CN112836784A - Magnetic moving target positioning method based on ant colony and L-M hybrid algorithm - Google Patents
Magnetic moving target positioning method based on ant colony and L-M hybrid algorithm Download PDFInfo
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Abstract
The invention discloses a magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm, which comprises the following steps: the method comprises the steps of enabling a magnetic moving target to be equivalent to a magnetic dipole array, establishing a magnetic dipole array model, and determining a magnetic field generated by the magnetic moving target at a measuring point, the magnetic moment of the magnetic moving target, and a magnetic moving target relational expression of the position relation between the magnetic moving target and the measuring point; when the magnetic moving target moves at a constant speed and the magnetic moment of the magnetic moving target is invariant, knowing the magnetic field generated by the magnetic moving target at a measuring point, performing least square optimization on the relational expression of the magnetic moving target to determine a nonlinear equation about the position of the magnetic moving target; under the condition that the initial state is unknown, the position of the magnetic moving target is solved by utilizing a hybrid algorithm combining an ant colony optimization algorithm and an L-M method, namely, an initial rough solution is obtained by utilizing the ant colony optimization algorithm, and then an optimal solution is obtained by utilizing the L-M method, so that the accurate positioning of the magnetic target is realized.
Description
Technical Field
The invention relates to the technical field of magnetic moving target positioning, in particular to a magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm.
Background
In recent years, the Levernberg-Marquardt algorithm (L-M method) is widely applied in the fields of three-dimensional information acquisition, building science, industrial design and the like. The Levernberg-Marquardt algorithm is a deformation of Newton's method, solves the optimal solution by minimizing the sum of squares of nonlinear objective functions, and can be used for passive magnetic positioning calculation. The calculation method is a compromise algorithm of a Newton method and a steepest descent method, and has the convergence rate of the Newton method and the convergence performance of the steepest descent method.
In the prior art, a shell of a vehicle is taken as a magnetic simulator, a magnetic field model of a measured target is established, unknown parameters are initially estimated, and the position of the target can be accurately estimated by using an L-M method. However, the L-M method also has the defect that the Newton method has high requirement on the initial value, and the L-M algorithm can find a good optimal solution within a certain range of the initial value from the true value; when the initial value is poor, an iterative divergence phenomenon occurs, so that a good optimal solution cannot be found, namely the positioning accuracy of the magnetic target is influenced.
Disclosure of Invention
The embodiment of the invention provides a magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm, which is used for solving the problems in the background technology.
The embodiment of the invention provides a magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm, which comprises the following steps:
establishing a receiving magnetic field platform by using a single three-component fluxgate sensor, and acquiring abnormal magnetic field data generated when a magnetic moving target passes through the receiving magnetic field platform;
the method comprises the steps of enabling a magnetic moving target to be equivalent to a magnetic dipole array, establishing a magnetic dipole array model according to the size of the magnetic moving target, and determining a magnetic field generated by the magnetic moving target at a measuring point, the magnetic moment of the magnetic moving target, and a magnetic moving target relational expression of the position relation between the magnetic moving target and the measuring point;
when the magnetic moving target moves at a constant speed, regarding the magnetic moment of the magnetic moving target as an invariant, knowing the magnetic field received at a measuring point, performing least square optimization on the relational expression of the magnetic moving target, and determining a nonlinear equation about the position of the magnetic moving target;
solving a nonlinear equation of the magnetic moving target position by adopting an ant colony optimization algorithm by combining abnormal magnetic field data to obtain a rough solution of the magnetic moving target position;
and taking the rough solution as an initial value, solving a nonlinear equation of the magnetic moving target position by adopting a Levernberg-Marquardt algorithm, and determining an accurate solution of the magnetic moving target position.
Further, the magnetic moving object includes: an automobile.
Further, the abnormal magnetic field data is: and subtracting the stable geomagnetic field data of the magnetic moving target before the magnetic moving target passes through the receiving magnetic field platform from the magnetic field data of the magnetic moving target when the magnetic moving target passes through the receiving magnetic field platform.
Further, determining the magnetic moving object relation specifically includes:
establishing a coordinate system by taking the center of the magnetic moving target as an origin, wherein the X-axis direction is the longitudinal direction of the magnetic moving target, and the Z-axis is vertically downward; fitting a magnetic moving target by an array of magnetic dipoles evenly distributed on the X axis, wherein the number of the magnetic dipoles is N, the center of the linear array of the magnetic dipoles is located at the origin, the magnetic moments of the magnetic dipoles in three directions are Mxi, Myi, Mzi, i is 1,2,3, N, and the magnetic field generated by the ith magnetic dipole at the measuring point P (X, y, z) is:
wherein r isiIs the distance from the ith magnetic dipole to the measurement point, (x)i,yi,zi) Is the coordinate position of the ith magnetic dipole;
the magnetic field generated by the magnetic dipole array at the measurement point P (x, y, z) is then:
further, the determining a non-linear equation about the position of the magnetic moving object specifically includes:
arranging a fluxgate sensor at a measuring point, wherein a Z 'axis of a fluxgate coordinate axis is vertically downward, and an included angle between an X' axis and a target course direction, namely an X axial direction is alpha; assuming that the magnetic moving target does uniform linear motion along the X direction, the speed is v, the sampling interval is DT, and the output (H ') of the fluxgate sensor at the j th time'xj,H'yj,H'zj) With magnetic moving target magnetic field (H)xj,Hyj,Hzj) The relationship of (1) is:
wherein, -pi ≦ α ≦ pi, and the parameter α is a fixed value for a magnetic moving target possessing a fixed direction of motion;
when the magnetic moving target passes through the measuring point, the fluxgate samples m times to obtain m groups of three-component magnetic moving target magnetic field data as follows:
and (3) establishing a linear equation system of the model by using the m-point sampling data:
H＝FM
wherein the content of the first and second substances,
M＝(Mx1,Mx2,···,MxN,My1,My2,···,MyN,Mz1,Mz2,···,MzN)T
H＝(Hx1,Hx2,···,Hxm,Hy1,Hy2,···,Hym,Hz1,Hz2,···,Hzm)T
the non-linear equation for the position of a magnetically moving target is as follows:
wherein F is a coefficient matrix related to the position of the magnetic moving target, M is a magnetic field model parameter, H is a magnetic field of the magnetic moving target, and the magnetic moving target function E is a nonlinear function of the positioning parameter (x, y, z, alpha).
Further, the ant colony optimization algorithm includes:
according to the number of parameters to be solved, the ant colony population is subjected to size setting and iteration frequency setting, and a magnetic motion objective function E determined by a nonlinear equation is used for initializing pheromones;
the ant colony optimization algorithm is an iterative algorithm, and the following operations are executed in each iteration:
a group of ants synchronously or asynchronously move between adjacent states of the nonlinear optimization problem, and the moving direction is selected by using pheromones and heuristic information associated in each state and adopting a state transition rule to gradually construct a feasible solution of the problem;
updating pheromones locally when each ant constructs solutions;
after all ants complete the construction of the solution, globally updating the pheromone according to the obtained solution;
the iterative process continues until a stop condition is satisfied; among the commonly used stopping conditions are the maximum run time or the maximum number of allowed solutions to be constructed.
Further, the Levernberg-Marquardt algorithm includes:
xk+1＝xk-[JT(xk)J(xk)+μkI]-1JT(xk)v(xk)
when mu iskAt increase, the Levernberg-Marquardt algorithm approaches the steepest descent method for small learning speeds:
when mu iskWhen dropping to 0, the Levernberg-Marquardt algorithm becomes Gaussian-Newton, and F (x) vT(x)v(x)。
The embodiment of the invention provides a magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm, which has the following beneficial effects compared with the prior art:
the invention provides a method for realizing accurate positioning of a magnetic target by utilizing a single three-component fluxgate sensor; under the condition that the initial state is unknown, the position of the magnetic moving target is solved by using a hybrid algorithm (ACO-LM method) combining an Ant Colony Optimization (Ant Colony Optimization) and an L-M method, namely, an initial rough solution is obtained by using an Ant Colony algorithm, and then an optimal solution is obtained by using the L-M method, so that the magnetic moving target is accurately positioned. In addition, the single fluxgate sensor has the characteristics of low price, convenience in carrying and installation and good engineering application prospect. In addition, the rationality and the feasibility of the hybrid algorithm are verified through theoretical simulation and an automobile experiment, and reference is provided for detection and positioning of a magnetic target in engineering.
Drawings
FIG. 1 is a magnetic dipole array model of a magnetic target provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of the movement of a magnetic target according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a target location experiment provided by an embodiment of the present invention;
FIG. 4a is a three-component magnetic field data of a first pass of a magnetic sensor by a vehicle according to an embodiment of the present invention;
FIG. 4b is a graph illustrating three-component magnetic field data for a second pass of the vehicle past the magnetic sensor in accordance with an embodiment of the present invention;
5-a1 illustrate data for positioning in the X direction for a first pass of a vehicle according to an embodiment of the present invention;
5-a2 are positioning results in the X direction for a first pass of a vehicle provided by an embodiment of the present invention;
5-b1 illustrate data for positioning in the Y direction for a first pass of a vehicle according to an embodiment of the present invention;
5-b2 illustrate the positioning results in the Y direction for a first pass of a vehicle provided by an embodiment of the present invention;
5-c1 illustrate data for positioning in the Z direction for a first pass of a vehicle according to an embodiment of the present invention;
5-c2 illustrate positioning results in the Z direction for a first pass of a vehicle provided by an embodiment of the present invention;
FIG. 5-d is a result of positioning an included angle with the X direction when the vehicle passes for the first time according to the embodiment of the present invention;
6-a1 shows data for a second pass of the vehicle in the X direction for positioning according to an embodiment of the present invention;
6-a2 are positioning results in the X direction for a second pass of the vehicle provided by embodiments of the present invention;
6-b1 illustrate data for a second pass of the vehicle in the Y direction for positioning according to embodiments of the present invention;
6-b2 are positioning results in the Y direction for a second pass of the vehicle provided by embodiments of the present invention;
6-c1 illustrate data for a second pass of the vehicle in the Z direction for positioning according to embodiments of the present invention;
6-c2 are positioning results in the Z direction for a second pass of the vehicle provided by embodiments of the present invention;
fig. 6-d shows the positioning result of the angle formed by the automobile and the X direction during the second pass according to the embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm, which comprises the following steps:
step 1: a receiving magnetic field platform is established by using a single three-component fluxgate sensor, and abnormal magnetic field data generated when a magnetic moving target passes through the receiving magnetic field platform are collected.
Step 2: and (3) enabling the magnetic moving target to be equivalent to a magnetic dipole array, establishing a magnetic dipole array model according to the size of the magnetic moving target, and determining a magnetic field generated by the magnetic moving target at the measuring point, the magnetic moment of the magnetic moving target and a magnetic moving target relational expression of the position relation between the magnetic moving target and the measuring point. Specifically, taking an automobile as an example, the automobile is about 4.4m long, and the three-magnetic dipole array model with equal intervals is established by taking the intervals as half of the length of the automobile.
And step 3: when the magnetic moving target moves at a constant speed, the magnetic moment of the magnetic moving target is regarded as an invariant, the magnetic field received at the measuring point is known, least square optimization is carried out on the relational expression of the magnetic moving target, and a nonlinear equation related to the position of the magnetic moving target is determined.
It should be noted that, according to the principle that a single magnetic dipole generates a magnetic field, a magnetic field model equation of the size and distance of the magnetic field and the magnetic moment of the target is listed, and according to the linear superposition principle, the abnormal magnetic field generated when the equivalent magnetic target passes through can be approximated by the magnetic fields generated by three magnetic dipoles distributed at different positions of the target.
And 4, step 4: and solving a nonlinear equation of the magnetic moving target position by adopting an ant colony optimization algorithm by combining the abnormal magnetic field data to obtain a rough solution of the magnetic moving target position. Specifically, the method comprises the steps of solving by adopting an ant colony optimization algorithm to obtain a rough solution of the position of the automobile, wherein the rough solution comprises the steps of setting the size of an ant colony according to the number of parameters to be solved, setting iteration times, initializing pheromones by an objective function determined by a nonlinear least square problem and setting pheromone updating rules.
And 5: and taking the rough solution as an initial value, solving a nonlinear equation of the magnetic moving target position by adopting a Levernberg-Marquardt algorithm, and determining an accurate solution of the magnetic moving target position. Specifically, an ant colony optimization algorithm is used for obtaining a rough solution of the position of the automobile as an initial solution of a Levernberg-Marquardt algorithm, and then an accurate solution about the position of the automobile is obtained by utilizing the characteristics of high precision and fast convergence of the Levernberg-Marquardt algorithm, wherein the accurate solution comprises the setting of iteration times and the setting of an iteration stopping condition of the Levernberg-Marquardt algorithm.
The specific analysis of the steps 1-5 is as follows:
magnetic target modeling generally adopts a magnetic dipole model. As shown in fig. 1, a coordinate system is established with the center of the magnetic target as the origin, the X-axis direction is the longitudinal direction of the target, generally the advancing direction thereof, and the Z-axis is vertically downward. Fitting the target with an array of magnetic dipoles evenly distributed on the X-axis, where the number of magnetic dipoles is N, the magnetic dipole line array is centered at the origin, the magnetic moments of the magnetic dipoles in three directions are Mxi, Myi, Mzi, i ═ 1,2,3, · · N, respectively, and the magnetic field generated by the ith magnetic dipole at the measurement point P (X, y, z) is:
wherein r isiIs the distance from the ith magnetic dipole to the measurement point, (x)i,yi,zi) Is the coordinate position of the ith magnetic dipole.
The magnetic field generated by the magnetic dipole array at the measurement point P (x, y, z) is then:
if the magnetic moment and distribution of the array are known, the magnetic field can be calculated at any point in space. Conversely, if the magnetic field distribution data in the space is known, the magnetic moment and the distribution position of the magnetic dipole equivalent to the magnetic moving target can be obtained by inversion, so that the position of the magnetic target can be obtained.
The fluxgate magnetic sensor is arranged at a measuring point, a Z 'axis of a fluxgate coordinate axis is vertically downward, and an included angle between an X' axis and a target heading (X axis) is alpha, as shown in FIG. 1. Assuming that the target does uniform linear motion along the X direction, the speed is v, the sampling interval is DT, and the speed when the target passes through is not long. Then the jth output (H ') of the flux gate'xj,H'yj,H'zj) With the target magnetic field (H)xj,Hyj,Hzj) The relationship of (A) is as follows:
where-pi ≦ α ≦ pi, and the parameter α is a fixed value for a magnetic target possessing a fixed direction of motion.
Setting the coordinate center position of the target at the jth sampling as Pj(xj,yj,zj) For a magnetic target moving on the ground, the coordinate P at the time of sampling at the j +1 th timej+1(xj+1,yj+1,zj+1) Comprises the following steps:
a batch of data may be collected as the target passes near the measurement system. The fluxgate samples m times, and m groups of three-component data can be obtained as follows:
with m-point sampled data, a linear system of equations for the model can be established:
H＝FM
wherein the content of the first and second substances,
M＝(Mx1,Mx2,···,MxN,My1,My2,···,MyN,Mz1,Mz2,···,MzN)T
H＝(Hx1,Hx2,···,Hxm,Hy1,Hy2,···,Hym,Hz1,Hz2,···,Hzm)T
the problem of localization of magnetic targets is in fact an optimization problem solving the following non-linear unconstrained equations:
where F is the coefficient matrix for the target location, M is the magnetic field model parameters, H is the target magnetic field, and the objective function E is a non-linear function of the localization parameters (x, y, z, α), which is a typical non-linear optimization problem. The unknown parameter has an initial position (x) of the central position of the target relative to the fluxgate at the first sampling1,y1,z1) Target individual magnetic dipole moment (M)xi,Myi,Mzi) The included angle alpha between the target course and the X' axis of the fluxgate is 3N +4 unknown numbers, wherein (M)xi,Myi,Mzi) Referred to as model parameters, (x)1,y1,z1α) is called a positioning parameter, it being clear that F is a parameter relating to positioningIs a non-linear function of (a). S nonlinear equations are established by using magnetic field data acquired by the fluxgate sensor, when S is more than 3N +4, the equation set is a contradiction equation set, an accurate solution cannot be obtained, only an approximate solution in the least square sense can be obtained, and E is (FM-H)T(FM-H) reaches a minimum value.
In order to solve the nonlinear optimization problem, the invention provides an ant colony and Levernberg-Marquardt mixed positioning algorithm (ACO-LM method), the global search optimization capability of the ant colony algorithm is combined with the local precise search capability of the L-M method, the ant colony algorithm is used for obtaining an initial rough solution, then the L-M method is used for obtaining an optimal solution, and the accurate positioning of the magnetic moving target is realized.
The Levernberg-Marquardt algorithm is:
xk+1＝xk-[JT(xk)J(xk)+μkI]-1JT(xk)v(xk)
the algorithm is equivalent to mukWhen increasing, it approaches the steepest descent method for small learning speeds:
when mu iskWhen the value falls to 0, the algorithm becomes gaussian-newton, where f (x) is equal to vT(x)v(x)。
The ant colony algorithm is an iterative algorithm, and the following operations are executed in each iteration: a group of ants move between adjacent states of a nonlinear optimization problem synchronously or asynchronously, and they use pheromones and heuristic information associated in each state to select moving directions by using state transition rules to gradually construct a feasible solution of the problem[8](ii) a Pheromones can be locally updated when each ant constructs solutions; after all ants complete the construction of the solution, the pheromone is globally updated according to the obtained solution. The iterative process continues until some stopping condition is met. Common stopping conditions are maximum run time or maximum number of allowed solutions to be constructed.
Because the ant colony algorithm has good global search capability, the optimization result is irrelevant to the initial value, only one initial value needs to be randomly generated in the variable distribution interval, the ant colony algorithm can quickly converge to the local area where the optimal solution of the target function is located, and a good initial value can be provided for the L-M method. Because the ant colony algorithm lacks the fine searching capability of a local area, the ant colony algorithm is easy to fall into stagnation in the later operation stage, and in order to improve the operation efficiency of the algorithm, the iteration times of the ant colony algorithm can be properly shortened and the number of ants can be reduced.
Magnetic moving object positioning simulation
The existing research shows that the three-dipole array model can well simulate the magnetic target. Assuming an equivalent three dipole magnetic moment of a magnetic target of (M)xi,Myi,Mzi)＝(2×104,3×104,2×104)Am2And i is equal to 1,2,3 magnetic dipole spacing of 2 m. The magnetic target center moves from the coordinate position (-150, -40,0) to the coordinate position (145, -40,0) in the positive X-axis direction at a speed V of 10 m/s. An included angle alpha between the X direction of the fluxgate and the X axis of the coordinate system is-30 degrees, the target moves in the XOY plane of the coordinate system, and the sampling interval of the acquisition system is 0.5 s. The magnetic target motion diagram is shown in figure 2 below.
When alpha is-30 degrees, the ant colony algorithm is used for enabling the hybrid algorithm to quickly converge to the vicinity of a true value, and then the L-M method is used for local operation, so that the simulation obtains a good positioning effect.
Magnetic target localization experiments
The positioning performance of the ACO-LM method will be verified experimentally by the magnetic target. A wide road which is far away from industrial facilities in the suburb of Western Ann and is in a stable magnetic field environment is selected for the experiment. The magnetic target is an automobile with dimensions of 4.55m × 1.8m × 1.88 m. The positive X direction of the magnetic sensor points to the driving direction of the automobile, the Z direction is vertical to the ground and faces downwards, and the Y direction, the X direction and the Z direction accord with a right-hand coordinate system. The automobile passes through the magnetic acquisition system at a speed of about 8.3m/s, the distance from the center of the automobile to the magnetic sensor in the Y direction is about 3m, the distance from the center of the automobile to the ground is about 1m, and an experimental schematic diagram is shown in FIG. 3.
The Levernberg-Marquardt algorithm solves the optimal solution by minimizing the sum of squares of the nonlinear objective functions, has high requirements on initial values, and cannot obtain the optimal solution when the initial values are not properly selected. The following describes the situation by selecting different initial values, using an L-M method to solve, randomly running for 30 times, and selecting simulation data of position true value parameters (-10M, -40M,0M, -30 °) for comparison. The results are shown in table 1:
TABLE 1L-M method solving effect when different initial values are taken
As can be seen from table 1, when the initial value is closer to the selected position true value, the L-M algorithm can find a good optimal solution; however, when the initial value is not properly selected, the algorithm cannot obtain the optimal solution and cannot converge to the vicinity of the true value. Aiming at the problem, the ant colony algorithm is introduced to form an ACO-LM method to solve the position parameters of the magnetic target. Setting the upper limit of the solution space of the ACO-LM method to be (500m,50m,10m and 50 degrees), setting the lower limit to be (-500m, -50m, -10m and-50 degrees), randomly operating for 30 times, similarly selecting the true position parameters (-10m, -40m,0m and-30 degrees), and obtaining the simulation result of x being-10.03 m, y being-40 m and z being 0.0003 m.
The experiment adopts a high-performance fluxgate magnetic sensor produced by Shunhua measuring equipment Limited liability company, the bandwidth is DC-1KHz, the linearity is not more than 0.01 percent FS, the three-axis orthogonality is not more than +/-0.2 degrees, and the noise is as low as 6pT RMS/Hz1 /2@1 Hz. The geomagnetic field can be regarded as stable within a period of time, a period of data is collected as the geomagnetic field before the experiment, and the geomagnetic field subtracted from the magnetic field data collected in the experiment process can be regarded as the target magnetic field. The automobile runs 2 times along the road edge, the X axis of the magnetic sensor is parallel to the X axis of the coordinate axis when the automobile passes for the first time, and the X axis of the magnetic sensor is wound around the seat when the automobile passes for the second timeThe axis X is rotated counterclockwise by about 30. And (3) intercepting the magnetic field data of 2s before and after the automobile equivalent center passes through the magnetic acquisition system every time to perform Butterworth low-pass filtering processing, wherein the processed magnetic target passing curve is shown in figure 4.
The three-dipole equidistant linear array model is selected to model the automobile, and the fitting error of different magnetic dipole intervals to the magnetic field change data is compared, so that the automobile can be well fitted through the magnetic field data with high precision when the magnetic dipole array interval is 2.2 m. The ACO-LM method provided by the present invention is used to position the motion trajectory of the vehicle, and the positioning results are shown in fig. 5 and fig. 6.
Since the vehicle travels straight in the X direction, the positional change in the X direction is an inclined straight line having a slope of the traveling speed of the vehicle with respect to the time axis, and there is substantially no change in the Y direction and the Z direction, so that the two directions are a horizontal straight line with respect to the time axis. From the positioning result, the positioning result is poor in a period of initial time because the magnetic field signal is weak when the automobile is far away from the magnetic sensor, the magnitude of noise is not negligible relative to the effective magnetic field signal, the signal-to-noise ratio is low, and the influence on positioning is large. As the automobile is closer to the magnetic sensor, the target magnetic field signal is gradually enhanced, the signal-to-noise ratio is improved, effective magnetic field data is more and more, and the positioning result is gradually improved. It can also be seen from the figure that the time node at which the positioning result is significantly improved occurs at a position approximately 0 in the X direction, when the vehicle is passing across the magnetic sensor, the magnetic field signal is strongest.
Meanwhile, the positioning effect of the automobile passing process twice under different numbers of magnetic dipole array models is compared by using the ACO-LM method, and the result is as follows:
TABLE 2 positioning effect under different models in the first pass
In table 2, V is the average velocity between 79s and 80s in the first pass, and Y, Z and α are the Y-direction distance, the Z-direction distance, and the angle with the X-direction when the time is 79.5 s.
TABLE 3 localization effects under different models for the second pass
In table 3, V is the average speed between 192.5s and 193.5s in the second pass, and Y, Z and α are the Y-direction distance, the Z-direction distance, and the angle to the X-direction when the time is 193 s.
The ACO-LM method is suitable for different numbers of magnetic dipole array models. By comparison, the positioning results based on the three-dipole model and the five-dipole model are closer to the actual situation (the distance from the center of the automobile to the Y direction of the magnetic sensor is about 3m, the positioning results in the Z direction in the 2-pass process are kept close to each other and about 1.2m), and the deviation of the positioning results based on the single-dipole model is large, which indicates that the positioning accuracy is also influenced by the number of model parameters.
In summary, the invention provides a hybrid algorithm which firstly uses the ACO algorithm to carry out rough solution and then uses the L-M method to carry out fine solution after determining a proper magnetic dipole array model under the condition that the initial position of the magnetic target is unknown, thereby overcoming the defect that the ant colony algorithm is easy to be stuck due to lack of local area fine search capability, and meeting the requirement of the L-M method on high initial value requirement.
Although the embodiments of the present invention have been disclosed in the form of several specific embodiments, and various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention, the embodiments of the present invention are not limited thereto, and any changes that can be made by those skilled in the art are intended to fall within the scope of the present invention.
Claims (7)
1. A magnetic moving target positioning method based on an ant colony and L-M hybrid algorithm is characterized by comprising the following steps:
establishing a receiving magnetic field platform by using a single three-component fluxgate sensor, and acquiring abnormal magnetic field data generated when a magnetic moving target passes through the receiving magnetic field platform;
the method comprises the steps of enabling a magnetic moving target to be equivalent to a magnetic dipole array, establishing a magnetic dipole array model according to the size of the magnetic moving target, and determining a magnetic field generated by the magnetic moving target at a measuring point, the magnetic moment of the magnetic moving target, and a magnetic moving target relational expression of the position relation between the magnetic moving target and the measuring point;
when the magnetic moving target moves at a constant speed, regarding the magnetic moment of the magnetic moving target as an invariant, knowing the magnetic field received at a measuring point, performing least square optimization on the relational expression of the magnetic moving target, and determining a nonlinear equation about the position of the magnetic moving target;
solving a nonlinear equation of the magnetic moving target position by adopting an ant colony optimization algorithm by combining abnormal magnetic field data to obtain a rough solution of the magnetic moving target position;
and taking the rough solution as an initial value, solving a nonlinear equation of the magnetic moving target position by adopting a Levernberg-Marquardt algorithm, and determining an accurate solution of the magnetic moving target position.
2. The ant colony and L-M hybrid algorithm-based magnetic moving object positioning method according to claim 1, wherein the magnetic moving object comprises: an automobile.
3. The ant colony and L-M hybrid algorithm-based magnetic moving object positioning method according to claim 1, wherein the abnormal magnetic field data is: and subtracting the stable geomagnetic field data of the magnetic moving target before the magnetic moving target passes through the receiving magnetic field platform from the magnetic field data of the magnetic moving target when the magnetic moving target passes through the receiving magnetic field platform.
4. The ant colony and L-M hybrid algorithm-based magnetic moving object positioning method according to claim 1, wherein determining the magnetic moving object relation specifically includes:
establishing a coordinate system by taking the center of the magnetic moving target as an origin, wherein the X-axis direction is the longitudinal direction of the magnetic moving target, and the Z-axis is vertically downward; fitting a magnetic moving target by an array of magnetic dipoles evenly distributed on an X axis, wherein the number of the magnetic dipoles is N, the center of the magnetic dipole linear array is positioned at an origin, magnetic moments of the magnetic dipoles in three directions are Mxi, Myi, Mzi, i is 1,2,3 and … N, and a magnetic field generated by the ith magnetic dipole at a measuring point P (X, y and z) is as follows:
wherein r isiIs the distance from the ith magnetic dipole to the measurement point, (x)i,yi,zi) Is the coordinate position of the ith magnetic dipole;
the magnetic field generated by the magnetic dipole array at the measurement point P (x, y, z) is then:
5. the ant colony and L-M hybrid algorithm-based magnetic moving object positioning method according to claim 4, wherein the determining a non-linear equation about the position of the magnetic moving object specifically comprises:
arranging a fluxgate sensor at a measuring point, wherein a Z 'axis of a fluxgate coordinate axis is vertically downward, and an included angle between an X' axis and a target course direction, namely an X axial direction is alpha; assuming that the magnetic moving target does uniform linear motion along the X direction, the speed is v, the sampling interval is DT, and the output (H ') of the fluxgate sensor at the j th time'xj,H'yj,H′zj) With magnetic field (H) of a magnetically moving targetxj,Hyj,Hzj) The relationship of (1) is:
wherein, -pi ≦ α ≦ pi, and the parameter α is a fixed value for a magnetic moving target possessing a fixed direction of motion;
when the magnetic moving target passes through the measuring point, the fluxgate samples m times to obtain m groups of three-component magnetic moving target magnetic field data as follows:
and (3) establishing a linear equation system of the model by using the m-point sampling data:
H＝FM
wherein the content of the first and second substances,
M＝(Mx1,Mx2,…,MxN,My1,My2,…,MyN,Mz1,Mz2,…,MzN)T
H＝(Hx1,Hx2,…,Hxm,Hy1,Hy2,…,Hym,Hz1,Hz2,…,Hzm)T
the non-linear equation for the position of a magnetically moving target is as follows:
wherein F is a coefficient matrix related to the position of the magnetic moving target, M is a magnetic field model parameter, H is a magnetic field of the magnetic moving target, and the magnetic moving target function E is a nonlinear function of the positioning parameter (x, y, z, alpha).
6. The ant colony and L-M hybrid algorithm-based magnetic moving object positioning method according to claim 5, wherein the ant colony optimization algorithm comprises:
according to the number of parameters to be solved, the ant colony population is subjected to size setting and iteration frequency setting, and a magnetic motion objective function E determined by a nonlinear equation is used for initializing pheromones;
the ant colony optimization algorithm is an iterative algorithm, and the following operations are executed in each iteration:
a group of ants synchronously or asynchronously move between adjacent states of the nonlinear optimization problem, and the moving direction is selected by using pheromones and heuristic information associated in each state and adopting a state transfer rule to gradually construct a feasible solution of the problem;
updating pheromones locally when each ant constructs solutions;
after all ants complete the construction of the solution, globally updating the pheromone according to the obtained solution;
the iterative process continues until a stop condition is satisfied; among the commonly used stopping conditions are the maximum run time or the maximum number of allowed solutions to be constructed.
7. The ant colony and L-M hybrid algorithm-based magnetic moving object locating method according to claim 1, wherein the levenberg-Marquardt algorithm comprises:
xk+1＝xk-[JT(xk)J(xk)+μkI]-1JT(xk)v(xk)
when mu iskAt increase, the Levernberg-Marquardt algorithm approaches the steepest descent method for small learning speeds:
when mu iskWhen dropping to 0, the Levernberg-Marquardt algorithm becomes Gaussian-Newton, and F (x) vT(x)v(x)。
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