The method of determining the corrective matrix of three-component magnetometer

 

Usage: the invention relates to the field of measurement of magnetic field induction in the three-component magnetometers, in particular for precision measurements of induction. Essence: using a modular magnetometer measure reorthogonalize three-axis measures the magnetic induction. Then, in a measure placed a three-component magnetometer, reproduce the exact value of the magnetic induction alternately along each axis measures constitute the instrument matrix of the three vector-columns of the measurement results of the magnetometer, normalized to the corresponding value, reproduced measure. On the measured reorthogonalization axis measures to build a matrix of its own axes in the orthogonal coordinate system of measures. On standardized instrument matrix axes identify corrective measures matrix magnetometer in its own orthogonal coordinate system. Effect: determining the correction without careful non-orthogonal orientation of the magnetometer in the orthogonal least, improving the accuracy of determining the corrective matrix. 1 table, 1 Il.

The invention relates to the field of measurement of magnetic field induction using (terrasond the value of magnetic field induction is based on identifying and accounting for systematic errors of measurement. One of the dominant components of the basic error is a static error.

It is known that the static error is determined by distorting the matrix of three-component magnetometer (see G. A. her granddaughter and others, the Angular error of measurement of the magnetic induction. In: Methods and tools for studying the structure of the geomagnetic field. - M, IZMIRAN, 1989, S. 161-168). There is proposed a method of determining lateral distorting elements of the matrix of three-component magnetometer using three measures of the magnetic induction in the conditions when the magnetometer and the measure of reorthogonalize. However, the known method does not allow one to determine all the elements distorting matrix, and therefore is not possible to find the correction matrix distorting.

There is also known a method for correcting results of measurement of three-component magnetometer (see U.S. patent No. 6130534, CL G 01 R 35/00, G 01 R 33/02, 2000), based on the determining the correction matrix. This way, the set of essential characteristics closest to the claimed and adopted for the prototype.

The known method includes the placement of the sensor, three-component magnetometer in the centre of the exemplary three-component measures the magnetic induction, a strict focus is in the center measures alternately reproduce the known values of the magnetic induction along each axis measures the registration of the output signals of the magnetometer in all its components, regulation of the output signals from the component to the corresponding signal from the measures, the construction of the normalized instrument square matrix of the normalized vector-column output signals using normalized for finding corrective matrix.

Factor hindering the achievement of specified following technical result when using the known method is a practical impossibility orientation of the three orthogonal sensitive axes of the magnetometer along three orthogonal axes measures. In the known method contains the following phrase: “We put calibrate (adjust) the sensor is a three-component magnetometer in the center of the reference measure magnetic induction and carefully Orient it so that the axis of the magnetometer coincide with the axes of the measures”. This prototype does not answer questions as to carry out a thorough orientation when working with the magnetometer orthogonal and non-orthogonal measure and the degree of thoroughness orientation is valid.

The challenge which healthy lifestyles is th result obtained by carrying out the invention is the ability to determine the corrective matrix magnetometer without careful non-orthogonal orientation of the magnetometer in the orthogonal least.

This technical result is achieved by the fact that in the present method of determining the corrective matrix of three-component magnetometer, including the placement of the sensor of the magnetometer in the centre of the exemplary three-component measures the magnetic induction, the orientation of the sensitive axis along the axes of the magnetometer measures the compensation of the external magnetic field, the replay to measure the exact values of the magnetic induction along its axis, the registration of all component measurement magnetometer magnetic field, reproducible measure, building a standardized instrument matrix of the normalized vector-columns of the measurement results and use it to find the corrective matrix, in contrast to the known method, preliminary, using modular magnetometer, measure reorthogonalize axes reference measure on which to build the matrix axes measuresin its own orthogonal coordinate system measures, then establish a three-component magnetometer, p is Noah and negative polarity along each axis measures when this register, the corresponding measurement results of all component magnetometer, which define the normalized instrument matrixaccording to the formula

wherethe results of the magnetometer measurement of the three components of the magnetic field, reproducible measure of positive and negative polarity;

then find distorting matrix of the magnetometer in the own coordinate system of measures by the formula

where- the distortion matrix of the magnetometer in its own coordinate system measures;- return matrix

which define adiagonal matrixresidual calibration coefficients of the magnetometer according to the formula

where- the elements of the matrixand reorthogonalize axes of the magnetometer according to the formula

where- portugoal.net the i-th and j-th magneticum>in its own orthogonal coordinate system of the magnetometer, which are distorting the matrix of the magnetometer according to the formula

and the required corrective matrixdefined as the inverse distorting.

The drawing shows a block diagram of the proposed method for determining the corrective matrix of three-component magnetometer.

The block diagram includes an exemplary three-component measure 1 magnetic induction (MI), in the workspace, which initially placed the modular magnetometer 2 to determine reorthogonalize measures, then the sensor 3 adjustable three-component magnetometer. The sensor 3 is connected to the measuring channel magnetometer and an analog-to-digital Converter 4, the output of which is connected to the input of the computer unit 5 to calculate the adjustment matrix of three-component magnetometer. The output unit magnetometer is also connected to the input of the computer device.

The inventive method of determining the corrective matrix of three-component magnetometer is as follows.

In the Central zone of the exemplary three-component measures 1 magnetic induction compensate the Earth's magnetic field and other external sources is

modules which measure precision modular magnetometer. Portugoal.net measures 1 between its axes 1 and 2 determine (see similar Angular error of measurement...) according to the formula

Similarly define other reorthogonalize E13by combination of fieldsandand E23on combinationand.

Then in the working area put the sensor 3 adjustable three-component magnetometer 4, the axis of which is oriented along the axes of the measures, and then along each axis measures 1 in turn reproduce measure accurately known value of the magnetic fieldorwhen positive and negative polarity, when it is measured with a magnetometer 4 corresponding vector-columns

The results of the measurement module magnetometer 2 (or pre-defined reorthogonalize measures 1field valuesreproduced by the measure, and the corresponding results of the measurements of the magnetometer 3, 4the boric matrix

and calculating on the set of the normalized matrix and reorthogonalize measures distortingand correctivematrices of the magnetometer in selected native orthogonal coordinate system of the magnetometer 4. This completes the definition of the offset matrix is completed. Subsequently, the magnetometer 3, 4 are removed from steps 1 and subsequent measurementsto adjust (correct) one of the following ways:

oror

wheretreatments of zero magnetometer;- dynamic measurement error.

In the first scheme adjusted for static measurement error, the second is a static error and goings of zeros in the third on a static error, zeros and dynamic error. In all schemes the main object is the adjustment matrix magnetometer in its own orthogonal coordinate system of the magnetometer.

The procedure for determining the correction matrix in its own orthogonal systemtechnology measuresnot obvious and requires a more detailed explanation. Consider a model of the distortion in the beginning for one-component magnetometer. The measurement result is a one-component magnetometerfor a single corecan be represented as the projection of the measured fieldon some single axis magnetometer

where the coefficienttakes into account the deviation from unity because of the imperfection of settings, instability and imperfection calibration one-component magnetometer,private care zero magnetometer axis. Another source of error is not a strict coincidence of the axis of the magnetometerwith the base axis.

Using this one-component model to a three-part magnetometer, we get that the vector-columns of the measurement resultsmeasured inductionand personal care zeros magnetometer

i.e., the distortion matrix transforms (“distorts”) on the magnitude and direction of the measured vector (true magnetic induction) in another vector (the result of a measurement minus the care of zero).

Distorting forms of works diagonal matrix of calibration coefficients magnetometerthe matrixcomposed of vector-row single axismagnetometer

It is obvious that the elements of each axisdepend on the choice of coordinate system (KS), respectively, the matrix axesand distortingalso depend on the choice of IC. Unlikethe matrixis diagonal and does not depend on the choice of coordinate system. It depends on the quality settings, stability and calibration of the magnetometer. The better tuning stability and calibration of the i-th component, the closer the calibration factorto unity. However, even strict equalitydoes not guarantee high measurement accuracy, because in about the new SC. Angular misalignments of the axes of the magnetometer affect accuracy. The closer on the wholeto a unit matrix, the better the magnetometer.

If the ratio isfield of external originreplace with field, reproducible measurealong its i-th axisi.e. in the positive direction, you will get normalized to the module field measures the vector-column. If you change the polarity of the field measures along its i-th axis, its axis is inverted and(module field measuresalways with a plus sign). It follows that the normalized instrument matrix

is (scalar) product of distorting matrix magnetometerthe matrix of the vector-columns axis measures. While the care of the zeros of the magnetometer and the residual external field vzaimokompensiruyutsya. Both matricesandshould be treated in the same IC, they depend on the choice of SC, but irresolute measurements, the adjustment matrix should beand only

whereas in the prototype as a corrective appearsthat's wrong (in the prototype are not taken into account and goings of zeros). In order to get the true corrective,you would additionally be multiplied byleft

I.e., if the matrixwas known in some SK, if known standardized instrumentadjustment would be determined in the same IC.

It is convenient to choose such orthogonal IC measures (ASCM), so you could simplify the exact expression of all elements of the matrix axes measuresthrough its reorthogonalize. Select OSCM with ortsfor example, so that the ORTOSCM coincided with the axis of measuresand the axis of measureslying in the plane of the vectors

as follows is expressed through its reorthogonalize:

where

The ratio of the above as an example. Own OSCM you could choose at least nine equitable ways to obtain similar expressions for the matrix axes through their reorthogonalize (six ways, when the matrix has three axes zero side item, and another three way, when the matrix has two axes of the zero element, and two non-zero element that is symmetric about the main diagonal are equal to each other). I.e. any of the three orthogonal axes can be expressed precisely and simply in one of 9 private orthogonal IC through reorthogonalize three axes.

So, found reorthogonalization measures build the matrix axesin one of their own was OSCM and are distorting the magnetometer in the same OSCM by the formula

Matrixcould be used for correction if the magnetometer would perform the subsequent measure in own OSCM without changing its orientation relative measures. But we are interested in the AI in its own orthogonal SC magnetometer (OKMAG). Note that by distorting found in OSCMyou can identify the unknown elements of the matrixand reorthogonalize axis magnetometerbecause these quantities do not depend on the choice of SC

where- .

By analogy with the above example, the expression of the matrix axes measuresin one of their own was OSCM choose one of your own OKMAG and determine in it the matrix axes of the magnetometer(the subscript “0” means belonging to their own OKMAG) through the found reorthogonalize axis magnetometer.

For example, let us choose an orthonormal basis OKMAGon the axes of the magnetometer so that

Where are matrix axes of the magnetometer in the selected OKMAG l0through the found reorthogonalize eij

where

So find activities distorting and its inverse (i.e., corrective) Maru repeat for different measuring ranges and, respectively, for each range find their distorting and corrective matrix in selected own OKMAG.

In some cases, further define and matrix connection s between the selected native OSCM and OKMAG

This relation follows from the following, again explaining the properties of all the above matrices

where- transposedbecause the matrixorthogonal, then

To test the capabilities of the proposed method in comparison with the method of the prototype using the automation system calculations MatLab computed the precision performance of the correction in the form of the maximum element of the matrix

for the prototype method;

for the proposed method

in conditions characterized by the maximum matrix elements: distortingaxis measuresand angular misalignment between the measure and magnetometer

The calculation results are shown in the table.

It can be shown that 708.gif">

As can be seen from the table, under adverse conditions, the correction in the method prototype does not improve, worsens the accuracy of the corrected magnetometer. However, data show significant accuracy advantages of the proposed method under all conditions. In particular, the inventive method allows accurate correction without careful non-orthogonal orientation of the magnetometer in the orthogonal least.

Claims

The method of determining the corrective matrix of three-component magnetometer, including the placement of the sensor of the magnetometer in the centre of the exemplary three-component measures the magnetic induction, the orientation of the sensitive axis along the axes of the magnetometer measures the compensation of the external magnetic field, the replay to measure the exact values of the magnetic induction along its axis, the registration of all component measurement magnetometer magnetic field, reproducible measure, building a standardized instrument matrix of the normalized vector-columns of the measurement results and use it to find the correction matrix, wherein the pre using modular magnetometer,gif">in its own orthogonal coordinate system measures, then establish a three-component magnetometer, and then in the center measures reproducing magnetic field BMialternately positive and negative polarity along each axis measures when this register, the corresponding measurement results of all component magnetometer, which define the normalized instrument matrix P according to the formula

wherethe results of the magnetometer measurement of the three components of the magnetic field, reproducible measure of positive and negative polarity,

then find distorting matrix of the magnetometer in the own coordinate system of measures by the formula

where- the distortion matrix of the magnetometer in its own coordinate system measures;- return matrix,

which define adiagonal matrixresidual calibration coefficients of the magnetometer according to the formula

where

where- portugoal.net the i-th and j-th magnetosensitive axis magnetometer, which build the matrix axes of the magnetometer l0in its own orthogonal coordinate system of the magnetometer, which are distorting the matrix of the magnetometer according to the formula

and the required corrective matrixdefined as the inverse distorting.

 

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