CN109975879A - A kind of magnetic dipole method for tracking target based on array of magnetic sensors - Google Patents
A kind of magnetic dipole method for tracking target based on array of magnetic sensors Download PDFInfo
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Abstract
Present disclose provides a kind of magnetic dipole method for tracking target based on array of magnetic sensors, which comprises step 1, establish dipole model of magnetic, the state variable of the magnetic dipole is determined according to the model；Step 2, according to the state variable, the motion state equation and observational equation of the magnetic dipole are obtained；Step 3, obtain the real-time residual quantity magnetic field in sensor array measurement magnetic field, Random Discrete sample point is generated by the method for Monte Carlo, bring the sample point into the motion state equation and the observational equation, it obtains mean value and covariance is estimated, complete the calculating of Kalman filtering gain and the update of state variable.
Description
Technical field
This disclosure relates to a kind of magnetic dipole method for tracking target based on array of magnetic sensors.
Background technique
With the Persisting exploitation of marine resources, sea area equity with border on the sea safety by countries in the world extensive concern with
Pay attention to, research fast and efficiently invades object detection and recognition method, borders on the sea defence capability with important military affairs for raising
Meaning.Magnetic spy survey technology is a kind of passive detection technology, because its can effectively make up acoustics near field, coastal waters detection it is insufficient by
To extensive concern both domestic and external.The magnetic anomaly regular signal around interesting target body is acquired by sensor array, it is emerging to obtain
The electromagnetic signature of interesting target, and then realize the identification of target and quickly position and track that there is important researching value.
The positioning of magnetic target and the most common method of tracking include two major classes: optimum position algorithm and filtering algorithm.Its
In, optimum position algorithm is typically established in more observation data basis, such as sensor network, magnetic gradient tensor system or
Person's boat magnetic flight survey line etc., by optimum estimation algorithm to obtain the characteristic parameters such as target position, magnetic moment.Filter tracking is calculated
Method is typically based on sensor array test constantly moving target magnetic field data, with realize to the real-time tracking of magnetic objective body with
State estimation, the extensive pass since good tracking performance is in the real-time the advantages that, by domestic and foreign scholars and researcher
Note.
But following problems exist in the prior art in researcher: in the past using sensor array to magnetic dipole specific item
The algorithm research of mark tracking concentrates on the nonlinear model adaptability of optimization algorithm, mainly leads in terms of inhibiting geomagnetic noise
Cross gradient system completion.Although magnetic gradient system can be very good to inhibit geomagnetic noise, but be limited by that baseline is too short, magnetic is terraced
Decay the factors such as fast for degree field, and magnetic gradient system is not suitable for the remote tracking with target.
It simultaneously include target magnetic anomaly in sensors measure magnetic fields when magnetic dipole target is close to array of magnetic sensors
Field and background earth's magnetic field.The prior art generally passes through the remote reference sensor method of setting, is sensed using reference sensor and measurement
The spatial coherence in earth's magnetic field between device, eliminate measurement magnetic field in earth magnetism background, obtain target magnetic anomaly field, i.e., by compared with
Reference sensor is set up in remote position, reference sensor only measure background and remaining sensor array at the same measure background with
The magnetic anomaly regular signal of target, in this way by handling to realize the purpose for eliminating the magnetic anomaly regular signal that background magnetic field obtains target.
However, there is two apparent defects for the method based on reference Magnetic Sensor: first, reference sensor and measurement sensor
Between distance be difficult to hold, when being closer, reference sensor be easy influenced by target magnetic anomaly, cause measure magnetic anomaly produce
Raw error；When the two distance farther out when, correlation decline between sensor causes the elimination of earth magnetism ambient field to be not thorough.Second,
Reliable ground magnetic environment is needed at the setting of reference sensor, with other magnetic disturbance sources are not influenced by the external world during guaranteeing work.
In addition, geomagnetic noise can also be effectively avoided by constructing magnetic gradient tensor system, however the decaying of magnetic gradient field is compared with magnetic couple
Pole subfield faster, is not appropriate for Long Range Target Tracking.
Summary of the invention
Present disclose provides a kind of magnetic dipole method for tracking target based on array of magnetic sensors, which comprises
Step 1, dipole model of magnetic is established, the state variable of the magnetic dipole is determined according to the model；Step 2, according to described
State variable obtains the motion state equation and observational equation of the magnetic dipole；Step 3, sensor array measurement is obtained
The real-time residual quantity magnetic field in magnetic field generates Random Discrete sample point by the method for Monte Carlo, brings the sample point into institute
State motion state equation and the observational equation, obtain mean value and covariance is estimated, complete the calculating of Kalman filtering gain with
The update of state variable.
Detailed description of the invention
In order to which the disclosure and its advantage is more fully understood, referring now to being described below in conjunction with attached drawing, in which:
Fig. 1 diagrammatically illustrates the magnetic dipole target following based on array of magnetic sensors of embodiment of the present disclosure offer
The method flow diagram of method；
Fig. 2 diagrammatically illustrates the magnetic dipole target following based on array of magnetic sensors of embodiment of the present disclosure offer
The method flow diagram of step 3 in method；
Fig. 3, which is diagrammatically illustrated, emulates magnetic dipole motion profile figure in the simulated example of embodiment of the present disclosure offer；
Fig. 4 A is diagrammatically illustrated in embodiment of the present disclosure offer simulated example and is emulated magnetic dipole in X-coordinate axial projection
Motion profile figure；
Fig. 4 B is diagrammatically illustrated in embodiment of the present disclosure offer simulated example and is emulated magnetic dipole in Y-coordinate axial projection
Motion profile figure；
Fig. 4 C is diagrammatically illustrated in embodiment of the present disclosure offer simulated example and is emulated magnetic dipole in Z coordinate axial projection
Motion profile figure；
Fig. 5 A diagrammatically illustrates the measurement magnetic field three-component in embodiment of the present disclosure offer simulated example at sensor 1；
Fig. 5 B diagrammatically illustrates x-component in the magnetic gradient field in embodiment of the present disclosure offer simulated example at sensor 1
Gradient of the magnetic field in x direction gradient, y-component field in y direction gradient and z-component field in the direction z；
Fig. 5 C diagrammatically illustrates the embodiment of the present disclosure and provides the residual quantity magnetic field of sensor 1,2 in simulated example；
Fig. 6 diagrammatically illustrates the motion profile figure of magnetic dipole in the embodiment of the present disclosure 1；
Fig. 7 A diagrammatically illustrates the error of X-coordinate axle projected footprint in the embodiment of the present disclosure 1；
Fig. 7 B diagrammatically illustrates the error of Y-coordinate axle projected footprint in the embodiment of the present disclosure 1；
Fig. 7 C diagrammatically illustrates the error of Z coordinate axial projection track in the embodiment of the present disclosure 1；
Fig. 8 diagrammatically illustrates the magnetic dipole target following based on array of magnetic sensors of embodiment of the present disclosure offer
The block diagram of system；
Fig. 9 diagrammatically illustrates the magnetic dipole target following based on array of magnetic sensors of embodiment of the present disclosure offer
The flow chart of step 3 in method.
Specific embodiment
Hereinafter, will be described with reference to the accompanying drawings embodiment of the disclosure.However, it should be understood that these descriptions are only exemplary
, and it is not intended to limit the scope of the present disclosure.In the following detailed description, to elaborate many specific thin convenient for explaining
Section is to provide the comprehensive understanding to the embodiment of the present disclosure.It may be evident, however, that one or more embodiments are not having these specific
It can also be carried out in the case where details.In addition, in the following description, descriptions of well-known structures and technologies are omitted, with
Avoid unnecessarily obscuring the concept of the disclosure.
Term as used herein is not intended to limit the disclosure just for the sake of description specific embodiment.It uses herein
The terms "include", "comprise" etc. show the presence of the feature, step, operation and/or component, but it is not excluded that depositing
Or add other one or more features, step, operation or component.
One embodiment of the disclosure provides a kind of magnetic dipole method for tracking target based on array of magnetic sensors,
Referring to Fig. 1, the method includes the steps the contents of 1~step 3:
Step 1, dipole model of magnetic is established, the state variable of the magnetic dipole is determined according to the model.
When the detection range of magnetic target body is greater than 3 times of its own size, objective body can be equivalent to magnetic dipole,
Magnetic dipole Vector Magnetic Field expression formula such as following formula.
In formula, μ0For permeability of free space, m is the total magnetic moment vector of objective body, r between target and sensor away from
From vector, r is the amplitude of distance vector r.
After coordinate system is established, magnetic dipole Vector Magnetic Field be can be written as such as 1 matrix form of formula.
Wherein, x0, y0, z0For the coordinate of the vector magnetic meter in three-dimensional system of coordinate, x, y, z is the magnetic in three-dimensional system of coordinate
The coordinate of dipole；Bx, By, BzProjection components for magnetic dipole magnetic vector in 3-D walls and floor, and mx, my, mzIt represents
For magnetic dipole magnetic moment vector in the projection components of three-dimensional coordinate reference axis, r is the distance between magnetic dipole and sensor vector
Amplitude, μ0For permeability of free space.Target is uniquely depended on for the magnetic field that any magnetic dipole target generates and is passed
The relative position of sensor and the magnetic moment of magnetic dipole.It is determined by independent six variables.
When sensor measures in ground magnetic environment, measurement magnetic field can be expressed as magnetic dipole anomalous field with
The stacking pattern in background earth's magnetic field such as following formula.
Bm=B+Be (13)
Wherein, Bm, B, BeRespectively represent total magnetic field, target magnetic anomaly field and the geomagnetic fieldvector at sensor.
Step 2, according to the state variable, the motion state equation and observational equation of the magnetic dipole are obtained.
According to dipole model of magnetic, the state variable of target is made of two parts during the tracking of target: description
The location parameter and speed parameter of target state；The magnetic moment parameter of target magnetism is described.Therefore described in time t moment
State variable is indicated by the vector expression of following state variables:
xt=[x (t), y (t), z (t), vx(t), vy(t), vz(t), mx(t), my(t), mz(t)] (2)
Wherein, x (t), y (t), z (t) respectively indicate t moment magnetic dipole in the direction x, the position in the direction y and the direction z,
vx(t), vy(t), vz(t) t moment magnetic dipole is respectively indicated in the direction x, the speed in the direction y and the direction z, mx(t), my(t),
mz(t) t moment magnetic dipole is respectively indicated in the direction x, the magnetic moment in the direction y and the direction z.
In view of the targets such as practical surface vessel and submarine navigation device move relatively slow, situations such as state is relatively stable,
The motion state that magnetic dipole target can be described with constant-velocity model, can satisfy real work demand.Target movement is described
State equation can be expressed as follows formula 14.
X (t)=x (t- Δ t)+Δ tvx(t-Δt)
Y (t)=y (t- Δ t)+Δ tvy(t-Δt)
Z (t)=z (t- Δ t)+Δ tvz(t-Δt)
vx(t)=vx(t-Δt) (14)
vy(t)=vy(t-Δt)
vz(t)=vz(t-Δt)
For the magnetic moment parameter of target, when posture changes in magnetic dipole target motion process, magnetic moment can also be sent out
Raw corresponding change, it is contemplated that magnetic dipole attitude motion state is unable to estimate and short time relatively stable etc. factors, Ke Yiyong
Permanent magnetic moment state equation is expressed as follows formula 15.
mx(t)=mx(t-Δt)
my(t)=my(t-Δt) (15)
mz(t)=mz(t-Δt)
According to the position parameter of target and magnetic moment parameter, the magnetic anomaly field at different sensors position can be obtained, when making
When measuring magnetic field with 3 magnetic field vector sensors, measurement field can be expressed asTherefore t moment
Observation output quantity z, observation output quantity is magnetic field value that sensor array is listed in actual observation in object tracking process, can be with
It is expressed as follows formula 16.
zt=[bx1(t), by1(t), bz1(t), bx2(t), by2(t), bz2(t), bx3(t), by3(t), bz3(t)] (16)
Wherein, bx1(t), by1(t), bz1(t) survey of the first sensor in X-direction, Y-direction and Z-direction is respectively indicated
Measure field, bx2(t), by2(t), bz2(t) measurement field of the second sensor in X-direction, Y-direction and Z-direction, b are respectively indicatedx3
(t), by3(t), bz3(t) measurement field of the 3rd sensor in X-direction, Y-direction and Z-direction is respectively indicated.
It can to sum up obtain, the state equation in magnetic dipole object tracking process is linear；And observational equation is non-linear
's.
Step 3, the real-time residual quantity magnetic field for obtaining sensor array measurement magnetic field, by the method for Monte Carlo generate with
Machine discrete sample point brings the sample point into the motion state equation and the observational equation, obtains mean value and covariance
The calculating of Kalman filtering gain and the update of state variable are completed in estimation.
In a kind of feasible mode, referring to fig. 2 and Fig. 9, the step 3 can be with 301- steps through the following steps
305 are realized, the method for step 3 is Monte Carlo kalman filter method, specifically:
Step 301, Initialize installation is carried out to Kalman filter, the state variable and its covariance is carried out just
Beginningization.
Define original state variable x0For 9 × 1 dimensional vectors；Initialize covarianceFor 9 × 9 matrixes,
x0=[x (0), y (0), z (0), vx(0), vy(0), vz(0), mx(0), my(0), mz(0)] (3)
Wherein, (0) x, y (0), z (0) are to be respectively magnetic dipole in the direction x, the position initial value in the direction y and the direction z；
vX(0), vy(0), vzIt (0) is magnetic dipole in the direction x, the velocity original value in the direction y and the direction z；mx(0), my(0), mz(0)
It is magnetic dipole in the direction x, the magnetic moment initial value in the direction y and the direction z.
Step 302, N number of sample point is generated at random according to monte carlo method, according to the sample point and the magnetic dipole
The motion state equation of son obtains state variable mean prediction and the covariance prediction of state variable.
It generates N number of sample point at random according to monte carlo method, is I=1,2 ..., N, sample point weight wi=1/N, i=1,2 ..., N；
Obtain the state variable mean prediction value x at n momentn|n-1Are as follows:
Obtain the covariance predicted value of the state variable at n momentAre as follows:
Wherein, c (i)~N (c；0, I), i=1,2 ..., N；Xn-1/n-1For the state variable mean value at n-1 moment, Dn-1|n-1
For the variable standard deviation at n-1 moment,N=2,3,4 ...；For the magnetic dipole
Motion state equation；Q is the covariance matrix of variable random error in state migration procedure.
Q value sets the random distribution for allowing for state variable, will lead to the error of tracking when Q value estimates bigger than normal
Increase, and tracking velocity is slack-off so that it cannot adapt to the randomness variation of target when Q value estimates less than normal.The disclosure is implemented
In example: Q value is 0.01*diag ([1 11 0.01 0.01 0.01 11 1])；Assume the random of variable position x, y, z
Distribution standard deviation is 0.1m, and speed vX、vy、vzThe random distribution standard deviation of variable is 0.01m/s, magnetic moment mx、my、 mzWith
Machine distribution standard deviation is 0.1Am2。
Step 303, N number of sample point is generated at random according to monte carlo method, according to the sample point, the magnetic dipole
The motion state equation and observational equation of son obtain observed quantity mean prediction, the prediction of observed quantity covariance, observed quantity and state
The cross covariance of variable is predicted.
It generates N number of sample point at random according to monte carlo method, is I=
0,1,2 ..., N, sample point weight wi=1/N, i=1,2 ..., N；
Obtain the observed quantity mean prediction value z at n momentn|n-1Are as follows:
Obtain the observed quantity covariance predicted value at n momentAre as follows:
Obtain the observed quantity at n moment and the cross covariance predicted value of state variableAre as follows:
Wherein: where c (i)~N (c；0, I), i=1,2 ..., N；Dn-1|n-1For the variable standard deviation at n-1 moment,
Xn-1/n-1For the state variable mean value at n-1 moment, xn|n-1For the state variable mean prediction value at n moment；N=2,3,4 ...；For the motion state equation of the magnetic dipole；For the observational equation of the magnetic dipole；R measures noise covariance matrix.
Noise covariance matrix R is measured, is determined by the sensor noise level used during actual tracking, in this public affairs
It opens in embodiment: assuming that the noise level of sensor is 1e-10(RMS), therefore corresponding observation covariance be R value is 1e-20*
diag([1 1 1 1 1 1])。
Step 304, it is predicted by the cross covariance of observed quantity covariance prediction, the observed quantity and state variable,
Calculate Kalman filtering gain estimation；Using the observed quantity mean prediction, Kalman filtering gain estimation with it is real-time poor
Magnetic field is measured, state variable mean value and its covariance matrix are updated.
K is estimated in the Kalman filtering gainnAre as follows:
The state variable mean value x at the n momentn|nAre as follows: xn|n=xn|n-1+Kn(zn-zn|n-1) (10)
The covariance matrix at the n momentAre as follows:
Wherein,For the observed quantity covariance predicted value at n moment,For the observed quantity and state variable at n moment
Cross covariance predicted value, xn|n-1For the state variable mean prediction value at n moment；zn|n-1For the observed quantity mean prediction at n moment
Value,For the covariance predicted value of the state variable at n moment；
ZnFor the residual quantity magnetic field that the n moment measures, can be indicated by following formula:
zn=[bx1(n)-bx2(n), by1(n)-by2(n), bz1(n)-bz2(n), bx2(n)-bx3(n), by2(n)-by3(n),
bz2(n)-bz3(n)]
Wherein, bx1(n), by1(n), bz1(n) n moment first sensor is respectively indicated in X-direction, the direction Y and Z-direction
Measurement field, bx2(n), by2(n), bz2(n) survey of the n moment second sensor in X-direction, Y-direction and Z-direction is respectively indicated
Measure field, bx3(n), by3(n), bz3(n) measurement of the n moment 3rd sensor in X-direction, Y-direction and Z-direction is respectively indicated
?.
The state variable mean value x at n momentn|nThe state variable as updated.
It should be noted that the embodiment of the present disclosure uses the acquisition in residual quantity magnetic field, it is to calculate to eliminate earth magnetism back by residual quantity
Scape, but synchronous signal also becomes target in the difference of sensor magnetic anomaly, and and non-primary observation magnetic anomaly) both guarantee to measure
In the process not by the interference in earth's magnetic field, and avoid the problem that the setting of reference sensor.
Below by simulated example, illustrates magnetic dipole residual quantity magnetic field and measure the characteristic of field and gradient magnetic.Emulate magnetic
As shown in figure 3, wherein black circles represent measurement magnetic field sensor, the magnetic moment for emulating magnetic dipole is fixed for dipole movement track
For [10,20,30] Am2.Magnetic dipole three coordinate axial projections motion profile such as Fig. 4 A, 4B, it is therein shown in 4C
Wave employs the oscillatory during simulating actual motion.
Two sensors measure magnetic fields such as Fig. 5 A, 5B, shown in 5C, the wherein measurement magnetic field three at Fig. 5 A representative sensor 1
Component, wherein three exemplary components in the magnetic gradient field at Fig. 5 B representative sensor 1, are followed successively by x-component magnetic field in the direction x
The gradient of gradient, y-component field in y direction gradient and z-component field in the direction z, the residual quantity magnetic field of Fig. 5 C representative sensor 1,2.
By Fig. 5 A, 5B, 5C as it can be seen that residual quantity magnetic field and sensor original measurement magnetic field on magnetic anomaly range value quite, and
Gradient magnetic is minimum.Therefore, when carrying out target following using residual quantity magnetic field, theoretically have identical as original measurement magnetic field
Tracking performance；And compared with using magnetic gradient field tracking, then there is farther detection range.
Step 305, the state variable mean value and its covariance matrix of the update are stored, return step 302 into
The update of row subsequent time state variable.
The process is iterative filtering process, and the estimation of the moment state variable is exported by the observational variable at each moment,
And its estimation (covariance matrix) of probability distribution, it is prepared, is led to by the state variable estimation that these variables are subsequent time
Cross the state variable x of step 304 updaten|nThe state variable mean value at n-1 moment (last moment) is become after return step 302
Xn-1/n-1。
Come below by a specific embodiment 1 to the effect for carrying out magnetic dipole tracking using disclosed method
It is illustrated:
Embodiment 1: emulation magnetic dipole tracking test
The motion profile of magnetic dipole is as shown in Figure 6；For realizing target following vector magnetic meter altogether there are three, sit
Mark is respectively (- 2m, 0,0), and (0,0,0), (2m, 0,0) is successively labeled as sensor 1,2,3.Pass through sensor 1,2 and sensing
Device 2,3 obtains residual quantity magnetic field bx1, by1, bz1 and bx2, by2, bz2 respectively.It is white that random Gaussian is superimposed on original residual quantity field
The system noise of noise simulation real work, the standard deviation of noise are 100pT.The residual quantity magnetic obtained using observation magnetic-field component
Are as follows:
zn=[bx1(n)-bx2(n), by1(n)-by2(n), bz1(n)-bz2(n), bx2(n)-bx3(n), by2(n)-by3(n),
bz2(n)-bz3(n)]
Kalman filtering (Extended Kalman Filter, EKF), Unscented kalman filtering is respectively adopted
Monte Carlo kalman filter method (the Monte that (Unscented Kalman Filter, UKF) and the disclosure propose
Carlo Kalman Filter, MCKF), realize magnetic dipole object real-time tracking.For the tracking for more preferably assessing algorithms of different
Performance, using 100 random experiments, using the assembly average of tracking error as judging quota.The emulation experiment of algorithms of different
Error result is as shown in Fig. 7 A, 7B, 7C, and wherein Fig. 7 A is the error of x coordinate axial projection track, and wherein Fig. 7 B is y-coordinate axis
The error of projected footprint, wherein Fig. 7 C is the error of z coordinate axial projection track.
Can be seen that EKF and UKF from Fig. 7 A, 7B, 7C has a similar tracking effect, the initial stage tracking effect of MCKF compared with
Difference, and later period tracking effect is substantially better than the tracking result of EKF/UKF.For qualitative, MCKF is in convergence rate compared with EKF/
UKF is slower, but after stablizing on tracking effect tracking accuracy highest.For quantitative analysis algorithms of different tracking performance, by three kinds
The tracking error calculating of tracking is enumerated as shown in table 1 (a), table 1 (b), table 1 (c).
Table 1 (a) x direction projection track following mean error (m)
Table 1 (b) y direction projection track following mean error (m)
Table 1 (c) z direction projection track following mean error (m)
It is listed in different time intervals in table 1, the tracking error average value of three direction projection tracks, wherein table 1
It (a) is the direction x, table 1 (b) is the direction y, and table 1 (c) is the direction z.From table 1 (a), table 1 (b) it can be seen that MCKF algorithm and EKF/
UKF algorithm is compared, and tracking error is larger in the 1-40 point at tracking initial stage, and then MCKF tracking error connects in 40-80 point
Be bordering on EKF/UKF as a result, stablize after 80-200 point in, the tracking accuracy of MCKF is substantially better than remaining two kinds of track algorithm；Table
1 (c) the result shows that, the MCKF tracking error in z direction projection track is suitable with EKF/UKF algorithm.In conclusion MCKF with
Track algorithm is slower than EKF/UKF algorithm in response speed, and MCKF algorithm is better than traditional in tracking accuracy after stabilization
EKF/UKF track algorithm.
In conclusion the beneficial effect of the disclosure includes but is not limited to:
(1) method of disclosure is simple, practical, and the dry of earth magnetism background in magnetic dipole object tracking process can be effectively suppressed
It disturbs.
(2) the more traditional magnetic gradient method of the method for the present invention, target following apart from it is upper advantageously.
(3) the Monte Carlo kalman filter method MCKF magnetic dipole tracking proposed in the present invention is more traditional
EKF, UKF magnetic dipole tracking tracking accuracy are higher.
In addition, another embodiment of the disclosure additionally provide a kind of magnetic dipole target based on array of magnetic sensors with
Track system, referring to Fig. 8, the system 800 comprises determining that state variable module 801, for establishing dipole model of magnetic, according to
The model determines the state variable of the magnetic dipole；State equation and observational equation module 802 are obtained, for according to institute
State variable is stated, the motion state equation and observational equation of the magnetic dipole are obtained；State variable update module 803,
For obtaining the real-time residual quantity magnetic field in sensor array measurement magnetic field, Random Discrete sample is generated by the method for Monte Carlo
Point brings the sample point into the motion state equation and the observational equation, obtains mean value and covariance is estimated, complete
The calculating of Kalman filtering gain and the update of state variable.
It will be understood by those skilled in the art that the feature recorded in each embodiment and/or claim of the disclosure can
To carry out multiple combinations or/or combination, even if such combination or combination are not expressly recited in the disclosure.Particularly, exist
In the case where not departing from disclosure spirit or teaching, the feature recorded in each embodiment and/or claim of the disclosure can
To carry out multiple combinations and/or combination.All these combinations and/or combination each fall within the scope of the present disclosure.
Although the disclosure, this field skill has shown and described referring to the certain exemplary embodiments of the disclosure
Art personnel are it should be understood that the spirit and scope of the present disclosure limited without departing substantially from the following claims and their equivalents the case where
Under, a variety of changes in form and details can be carried out to the disclosure.Therefore, the scope of the present disclosure should not necessarily be limited by above-mentioned reality
Example is applied, but should be not only determined by appended claims, is also limited by the equivalent of appended claims
It is fixed.
Claims (10)
1. a kind of magnetic dipole method for tracking target based on array of magnetic sensors, which is characterized in that the described method includes:
Step 1, dipole model of magnetic is established, the state variable of the magnetic dipole is determined according to the model；
Step 2, according to the state variable, the motion state equation and observational equation of the magnetic dipole are obtained；
Step 3, the real-time residual quantity magnetic field for obtaining sensor array measurement magnetic field generates Random Discrete by the method for Monte Carlo
Sample point brings the sample point into the motion state equation and the observational equation, obtains mean value and covariance is estimated, complete
At the calculating of Kalman filtering gain and the update of state variable.
2. the method according to claim 1, wherein the dipole model of magnetic includes:
When the detection range of magnetic target body is greater than 3 times of its own size, objective body can be equivalent to magnetic dipole, magnetic dipole
Sub-vector magnetic field matrix expression is as follows:
Wherein, x0, y0, z0For the coordinate of the vector magnetic meter in three-dimensional system of coordinate, x, y, z is the magnetic dipole in three-dimensional system of coordinate
The coordinate of son；Bx, By, BzProjection components for magnetic dipole magnetic vector in 3-D walls and floor, and mx, my, mzRepresent magnetic couple
For extremely sub- magnetic moment vector in the projection components of three-dimensional coordinate reference axis, r is the width of the distance between magnetic dipole and sensor vector
Degree, μ0For permeability of free space.
3. the method according to claim 1, wherein the vector table that the state variable passes through following state variables
It is indicated up to formula:
xt=[x (t), y (t), z (t), vx(t), vy(t), vz(t), mx(t), my(t), mz(t)] (2)
Wherein, x (t), y (t), z (t) respectively indicate t moment magnetic dipole in the direction x, the position in the direction y and the direction z, vx(t),
vy(t), vz(t) t moment magnetic dipole is respectively indicated in the direction x, the speed in the direction y and the direction z, mx(t), my(t), mz(t) divide
Not Biao Shi t moment magnetic dipole in the direction x, the magnetic moment in the direction y and the direction z.
4. the method according to claim 1, wherein the motion state equation of the magnetic dipole is linear side
Journey.
5. the method according to claim 1, wherein the observational equation of the magnetic dipole is nonlinear equation.
6. the method according to claim 1, wherein the step 3 includes:
Step 301, Initialize installation is carried out to Kalman filter, the state variable and its covariance is initialized；
Step 302, N number of sample point is generated at random according to monte carlo method, according to the sample point and the magnetic dipole
Motion state equation obtains state variable mean prediction and the covariance prediction of state variable；
Step 303, N number of sample point is generated at random according to monte carlo method, according to the fortune of the sample point, the magnetic dipole
Dynamic state equation and observational equation obtain the mutual of observed quantity mean prediction, the prediction of observed quantity covariance, observed quantity and state variable
Covariance prediction；
Step 304, it is predicted, is calculated by the cross covariance of observed quantity covariance prediction, the observed quantity and state variable
Kalman filtering gain estimation；Utilize the observed quantity mean prediction, Kalman filtering gain estimation and real-time residual quantity magnetic
, update state variable mean value and its covariance matrix；
Step 305, the state variable mean value and its covariance matrix of the update are stored, return step 302 carries out down
The update of one moment state variable.
7. according to the method described in claim 6, it is characterized in that, the step 301 includes: to define original state variable x0It is 9
× 1 dimensional vector；Initialize covarianceFor 9 × 9 matrixes,
x0=[x (0), y (0), z (0), vx(0), vy(0), vz(0), mx(0), my(0), mz(0)] (3)
Wherein, (0) x, y (0), z (0) are to be respectively magnetic dipole in the direction x, the position initial value in the direction y and the direction z；vX(0),
vy(0), vzIt (0) is magnetic dipole in the direction x, the velocity original value in the direction y and the direction z；mx(0), my(0), mzIt (0) is magnetic dipole
Son is in the direction x, the magnetic moment initial value in the direction y and the direction z.
8. according to the method described in claim 6, it is characterized in that, the step 302 includes:
It generates N number of sample point at random according to monte carlo method, is Sample point weight wi=1/N, i=1,2 ..., N；
Obtain the state variable mean prediction value x at n momentn|n-1Are as follows:
Obtain the covariance predicted value of the state variable at n momentAre as follows:
Wherein, c (i)~N (c；0, I), i=1,2 ..., N；Xn-1/n-1For the state variable mean value at n-1 moment, Dn-1|n-1For n-1
The variable standard deviation at moment, For the magnetic dipole
Motion state equation；Q is the covariance matrix of variable random error in state migration procedure.
9. according to the method described in claim 6, it is characterized in that, the step 303 includes:
It generates N number of sample point at random according to monte carlo method, is Sample point weight wi=1/N, i=1,2 ..., N；
Obtain the observed quantity mean prediction value z at n momentn|n-1Are as follows:
Obtain the observed quantity covariance predicted value at n momentAre as follows:
Obtain the observed quantity at n moment and the cross covariance predicted value of state variableAre as follows:
Wherein, c (i)~N (c；0, I), i=1,2 ..., N；Dn-1|n-1For the variable standard deviation at n-1 moment, Xn-1/n-1When for n-1
The state variable mean value at quarter, xn|n-1For the state variable mean prediction value at n moment； For the motion state equation of the magnetic dipole；For the observational equation of the magnetic dipole；R measures noise covariance matrix.
10. according to the method described in claim 6, it is characterized in that, the step 304 includes:
K is estimated in the Kalman filtering gainnAre as follows:
The state variable mean value x at the n momentn|nAre as follows: xn|n=xn|n-1+Kn(zn-zn|n-1) (10)
The covariance matrix at the n momentAre as follows:
Wherein,For the observed quantity covariance predicted value at n moment,For the observed quantity at n moment and the mutual association of state variable
Variance predicted value, xn|n-1For the state variable mean prediction value at n moment；zn|n-1For the observed quantity mean prediction value at n moment,For the covariance predicted value of the state variable at n moment；ZnThe residual quantity magnetic field measured for the n moment.
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