CN106908058B - Method for determining aperture of geomagnetic positioning array - Google Patents

Abstract

The invention provides a method for determining the aperture of a geomagnetic positioning array. Step one, constructing a geomagnetic sensor array formed by scalar magnetic sensors, and recording geomagnetic total field intensity through each scalar magnetic sensor; step two, calculating a time and space dual difference function between the two scalar sensors; solving a mixed partial derivative of the dual difference function on a certain coordinate variable and an array aperture variable, enabling the mixed partial derivative to be equal to zero aiming at a certain coordinate variable, and solving a theoretical optimal array aperture at a specific position; and step four, determining the actual optimal array aperture according to the environmental noise and the positioning precision. The method for determining the aperture of the geomagnetic positioning array can ensure that a locator can select the minimum array to position a magnetic target on the premise of meeting the requirement of positioning accuracy, so that the array is convenient to arrange, the maneuverability and the reliability of the geomagnetic positioning array are improved, and the array is more practical.

Description

Method for determining aperture of geomagnetic positioning array

Technical Field

The invention relates to a method for tracking and positioning a magnetic target, in particular to a method for determining an optimal aperture of an array.

background

the geomagnetic field is a natural physical field of the earth and is formed by overlapping magnetic field components with different change laws. Considering the time-varying characteristics of the geomagnetic field, the geomagnetic field that varies rapidly with time is called the varying magnetic field of the earth, and the geomagnetic field that varies slowly or substantially constantly with time is called the steady magnetic field of the earth.

The geomagnetic field is an important physical quantity reflecting the processes of universe evolution, earth evolution, geological structure evolution, seismic activity and the like. The magnetic field is utilized to position the target, which has important application significance in the aspects of geological monitoring, energy mineral deposit exploration, crash and sunken ship search and rescue, medical diagnosis and the like.

Depending on the characteristics of the geomagnetic field, the geomagnetic field can be applied to many fields, and in various application fields, it is an important task to accurately determine the position of a target object. For example, cargo rescue, beach rescue, port and ship monitoring of submerged ships, which are required to be performed, need to accurately and quickly locate underwater targets. The average sea depth of yellow sea in China is 50 meters, and the sea in the east China is mostly a continental shelf of 200 meters, and under the environment, sea conditions and target noise are the largest factors for determining sonar detection distance. While detection based on magnetic fields does not take these factors into account. Due to the presence of the magnetic target, the induced magnetic field generated by the magnetic target can cause a change in the magnetic field distribution in the space, thereby generating a magnetic anomaly in the space. Therefore, the magnetic measurement technology is a very effective method, and people can obtain the positioning information (such as geometric parameters, position parameters and the like) of the target object through the inversion of the magnetic anomaly.

In positioning a magnetic target, a vector sensor capable of measuring a geomagnetic component is generally required. In the positioning process, six parameters of the target need to be determined to finally determine the position and the characteristics of the target, including the space coordinates of the target and the magnetic moment components in all directions under the space coordinates. Therefore, at least 2 vector sensors capable of measuring three directional field components are required.

in the measurement process of the vector sensor, the sensor is installed in a complex way, and the attitude and the direction are strictly corrected during installation. When the angle error of the sensor is 0.05 °, the measured geomagnetic error is approximately 50nT or so. Therefore, the influence of attitude and orientation changes still needs to be compensated in real time during the movement process, and other high-precision positioning systems need to be used for correcting the attitude and the orientation. Meanwhile, due to the influence of the change of the geomagnetic field along with time and the low resolution of the vector sensor, the measurement distance cannot be too far. Compared with vector sensing, a scalar sensor for detecting the total geomagnetic field, such as the optical pumping magnetometer, has high resolution, and the measured total geomagnetic field value cannot change due to small attitude change, so that the optical pumping magnetometer does not need attitude and azimuth calibration during installation and use and is very convenient. Therefore, the scalar sensors are used for forming the array, so that the positioning of the target is significant.

disclosure of Invention

The invention aims to provide a method for determining the aperture of a geomagnetic positioning array, which can realize high-precision tracking and positioning of a magnetic target.

The purpose of the invention is realized as follows:

Step one, constructing a geomagnetic sensor array formed by scalar magnetic sensors, and recording geomagnetic total field intensity through each scalar magnetic sensor; step two, calculating a time and space dual difference function between the two scalar sensors; solving a mixed partial derivative of the dual difference function on a certain coordinate variable and an array aperture variable, enabling the mixed partial derivative to be equal to zero aiming at a certain coordinate variable, and solving a theoretical optimal array aperture at a specific position; and step four, determining the actual optimal array aperture according to the environmental noise and the positioning precision.

The present invention may further comprise:

1. The first step specifically comprises: the distance D between the scalar magnetic sensor and the origin o is defined as the array aperture, and when the target is located at the (x, y, z) coordinate point, the measurement T of the scalar magnetic sensor i is_iComprises the following steps:

Wherein: t is₀The magnitude of the magnetic field is set to be non-target, i is 1,2,3,4,5 …, the local declination angle and declination angle are respectively theta,P_mIs the target magnetic moment vector and is,is the displacement vector of the scalar magnetic sensor to the target,

Bysolving the equation set to obtain x, y, z, | P_m(x, y, z) determines the spatial position of the target, | P_mAnd I, preliminarily judging the tonnage of the target.

2. the second step specifically comprises: let t₀The measurement value of the time scalar magnetic sensor i is T_i(t₀,x_i,y_i,z_i)，ΔT(t-t₀) Delta T as the increment of the geomagnetic value with time_M(t-t₀,x_i,y_i,z_i) Is t-t₀the scalar magnetic sensor i measurement value increment caused by target movement in the time period; measuring the value T at time T_i(t,x_i,y_i,z_i)＝T_i(t₀,x_i,y_i,z_i)+ΔT(t-t₀)+ΔT_M(t-t₀,x_i,y_i,z_i) (ii) a Scalar magnetic sensor j measures value T at time T_j(t,x_j,y_j,z_j)＝T_j(t₀,x_j,y_j,z_j)+ΔT(t-t₀)+ΔT_M(t-t₀,x_j,y_j,z_j)

Order to

By Delta T_ijthe target is positioned independently of the time variation of the geomagnetic field, and the influence of the nonuniform spatial distribution is eliminated.

3. The third step specifically comprises: delta T_ijis a function of four variables, x, y, z, D, let Δ T_ijf (x, y, z, D), for a certain y value, in the y-axis direction, for Δ T_ijDifferentiating to obtain

In the formulaMiddle, delta (delta T)_ij) Can not be less than instrument noise and environmental noise Delta T_mini.e. delta (delta T)_ij) There is a lower limit Δ T_minAnd delta y represents uncertainty of y, the uncertainty delta y is reduced, the positioning precision is improved, and the likeReaching a maximum, when the target is at position y,is a function of D, finds D, makesTo a maximum, i.e. whenAnd solving D to obtain the theoretically optimal array aperture.

4. The fourth step specifically comprises:

determining instrument and environment noise delta T_min，

Determining the positioning accuracy delta y of the target_min，

Solving for specific yThe set of D-values of (a),

Fourthly, solving the intersection of the D sets corresponding to all the y,

The method for determining D value in the x-axis and z-axis directions is the same as that in the y-axis direction,

Sixthly, solving intersection set of three D value sets of the x axis, the y axis and the z axis, and selecting the minimum value D in the intersection set.

The invention provides a method for determining the optimal array aperture and a principle followed in practical application, and provides a feasible technology for constructing a scalar magnetic sensor positioning array. The main characteristics of the invention include:

1. The geomagnetic sensor array shown in fig. 1 is constructed, five scalar magnetic sensors record geomagnetic total field intensity, time and space dual difference functions between the two scalar sensors are calculated, mixed partial derivatives of the dual difference functions to a certain coordinate variable and array aperture variables are solved, the mixed partial derivatives are made equal to zero aiming at a certain coordinate variable, and array aperture values meeting the equation, namely the theoretically optimal array aperture at a specific position, are solved.

2. in practical application, the actual optimal array aperture is determined according to the environmental noise and the positioning precision. The following principles are followed to determine the actual optimal array aperture: aiming at a certain coordinate variable, the first-order partial derivative of the dual difference function of the two sensors along with the certain coordinate variable is more than or equal to the ratio of the environmental noise to the positioning precision, and the array aperture set meeting the inequality is solved. And solving the intersection of the array aperture sets corresponding to all the coordinate variables. And obtaining the actual optimal array aperture set which meets the positioning precision requirement in the coordinate direction.

3. and determining the actual optimal array aperture set in the directions of the other coordinate axes, and determining the minimum value of the optimal array aperture according to the actual optimal array aperture set corresponding to all the coordinate axes. And (3) solving the optimal array aperture sets on the other two coordinate axes by using the same principle as the principle in the part 2, solving an intersection of the three optimal array aperture sets on the x, y and z axes, and selecting the minimum value of the optimal array aperture in the intersection, namely the minimum optimal array aperture value.

4. For all coordinate variables, the method is theoretically infinite and has no feasibility of implementation, so that the method is characterized in practical application by the following steps: and selecting limited discrete coordinate values to realize calculation in the target positioning coordinate range.

According to the invention, the scalar magnetic sensor array is built, and the influence of the array aperture on the positioning precision is analyzed and researched based on the geomagnetic total field positioning theory, so that the selection basis of the array aperture is provided. The method for determining the aperture of the geomagnetic positioning array can ensure that a locator can select the minimum array to position a magnetic target on the premise of meeting the requirement of positioning accuracy, so that the array is convenient to arrange, the maneuverability and the reliability of the geomagnetic positioning array are improved, and the array is more practical.

Drawings

FIG. 1 is a schematic view of a magnetic positioning array scheme;

FIG. 2 is a schematic diagram of a simulation experiment area;

FIG. 3Curve with D;

FIG. 4Curve with D;

FIGS. 5 a-5 c different y valuesGraph with D;

Δ T for the SUV vehicle of FIGS. 6 a-6 d_ijThe theoretical curve and the experimental curve of (1);

FIG. 7D values Table 1 which meet the accuracy requirements;

Fig. 8 automotive positioning experimental data table 2.

Detailed Description

The invention provides a theoretical method and an actual determination principle of the array optimal aperture value, thereby realizing high-precision tracking and positioning of a magnetic target. The aperture is the distance of each sensor of the array to the center of the array, characterizing the size of the spatial scale of the array. The invention realizes the positioning of the magnetic target through the geomagnetic total field sensor array, obtains the relation between the array aperture and the target positioning precision according to the geomagnetic total field positioning theory, and provides a determination principle and a specific method of the optimal aperture on the basis of meeting the positioning precision requirement, so that a locator can select the minimum array to realize the positioning of the magnetic target on the premise of meeting the positioning precision requirement, the array is convenient to arrange, the maneuverability and the reliability of the geomagnetic positioning array are improved, and the array is more practical. The invention is further described below by way of example:

The method comprises the following steps: as shown in fig. 1, a magnetometer array is constructed with scalar magnetic sensors, the sensors being spaced from the origin o by a distance D, defined as the array aperture. The measured value T of the magnetic sensor i when the target is at the (x, y, z) coordinate point_iComprises the following steps:

Wherein: t is₀is the magnitude of the field without a target. i is 1,2,3,4,5 … with local magnetic declination angle and declination angle being theta,P_mIs the target magnetic moment vector.Is the displacement vector of the sensor to the target,X, y, z, | P can be solved by the equation set of formula (1)_m(x, y, z) determines the spatial position of the target, | P_mAnd I, preliminarily judging the tonnage of the target.

step two: and calculating a time and space dual difference function between the two scalar sensors to eliminate the influence of the time variation and space distribution abnormality of the geomagnetic field.

Let t₀The measured value of the time sensor i is T_i(t₀,x_i,y_i,z_i)，ΔT(t-t₀) Delta T as the increment of the geomagnetic value with time_M(t-t₀,x_i,y_i,z_i) Is t-t₀The increment of sensor i measurements caused by the movement of the target over the time period. Measuring the value T at time T_i(t,x_i,y_i,z_i)＝T_i(t₀,x_i,y_i,z_i)+ΔT(t-t₀)+ΔT_M(t-t₀,x_i,y_i,z_i). Sensor j measures value T at time T_j(t,x_j,y_j,z_j)＝T_j(t₀,x_j,y_j,z_j)+ΔT(t-t₀)+ΔT_M(t-t₀,x_j,y_j,z_j)

Order toBy Delta T_ijThe target is positioned independently of the time variation of the geomagnetic field, and the influence of the nonuniform spatial distribution is eliminated.

step three: the optimal array aperture is theoretically calculated.

ΔT_ijis a function of four variables, x, y, z, D, let Δ T_ijF (x, y, z, D). In the y-axis direction, for a certain y-value, for Δ T_ijDifferentiating to obtain

In the formula (3), Δ (Δ T)_ij) Can not be less than instrument noise and environmental noise Delta T_mini.e. delta (delta T)_ij) There is a lower limit Δ T_min. The uncertainty of y is expressed by delta y, and the positioning precision can be improved by reducing the uncertainty delta yReaching a maximum, when the target is at position y,Is a function of D, finding D,Make itTo a maximum, i.e. whenAnd solving D to obtain the theoretically optimal array aperture.

Step four: and determining the actual optimal array aperture value according to the optimal array aperture determination principle.

Determining instrument and environment noise delta T_min。

Determining the positioning accuracy delta y of the target_min。

solving for specific yThe set of D values of (a).

and fourthly, solving intersection of the D sets corresponding to all the y.

Method for determining D value in x-axis and z-axis directions is the same as that in y-axis direction

Sixthly, solving intersection set of three D value sets of the x axis, the y axis and the z axis, and selecting the minimum value D in the intersection set.

Due to the limited number of devices, the positioning experiment is implemented by constructing an array as shown in FIG. 1 by using four sensors. The aperture of the square array is D, and the located target automobile runs in the reverse direction parallel to the y axis, is 32.02m away from the y axis, and is uniform from y equal to 32.8m to y equal to-41 m, as shown in fig. 2. The local magnetic inclination angle is 63.3 degrees and the declination angle is-10.34 degrees, the local magnetic inclination angle is converted into a measurement coordinate system, the inclination angle is 58.83 degrees and the declination angle is 120 degrees. Target moment | P_m|＝550Am². Fig. 3 shows the difference Δ T of the sensor calculated according to the equations (1) and (2) when y is-40 m₃₄Curve of partial derivative of y with D. When D is 32m, the curve has a maximum value, 32m is the theoretical optimal aperture, and the positioning precision is highest at the moment. 0.6pT noise of sensor CS-L and 10pT environmental noise, if the target positioning accuracy is 1m, the requirement on the curve of FIG. 3 is satisfiedIn fact D ∈ (9,43.5) U (47,91) mall meet the requirements, can be taken D_min9 m. FIG. 4 shows the second partial derivative when y is-40 mCurve with D. Second partial derivativethe values of D are 32m and 59m, corresponding to a first derivative functionThere is a maximum that occurs. D the selection of 32m and 59m is the theoretically optimal array aperture.

FIG. 5 shows the different values of yGraph with D. When the environmental noise is 10pT, if the target location accuracy is 1m, the range of D values satisfying the accuracy requirement is calculated from the data of FIG. 5, as shown in Table 1. And (3) solving intersection of the D value sets meeting the precision requirement in the table 1 to obtain: d ∈ (4.5,16.5) U (21,25) U (28.5,32.5) U (36,53) m. Selecting the minimum D in the intersection_min4.5m as the final actual array aperture.

Four cesium optical pump magnetometers CS-L are arranged in suburbs according to the graph shown in FIG. 2, a positioned target automobile runs in a reverse direction in parallel to the y axis, x is 32.02m, a total geomagnetic field measurement data curve is shown in FIG. 6, and points x in the graph represent actual measurement difference values delta T of the two magnetometers₁₄,ΔT₂₄,ΔT₃₄The point corresponding to position y, according to equation (2), t₀the car is selected at the moment when y equals 32.8 m. In the figure, the horizontal axis represents the position y e (-40,35) of the vehicle in m, and the vertical axis represents the total geomagnetic field difference Δ T_ijAnd the unit is nT. In the experiment, D is 6m, 4m, 2m and 1m, and the automobile magnetic moment | P_m|＝550Am². The solid line in fig. 7 is the geomagnetic total field difference value Δ T calculated using the software simulation equations (1) and (2)_ijVersus position y. The calculation result of the automobile driving range of y from-41 m to 32.8m is consistent with the experimental data, the description of the far-field magnetic dipole on the automobile magnetic field model is proved to be correct, and the time-varying geomagnetic field is eliminatedThe effects of the chemometric and spatial anomalous fields, i.e. equations (1) and (2), are correct.

According to the formulas (1) and (2), the experimental data Δ T in FIG. 6 is used_ijThe position (x, y) of the car at each time is calculated as the result of the magnetic field localization of (x, y), see table 2. In Table 2 (x)₀，y₀) Is the actual position of the car, (x, y) is the position theoretically calculated from the geomagnetic measurement data, the unit m, Δ r is the distance between the theoretical point and the actual point,Is the average, in m, representing the positioning accuracy,the smaller the size, the higher the positioning accuracy. When the positioning precision is 1m, simulation shows that the minimum D is_min4.5 m. As D increases from 1m to 4m in table 2,And the positioning precision is increased from 9.94m to 1.58m, which is basically consistent with the result of simulation calculation.

Claims (3)

1. A method for determining the aperture of a geomagnetic positioning array is characterized in that: step one, constructing a geomagnetic sensor array formed by scalar magnetic sensors, and recording geomagnetic total field intensity through each scalar magnetic sensor; step two, calculating a time and space dual difference function between the two scalar sensors; solving a mixed partial derivative of the dual difference function on a certain coordinate variable and an array aperture variable, enabling the mixed partial derivative to be equal to zero aiming at a certain coordinate variable, and solving a theoretical optimal array aperture at a specific position; fourthly, determining the actual optimal array aperture according to the environmental noise and the positioning precision;

The second step specifically comprises: let t₀The measurement value of the time scalar magnetic sensor i is T_i(t₀,x_i,y_i,z_i)，ΔT(t-t₀) Delta T as the increment of the geomagnetic value with time_M(t-t₀,x_i,y_i,z_i) Is t-t₀The scalar magnetic sensor i measurement value increment caused by target movement in the time period; measuring the value T at time T_i(t,x_i,y_i,z_i)＝T_i(t₀,x_i,y_i,z_i)+ΔT(t-t₀)+ΔT_M(t-t₀,x_i,y_i,z_i) (ii) a Scalar magnetic sensor j measures value T at time T_j(t,x_j,y_j,z_j)＝T_j(t₀,x_j,y_j,z_j)+ΔT(t-t₀)+ΔT_M(t-t₀,x_j,y_j,z_j)

Order to

By Delta T_ijThe target is positioned, the time variation of the geomagnetic field is irrelevant, and the influence of the uneven spatial distribution is eliminated;

The third step specifically comprises: delta T_ijIs a function of four variables, x, y, z, D, let Δ T_ijf (x, y, z, D), for a certain y value, in the y-axis direction, for Δ T_ijDifferentiating to obtain

In the formulaMiddle, delta (delta T)_ij) Can not be less than instrument noise and environmental noise Delta T_minI.e. delta (delta T)_ij) There is a lower limit Δ T_minAnd delta y represents uncertainty of y, the uncertainty delta y is reduced, the positioning precision is improved, and the likeReaching a maximum, when the target is at position y,Is a function of D, finds D, makesTo a maximum, i.e. whenAnd solving D to obtain the theoretically optimal array aperture.

2. the method of claim 1, wherein the first step specifically comprises: the distance D between the scalar magnetic sensor and the origin o is defined as the array aperture, and when the target is located at the (x, y, z) coordinate point, the measurement T of the scalar magnetic sensor i is_iComprises the following steps:

Wherein: t is₀The magnitude of the magnetic field is set to be non-target, i is 1,2,3,4,5 …, the local declination angle and declination angle are respectively theta,P_mis the target magnetic moment vector and is,Is the displacement vector of the scalar magnetic sensor to the target,

Bysolving the equation set to obtain x, y, z, | P_m(x, y, z) determines the spatial position of the target, | P_mAnd I, preliminarily judging the tonnage of the target.

3. the method of claim 1, wherein the step four includes:

Determining instrument and environment noise delta T_min，

Determining the positioning accuracy delta y of the target_min，

Solving for specific yThe set of D-values of (a),

Fourthly, solving the intersection of the D sets corresponding to all the y,

The method for determining D value in the x-axis and z-axis directions is the same as that in the y-axis direction,

Sixthly, solving intersection set of three D value sets of the x axis, the y axis and the z axis, and selecting the minimum value D in the intersection set.