CN106912105B - Three-dimensional positioning method based on PSO _ BP neural network - Google Patents
Three-dimensional positioning method based on PSO _ BP neural network Download PDFInfo
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Abstract
The invention designs a terminal three-dimensional positioning method of a BP neural network based on Particle Swarm Optimization (PSO), which can be widely applied to the field of wireless positioning. The method comprises the following steps: and measuring distance data between a plurality of base stations and the terminal in a certain area. And sequencing the measured distances from small to large, selecting four base stations with the closest distances, and calculating the position of the terminal with the non-line-of-sight influence by using the four base stations through a least square method. And calculating the positions of all terminals with non-line-of-sight distances, and calculating the three-dimensional direction angle from each base station to the terminal. And finally, taking the obtained terminal position coordinate, the distance from the base station to the terminal and the three-dimensional direction angle as a characteristic value input layer of the PSO _ BP neural network, wherein the output layer is the corrected terminal position coordinate. The invention optimizes the BP neural network by utilizing the PSO algorithm, the obtained result eliminates the terminal position measurement error caused by non-line-of-sight factors, and the proposed algorithm has the advantages of stable performance, fast algorithm convergence, high positioning precision and the like, and is suitable for popularization and use.
Description
Technical Field
The invention designs a terminal three-dimensional positioning method of a BP neural network optimized based on a particle swarm algorithm, which can be widely applied to the field of wireless positioning.
Background
With the rapid development of wireless communication networks and mobile internet, providing Location Based Service (LBS) has become one of the most promising services with market prospect and development potential. From traditional GPS navigation to electronic commerce, catering platforms and other consumption information services and social software based on geographical positions, the basis for realizing the functions is to acquire the position of a handheld terminal (including a mobile phone or a tablet and other devices) of a user.
Although commercial GPS has been widely used with the development of smart phones, GPS positioning performance is poor in many scenarios such as indoors, underground, urban areas where high buildings stand, and the like. Compared with a GPS, the positioning system based on the wireless network base station has the advantages of wide coverage range, high signal quality and strong mobile terminal desire of a user, meanwhile, based on the wireless network base station, an operator has clear profit mode for promoting positioning service, and besides basic data service, the positioning system can also promote the business development of the operator by providing value-added service for the user. Therefore, the positioning technology based on the wireless communication base station has wide application prospect and great commercial value.
Limited by conditions such as positioning time, positioning precision, complex indoor environment and the like, especially in a three-dimensional positioning environment, a relatively perfect positioning technology cannot be well utilized at present. Taking an indoor environment as an example, the radio signal can be reflected many times by a wall surface, refracted and absorbed by an indoor object, and the like in the transmission process. These physical factors can cause noise in the information measured by the communication base station, such as distance, angle, etc. How to obtain accurate estimation of the position information based on the noisy measurements is also a problem to be solved when the communication base station realizes the positioning of the terminal.
The algorithm with strong innovation and realizability for solving and analyzing the mobile terminal positioning related problems under the three-dimensional condition can be rapidly deployed in the modern commercial communication network, and great social and economic benefits are brought.
Disclosure of Invention
The invention provides a terminal three-dimensional positioning method based on a PSO _ BP neural network, aiming at the problem that the terminal positioning method under the condition of multiple indoor base stations in the prior art is low in precision.
There will be a plurality of base stations in an area, from the location (mx) where the terminal is locatedi,myi,mzi) The four base stations which are not in the same plane before being selected from near to far, and the distances measured by the TDOA technology from the terminal to the base stations are r1i,r2i,r3i,r4iHas r of1i≤r2i≤r3i≤r4i。
And calculating the position of the terminal containing the non-line-of-sight error by the measured distances from the four base stations to the mobile terminal, and estimating by adopting a least square method. The least-squares estimated position of the three-dimensional coordinates is
Using the AOA method, the base station coordinates (bx) are calculatedj,byj,bzj) To the three-dimensional terminal position estimated by the base stationDetermined three-dimensional direction angle
Position error and azimuth error generation are generated by 2 components, respectively by non-line-of-sight propagation errorsAnd measurement error 2 parts.
And (3) constructing a BP neural network, wherein input characteristic values of the network are the position of the terminal, the distance between a base station and the terminal and the three-dimensional AOA direction angle. The network is multilayer, the hidden layer structure is determined after optimization, and the output layer is the final predicted terminal point position.
And optimizing the BP neural network by adopting a PSO algorithm, and establishing a PSO _ BP neural network algorithm model.
And carrying out error analysis on the PSO _ BP neural network by using the collected sample data after partial processing, and determining a better network structure through the error analysis of the neural network.
And (3) firstly training the BP neural network by using a PSO algorithm and then carrying out secondary optimization by using a gradient descent method by using the data sample which is converted into the characteristic value after being completely processed, and finally determining the weight threshold parameter of the network. The network achieves accurate location (x) of the terminal point from the feature vector M to the samplei,yi,zi) The function mapping relation eliminates the error caused by non-line-of-sight distance of the environment, and obtains a more accurate terminal point position.
The invention initially estimates the position of the terminal according to the multiple base stations in the three-dimensional space, extracts the estimated position coordinates, the distance from the base stations to the terminal and the three-dimensional space azimuth angle from the base stations to the terminal as characteristic value input vectors, and the characteristic value vectors better reflect the relative relationship between the position of the terminal and the base stations and the terminal and can reflect non-line-of-sight factors and relevant factors influenced by measurement errors. Extracting a characteristic quantity data set from a sample point, training in a BP neural network, optimizing an error function according to a PSO algorithm, and iterating to the vicinity of a minimum value point of the error function by small step length by gradient descent when converging to a region. And performing error analysis on the error function, comprehensively determining the structure of the network through a learning curve, and performing operations such as whether to increase the data volume. And after the network structure is determined and the network is trained, obtaining a more accurate terminal position point under the condition of eliminating non-line-of-sight errors and measurement errors. The method has the advantages of high convergence speed and high accuracy, is suitable for various specific environments, and is suitable for popularization and use.
Drawings
FIG. 1 is a flow chart of a process for carrying out the method of the present invention;
FIG. 2 is a schematic diagram of four base stations determining the location of a terminal;
FIG. 3 is a schematic diagram of a three-dimensional AOA azimuth from a base station to a terminal point in the present invention; (ii) a
FIG. 4 is a topology diagram of a BP network in the present invention;
FIG. 5 is a schematic diagram of a process for optimizing BP neural network parameters by using a PSO algorithm in the present invention;
FIG. 6 is a flow chart of the algorithm process of the PSO _ BP neural network-based terminal three-dimensional positioning method in the invention.
Detailed Description
The three-dimensional terminal positioning method based on the PSO _ BP neural network of the present invention will be further described in detail below, and fig. 1 is a flowchart of an implementation process of the present invention, and the specific implementation steps are as follows:
s1. TongIn the process of calculating the distance between the base station and the terminal through radio signal propagation, the influence of non-line-of-sight exists, and the influence can cause deviation when the terminal is positioned by multiple base stations. There will be a plurality of base stations in an area, from the location (mx) where the terminal is locatedi,myi,mzi) The first four base stations are selected from near to far, and the coordinates of the four base stations are respectively named as (bx) in sequence1,by1,bz1),(bx2,by2,bz2),(bx3,by3,bz3),(bx4,by4,bz4). FIG. 2 is a schematic diagram of four base stations determining the location of a terminal, where a first ranging coverage area (A), a second ranging coverage area (B), a third ranging coverage area (C) and a fourth ranging coverage area (D) are spherical surfaces with the four base stations as the sphere centers, respectively, and the coverage areas of the four base stations intersect with a terminal M, and when the four base stations are not in the same plane, the distances measured by the TDOA technique from the terminal to the base stations are r1i,r2i,r3i,r4iHas r of1i≤r2i≤r3i≤r4i. The invention discusses the situation of four out-of-plane base stations, and the first 5 base stations are continuously selected in one plane at the current four base stations, and so on.
S2, calculating the position of the terminal containing the non-line-of-sight error by the measured distance from the four base stations to the mobile terminal, wherein the four balls may not intersect with one point due to the existence of the measurement error, and estimating by adopting a least square method to reduce the influence of the error. The least-squares estimated position of the three-dimensional coordinates is
In S2, when the distance measurement between the bs and the ue is error-free, it can be crossed to a point, and four equations are listed according to the distance formula between two points:
the coordinates of the i point (mx)i,myi,mzi) The matrix of (d) is represented as:
because of the measurement error, the four spheres can not intersect with one point, and in order to reduce the influence of the error, the data is processed by adopting a least square method. Least squares estimated position of three-dimensional coordinates ofThen
Solving by using a least square method to obtain:
wherein
Since the invention is concerned with 4 non-coplanar base stations, n is 4. The case of more than 4 base stations can be calculated according to this formula.
S3, calculating the coordinates (bx) of the base station by using the AOA methodj,byj,bzj) To the three-dimensional terminal position estimated by the base stationDetermined three-dimensional direction angleFIG. 3 is a schematic diagram of three-dimensional AOA azimuth angle from a base station to a terminal point, showing a base station MiTo terminal BiThe three-dimensional azimuth angle of (a),is an error-free three-dimensional orientation angle. The input eigenvalue vector of the PSO BP neural network is M.
Since the invention is based on 4 noncoplanar base stations as a special example, n is 4. The case of more than 4 base stations can be expressed in this general form.
S4, the position error and the azimuth error are generated by 2 parts, wherein the estimated position coordinate of the terminalAnd error-free position coordinates (x)i,yi,zi) The error between is a non-line-of-sight propagation errorAnd measurement errorThen there is
From base station position coordinates (bx)j,byj,bzj) Estimating a location to a terminalThree-dimensional direction angle ofAlso including errors due to non-line-of-sight factorsAnd measurement errorIs provided withWhereinIs an error-free three-dimensional orientation angle.
And S5, constructing a BP neural network, wherein the BP neural network consists of an input layer, a hidden layer and an output layer. The input eigenvalue vector is M. The input feature vector is 3n +4 dimensional. In the invention, n is 4. The output layer is 3-dimensional, and the output layer is the required accurate terminal position coordinates. The hidden layer is a plurality of layers, and the hidden layer structure is determined by error analysis of a neural network learning curve. Fig. 4 is a topology diagram of the BP network.
In S5, the hidden layer transfer function tansig function of the BP neural network is expressed as:the input value may be any value and the output value has a value range of [ -1,1 []. The output layer is composed of 3 neurons and adopts a linear transfer function fo(x) Kx. The output vector is [ x ]i,yi,zi]TThis vector element is the coordinate accurate value after the error is eliminated. Let the actual position corresponding to the sample point i be
The error function isW and B are the weight and threshold parameters of the network. And | | is a norm symbol, and m is the number of input samples.
S6, constructing a BP neural network according to S5, searching a global minimum solution of an error function in a defined domain of a given characteristic value by adopting the PSO algorithm, and after the PSO algorithm converges to a small region and terminates iteration, searching the minimum solution by adopting a gradient descending mode locally and secondarily with a small step length. FIG. 5 is a schematic diagram of a process for optimizing BP neural network parameters by a PSO algorithm.
In S6, the PSO algorithm is described mathematically as:
within the D-dimensional search space, a population contains N particles, counted as X ═ X1,...,xN]TThe rate of change of position of the particle i is denoted vi=[vi1,vi2,...,viD]TThe position of which is denoted as xi=[xi1,xi2,...,xiD]TWherein i is 1, 2.. times.n; the optimal position found by particle i itself up to the current iteration is denoted pi=[pi1,pi2,...,piD]TThe optimal position found by all particles up to now is denoted pg=[pg1,pg2,...,pgD]TAfter finding these two values, the particle is updated by the following equation:
vid(t+1)=ω(t)vid(t)+c1r1(pid-xid(t))+c2r2(pgd-xid(t))
xid(t+1)=xid(t)+vid(t+1)
wherein, i is 1,2, and N, D is 1, 2; c. C1,c2Is a learning factor, is a non-negative constant, generally set to 2; r is1,r2Is at [0,1 ]]A random number within; ω (t) is the inertial weight; t is the number of iterations; t ismaxIs the maximum iteration number; v. ofid(t),xid(t) is the current velocity and position of particle i, respectively; p is a radical ofidIs the individual optimal position found by particle i;
as shown in fig. 6, it is a flowchart of the algorithm process of the terminal three-dimensional positioning method based on the PSO _ BP neural network, and the PSO _ BP algorithm specifically includes the following steps:
(1) and initializing parameters. These parameters include the size of the population, the number of iterations, the learning factor, the speed, the location.
(2) And establishing the BP neural network according to the input function, the hidden layer function, the output function and the excitation function. Randomly generating a particle group Xi=[xi1,xi2...,xiN]TAnd i is 1, 2.. times.n, elements contained in each particle are all weight values W and threshold values B on the BP neural network, and the elements in W and B are correspondingly and regularly placed in a one-dimensional vector X according to a certain front-back sequence.
In the formula, i is the number of particles, and n is the number of particle groups.
(3) And calculating the fitness value of the evaluation function of each particle through the BP network. Initializing parameters of the BP neural network, and respectively bringing the weight and the threshold contained in each particle of the particle swarm determined in the step (2) into the BP neural network. Inputting the characteristic value matrix into the BP network of each particle to obtain a training output vector Pi outputThe fitness value of the particle at this time is the error function E (W, B) of the network:
in the formula, Pi outputOutputting a vector for the network; pi realA desired output vector; and | | is a norm symbol, and m is the number of input samples.
(4) Calculating XiAnd (i ═ 1, 2.. once, n), comparing the fitness value of the current particle with the previous best fitness value, and replacing the smaller value of the two with the local extreme value of the current particle. And then selecting the current global extremum with the smallest fitness value of all the particles.
(5) Updating the speed and position of each particle in each iteration process according to the position and speed iteration formula described in the PSO algorithm mathematical model;
velocity update formula: v. ofid(t+1)=ω(t)vid(t)+c1r1(pid-xid(t))+c2r2(pgd-xid(t))
Location update formula: x is the number ofid(t+1)=xid(t)+vid(t+1)
(6) And (4) calculating the fitness value of the new particle, and updating the individual extreme value and the group extreme value of the particle according to the fitness value of each particle of the particle swarm at the moment according to the step (4).
(7) And (4) exiting the PSO algorithm after the maximum iteration number is met or the set error standard is met, and otherwise, returning to the step (2).
(8) The weight and the threshold contained in the optimal particles obtained by the particle swarm optimization are given to the BP network for secondary optimization, the process of descending according to a gradient rule is used for searching the optimal solution during the secondary optimization, the weight and the threshold trained by the PSO algorithm are close to global optimal, because the PSO algorithm is possibly long in flight step length and cannot completely reach the optimal state when the PSO algorithm is stopped, a small-learning-efficiency BP network is arranged at the last position for further small-range small-step-length search. And if the searched result is better than the result before searching, outputting the result, and otherwise, keeping the original result unchanged.
And S7, carrying out error analysis on the PSO _ BP neural network by using the collected sample data after partial processing, and determining a better network hidden layer structure through the error analysis of the neural network.
The hidden layer structure of the neural network in S7 is related to the scene, and the more complex the scene, the more complex the network structure should be. Whether the network is under-fit or over-fit can be seen through the variance and deviation curve in the learning curve of the neural network. And taking different measures to adjust the strategy for different situations. These common measures include but are not limited to: (1) extracting a new characteristic quantity; (2) the data volume of the training sample; (3) the size of the penalty term factor; (4) increase and decrease of the number of network layers or the number of neurons.
When a neural network algorithm is established, a simple network is constructed firstly, the simple network is trained, a learning curve is drawn, and what the deviation and variance curve are in the learning curve of the simple network is judged. And determining which measure or measures are adopted to cooperate with the improved neural network according to the learning curve so that the neural network has proper fitting performance, thereby improving the generalization performance of the network.
And S8, training a PSO _ BP neural network to determine weight threshold parameters of the network by using the data samples which are converted into the characteristic values after all processing. Thus, the network learns error information caused by non-line-of-sight factors and measurement errors in a specific environment, and finally realizes the slave feature vector.
The invention provides a PSO _ BP neural network-based terminal three-dimensional accurate positioning method, which is suitable for various specific environments, particularly environments with more irregular obstacles, obvious scattering and multipath phenomena, such as large-scale shopping malls, underground tunnels, mountain areas and the like, and is a practical positioning technology. The method calculates the accurate position of the terminal according to the coordinate information of the actually measured terminal position in the three-dimensional space. And extracting a terminal point coordinate, a distance from the base station to the terminal and a three-dimensional azimuth angle from the base station to the terminal from the actually measured terminal position as characteristic values, and calculating by a PSO _ BP neural network algorithm to obtain the accurate position of the target. The three-dimensional terminal positioning method provided by the invention can effectively learn the non-line-of-sight error influence brought by the environment and the error influence brought by measurement through the neural network, and has the advantages of high feasibility, adaptation to specific environment and high precision. Can be popularized and used.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. A terminal three-dimensional positioning method based on a PSO _ BP (Particle Swarm Optimizer _ Error Back Propagation Particle Swarm optimization _ Error Back Propagation) neural network is characterized in that:
s1, in the process of calculating the distance from a base station to a terminal through radio signal propagation, the influence of non-line-of-sight exists, and the influence can cause deviation when the multi-base-station positioning terminal is in error; there will be a plurality of base stations in an area, from the location (mx) where the terminal is locatedi,myi,mzi) The first four base stations are selected from near to far, and the coordinates of the four base stations are respectively named as (bx) in sequence1,by1,bz1),(bx2,by2,bz2),(bx3,by3,bz3),(bx4,by4,bz4) When the four base stations are not in the same plane, the distances measured by the TDOA (Time Difference of array Time Difference) technique from the terminal to the base stations are r1i,r2i,r3i,r4iHas r of1i≤r2i≤r3i≤r4i(ii) a The invention discusses the situation of four base stations which are not in a plane, and when the current four base station points are in one plane, the adjacent fifth base station is selected in sequence; similarly, when the first five selected base stations are in one plane, sequentially selecting the adjacent sixth base station until all the selected base stations are not in the same plane;
s2. moving from four base stationsThe measured distance of the terminal is calculated to the position of the terminal containing non-line-of-sight error, because of the measurement error, four spheres may not intersect with one point, in order to reduce the influence of the error, least square method estimation is adopted, and the least square estimation position of the three-dimensional coordinate is
S3, calculating coordinates (bx) of a base station by utilizing an AOA (Activity On Arrow arrival angle intersection positioning) methodj,byj,bzj) To the three-dimensional terminal position estimated by the base stationDetermined three-dimensional direction angleThe input eigenvalue vector of the PSO _ BP neural network is M, and since the present invention is studied based on 4 non-coplanar base stations as a special example, n is 4; the case of more than 4 base stations can be expressed in this general form, where
S4, the position error and the azimuth error are generated by 2 parts, wherein the estimated position coordinate of the terminalAnd error-free position coordinates (x)i,yi,zi) The error between is a non-line-of-sight propagation errorAnd measurement errorThen there is
From base station position coordinates (bx)j,byj,bzj) Estimating a location to a terminalThree-dimensional direction angle ofAlso including errors due to non-line-of-sight factorsAnd measurement errorIs provided withWhereinIs an error-free three-dimensional orientation angle;
s5, constructing a BP neural network, wherein the BP neural network consists of an input layer, a hidden layer and an output layer; the input characteristic value vector is M, the input characteristic vector is 3n +4 dimensions, n is 4 in the invention, the output layer is 3 dimensions, the output layer is the accurate terminal position coordinate, the hidden layer is multilayer, the hidden layer structure is determined by the error analysis of the neural network learning curve;
s6, constructing a BP neural network according to S5, searching a global minimum solution of an error function in a defined domain of a given characteristic value by adopting the PSO algorithm, and after the PSO algorithm converges to a small region and terminates iteration, searching the minimum solution by adopting a gradient descent mode locally and secondarily with a small step length;
s7, carrying out error analysis on the PSO _ BP neural network by using the collected sample data after partial processing, and determining a better network structure through the error analysis of the neural network;
s8, training a PSO _ BP neural network to determine weight threshold parameters of the network by using data samples which are converted into characteristic values after being processed completely, so that the network learns error information caused by non-line-of-sight factors and measurement errors in a specific environment, and finally realizing accurate position (x) from the characteristic vector M to the samplei,yi,zi) The function mapping relation eliminates errors and obtains a more accurate position.
2. The PSO _ BP neural network-based terminal three-dimensional positioning method according to claim 1, characterized in that: the method as claimed in step S1 of claim 1, wherein when there are multiple base stations located at the same time, the nearest four base stations are adaptively selected to locate the terminal, and the distances between the four base stations and the terminal measured by TDOA technique are sorted from small to large; since the closer the distance, the smaller the error due to non-line-of-sight effects, and thus the smaller the estimation error used as a position.
3. The PSO _ BP neural network-based terminal three-dimensional positioning method according to claim 1, characterized in that: the method of claim 1, step S3, utilizing the three-dimensional terminal position coordinates estimated in step S2Calculate the three-dimensional direction angleThe input characteristic vector M of the neural network is formed by the position coordinates, the three-dimensional direction angles and the distance data between the base station and the terminal estimated by the least square method, the combination of the characteristic vectors is complete, and the position can be accurately predicted, so that the information of the position of the terminal after the influence of non-line of sight can be comprehensively reflected.
4. The PSO _ BP neural network-based terminal three-dimensional positioning method according to claim 1, characterized in that: the step S5 of claim 1, wherein the error function of the BP neural network constructed in S4 is optimized by PSO algorithm; the BP neural network uses a gradient descent method to carry out local optimization on an error function in the back propagation learning process, the selection of an initial feasible solution is greatly depended on, and the PSO algorithm can carry out global optimization in the definition domain of the characteristic value.
5. The PSO _ BP neural network-based terminal three-dimensional positioning method according to claim 1, characterized in that: the PSO _ BP algorithm in step S6 of claim 1 specifically comprises:
s6-1, using a PSO algorithm to carry out global optimization on the error function of the BP neural network in the S5, wherein the PSO algorithm has good global optimization performance;
s6-2, the gradient descent algorithm has good local optimization performance; the PSO algorithm iterates in a global range by a larger particle flight step length, when the iteration reaches a termination condition, local optimization is further performed by a gradient descent algorithm with a smaller learning factor to reach an accurate value which enables an error function to be minimum, and therefore better weight and threshold network parameters are obtained.
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