One-point positioning method based on magnetic gradient tensor invariantTechnical field
The invention belongs to magnetic detection technical fields, are related to a kind of novel magnetic object localization method.This method utilizes magnetic ladderDegree tensor invariant is derived from, and the position of magnetic target can be uniquely solved in ground magnetic environment, and have not by appearanceThe characteristic that state variation influences.
Background technique
Due to the presence in earth's magnetic field, ferrimagnet is made to be magnetized, to show magnetic characteristic, generates magnetic field, in this wayMagnetic field superposition will cause earth magnetism field distortion on earth's magnetic field, this phenomenon is known as magnetic anomaly phenomenon.Magnetic anomaly detection skillArt utilizes magnetic anomaly phenomenon, and magnetic target is positioned and recognized by observing and analyzing anomalous field.Magnetic anomaly detection skillArt due to have many advantages, such as it is light it is easy, high-efficient, at low cost, concealment is good, anti-interference strong, have high military significanceWith civilian value.
The development of magnetic anomaly detection technology mainly experienced the total measurement in magnetic field, magnetic-field component and gradiometry, magnetic gradientTensor measuring three phases.Magnetic gradient Tensor measuring has overwhelming advantage compared to traditional magnetic-field measurement, maximum excellentPoint is the interference that can effectively overcome earth's magnetic field, improves the positioning accuracy of magnetic target.Magnetic gradient tensor localization method can be realNow to the accurate positioning of target, but it is higher to the movement needs of carrying platform, and the motor-driven of platform can bring positioning result very greatlyInterference.
Magnetic gradient tensor invariant, be magnetic gradient tensor carry out certain operation obtain it is some not with coordinate system change and becomeThe scalar of change, common invariant has mark, characteristic value, Frobenius norm of magnetic gradient tensor etc., because magnetic gradient tensor is notVariable has the property not changed with the variation of coordinate system, therefore is very suitable for positioning of the mobile platform to target,Through becoming research hotspot both domestic and external.
Summary of the invention
The technical problem to be solved by the present invention is to propose a kind of locating magnetic objects method suitable for mobile platform.InstituteMethod is proposed using the position vector and the smallest characteristic value pair of magnetic gradient tensor matrix absolute value of measurement point and magnetic target formationThe vertical relation between feature vector answered, solves magnetic target position.Since this vertical relation is by gradient tensorInvariant is derived from, therefore mentioned localization method has the advantage not changed with coordinate system, is suitable for mobile platform.
The present invention is achieved by the following technical solutions: a kind of locating magnetic objects method, magnetic target A contain ferromagneticProperty substance, be magnetized in earth magnetic field, generate magnetic field.Cartesian coordinate system is established centered on carrier, magnetic target A is located atP0Point has any one measurement point P in the magnetic field of magnetic target A1Point, P1It puts and is the position vector between magnetic target Ar1。
Measure P1The gradient tensor G of point1, and solve the characteristic value of this gradient tensor matrix, take wherein absolute value it is the smallestThe corresponding feature vector of characteristic value is V1.Because of position vector and the smallest feature of absolute value that measurement point and magnetic target are formedIt is vertical to be worth corresponding feature vector, can obtain
V1·r1=0 (1)
By O, P0、P1Space geometry relationship, it is available using vector operation:
It is available afterwards to bring the equation in (2) formula into (1):
(3) feature vector V in formula1It can be obtained by measurement, vectorIt is known that position vector r can be expressed as (x0,y0,z0).Therefore formula (3) is the ternary homogeneous linear equations for containing only unknown vector r.
During actual measurement, inevitably there is error.Firstly, the measurement of magnetic gradient tensor element is used based on micro-Point difference approximation Equivalent Calculation, will lead to the feature vector of solution, there are errors.Then, sensor array structure installation is inclinedDifference, measures noise, and carrier magnetic interference etc. can equally impact calculating.Therefore, measurement point P1Point is formed with magnetic target APosition vector feature vector corresponding with the gradient tensor the smallest characteristic value of matrix absolute value being calculated be not absolutely hang downDirectly,It is approximately equal toIt solvesThe minimum value of absolute value could accurately obtain x0,y0,z0。To solve this problem, it enablesConstruct objective function are as follows:
F=max (| f1|) (4)
Using optimization algorithm to x in formula (4)0,y0And z0It optimizes, so that f is minimum, obtained x at this time0,y0And z0Value be magnetic target A position.The optimization algorithm of solution formula (4) is needed exist for using heuristic value, wherein grainIt is best that subgroup optimization algorithm solves effect.
When concrete application, n measurement point P is selected in the magnetic field of magnetic target A1、P2、……PnMeasure magnetic target A'sMagnetic gradient tensor, gets f1、f2、……fn, building objective function f=max (| f1|,|f2|……|fn|), the magnetism acquiredThe position of target A is more acurrate.Measurement point is more, and it is more accurate that the location parameter of magnetic target A solves, and measurement point is fewer, magnetic meshThe location parameter solution for marking A is faster.
A kind of locating magnetic objects method of the present invention, has the following beneficial effects: compared with prior art
1. the present invention need to only measure the magnetic gradient tensor of 1 position, solution procedure is simple, and solving speed is fast, and convenient for realIt applies.
2. localization method of the invention, because being derived from using magnetic gradient tensor data, it is possible in ground magnetic environmentMiddle application, and solving result is unique.
3. localization method of the invention is derived from, not by coordinate using the feature vector of magnetic gradient tensor Matrix SolvingIt is the influence of transformation, can be applied to mobile platform.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show belowThere is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only thisSome embodiments of invention for those of ordinary skill in the art without creative efforts, can be withIt obtains other drawings based on these drawings.
Fig. 1 is the space schematic diagram of locating magnetic objects Method And Principle of the present invention.
Fig. 2 is cross magnetic gradient Tensor measuring system.
Fig. 3 particle swarm optimization algorithm effect picture.
The time of Fig. 4 particle swarm optimization algorithm consumption and optimal solution schematic diagram.
Specific embodiment
To make the object, technical solutions and advantages of the present invention clearer, technical solution of the present invention will be carried out belowDetailed description.Obviously, the described embodiment is only a part of the embodiment of the present invention, instead of all the embodiments.It is based onEmbodiment in the present invention, those of ordinary skill in the art without making creative work it is obtained it is all itsIts embodiment belongs to the range that the present invention is protected.
Technical solution of the present invention is described in detail with reference to the accompanying drawing.
Embodiment 1
Cross magnetic gradient Tensor measuring system is denoted as respectively as shown in Fig. 2, there is 4 three axis fluxgate magnetometers in figure1,2,3,4, wherein 2 and 4 center passes through x-axis, the centre distance between the two is also that the center that parallax range is L, 1 and 3 passes through yAxis, the parallax range of the two are also L.Cartesian coordinate system is established using measuring system center as origin, three of vector magnetic meterAxis is consistent with three axis directions of coordinate system.
Magnetic target A is located at P0Point, coordinate are (x0,y0,z0).Take measurement point P1For cross magnetic gradient Tensor measuring systemCenter is origin, then P1Point coordinate is (0,0,0).Coordinate origin is to magnetic target P0The position vector of point is r, then P1Point arrives magneticThe position vector of property target is
P1The corresponding feature vector of the point the smallest characteristic value of gradient tensor matrix absolute value is V1.Utilize measurement point and magnetismThe position vector feature vector corresponding with the smallest characteristic value of measurement point gradient tensor matrix absolute value that target is formed is approximate to hang downStraight relationship can construct following equation: f in measurement point1=V1·(x0,y0,z0).Then objective function be f=max (| f1|)。Objective function f is optimized by heuristic value, f obtains corresponding x when minimum value0,y0,z0As magnetic targetPosition.
Embodiment 2: how objective function is solved
After the completion of objective function building, selects reasonable algorithm to be solved and be also very important.By testing, weIt was found that target function type (4) needs to be solved using heuristic value.And with population in heuristic valueIt is best that optimization algorithm solves effect.Here it is illustrated by taking the objective function f that embodiment 1 constructs as an example.
One kind that PSO algorithm belongs to heuristic value is similar with simulated annealing, it is also from solving at randomHair finds optimal solution by iteration, it is also the quality that solution is evaluated by fitness, it is arrived most by following current searchThe figure of merit finds global optimum.This algorithm is realized with it to be easy, precision height, restrains the advantages that fast, in solving practical problemsIllustrate its superiority.
L takes 0.5m, sensor accuracy 0.1nT.Magnetic target location A be (- 30,20,30), magnetic away from amplitude be 1 ×104Am2, magnetic takes away from the azimuth in directionInclination angle takesAssuming that the magnetic field of the earth is 5 × 104NT, geomagnetic inclination take 50 degree,Geomagnetic declination takes -10 degree.In these cases, the objective function f solved to embodiment 1 is optimized.Particle swarm optimization algorithmEffect of optimization it is as shown in Figure 3.The position coordinates that optimization algorithm solves the time and solution that use are as shown in Figure 4.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, anyThose familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all containLid is within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.