CN115278870A

CN115278870A - Improved genetic ant colony hybrid positioning method and device based on TDOA selection

Info

Publication number: CN115278870A
Application number: CN202210860345.9A
Authority: CN
Inventors: 刘洋; 韩宇飞; 雷雪梅; 刘中艳; 陈泽
Original assignee: Inner Mongolia University
Current assignee: Inner Mongolia University
Priority date: 2022-07-21
Filing date: 2022-07-21
Publication date: 2022-11-01

Abstract

The invention relates to an improved genetic ant colony hybrid positioning method and device based on selection of TDOA (time difference of arrival), belongs to the technical field of wireless positioning, and can improve the solving efficiency and convergence in a solving space and solve the problem of poor positioning accuracy of the traditional TDOA algorithm under a non-line-of-sight condition; the method comprises the following steps: s1, finding a base station combination with a minimum residual error subset as a reference point required by positioning; s2, substituting the TDOA value of the reference point into a Chan algorithm for solving to obtain a rough coordinate estimation result; s3, taking the rough coordinate estimation result as a node coordinate of the genetic ant colony algorithm to carry out global search, and taking the node containing the most pheromones as an optimal solution; and S4, substituting the optimal solution as an initial value into a Taylor algorithm to carry out iterative solution to obtain a final target positioning result.

Description

Improved genetic ant colony hybrid positioning method and device based on TDOA selection

Technical Field

The invention relates to the technical field of wireless positioning, in particular to an improved genetic ant colony hybrid positioning method and device based on selection of TDOA.

Background

In recent years, the construction speed of the 5G network is very high, with the coming of the 5G era, the 5G as a physical network can provide various capabilities and services, the 5G positioning and communication are integrated, and the advantage of one-network-multiple-use is reflected to the greatest extent. The 5G wireless network differs from the conventional macro cellular network mainly in that it can provide effective gain for the basic data required for mobile positioning. In a 5G network, small cell and D2D transmissions will dominate, such an arrangement shortens the distance between the base station and the mobile device, shorter distances will increase line of sight (LOS) probability, and the increase in wireless network bandwidth will make the positioning more accurate. The 5G positioning is mainly used in a downlink positioning (O-TDOA) method, in which the Reference Signal Time Difference (RSTD) based on a dedicated Positioning Reference Signal (PRS) transmitted by two base stations is observed (i.e., measured) at a user, thereby defining a hyperbola where the user is located. Then, the time difference of arrival RSTD generated by the downlink positioning reference signals PRS sent by a plurality of different base stations can be analyzed and calculated, and finally the actual position coordinate is obtained.

In practical application, propagation environments can be divided into line-of-sight propagation and non-line-of-sight propagation, and NLOS propagation directly affects measurement accuracy of TDOA observed quantity, so that accuracy and stability of a positioning algorithm are reduced essentially, and the problem is urgently needed to be solved. Currently, the solution to the problem of NLOS error in positioning algorithms mainly focuses on the following three schemes, the first, identifying LOS and NLOS paths. The method needs to firstly identify and judge an LOS path and an NLOS path through an identification algorithm, abandons the NLOS path, and only selects the LOS path for positioning analysis, but the method has great limitation, and effective positioning can not be carried out when the LOS path is extremely weak or only the NLOS path is available. Second, NLOS error modeling. Modeling the NLOS error first and then reducing the NLOS error in the observed quantity using a predictive model, but this method has great difficulty in practical application and uncertainty because the propagation model of the signal is very complex in the actual positioning environment. Thirdly, optimizing a positioning resolving process by utilizing an optimization theory. For the third kind, in the prior art, improvement is made on the basis of a two-step Weighted Least Square (WLS) algorithm so as to improve the positioning accuracy, two-step positioning is performed on the basis of a factor graph algorithm, adaptive TOA estimation positioning is performed on the basis of prior knowledge of LOS/NLOS, NLOS is classified by a machine learning method so as to improve the positioning accuracy, or a Convolutional Neural Network (CNN) is used for identifying an impulse response diagram of a channel, so that the purpose of identifying the LOS/NLOS channel with high accuracy is achieved. The positioning method can improve the positioning accuracy to a certain extent or at a certain aspect and a certain stage, but still cannot meet the requirement on high positioning accuracy in the NLOS environment.

Accordingly, there is a need to develop a new improved TDOA-based genetic ant colony hybrid location approach to address the deficiencies of the prior art to address or mitigate one or more of the above-mentioned problems.

Disclosure of Invention

In view of this, the present invention provides an improved genetic ant colony hybrid positioning method and apparatus based on TDOA selection, which can improve the solution efficiency and convergence in the solution space, and improve the problem of poor positioning accuracy of the conventional TDOA algorithm in non-line-of-sight.

In one aspect, the present invention provides a method for improved genetic ant colony hybrid localization based on selection of TDOA, the steps of the method comprising:

s1, finding a base station combination with a minimum residual error subset as a reference point required by positioning;

s2, substituting the TDOA value of the reference point into a Chan algorithm for solving to obtain a rough coordinate estimation result;

s3, taking the rough coordinate estimation result as a node coordinate of the genetic ant colony algorithm to carry out global search, and taking the node containing the most pheromones as an optimal solution;

and S4, substituting the optimal solution as an initial value into a Taylor algorithm to carry out iterative solution, and obtaining a final target positioning result.

The above-described aspect and any possible implementation manner further provide an implementation manner, and the content of step S1 includes:

s11, selecting all base station combinations with the number of M from the total set of base stations; m is a positive integer not less than 4;

s12, calculating residual errors of all base station combinations, screening by using a minimum residual error method, and taking the base station combination with the minimum residual error subset as a reference point required by positioning;

the residual is defined as the difference between the range-difference observed value and the predicted value calculated using the intermediate position.

In the foregoing aspect and any possible implementation manner, there is further provided an implementation manner, where the content of the global search for the node coordinates by the genetic ant colony algorithm in step S3 includes:

s31, processing the node coordinates mainly by using a genetic algorithm, quickly generating initial pheromones, and randomly distributing the initial pheromones in a solution space while ensuring global convergence;

s32, searching by adopting an improved ant colony algorithm: and according to the pheromone, the optimal solution is searched from multiple points, so that the efficiency of solving the optimal solution in the whole situation is improved by utilizing the advantage of positive feedback.

As for the above-mentioned aspect and any possible implementation manner, there is further provided an implementation manner, and the specific content of step S31 includes:

coding the coded object by adopting a real number coding mode so as to process complex variable constraint conditions;

randomly generating an original population in a target search space by adopting a failure sequence, setting the number of individuals of the original population, and determining the value range of each individual in the population;

determining a fitness function;

determining a genetic operator;

preserving part of excellent individuals in the existing solution by adopting an elite preservation strategy, so that the excellent individuals directly become members of the next generation of population;

repeating the calculation process of the genetic algorithm until a preset termination condition is met, and then taking the currently selected optimal individual as an output result;

and generating pheromones according to the output result.

The above-described aspects and any possible implementations further provide an implementation in which the pheromone includes: coordinate data of the optimal individual and randomly generated data.

As for the above-mentioned aspect and any possible implementation, there is further provided an implementation that the fitness function is:

wherein the content of the first and second substances,

R_iindicating the distance from the real coordinates of the moving object to the ith base station,

distance, n, from the estimated coordinate position of the moving object to the ith base station_iRepresenting the noise error subject to a gaussian distribution, M being the number of base stations.

The above-described aspect and any possible implementation further provide an implementation, and when determining the genetic operator, the cross probability value is 0.9, and the mutation probability value is 0.05.

As to the above-mentioned aspect and any possible implementation manner, there is further provided an implementation manner, and the specific content of step S32 includes:

searching according to a search rule, and migrating according to the migration probability;

the expression of the migration probability P for an ant k moving from position i to position j at time t is:

where α is the pheromone elicitor, β is the desired elicitor, t is the time, η_ijRepresenting the visibility of the path (i, j), τ_ij(t) indicates the amount of pheromones present on the path (i, j) at time t; allowed is a set of coordinate points to be accessed by the ant k, s is a coordinate point in allowed, and eta is_isExpressing the degree of inspiration from the i coordinate to the s coordinate;

and (3) updating pheromones: the path pheromone strengths and pheromone increments are updated.

As to the above-mentioned aspect and any possible implementation manner, there is further provided an implementation manner that the pheromone increment left by the kth ant in each traversal of the path (i, j) is:

in the formula, L_kRepresenting the path length of the pheromone left by the ant k, and Q is the total pheromone amount traversed by the ant colony once;

the intensity of the pheromone existing on the path (i, j) at time t +1 is:

τ_i,j(t+1)＝(1-ρ)τ_i,j(t)+Δτ_i,j(t,t+1)，

in the formula, τ_ij(t) represents the amount of pheromones present on the path (i, j) at time t, (1- ρ) represents the pheromone residual coefficient, Δ τ_ij(t, t + 1) represents the pheromone increment of the ant colony population traversed once in time (t, t + 1);

denotes pheromone increment for ant number k at time (t, t + 1).

In another aspect, the present invention provides an improved genetic ant colony hybrid localization apparatus based on TDOA selection, comprising a memory, a processor, and a computer program stored in the memory and operable on the processor, wherein: the processor, when executing the computer program, performs the steps of any of the methods described above.

Compared with the prior art, one of the technical schemes has the following advantages or beneficial effects: the algorithm improves the solving efficiency and convergence in the solving space, and solves the problem that the traditional TDOA algorithm is poor in positioning accuracy under non-line-of-sight;

another technical scheme among the above-mentioned technical scheme has following advantage or beneficial effect: simulation experiment results show that the positioning algorithm has better positioning accuracy and stability compared with other algorithms, and is closest to the lower boundary of Cramer-Rao.

Of course, it is not necessary for any product to achieve all of the above-described technical effects simultaneously in the practice of the invention.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

FIG. 1 is a flowchart of a method for improved TDOA-based hybrid location of genetic ant colonies provided by an embodiment of the present invention;

FIG. 2 is a schematic diagram of a TDOA location provided by one embodiment of the present invention;

FIG. 3 is a flow chart of an improved genetic ant colony algorithm provided by one embodiment of the present invention;

FIG. 4 is a flow chart of a minimum residual weighting Chan-Taylor joint algorithm according to an embodiment of the present invention;

FIG. 5 is a graph comparing the convergence performance of the GA-ACO hybrid algorithm provided by one embodiment of the present invention;

FIG. 6 is a graph comparing the performance of the RWC-GAA-T algorithm for different numbers of base stations according to an embodiment of the present invention;

FIG. 7 is a CDF versus RMSE curve for the RWC-GAA-T algorithm at different numbers of base stations, according to an embodiment of the present invention;

FIG. 8 illustrates positioning root mean square error under different base stations according to an embodiment of the present invention;

fig. 9 is a comparison of RMSE performance of each algorithm under different base stations, where (a) BS =4, (b) BS =5, (c) BS =6, and (d) BS =7;

fig. 10 is a graph of CDF versus RMSE for various algorithms at different base stations, where (a) BS =4, (b) BS =5, (c) BS =6, and (d) BS =7, according to an embodiment of the present invention;

FIG. 11 is a plot of root mean square error for different base station radii as provided by an embodiment of the present invention;

fig. 12 is a graph of the percentage improvement in performance of the RWC-GAA-T algorithm for 7 base stations according to an embodiment of the present invention.

Detailed Description

In order to better understand the technical scheme of the invention, the following detailed description of the embodiments of the invention is made with reference to the accompanying drawings.

It should be understood that the described embodiments are only some embodiments of the invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.

Aiming at the problem that the traditional TDOA (time difference of arrival) positioning algorithm cannot achieve a good positioning effect under a non line of sight (NLOS) propagation condition, the invention provides an improved genetic ant colony hybrid positioning algorithm based on TDOA selection. Firstly, a screening combination mode of a Chan algorithm for a base station in position estimation is improved by using a minimum residual error principle, different weights are given in a weighting process to increase grouping discrimination, then estimated coordinates obtained by the improved Chan algorithm are used as node positions of the ant colony algorithm, a generation process of initial pheromones of the ant colony algorithm is optimized by using a genetic algorithm, finally estimated coordinates solved by the improved algorithm are used as initial values of a Taylor algorithm, and a final positioning result is solved through iteration. Fig. 1 is a flow chart of the positioning method of the present invention.

1. Positioning model of the invention

1.1TDOA measurement model

The TDOA-based location model may also be referred to as a hyperbolic location model from the perspective of the geometric model. In practical situations, because the calculation difficulty of the transmission time of signals in the air is large, and accurate synchronization of two end times cannot be achieved, the TDOA location uses the time difference between the mobile target position and two base stations as an observed quantity, converts the time difference into a distance difference by using the radio propagation speed, and then establishes a geometric relation equation, wherein the coordinate of the mobile target position is the intersection point coordinate of the two hyperbolic curves. The TDOA location principle is shown in fig. 2.

TDOA positioning requires at least three base stations to participate in positioning, assuming BS₁，BS₂，BS₃For reference base station, the position coordinates are respectively (x)₁,y₁),(x₂,y₂),(x₃,y₃) The location coordinate of the moving object is (x, y), the TDOA location is to select the serving base station as the reference, and assume that the serving base station is base station 1.r is a radical of hydrogen_iDenotes the distance, r, between the base station i and the target location_i,1Indicating the difference between the distance from the base station 1 to the target position and the distance subtracted from the distance from the ith base station to the target position.

The relation equation of the base station and the target position is as follows:

a system of equations for the relationship between (x, y) and the distance difference can be established according to equation (1):

wherein r is_i1＝r_i-r₁＝ct_i1＝c(t_i-t₁) I = 2.. N, c is the signal propagation speed, t_iTOA time, t, for a signal from a target location to arrive at the ith slave base station₁Is the TOA time at which the signal from the target location arrives at the primary base station. The equation set (2) is simplified to obtain:

in formula (3)

The position coordinates of the moving object can be finally solved by equation (3).

1.2 Wireless location error Source analysis

The signal-related data (such as TDOA, TOA, AOA, etc.) measured under the condition of non-line-of-sight cannot correctly reflect the geometric relationship between the target to be measured and the base station. In the actual measurement of the TDOA technology, the measured time value is much higher than the actual value due to the influence of non-line-of-sight, and a large position difference is reflected on the distance position.

If N base stations participate in the positioning of the moving target, r is used_iIndicating the measured distance between the moving object and the ith base station,

representing the actual distance between the moving target and the ith base station, the distance model of the moving target can be expressed as:

where c is the signal propagation velocity, t_iPropagation time, n, of signal from moving object to ith base station_iIs the systematic measurement error, omega, of zero mean-compliant Gaussian distribution under line-of-sight propagation conditions_iRepresenting non-line-of-sight propagation errors, omega, when only line-of-sight is propagating_i Is 0.

2. Improved positioning algorithm

2.1 minimum residual weighting Algorithm

The TDOA positioning algorithm in the three-dimensional space needs at least 4 base stations for positioning, all base station combinations with the number equal to 4 are selected from the total number of the base stations, then the position estimation of each combination is respectively solved, and the LOS propagation path is judged. The traditional residual weighting algorithm uses an exhaustive method, but when the number of base stations is large, the calculation complexity is greatly increased by the method. In order to effectively reduce the computational complexity, the invention replaces the traditional exhaustive method by selecting the base station combination with the minimum residual error subset to reduce the computational complexity. The specific algorithm steps are as follows.

(1) Assuming that M base stations are located and the number of TDOA measurements is M, then M = M-1, and first a combination of TDOA measurements is screened for which the number of base stations is 4:

where N represents the number of combinations with the minimum number of base stations required and the index set for TDOA measurements is defined as S_k|k＝1,2,...,M}。

(2) Coordinate vector of target object

Is calculated using a least squares method, the residual of each group is represented as the difference between the distance-difference observed value and the predicted value calculated using the intermediate position, each combination from a subset of the N base station combinations is filtered using a minimum residual method, and the calculation is performed for each combination

Find out to have the minimum

And will index set S_kIs updated to S_minSetting a minimum combination selected from the N combinations of base stations

Is defined as follows:

r for measuring distance between base station and moving object_iIndicating that the base station is marked X_i，S₁Indicating that M base stations complete the entire set of packets,

representing the position of a target estimated jointly by M base stationsAnd (4) coordinates. The residual error is normalized, the influence of the number of the positioning base stations on the weight value can be effectively eliminated, and the normalized residual error can be defined as follows:

(3) Set of complement S_minA total of P elements, each element in Q is put into the complementary set S_minIn (3), a new index set S is formed_kI =1,2,. So, N-P }, at which point a new S_kThe number of the elements in (1) is P +1. For N-P new combinations, recalculating

Find out with the minimum

Combinations of (a) and (b).

For example, P +1 base stations are selected from the total station, and the minimum of N-P base station combinations is set

Is defined as follows:

(4) Then compare

And

if it is used

Shows that the LOS propagation path of the base station combination is superiorIn the last combination, the position estimate is added to the final position estimate set, and S is updated_minAnd repeating the above steps until

When the combination of different base stations is not changed along with the selection, the propagation path of the currently selected base station is LOS propagation, and when the size of the index set is M, the operation is ended and the next step is carried out.

(5) And weighting all the position estimation values obtained by calculation in the previous step according to the residual error to obtain a final position estimation result.

Where V is the number of location estimates obtained.

Considering that the weighting process of the traditional residual weighting algorithm is that the size of the residual value is inversely proportional to the error size of the NLOS under no special condition. When the number of LOS base stations is significantly greater than that of NLOS base station combinations, a larger residual error is generated, and a higher weight can be given to the LOS base station combinations. However, when the number of NLOS base stations is significantly greater than the number of LOS base station combinations, the effect of directly taking the inverse of the residual value as the weight in the conventional residual weighting algorithm and the whole process is not ideal, and the residual value may be significantly smaller than the NLOS error. In this case, the invention takes the high power of the residual as the weight function in the above calculation process, and takes n =2, which has the advantage that the change of the function value can be more obvious, as shown in formula (12)

The principle of the minimum residual error weighting algorithm is mainly to solve the minimum from the positioning base station combination

Combining and complementing information of redundant base stationsGradually adding the LOS base station data into a new index set, gradually reducing the index set by using a minimum residual error criterion, continuously repeating iteration according to the minimum residual error criterion until an optimal estimated value appears, and finally weighting the position estimated value according with the minimum residual error criterion, so that the utilization rate of the LOS base station data is improved, and the calculation complexity of the traditional residual error weighting algorithm is also reduced.

2.2 improved genetic Ant colony hybrid Algorithm

The ant colony algorithm has the problem of slow resolving speed due to the shortage of pheromones in the initial resolving stage, and the genetic algorithm has the problem of low precision resolving efficiency due to the incapability of effectively utilizing feedback information. In order to solve the problems of the two algorithms, the genetic algorithm and the improved ant colony algorithm are combined, and the rapidity and the accuracy of the two heuristic algorithms are fully utilized to make up for the defects of the two algorithms. The basic idea of the hybrid algorithm is divided into two parts, the genetic algorithm is mainly used in the early stage of the algorithm, initial pheromones are quickly generated by fully utilizing the genetic algorithm as an improved ant colony algorithm, and the initial pheromones are randomly distributed in a solution space while global convergence is ensured; and the improved ant colony algorithm is adopted for searching in the later stage of the fusion algorithm, the improved ant colony algorithm searches for the optimal solution from multiple points through strong parallel capability according to the initial pheromone generated in the earlier stage, and the efficiency of solving the optimal solution in the whole situation is improved by utilizing the advantage of positive feedback. The specific design steps are as follows:

(1) The invention adopts a real number coding mode to code the coded object, is convenient to process complex variable constraint conditions, and can ensure that the optimal result is obtained under the condition of maximum population quantity without frequently operating the coding.

(2) The method adopts the Faure sequence to randomly generate an original population in a target search space, sets the number of original population individuals of the genetic algorithm to be 50, and sets a proper value range for each individual in the population, wherein the operation efficiency of the genetic algorithm has a direct relation with the value range, the proper value can improve the solving efficiency of the algorithm, and the individual in the population represents the initial guess position of the moving target.

(3) A suitable fitness function is selected.

Suppose (x)_i,y_i,z_i) To represent the true coordinate position of the moving object, the estimated coordinate position is noted

The distance from the real coordinate of the moving target to the ith base station is recorded as R_iThe distance from the estimated coordinate position of the moving object to the ith base station is recorded as

Noise error n_iObeying the gaussian distribution, the distance difference Δ R between the obtained real coordinate and the estimated coordinate is:

the fitness function of the present invention can be expressed as:

(4) And (4) selecting a genetic operator.

The operation method of the selection operator is determined as a roulette selection method, and the excellent individuals of the next generation are selected according to the proportion of the fitness value of the individuals in the population to the population fitness value. The selected probability for good individuals is:

the cross probability value set by the invention is P_cAnd =0.9, selecting a two-point crossing method by the operation mode of a crossing operator, randomly exchanging specific gene segments in two excellent individuals according to a preset crossing probability, and recombining to obtain the excellent individuals with new properties.

The variation probability value set by the invention is P_m=0.05, mutation operatorThe operation mode of the method selects a uniform mutation method, gene mutation points in a designated population are randomly replaced according to the mutation probability, and the operation of a mutation operator is the key for maintaining the population diversity in the genetic algorithm, so that the local search capability of the algorithm is favorably improved, and the local optimal solution in the mixed algorithm is avoided.

(5) And an elite retention strategy is adopted, part of excellent individuals in the existing solution are retained, and the excellent individuals do not need to continuously participate in the genetic process and directly become members of the next generation of population, so that the global effect of the genetic algorithm can be effectively improved.

(6) The calculation process is repeated until the system determines that the termination condition is reached, and the optimal individual now selected is output as a result.

(7) And generating pheromone, wherein the pheromone is composed of two parts, the first part is the pheromone which is obtained by using the optimal solution coordinate obtained by genetic algorithm, and the second part is a part of the pheromone which is randomly generated. Initial time pheromone generation rule:

τ′_s＝τ′_c+τ′_G (16)

wherein: τ'_cIs a pheromone constant randomly generated on the ant colony algorithm path; τ'_GIs a pheromone generated by a genetic algorithm.

(8) In the path selection, the ant colony judges the intensity of the pheromone left on each branch at each node, and selects a path with a large pheromone amount, because the more ants select the path, the more pheromone amount of the path, and the positive feedback mechanism is also the reason for high solving efficiency of the ant colony algorithm.

The moving direction of the ant at the time t (t is not equal to 0) is determined by the accumulation amount of pheromones on each path, the accumulation amount of the pheromones is related to the length of the path, and the transition probability of the ant k from the position i to the position j

The mathematical model of (a) is as follows:

alpha is a pheromone heuristic factor, beta is a desired heuristic factor, rho is the volatility of the pheromone, the pheromone residual coefficient is expressed by (1-rho) and rho is satisfied (0 ≦ rho)<1) M is the number of individuals in the ant colony, Q is the total pheromone amount traversed by the ant colony, eta_ijRepresenting path (i, j) visibility, typically taken as eta_ij＝1/d_ijτ is the amount of pheromones existing on the path (i, j) at time t_ij(t) indicates that the probability that the ant k moves from i to j at time t is

allowed is a set of coordinate points to be accessed by the ant k, s is a coordinate point in allowed, and eta is_isRepresenting the degree of inspiration, τ, from the i-coordinate to the s-coordinate_ij(t) represents the amount of pheromones existing on the route (i, j) at time t.

(9) And (3) updating the pheromone, and assuming that the ant colony has completed one traversal at the time t, updating the pheromone according to the formula (18) to the formula (19) at the time t +1.

τ_i,j(t+1)＝(1-ρ)τ_i,j(t)+Δτ_i,j(t,t+1) (18)

L in the formula_kRepresents the path length of the pheromone left by ant k, delta tau_ijRepresenting the pheromone increment for each traversal on the path (i, j),

represents the pheromone increment left by the kth ant for each traversal on the path (i, j),

denotes pheromone increment, Δ τ, of ant number k at time (t, t + 1)_ij(t, t + 1) represents the pheromone increment for which the ant colony population has traversed once in time (t, t + 1).

The process of improving the genetic ant colony mixing algorithm is shown in fig. 3.

2.3Chan-Taylor joint algorithm

The node coordinates on the path containing the most pheromones, which are obtained after the genetic ant colony hybrid algorithm is subjected to global search, namely the optimal position solution roughly estimated by the Chan algorithm, is not related to the use of the optimal path, and only the optimal position solution is output as the initial value of the Taylor algorithm, and the idea is as follows.

Firstly, using coordinate values of an estimated target obtained by an improved Chan algorithm as node coordinates required in the ant colony algorithm, and generating initial pheromones required by part of the ant colony algorithm by a genetic algorithm through selection, intersection and variation operations; then, carrying out global search by using an ant colony algorithm, and selecting node coordinates on the path containing the most pheromones, namely an initial optimal position solution; and finally, substituting the screened optimal position solution into the Taylor algorithm to be used as an initial value of the Taylor algorithm for iterative solution.

Assume that the coordinates of the base station in three-dimensional space are (x)_i,y_i,z_i) The total number of the base stations is N (N is more than or equal to 4), the position coordinates of the moving target are represented by (x, y, z), and r is_iRepresenting the measured distance between the moving object and the base station, the first base station is usually selected as the master serving base station among a plurality of base stations, the remaining base stations are set as slave base stations, r_i1Is the difference in measured distance from the moving target to the serving base station to the base station. From equation (1), the following can be derived:

x of the above formula_i1,y_i1,z_i1May be respectively represented as x_i1＝x_i-x₁，y_i1＝y_i-y₁，z_i1＝z_i-z₁Simplifying to obtain:

in formula (22):

now assume x, y, z, r₁Are all wirelessly related, let z = [ x y z r₁]^TThe measurement error vector is expressed by psi, and the matrix form of equation (22) is:

h＝Gz⁰+Ψ (24)

wherein z corresponds to a true position z⁰,

If the measurement error Ψ follows a Gaussian distribution, a weighted least squares solution (24) can be applied:

Σ in formula (26)^-1Is a weight matrix.

∑＝E(ΨΨ^T)＝C²BQB (27)

Where Σ is the covariance matrix of the measurement error Ψ,

Q＝E(nn^T) Is the covariance matrix of the delay error, c is the propagation speed of the radio signal,

the target location may be considered to approach a constant when the target location is particularly far from the base station. Suppose B ≈ r_aI, then

Instead of Σ, we can approximate with Q, the available equation is transformed as follows:

the Chan algorithm obtains an initial value of the target position and the first weighted least square is finished.

In case of small noise conditions:

due to h⁰＝G⁰z⁰The recombination of formula (24) and formula (29) gives:

Ψ＝Δh-ΔGz⁰ (30)

let z = z⁰+ Δ z, an expression for Δ z and z covariance matrices may be obtained by combining equation (27) and equation (30):

bn = Ψ/C in equation (31), and the vector z is such that one element is z₁,z₂,z₃,z₄The estimation error of the element corresponding to z is e₁,e₂,e₃,e₄Then z is₁＝x⁰+e₁，z₂＝y⁰+e₂，z₃＝z⁰+e₃，

Is an expression for an element of z, using z in the vector z₁,z₂,z₃The elements are respectively subtracted by x of the base station with the number of 1 on three coordinate axes₁,y₁,z₁Then, the square operation is performed on the processed elements to obtain the following linear equation set expression:

Ψ′＝h′-G′z′ (32)

where Ψ' represents a new error vector, and:

the least squares calculation for equation (32) yields:

where Σ 'is an approximate covariance matrix of Ψ' and:

finally, a second minimum weighting result is obtained:

completing the work and solving the minimum residual weighted Chan algorithm to obtain the position coordinate marking (x)₀,y₀,z₀) After the initial value of the Taylor algorithm is obtained, the Taylor algorithm in the three-dimensional space is deduced, and the specific work is as follows.

Now, assuming that the number of base stations in the three-dimensional space is N (N is larger than or equal to 4), the position coordinates of the moving object are represented by (x, y, z), and the coordinates of the base stations can be represented by (x, y, z)_i,y_i,z_i) By (x)₀,y₀,z₀) Expressing initial estimation coordinates of Taylor algorithm, setting the main base station as the first base station, measuring noise obeying zero mean Gaussian distribution, and estimating error between the real position and the initial estimation position to be sigma_x,σ_y,σ_z。

From the geometric model of TDOA locations, the function is defined as follows:

the following formula is simplified:

f_i(x,y,z)＝r_i1 (38)

the relationship of the real coordinates to the initial estimated coordinates can be expressed as:

(x) in expansion (30) using Taylor series expansion₀,y₀,z₀) And discarding more than two orders can be obtained:

wherein the partial derivative term values are:

formula (40) can be converted into

Order to

The error vector from which the measurement can be derived is:

Ψ＝h-Gσ (44)

letting the error function ψ =0, according to the weighted least squares method, the following results are obtained:

σ＝(G^TQ^-1G)^-1G^TQ^-1h (45)

where Q represents the covariance matrix of the measurement errors, assuming that the measurement errors are independent of each other,

table-expressing the variance of the measurement error for each base station, we can then obtain:

the Taylor series expansion method is one of iterative algorithms, and the estimated initial position coordinate becomes (x) with the next iteration₀+σ_x,y₀+σ_y,z₀+σ_z) Setting a threshold value mu, when |. Sigma_x|+|σ_y|+|σ_zEnding the iteration when | is less than or equal to mu, otherwise, if | sigma |, ending the iteration_x|+|σ_y|+|σ_z|>Mu, repeating the derivation process, and solving the estimated coordinates by using a least square method. It is also possible to initially preset a maximum number of iterations N, when N are completed, σ_x|+|σ_y|+|σ_zAnd if the | is less than or equal to mu, forcibly exiting the iteration.

The steps of the minimum residual weighted Chan-Taylor joint algorithm based on TDOA are shown in FIG. 4.

2.4 improving the positioning Algorithm Overall procedure

Firstly, a combination mode of screening base stations is improved by using a minimum residual error principle, an index set is gradually reduced, iteration is continuously repeated according to the minimum residual error principle until an optimal TDOA measured value combination appears, the obtained TDOA value is substituted into a Chan algorithm and solved, and an original first order item is converted into a high order item of a residual error function in a weighting process. And then, taking the obtained result as a node required for generating an improved genetic ant colony hybrid algorithm to solve, wherein the task of improving the genetic ant colony hybrid algorithm is to find an optimal solution with the most distributed pheromones from the nodes. And finally, taking the optimal solution as an initial value of the Taylor algorithm, repeatedly comparing the settings of the error threshold value in the iterative solving process through the Taylor algorithm, if the conditions are not met, re-iteratively solving, if the conditions are met, ending the iteration, and outputting a final target position result.

As shown in fig. 1, the positioning algorithm specifically includes the following steps:

firstly, grouping 4 base stations in the whole positioning range space by using an improved residual weighted Chan algorithm, then recording rough coordinate estimation values obtained by calculation after grouping, and finally outputting estimation value results as node coordinates of an improved genetic ant colony algorithm, wherein the node coordinates are represented as P_i(x_i,y_i,z_i)。

Secondly, the coordinates P of the nodes are calculated by using an improved genetic ant colony mixing algorithm_i(x_i,y_i,z_i) And carrying out global search, and outputting the node containing the most pheromones as an optimal solution to an initial value of a Taylor algorithm, wherein the initial value has higher positioning accuracy under the NLOS environment.

And thirdly, iteratively solving by using a Taylor algorithm to obtain a final target.

3. Simulation results and analysis

The invention carries out matlab simulation on a three-dimensional improved genetic ant colony hybrid positioning algorithm (RWC-GAA-T algorithm) under the NLOS environment, firstly analyzes the influence of the number of base stations on the positioning precision, and then carries out comparative analysis with the positioning performance of several algorithms. The algorithm parameters are set as follows: the total number of 7 base stations is (0, 0), (350, 600, 20), (700, 0, 30), (-350, 600, 30), (-700, 0, 40), (-350, -600, 50), (350, -600, 35), the channel model adopts the downtown scene of the T1P1 channel model, the radius of the base station is 400M, the number of individuals in the genetic algorithm population M =50, and the cross probability P_C=0.9, probability of mutation P_m=0.01, the number m =20 of ants in the ant colony algorithm, α =0.8, β =0.2, ρ =0.7, and the maximum number of iterations of both algorithms is 100. The TDOA measurements are run 200 times without parameter changes and averaged, assuming that the TDOA measurement errors are independent of each other.

As shown in fig. 5, the improved genetic ant colony mixing algorithm was first compared with the convergence and optimum accuracy of the genetic algorithm and the ant colony algorithm. It can be seen from the figure that the initial convergence speed of the genetic algorithm is the fastest, the improved algorithm is slightly slower than the genetic algorithm, and the convergence speed of the ant colony algorithm is the slowest, because the improved algorithm inherits the global fast convergence characteristic of the genetic algorithm in the initial stage. The improved algorithm has the highest optimal solution precision, and the ant colony algorithm is the next one, and the genetic algorithm is the lowest, because the improved algorithm can be regarded as the ant colony algorithm with a better initial value, the optimal solution precision can be higher.

As a result, as shown in fig. 6, the positioning accuracy of the RWC-GAA-T algorithm tends to increase with the number of base stations, and when there are 7 base stations participating in positioning, the positioning accuracy of the algorithm is greatly improved compared with that when only 4 base stations participate in positioning. It can be seen that more redundant base stations can directly help the positioning accuracy of the algorithm, because more available redundant TDOA measurement data are generated with the increase of the number of base stations, and the measurement data of the redundant base stations are fully utilized under the condition that only 4 base stations can complete positioning, the algorithm can have more different base station grouping schemes, so that the problems of less measurement data and larger positioning error caused by larger NLOS error interference are avoided, and the positioning accuracy can be improved.

As shown in fig. 7, it can be seen more intuitively that the positioning performance of the algorithm improves as the number of base stations increases, and the probability of the error distribution in the smaller root mean square is higher as the number of base stations is larger.

As shown in FIG. 8, the RWC-GAA-T algorithm proposed by the present invention is significantly better than other positioning algorithms under the condition that the basic parameters are consistent and the lowest positioning base station is satisfied, and is closest to the lower CRLB boundary. The positioning performance of the RWC-T algorithm is second only to that of the RWC-GAA-T algorithm, and the worst positioning performance is the Chan algorithm because the algorithm is greatly influenced by non-line-of-sight errors. With the increasing number of base stations participating in positioning, the positioning accuracy of all algorithms is improved, and the root mean square error is gradually reduced.

As shown in FIG. 9, the RWC-GAA-T algorithm has the best positioning performance, which is closest to the lower bound of CRLB and second to the RWC-T algorithm, and the problem that the positioning decline of the original algorithm in the NLOS environment is improved by adding the improved genetic ant colony hybrid algorithm is shown. With the increase of the number of base stations, the positioning performance of the Taylor algorithm in the NLOS environment is gradually superior to that of the Chan algorithm and that of the Rwgh algorithm. The root mean square error of all algorithms is increased compared with that in an LOS environment, which shows that the error interference propagated by NLOS still has great influence on the positioning performance. However, it can also be seen that the accuracy of the RWC-GAA-T algorithm is always higher than that of other algorithms because the algorithm is changed in that the existing base stations are grouped by using a Chan algorithm based on minimum residual weighting, different weights are given according to the interference situation of the NLOS error to reduce the NLOS error, and the finally obtained coordinates generate the node positions required in the ant colony algorithm. And then, carrying out global search by utilizing the improved genetic ant colony algorithm, taking the optimal position coordinate as an initial coordinate of the Taylor algorithm, and obtaining a target estimation value through a continuous iteration process. The algorithm reduces the NLOS error twice, and greatly reduces the interference of the NLOS. Although the root mean square error values of all the algorithms rise with the increase of the ranging errors, the increase range of the RWC-GAA-T algorithm is relatively gentle, and the algorithm is relatively high in anti-jamming capability and relatively stable in positioning performance.

As shown in fig. 10, the RWC-GAA-T algorithm has the best positioning performance, and when only 4 base stations participate in positioning, the rms error is more than 80% and less than 25m, the chan algorithm has the worst positioning performance, and 80% of the rms error is less than 38m. As the number of base stations increases, the performance of all the algorithms is improved, and when the number of the base stations increases to 7, the RWC-GAA-T algorithm has the root mean square error of less than 21m, which exceeds 80%, and can obtain better positioning effect in the NLOS environment as shown in FIG. 10 (d). The figure shows the advantages of the improved algorithm compared with the rest algorithms in NLOS environment, which proves the good positioning performance.

As shown in fig. 11, the root mean square errors of all the algorithms increase with the increase of the radius of the base station, wherein the increment of the Chan algorithm is the largest, the increment of the root mean square errors of the RWChan-Taylor algorithm and the RWC-GAA-T algorithm is the second largest, the increment of the root mean square errors of the RWChan-Taylor algorithm and the RWC-GAA-T algorithm is smaller, and the root mean square errors of the RWC-GAA-T algorithm are the smallest. The interference of non-line-of-sight errors is larger and larger along with the increase of the radius of the base station, and compared with other algorithms, the RWC-GAA-T algorithm has more obvious advantages.

The calculation method of the lifting percentage in fig. 12 is as follows:

in fig. 12, in order to more intuitively see the performance change of the algorithm proposed by the present invention compared with other algorithms, the Chan algorithm is also used as a standard reference algorithm for comparison, and the performance improvement conditions of the RWChan-Taylor algorithm and the RWC-GAA-T algorithm compared with the conventional Chan algorithm are compared. The improved algorithm is improved to a larger extent, and the RWC-GAA-T algorithm is improved by about 20 percent compared with the RWC-Taylor algorithm. The RWC-GAA-T algorithm plays an effective restraining role on NLOS errors in the NLOS environment, and is suitable for solving the positioning problem in the NLOS environment.

The above provides a detailed description of an improved genetic ant colony hybrid location method based on TDOA selection according to an embodiment of the present application. The above description of the embodiments is only for the purpose of helping to understand the method of the present application and its core ideas; meanwhile, for a person skilled in the art, according to the idea of the present application, the specific implementation manner and the application scope may be changed, and in summary, the content of the present specification should not be construed as a limitation to the present application.

Claims

1. An improved genetic ant colony hybrid location method based on selection of TDOA, the method comprising the steps of:

2. The method for improved genetic ant colony hybrid location based on TDOA selection as recited in claim 1, wherein the step S1 comprises:

the residual is defined as the difference between the observed value of the distance difference and the predicted value calculated using the intermediate position.

3. The improved genetic ant colony hybrid location method based on TDOA selection as recited in claim 1, wherein the global search of node coordinates by the genetic ant colony algorithm in step S3 comprises:

4. The method for improved genetic ant colony hybrid location based on TDOA selection according to claim 3, wherein the specific contents of step S31 include:

determining a fitness function;

determining a genetic operator;

and generating pheromone according to the output result.

5. The method for improved genetic ant colony hybrid location based on selective TDOA as claimed in claim 4, wherein said pheromones comprise: coordinate data of the optimal individual and randomly generated data.

6. The improved TDOA-based genetic ant colony hybrid location method as recited in claim 4, wherein said fitness function is:

wherein, the first and the second end of the pipe are connected with each other,

R_iindicating the distance of the real coordinates of the moving object to the ith base station,

indicating the distance, n, from the estimated coordinate position of the moving object to the ith base station_iRepresenting the noise error subject to a gaussian distribution, M being the number of base stations.

7. The improved TDOA-based genetic ant colony hybrid location method as recited in claim 4, wherein the crossover probability value is 0.9 and the mutation probability value is 0.05 when determining the genetic operator.

8. The method for improved genetic ant colony hybrid location based on TDOA selection according to claim 4, wherein the specific content of step S32 includes:

searching according to a search rule, and migrating according to migration probability;

where α is the pheromone elicitor, β is the desired elicitor, t is the time, η_ijRepresenting path (i, j) visibility,. Tau_ij(t) indicates the amount of pheromones present on the path (i, j) at time t; allowed is a set of coordinate points to be accessed by the ant k, s is a coordinate point in allowed, and eta is_isRepresenting the degree of inspiration from the i coordinate to the s coordinate;

and (3) updating pheromone: the path pheromone strengths and pheromone increments are updated.

9. The method for improved genetic ant colony hybrid location based on selective TDOA of claim 8, wherein the pheromone increment left by the kth ant per traversal on path (i, j) is:

in the formula, L_kExpressing the path length of the pheromone left by the ant k, and Q is the total amount of the pheromone traversed by the ant colony once;

the intensity of the pheromone existing on the path (i, j) at time t +1 is:

τ_i,j(t+1)＝(1-ρ)τ_i,j(t)+Δτ_i,j(t,t+1)，

in the formula, τ_ij(t) represents the amount of pheromone present on the path (i, j) at time t, (1- ρ) represents the pheromone residual coefficient, Δ τ_ij(t, t + 1) represents the pheromone increment of the ant colony population traversed once in time (t, t + 1);

denotes pheromone increment for ant number k at time (t, t + 1).

10. An improved TDOA-based genetic ant colony hybrid location apparatus comprising a memory, a processor, and a computer program stored in said memory and operable on said processor, wherein: the processor when executing the computer program realizes the steps of the method according to any of claims 1-9.