CN116184512A - Vector sensor network real-time positioning method and system based on magnetic moment invariants - Google Patents
Vector sensor network real-time positioning method and system based on magnetic moment invariants Download PDFInfo
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Abstract
A vector sensor network real-time positioning method and system based on magnetic moment invariants belongs to the field of magnetic anomaly detection and solves the problems of low actual positioning performance, poor instantaneity and poor positioning accuracy of a traditional network positioning method. The technical key points of the invention are as follows: in distributed magnetic sensor network positioning, real-time magnetic field information observed by magnetic sensor nodes is inverted, and a method for constructing cost functions with fewer solving parameters is provided based on magnetic moment invariants, so that the parameters required to be solved are reduced. The invention is suitable for actual outdoor positioning scenes.
Description
Technical Field
The invention belongs to the field of magnetic anomaly detection, and particularly relates to the field of vector magnetic sensing network positioning.
Background
Since the magnetic permeability of ferromagnetic objects is higher than that of most media such as air, water, seawater, soil, etc., the geomagnetic field around them is disturbed, and Magnetic Anomaly Detection (MAD) is a method for detecting magnetic disturbance. Specifically, when there is relative movement between the sensor and the observed object, the voltage information output by the sensor contains magnetic field variation information of unknown object characteristics. This physical phenomenon allows the obtained magnetic anomaly signature to be an important clue to hidden target detection, localization, especially in cross-media detection scenarios.
The analysis of locating the target object based on the detection of magnetic anomalies adopts a vector magnetic sensing network mode at present, and the inversion algorithm is utilized to solve the problem based on the acquisition of magnetic anomaly information. With the recent trend of miniaturization and low cost of magnetic sensors, a large-scale application of sensor networks to detect targets has become possible. The traditional full-parameter positioning solution method is mostly applied to indoor scenes such as medicine, positioning is carried out through more than 5 sensor nodes, the arrangement positions of the sensors in outdoor scenes are often sparse randomly, and the actual positioning performance of the method is low. Meanwhile, under the condition that magnetic dipole equivalence is carried out by a magnetic anomaly signal source, 6 parameters, including 3 position quantities and 3 magnetic moment quantities, need to be solved in the positioning parameter inversion of the target object. The traditional full-parameter inversion algorithm solves the 6 parameters simultaneously, and has poor real-time performance and positioning accuracy. Therefore, the method has high positioning real-time performance and can be applied to actual outdoor positioning scenes under the sparse network condition.
For the construction of cost functions, the conventional inversion algorithm is a full parameter solution (APS), i.e., a method of constructing a cost function that includes 6 parameters (3 position quantities and 3 magnetic moment quantities). Therefore, the cost function F of the APS algorithm APS Can be defined as follows:
wherein the superscript e represents the estimate.
Since this strategy requires simultaneous solution of 6 parameters, it is at least necessary to construct a system of equations comprising 6 non-linear equations, i.e. at least two three-axis magnetic sensors can be used for the solution. However, the cost function is less time-efficient, and for this problem, the solution in the related literature is to improve the optimization algorithm, such as by a combination algorithm of PSO and LM, to improve performance. In addition, in order to obtain better positioning accuracy in practical application, such as a small-range capsule endoscope positioning tracking research, more than 5 triaxial sensors are used for positioning, namely, solving performance is improved by improving the information quantity of the magnetic sensors. However, this method is difficult to apply to real-time positioning applications of a wide range of sparse sensor node networks. The reason for this is that improving the optimization algorithm, increasing the number of sensors, etc. does not change the essence of the APS algorithm that requires a parameter search in a 6-dimensional solution space. Since there are a large number of extreme points in the solution space with high dimensionality, the solution is easy to trap into local extreme values. Therefore, the separation of the position quantity and the magnetic moment quantity, and the construction of the cost function under the low-dimensional solution space are key to improving the real-time positioning performance.
Disclosure of Invention
The invention provides a vector sensor network real-time positioning method and system based on magnetic moment invariants, which solve the problems of low actual positioning performance, poor real-time performance and poor positioning precision of the traditional network positioning method.
A vector sensor network real-time positioning method based on magnetic moment invariants, the method comprising:
establishing a positioning analysis model according to the target;
defining a cost function according to a magnetic moment consistency principle;
obtaining the position information of the target and the magnetic field information at the corresponding position point according to the model;
substituting the position information of the target and the magnetic field information at the corresponding position point into the cost function;
selecting an optimization solving algorithm according to the model to obtain a plurality of groups of magnetic moment solving and iteration of the target;
obtaining positioning information according to the difference of multiple groups of magnetic moment quantities;
and (3) averaging a plurality of groups of magnetic moment amounts according to the positioning information to obtain the magnetic moment amount of the target, thereby completing the vector sensor network real-time positioning method based on the magnetic moment invariants.
Further, the target is equivalent to an actually positioned target as a magnetic dipole, and the magnetic field is expressed as follows:
wherein μ0 ＝4π×10 -7 H/m is vacuum permeability, r= [ x, y, z]Representing the relative positional relationship between the magnetic dipole and the observation point, m= [ m ] x ,m y ,m z ]Is the magnetic moment of the target.
Further, the magnetic field is denoted b= kAm,
where k is the constant term μ 0 And/4 pi, A is a position vector matrix.
Further, the position vector matrix specifically includes:
further, the cost function is:
wherein ,
m xi e (i=1, 2, … n) is the estimated magnetic moment value of the x-axis, m, calculated for the ith sensor yi e and mzi e The estimated magnetic moment values for the ith sensor y-axis and z-axis, respectively.
Further, the variability of the plurality of sets of magnetic moment amounts is represented by a standard deviation function σ.
Further, the target magnetic moment is:
a computer device comprises a memory and a processor, wherein a computer program is stored in the memory, and when the processor runs the computer program stored in the memory, the processor executes the vector sensor network real-time positioning method based on magnetic moment invariants.
A computer readable storage medium for storing a computer program for executing the method for real-time positioning of a vector sensor network based on magnetic moment invariants.
The vector sensor network real-time positioning method based on the magnetic moment invariants can be realized by adopting computer software, so that the vector sensor network real-time positioning system based on the magnetic moment invariants is correspondingly also claimed and comprises the following steps:
modeling means for establishing a positioning analysis model from the target;
means for defining a cost function;
receiving means for obtaining position information of the object and magnetic field information at the corresponding position points;
the computing device is used for substituting the position information of the target and the magnetic field information at the corresponding position points into the cost function, selecting an optimization solving algorithm, and obtaining a plurality of groups of magnetic moment solving and iteration of the target;
and the computing device is used for obtaining positioning information according to the difference of the magnetic moment quantities, and obtaining a target magnetic moment quantity by averaging the magnetic moment quantities.
The invention has the beneficial effects that:
the vector sensor network real-time positioning method and system based on the magnetic moment invariants have higher solving speed and solving precision when carrying out positioning solving, have obvious improvement on positioning instantaneity and positioning accuracy compared with the traditional APS algorithm, and have greater significance in practical application. This advantage results from the construction of the cost function, which results in a reduction of the parameters of the required solution. After the parameters to be solved are reduced, the cost function solution space is optimized, and the positioning accuracy can be greatly improved. Through Monte Carlo simulation comparison, under the same condition particle swarm algorithm (100 search particles), the solving accuracy of the traditional algorithm is about 20%, 35% and 50% respectively in the solving time of 0.1s, 0.3s and 1.0s, and the solving accuracy of the method is about 30%, 95% and 99% respectively.
The invention is suitable for actual outdoor positioning scenes.
Drawings
FIG. 1 is a distributed sensor network observation model according to an embodiment;
fig. 2 is a flow chart of a real-time positioning method of a vector sensor network based on magnetic moment invariants according to the first embodiment and the second embodiment.
Detailed Description
Embodiment one: the present embodiment will be described with reference to fig. 1 and 2.
The embodiment of the method for positioning the vector sensor network in real time based on the invariant magnetic moment comprises the following steps:
establishing a positioning analysis model according to the target;
defining a cost function according to a magnetic moment consistency principle;
obtaining the position information of the target and the magnetic field information at the corresponding position point according to the model;
substituting the position information of the target and the magnetic field information at the corresponding position point into the cost function;
selecting an optimization solving algorithm according to the model to obtain a plurality of groups of magnetic moment solving and iteration of the target;
obtaining positioning information according to the difference information of multiple groups of magnetic moment amounts;
and (3) averaging a plurality of groups of magnetic moment amounts according to the positioning information to obtain the magnetic moment amount of the target, thereby completing the vector sensor network real-time positioning method based on the magnetic moment invariants.
Specifically:
as shown in figure 1, n magnetic sensors are adopted to form a distributed sensor network observation model, and magnetic anomaly detection is carried out on a targetMeasuring under the same observation coordinate system C, from the position s i Sensor observation network consisting of n triaxial magnetic sensors at (i=1, 2, … n). When there is a magnetic dipole at the p-point, the pass-through type
The magnetic field value under the observation coordinate system at each observation point can be known. Considering the randomness of the gestures of the vector sensors when the nodes are arranged, the rotation matrix R is used for representing the orientation of each three-axis sensor, and then the actual observation magnetic field of the ith sensor is obtained:
wherein Gi The geomagnetic field component observed by the ith sensor may be considered a constant for a short period of time, and may be removed by previous observations in subsequent signal processing; n (N) i The background noise is the corresponding observation; for the random attitude R of the sensor, the corresponding attitude of the sensor may be specified when the sensor is laid out or the corresponding attitude information may be acquired by equipping the attitude sensor.
Can be made without taking into account the observation noise N i The observation field is correspondingly preprocessed. Under the observation coordinate system C, the magnetic anomaly information of the ith sensor can be obtained by the following formula:
B i (m,r i )：
based on the model, inversion of the position and magnetic moment of the target object can be achieved according to the position information of the sensor and the preprocessed magnetic field information.
Observe FIG. 1 and formula
It can be known that, for different sensors, the magnetic moments of the magnetic dipoles are identical in the sensed magnetic anomaly information under the same coordinate system at the same moment, so that the magnetic moment information is taken as a known invariant, and a magnetic moment invariant MMI (Magnetic Moment Invariant) algorithm is proposed to reduce the search dimension of the magnetic positioning problem.
The magnetic moment invariant algorithm provided by the embodiment has higher solving speed and solving precision when carrying out positioning solving, and has obvious improvement on positioning instantaneity and positioning accuracy compared with the traditional APS algorithm.
Embodiment two: the present embodiment will be described with reference to fig. 2.
The present embodiment is a further illustration of the target in the vector sensor network real-time positioning method based on magnetic moment invariants in the first embodiment.
The object of this embodiment is to equate the positioning object to a magnetic dipole, the magnetic field is expressed as follows:
wherein μ0 ＝4π×10 -7 H/m is vacuum permeability, r= [ x, y, z]Representing the relative positional relationship between the magnetic dipole and the observation point, m= [ m ] x ,m y ,m z ]Is the magnetic moment of the target.
Specifically:
from the above equation, there is a nonlinear coupling relationship between the position quantity r and the magnetic moment m, which is difficult to translate
The cancellation process is performed to extract the independent position quantity r or magnetic moment quantity m, so that the localization problem is often attributed to an optimization solution problem. The solving flow of the whole method is shown in fig. 2, and it can be known that under the conditions of observation information and solving model confirmation, the key of target positioning solving is the construction of a cost function and the selection of a solving algorithm, which directly affects the solving speed and precision.
Embodiment III:
the present embodiment is a further illustration of the magnetic field representation in the vector sensor network real-time positioning method based on magnetic moment invariants described in the second embodiment.
The magnetic field according to the present embodiment is expressed as
B＝kAm，
Where k is the constant term μ 0 And/4 pi, A is a position vector matrix.
Specifically: the magnetic field representation described in this embodiment is first converted into the following form:
further simplified into
B＝kAm。
If the position information of the target object and the magnetic field information at the corresponding position point are known, the magnetic moment of the target object can be obtained as follows:
m＝A -1 B/k
embodiment four:
the present embodiment is a further illustration of the position vector matrix described in the vector sensor network real-time positioning method based on magnetic moment invariants described in the third embodiment.
The position vector matrix described in this embodiment is specifically:
fifth embodiment:
the present embodiment is a further illustration of the cost function described in the vector sensor network real-time positioning method based on magnetic moment invariants in the first embodiment.
The cost function described in this embodiment is:
wherein ,
m xi e (i=1, 2, … n) is the estimated magnetic moment value of the x-axis, m, calculated for the ith sensor yi e and mzi e The estimated magnetic moment values for the ith sensor y-axis and z-axis, respectively.
Specifically:
from the following components
m＝A -1 B/k
It can be seen that:
according to the analysis, the magnetic moment is defined as constant in the optimization problem, only the position quantity needs to be solved, and the solving parameters of the problem are reduced from 6 to 3, so that the cost function can be constructed by utilizing the MMI principle in the embodiment, the searching speed can be improved, and the complexity of the searching space can be reduced.
Embodiment six:
the present embodiment is a further illustration of the differences between the multiple sets of magnetic moment amounts in the vector sensor network real-time positioning method based on the magnetic moment invariants in the first embodiment.
The variability of the magnetic moment amounts of the plurality of groups described in this embodiment is represented by a standard deviation function sigma.
Specifically:
under the observation condition of the sensor network shown in fig. 1, a certain estimated position p e Can obtain n groups of magnetic moment values m 1 e ,m 2 e ,…m n e . According to MMI principle, p is theoretically e For correct estimation, there is m 1 e ＝m 2 e ,…＝m n e . The cost function F defining the MMI algorithm can thus be set by the differences between the multiple magnetic moment values MMI The difference between the magnetic moment values is represented by a standard deviation function sigma.
Embodiment seven:
this embodiment is a further illustration of the magnetic moment of the target in the method for real-time positioning of a vector sensor network based on magnetic moment invariants according to the first embodiment.
The target magnetic moment amounts described in this embodiment are:
after solving the position quantity, the formula can be calculated
The average value of the plurality of magnetic moments is calculated, so that the magnetic moment of the target object is solved.
Embodiment eight:
the embodiment of the real-time positioning system of the vector sensor network based on the invariant magnetic moment comprises:
modeling means for establishing a positioning analysis model from the target;
means for defining a cost function;
receiving means for obtaining position information of the object and magnetic field information at the corresponding position points;
the computing device is used for substituting the position information of the target and the magnetic field information at the corresponding position points into the cost function, selecting an optimization solving algorithm, and obtaining a plurality of groups of magnetic moment solving and iteration of the target;
and the computing device is used for obtaining positioning information according to the difference of the magnetic moment quantities, and obtaining a target magnetic moment quantity by averaging the magnetic moment quantities.
Claims (10)
1. A vector sensor network real-time positioning method based on magnetic moment invariants is characterized by comprising the following steps:
establishing a positioning analysis model according to the target;
defining a cost function according to a magnetic moment consistency principle;
obtaining the position information of the target and the magnetic field information at the corresponding position point according to the model;
substituting the position information of the target and the magnetic field information at the corresponding position point into the cost function;
selecting an optimization solving algorithm according to the model to obtain a plurality of groups of magnetic moment solving and iteration of the target;
obtaining positioning information according to the difference of multiple groups of magnetic moment quantities;
and (3) averaging a plurality of groups of magnetic moment amounts according to the positioning information to obtain the magnetic moment amount of the target, thereby completing the vector sensor network real-time positioning method based on the magnetic moment invariants.
2. The method for real-time positioning of a vector sensor network based on magnetic moment invariants according to claim 1, wherein the target is a magnetic dipole equivalent to an actual positioning target, and the magnetic field is expressed as follows:
wherein μ0 ＝4π×10 -7 H/m is vacuum permeability, r= [ x, y, z]Representing the relative positional relationship between the magnetic dipole and the observation point, m= [ m ] x ,m y ,m z ]Is the magnetic moment of the target.
3. The real-time positioning method of the vector sensor network based on the magnetic moment invariants according to claim 2, wherein the magnetic field is expressed as:
B＝kAm，
where k is the constant term μ 0 And/4 pi, A is a position vector matrix.
4. The method for positioning the vector sensor network in real time based on the invariant of magnetic moment according to claim 3, wherein the position vector matrix is specifically:
5. the real-time positioning method of a vector sensor network based on magnetic moment invariants as set forth in claim 1, wherein the cost function is:
wherein ,
m xi e (i=1, 2, … n) is the estimated magnetic moment value of the x-axis, m, calculated for the ith sensor yi e and mzi e The estimated magnetic moment values for the ith sensor y-axis and z-axis, respectively.
6. The method for real-time positioning of a vector sensor network based on magnetic moment invariants according to claim 1, wherein the variability of the magnetic moment amounts of the plurality of groups is represented by a standard deviation function sigma.
7. The real-time positioning method of the vector sensor network based on the magnetic moment invariants as set forth in claim 1, wherein the magnetic moment of the target is:
8. a computer device comprising a memory and a processor, the memory having a computer program stored therein, the processor performing a method of real-time localization of a vector sensor network based on magnetic moment invariants according to any one of claims 1-7 when the processor runs the computer program stored in the memory.
9. A computer readable storage medium for storing a computer program for executing a method for real-time localization of a vector sensor network based on magnetic moment invariants as set forth in any one of claims 1 to 7.
10. A vector sensor network real-time positioning system based on magnetic moment invariants, the system comprising:
modeling means for establishing a positioning analysis model from the target;
means for defining a cost function;
receiving means for obtaining position information of the object and magnetic field information at the corresponding position points;
the computing device is used for substituting the position information of the target and the magnetic field information at the corresponding position points into the cost function, selecting an optimization solving algorithm, and obtaining a plurality of groups of magnetic moment solving and iteration of the target;
and the computing device is used for obtaining positioning information according to the difference of the magnetic moment quantities, and obtaining a target magnetic moment quantity by averaging the magnetic moment quantities.
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