizing the input training set sample through a function, and reducing the influence of a large attribute value on a small attribute value;
s106, traversing all the parameters c and g by a grid search method, and calculating results of all the parameters;
s107, sequencing the accuracy of the training results by using cross validation, and obtaining a parameter combination with the highest accuracy as the optimal parameter of the model after traversing all possible results;
s108, inputting the first part and the second part into a vector machine to obtain coordinate data;
s109, inputting the training result into the trained support vector machine model, and performing inverse normalization on the obtained result to obtain a decision coefficient R2And a root mean square error;
s110, obtaining a determination coefficient R2Comparing and judging the error with the root mean square error, and comparing the quality of the training model;
and when the S111 region is positioned, inputting the acquired real-time TDOA value into the support vector machine model, so as to obtain a real-time coordinate value.
Example 2:
s101, TDOA data of an area to be positioned is obtained, and data are obtained by receiving the absolute time difference of arrival of two signals through a base station;
s102, acquiring user position data, and obtaining a user position corresponding to TDOA data by inputting the TDOA data;
s1031 preprocesses the collected TDOA data and the collected user position data and divides the data into a first part and a second part;
s1032, dividing the first part into four parts, and dividing the second part into one part;
s104, the data sets of the first part and the second part are linear inseparable, the data sets are mapped to a high-dimensional space through a proper kernel function, and a linear discriminant function is constructed in the high-dimensional space;
s105, normalizing the input training set sample through a function, and reducing the influence of a large attribute value on a small attribute value;
s106, traversing all the parameters c and g by a grid search method, and calculating results of all the parameters;
s107, sequencing the accuracy of the training results by using cross validation, and obtaining a parameter combination with the highest accuracy as the optimal parameter of the model after traversing all possible results;
s108, inputting the first part and the second part into a vector machine to obtain coordinate data;
s109, inputting the training result into the trained support vector machine model, and performing inverse normalization on the obtained result to obtain a decision coefficient R2And a root mean square error;
s110, obtaining a determination coefficient R2Comparing and judging the error with the root mean square error, and comparing the quality of the training model;
and when the S111 region is positioned, inputting the acquired real-time TDOA value into the support vector machine model, so as to obtain a real-time coordinate value.
Example 3:
s101, TDOA data of an area to be positioned is obtained, and data are obtained by receiving the absolute time difference of arrival of two signals through a base station;
s102, acquiring user position data, and obtaining a user position corresponding to TDOA data by inputting the TDOA data;
s103, preprocessing the acquired TDOA data and the user position data, and dividing the data into a first part and a second part;
s1041, the data sets of the first part and the second part are linear inseparable, the data sets are mapped to a high-dimensional space through a proper kernel function, and a linear discriminant function is constructed in the high-dimensional space;
s1042 maps the input space of the introduced kernel function to a high-dimensional space and converts the operation of the high-dimensional space into the operation of the kernel function of a low-dimensional space, so that the workload of calculation is greatly reduced, and the situation of dimension disaster is avoided.
S105, normalizing the input training set sample through a function, and reducing the influence of a large attribute value on a small attribute value;
s106, traversing all the parameters c and g by a grid search method, and calculating results of all the parameters;
s107, sequencing the accuracy of the training results by using cross validation, and obtaining a parameter combination with the highest accuracy as the optimal parameter of the model after traversing all possible results;
s108, inputting the first part and the second part into a vector machine to obtain coordinate data;
s109, inputting the training result into the trained support vector machine model, and performing inverse normalization on the obtained result to obtain a decision coefficient R2And a root mean square error;
s110, obtaining a determination coefficient R2Comparing and judging the error with the root mean square error, and comparing the quality of the training model;
and when the S111 region is positioned, inputting the acquired real-time TDOA value into the support vector machine model, so as to obtain a real-time coordinate value.
In the embodiment, the support vector machine is a method based on the statistical learning theory, which attracts more and more attention in the aspects of theoretical research and practical application, the support vector machine method of regression estimation is widely used in the fields of identification, prediction, modeling and control of a nonlinear system, the establishment of a model does not need too much artificial intervention,
FIG. 5 shows the parameters of the support vector machine, and the hyperplane function expression is:
f(x)＝wTx+b (1-1)
wherein w is the normal vector of the hyperplane, x is the point on the plane, b represents the distance from the hyperplane to the origin,
wherein the coefficients w and b can obtain the objective function of the soft interval support vector machine by the formula (1-1):
Figure BDA0002310122220000061
wherein, C is a penalty coefficient and is used for balancing the complexity and the loss error of the model; l isεFor the loss function, the expression is:
Figure BDA0002310122220000062
for the regression data points, a relaxation variable ξ was introducedi，
Figure BDA0002310122220000063
Representing how far the corresponding point is from the other side of the classification error,
the loss function (1-3) is brought to (1-2) to obtain:
Figure BDA0002310122220000064
wherein
Figure BDA0002310122220000071
The double gradient theory is used to solve equations (1-4), establishing the lagrangian equation:
Figure BDA0002310122220000072
wherein the content of the first and second substances,
Figure BDA0002310122220000073
αi，
Figure BDA0002310122220000074
in order to be a lagrange multiplier,
Figure BDA0002310122220000075
in order to relax the variable-influencing factor,
to pair
Figure BDA0002310122220000076
The partial derivatives are obtained:
Figure BDA0002310122220000077
simplified (1-6 formula) to obtain
Figure BDA0002310122220000078
Wherein the content of the first and second substances,
Figure BDA0002310122220000079
the data set is mainly passed through a kernel function K (x) in the nonlinear regressioni,xj)φ(xi)Tφ(xj) Mapping to a high-dimensional feature space and performing linear regression,
Figure BDA00023101222200000710
wherein the content of the first and second substances,
Figure BDA00023101222200000711
in order to avoid the situation of "dimension disaster", the support vector machine algorithm can map the input space of the introduced kernel function to the high-dimensional space and convert the operation of the high-dimensional space into the operation of the kernel function of the low-dimensional space, so that the workload of calculation is greatly reduced, fig. 6 is a nonlinear mapping of the kernel function, the gaussian kernel function is the most commonly applied kernel function, also called Radial Basis Function (RBF), can map data to infinite dimensions:
K(xi,xj)＝exp(-γ||xi-xj||2),γ＞0 (1-9)
wherein gamma represents the distance from any point in space to a point on the hyperplane,
the central idea of the support vector machine algorithm is to select a subset with obvious characteristics in a training data set as a support vector, SV for short, the linear division of the characteristic subset represents the linear division of the whole data set, the support vector machine algorithm improves the classification accuracy and reduces the complexity of operation at the same time, thereby greatly reducing the calculated amount,
in the classification regression algorithm of the support vector machine, the selection of the kernel function is very important, the kernel function can convert the dot product operation in a high-dimensional characteristic space into the kernel function of a low-dimensional input space for operation, different support vector machines trained by different kernel functions are different, the selection of the proper kernel function can improve the classification and regression precision, it improves the position accuracy, and commonly used kernel functions are as follows, such as linear kernel function, polynomial kernel function, gaussian kernel function, RBF kernel function, and logistic kernel function, etc., because the statistical result of the actual signal distribution characteristics is very similar to gauss distribution, therefore, the RBF kernel function is selected, after training by using different kernel functions, the RBF kernel root mean square error is minimum, the RBF mean square error is 1.00146151, the root mean square errors of other three are respectively calculated to be 1.20194, 1.3275195 and 3.416845, the RBF kernel is thus selected, and the following equations (1-10) are expressions of the Gaussian kernel:
Figure BDA0002310122220000081
where σ is the bandwidth of the Gaussian kernel,
when selecting function parameters, the RBF kernel function comprises a penalty constant term C and a parameter G of the RBF, so that the parameters are necessarily optimized, at present, the general use methods of parameter optimization are grid optimization, ga optimization and pso optimization, wherein a grid optimization method is the simplest and most effective, but the parameter optimization methods all have the most important precondition that a test set label is known, but the invention assumes that a regression algorithm is used under the condition that the test set label is not known, so that the optimal C and G are searched by using a Cross Validation (Cross Validation),
in order to optimize the performance of the support vector machine, the present invention compares the root mean square error with the decision coefficient for different number of samples within 25 × 2m3, and when the number of samples is 4500, the root mean square error is the lowest and the decision coefficient is close to the maximum, so the present invention selects 4500 as the training data sample to train the support vector machine.
The specific steps of the training process of the support vector machine are summarized as follows:
step 1: the invention uses TDOA value, inputs necessary information into the network through training test, usually the more sample data, the closer the training result is to the target result, but this will increase the difficulty of data collection and data analysis, in order to use the minimum sample to get the best effect, the invention above compares the relation of sample quantity and training effect, in the simulation process in this subject, finally chooses 4500 sample data to train, the upper limit of training times is set to 6000 times,
step 2: using functions
Figure BDA0002310122220000091
The input training set samples are normalized, the influence of the large attribute value on the small attribute value is reduced,
step 3: mapping the dataset to a high-dimensional space using equations (1-10), constructing a linear discriminant function in the high-dimensional space,
step 4: traversing all c and g parameters by a grid search method, calculating results of all parameters, sequencing the accuracy of the trained results by cross validation, obtaining a proper classifier after traversing all possible results,
step 5: inputting the test set into a trained model, and performing inverse normalization on the obtained result to obtain a decision coefficient R2And the root mean square error, judging the quality of the training model according to the two parameters,
step 6: when the area is positioned, the acquired real-time TDOA value is input into the support vector machine model, so as to obtain a real-time coordinate value,
the input of the support vector machine algorithm is 3 TDOA values, the coordinate value corresponding to the TDOA value is output, the positioning accuracy of the algorithm is analyzed from the X direction, the Y direction and the Z direction respectively, and the three-dimensional space 25 × 2m is shown in the figure 73Sampling interval of 0.5m, total10000 points are sampled, a plurality of 10000 sampling points are randomly selected as training samples, the proportion of a test set to a training set is generally 1:4,
in order to compare the positioning accuracy of the algorithm with that of the traditional algorithm, the Chan, Taylor and the algorithm of the invention are compared under the condition of different TDOA difference values, as shown in FIG. 8, it can be seen from FIG. 8 that the root mean square error of the Taylor algorithm is far greater than that of the Chan algorithm, because the Taylor algorithm needs to be recursively solved according to the initial position, the initial estimated position has a great influence on the final solving result, so the root mean square error is relatively large; the Chan algorithm is actually a solution of a non-recursive hyperbolic equation set, the complexity of the Chan algorithm is smaller than that of Taylor, and position coordinates can be solved through two iterations, so the root mean square error of the Chan algorithm is smaller than that of Taylor.
With the increase of the number of positioning points, more and more time is used for locating the Chan algorithm and the Taylor, the time used for the three algorithms under different positioning points is compared, as shown in FIG. 9, it can be seen from the figure that the time used for locating the Taylor algorithm and the Chan algorithm is far longer than that of the algorithm because the complexity of resolving the coordinates of the Taylor algorithm and the Chan algorithm is higher than that of the algorithm, the time used for locating the Taylor algorithm and the Chan algorithm is used for resolving the TDOA for ultra-wideband indoor positioning, a certain time is spent in training the model, the time used for locating the sample point after the model is trained is basically less than 1s, and the real-time performance of the algorithm is far better than that of the traditional positioning algorithm under the condition of equivalent positioning accuracy,
after the support vector machine network is trained, the 3D positioning result of the algorithm is shown in FIG. 10, the error between the estimated position and the actual position of the tag is 10.15cm, and the correctness of the simulation result is verified better.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (10)

1. An ultra-wideband indoor positioning method based on a support vector machine is characterized by comprising
Obtaining TDOA data of an area to be positioned, and obtaining the data by receiving the absolute time difference of arrival of two signals through a base station;
acquiring user position data, and obtaining a user position corresponding to the TDOA data by inputting the TDOA data;
preprocessing the collected TDOA data and the user position data, and dividing the data into a first part and a second part;
and inputting the first part and the second part into a vector machine to obtain coordinate data.
2. The ultra-wideband indoor positioning method based on support vector machine according to claim 1, further comprising, before inputting the first part and the second part into a vector machine to obtain coordinate data:
and the data sets of the first part and the second part are linear inseparable, the data sets are mapped to a high-dimensional space through a proper kernel function, and a linear discriminant function is constructed in the high-dimensional space.
3. The ultra-wideband indoor positioning method based on support vector machine according to claim 2, wherein after the data sets of the first part and the second part are linearly inseparable, the data sets are mapped to a high-dimensional space by a suitable kernel function, and a linear discriminant function is constructed in the high-dimensional space, the method further comprises:
and normalizing the input training set sample through the function, so that the influence of the large attribute value on the small attribute value is reduced.
4. The ultra-wideband indoor positioning method based on support vector machine according to claim 3, after normalizing the input training set samples by the function to reduce the influence of the large attribute value on the small attribute value, further comprising:
and traversing all the parameters c and g by a grid search method, and calculating results of all the parameters.
5. The method of claim 4, wherein between traversing all c and g parameters by a grid search method, calculating the results of all parameters and inputting the first portion and the second portion into a vector machine, obtaining coordinate data, further comprising:
and sequencing the accuracy of the training results by using cross validation, and obtaining a parameter combination with the highest accuracy as the optimal parameter of the model after traversing all possible results.
6. The method of claim 5, wherein after inputting the first portion and the second portion into a vector machine to obtain coordinate data, further comprising:
inputting the training result into the trained support vector machine model, and performing inverse normalization on the obtained result to obtain a decision coefficient R2And root mean square error.
7. The support vector machine-based ultra-wideband indoor positioning method of claim 6, wherein the training result is input into the trained support vector machine model, and the obtained result is subjected to inverse normalization to obtain a decision coefficient R2And after the root mean square error, further comprising:
will obtain the determination coefficient R2And comparing and judging with the root mean square error, and comparing the quality of the training model.
8. The ultra-wideband indoor positioning method based on support vector machine according to claim 7, wherein the decision coefficient R is obtained2Comparing and judging with the root mean square errorAfter comparing the quality of the training model, the method further comprises:
when the region is positioned, the acquired real-time TDOA value is input into the support vector machine model, and then the real-time coordinate value can be obtained.
9. The method of support vector machine-based ultra-wideband indoor positioning as claimed in claim 1, wherein in pre-processing the collected TDOA data and the user location data into a first part and a second part:
the dividing ratio of the first part is four parts, and the dividing ratio of the second part is one part.
10. The ultra-wideband indoor positioning method based on support vector machine according to claim 2, wherein, when the data sets of the first part and the second part are linearly inseparable, the data sets are mapped to a high-dimensional space by a suitable kernel function, and in constructing a linear discriminant function in the high-dimensional space:
the input space of the introduced kernel function is mapped to the high-dimensional space, and the operation of the high-dimensional space is converted into the operation of the kernel function of the low-dimensional space, so that the workload of calculation is greatly reduced, and the situation of dimension disaster is avoided.
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