RU2530778C2 - Method for magnetic navigation on geomagnetic sections - Google Patents

Abstract

FIELD: physics, navigation.

SUBSTANCE: disclosed is a method for magnetic navigation on geomagnetic sections. In the method, navigation is carried out not by comparing the observed field with a reference field, but by correlation of constructed geomagnetic sections on said fields. Anomalies created by objects lying higher than the level of the earth's surface or the sea floor are considered interference and do not take part in the navigation process. Also, anomalies lying deeper than a given level and without a clear shape are also excluded.

EFFECT: high reliability of navigation.

Description

The invention relates to the field of navigation through geophysical fields and can be used when navigating air carriers in hard-to-reach areas, navigating underwater vehicles when searching for mineral deposits at great depths in water areas, and when navigating an air carrier measuring a modern magnetic field using old reference magnetic field maps, containing random errors, false anomalies due to variations in the geomagnetic field, coordination errors and data linking.

There is a method of determining their place by ships and aircraft on the topography of the seabed or terrain, respectively [1].

There is also a technical solution in this area when determining its place by the carrier of magnetometric equipment according to the reference magnetic field of the Earth [2].

Of the known methods and technical solutions, both sources [1, 2] are closest to the claimed solution. Both decisions are based on common with the declared actions on the features measured from the carrier (relief, magnetic field) and the reference values of the feature being studied, presented in the form of a map.

A disadvantage of the known methods [1, 2] is that navigation in a magnetic field cannot be carried out in all territories and waters of the globe, because many regions do not have enough density for navigation to observe the Earth’s reference magnetic field, and there are even “empty” areas where there are no magnetic surveys. When navigating a terrain, the same medium cannot determine its position above the terrain and in the water areas. By a magnetic field, for example, an air carrier can navigate both over territories and in water areas. The aim of the present invention is the possibility of magnetic navigation in any region of the globe where magnetic navigation by known methods is performed with a large error or even cannot be performed at all.

The goal is achieved by the fact that the measurement of the module of the Earth's magnetic field on the profile from a mobile carrier.

A reference map of the Earth’s magnetic field in the region under study, measurements of the Earth’s magnetic field from the carrier, coordinates of the starting point and a regular system of approximate coordination of the carrier.

Moreover, according to the invention, geomagnetic sections are constructed from the reference and measured fields according to the selected parameters for converting the field into a section (field, object coordinates, magnetic masses and distribution in the context of the similarity function) in a given interval of field observation and a given interval of depths, exclude false and partially falling into the anomaly section window, the objects determine the exact coordinates of the carrier by comparing in a given interval the geomagnetic section obtained from the magnetic field 3 measured using the on-board system mli, with reference geomagnetic sections obtained following the reference field by calculation a functional type correlation function and the search for an extremum of the function.

Such a constructive implementation of the method of expanding the areas of application of magnetic field navigation allows navigation in areas where the magnetic reference field is poorly studied or in some places and even completely absent.

To construct a geomagnetic section, a quantitative interpretation of all the anomalies of the observed and reference fields is required. The quantitative interpretation of magnetic anomalies involves solving the direct and inverse problems of magnetic exploration.

The solution of a direct problem is often an integral part of the procedure for solving the inverse problem. The parameters of the anomaly-forming objects are determined by the observed anomalies. This is typical for remote water areas, where information about the parameters of anomaly-forming objects can be taken mainly only by analogy. In solving the inverse problem of magnetic exploration, the similarity between the theoretical and observed anomaly is used. As a result of solving the inverse problem, the shape, size, depth, and magnetization of magnetically disturbing objects are estimated.

The main method for solving the inverse problem is based on the selection of such a magnetically disturbing object, which creates a theoretical anomaly similar to the observed one. Theoretical anomalies are calculated by setting the expected parameters of the anomaly-forming objects or by enumerating various values of these parameters. One way to solve this problem is to find the minimum of a certain functional of the type:

$$F_{\mathrm{one}}={\displaystyle \sum {}_j^m|\; |\; |T\left(x_j\right)-\alpha \left(x_j\right)|\; |\; |{}^i=\min ,\left(\mathrm{one}\right)}$$

where T (x _j ) are the values of the observed field specified at points x _j ; α (x _j ) - values of the selected (theoretical) field from the anomaly of the forming object; m is the number of points; i is the degree of functionality, which can take the values 1 or 2.

However, the minimum of the functional Ф ₁ does not yet guarantee the similarity of the shape of the associated curves. The minimum guarantees only the proximity of the compared amplitudes. As a result, the features of the experimental (observation and / or reference) field, which determines the shape of the anomaly-forming objects, are absent in the theoretical field.

As follows from the practice of interpretation, the selection of magnetically disturbing objects by minimizing the functional Ф ₁ can lead to a fairly reliable approximation of the reference and observed fields by the selected bodies. However, the selected masses, if there are no restrictions on them, can receive unrealistic values. This is characteristic of any active minimizing the functional f ₁ methods.

The use of passive methods looks completely different when instead of criterion (1), the selection of masses of magnetically disturbing objects is carried out by sorting the theoretical curves and detecting such palette plots, for example, by maximum correlation, without “violent” minimizing the functional Ф ₁ [3].

Minimization of the functional Ф ₁ is a necessary but insufficient procedure. A sufficient procedure will be considered one that minimizes Φ ₁ and maximizes the similarity between α (x) and T (x). The correlation coefficient r (T, α) can serve as a similarity criterion.

Let the experimental and theoretical curves have zero mean and equal variances [4]. Then the correlation coefficient between the theoretical and experimental curves is written in the form:

$$r\left(T,\alpha \right)=\frac{{\displaystyle \sum {}_{j=\mathrm{one}}^{m}T\left(x_j\right)\cdot \alpha \left(x_j\right)}}{{\sigma }^2}\left(2\right)$$

If the theoretical anomaly differs from that observed in the variance, then it should be normalized. The theoretical anomaly is normalized according to the observed one after bringing it and the observed one to zero mean.

$$|\; |\; |{\displaystyle \sum _{j=\mathrm{one}}^m{T}_j}|\; |\; |=\beta |\; |\; |{\displaystyle \sum _{j=\mathrm{one}}^m{\alpha }_j}|\; |\; |$$

Then, the difference between the observed curve and the normalized theoretical will serve as a hindrance to selection or a measurement error, or a measure of the mismatch between the theoretical curve and the one observed in the conditional probability method [4]. Based on this difference, the interference variance σ ^{2 is} calculated.

The maximum similarity between α and T will be subject to:

$$F_2={\displaystyle \sum {}_j^{m}T\left(x_j\right)\cdot \alpha \left(x_j\right)=\max \left(3\right)}$$

The most effective criterion for similarity will be a criterion that combines both functionalities Ф ₁ and Ф ₂

$$\lambda =\frac{F_2}{F_{\mathrm{one}}}$$

Obviously, the maximum similarity of the experimental and theoretical curves will be at maximum λ.

The application of the λ criterion is associated with great difficulties. Most simply, this problem is solved by enumeration.

Due to the fact that the a priori information used in the interpretation is specified with an error or is probabilistic, the obtained values of the shape and depth of magnetically disturbing objects are not unambiguous. Therefore, the results of interpretation in the context should be shown in a certain confidence interval. Such intervals determine the contour within which the object is located with a given probability. In other words, moving an object inside this interval from one point to another does not cause a significant change in λ. We call this contour the geometrical place of existence of the object or the contour of ambiguity of interpretation. The geological section should be built taking into account this ambiguity. The larger this contour, the less reliable the interpretation. Thus, the size of the contour of ambiguity can be taken as a characteristic of the reliability of the corresponding selected magnetically disturbing object. This is nothing more than an estimate of the confidence interval, which is very important in the interpretation. If we sort through various objects, then the one that has the minimum area of the contour of ambiguity is most reliably selected. The difference in the contours of the ambiguity will depend both on the reliability of a priori ideas about objects and on the level of noise present in the observed field. As noise, we mean not only measurement errors, but also uninterpreted anomalies.

We divide the lower geological half-space Г (х, h) into unit cells Δx × Δh (Δx≤Δh, the minimum Δx is the distance between the observation points) and we will sequentially place objects from which the theoretical effect is calculated [5]. If the interval Δh is equal to Δx, where Δx is the observation step along the profile and / or between the profiles (Δx = Δу) (for example, in the digital map model), then we will not miss a single point at which the center of mass of the real disturbing object. When we get to such points, we must obtain the maximum of the λ criterion, and calculations carried out at neighboring points allow us to estimate the contour of the ambiguity of the position of the center of the magnetically disturbing object [4].

The implementation of functional (4) can be carried out using the modification method of inverse probabilities [4].

Let the theoretical α (x) and the observed T (x) anomalies be given. To assess the similarity, the correlation sum is used:

$${\mu }_{\mathrm{one}}={\displaystyle \sum {}_{i=\mathrm{one}}^{n}T\left(x_i\right)\cdot \alpha \left(x_i\right)\left(5\right)}$$

and rms difference:

$${\sigma }^2={\displaystyle \sum {}_{i=\mathrm{one}}^n\frac{{\left[T\left(x_i\right)-\alpha \left(x_i\right)\right]}^2}{n-\mathrm{one}}}\left(6\right)$$

where n is the number of points on the profile. Then the measure of the reliability of the selected model is an indicator of the likelihood coefficient:

$$\mu =-\frac{{\displaystyle \sum {}_{i=\mathrm{one}}^n{\alpha }^2\left(x_i\right)}}{2{\sigma }^2}+\frac{{\displaystyle \sum {}_{i=\mathrm{one}}^{n}T\left(x_i\right)\alpha \left(x_i\right)}}{{\sigma }^2}\left(7\right)$$

Moreover, the normalized α (x _i ) = α (x _i ) · β, where α ₁ (x _i ) is the anomaly of unit amplitude, is considered as a theoretical anomaly;

$$\beta =\frac{{\displaystyle \sum {}_{i=\mathrm{one}}^n|\; |\; |T\left(x_i\right)|\; |\; |}}{{\displaystyle \sum {}_{i=\mathrm{one}}^n|\; |\; |{\alpha }_{\mathrm{one}}\left(x_i\right)|\; |\; |}}\left(8\right)$$

provided that T and α are centered on the comparison interval, i.e.

$${\displaystyle \sum {}_{i=\mathrm{one}}^{n}T\left(x_i\right)={\displaystyle \sum {}_{i=\mathrm{one}}^n\alpha \left(x_i\right)=0\left(9\right)}}$$

The likelihood coefficient λ ₁ is determined from the expression:

λ ₁ = exp (µ);

The conditional probability of detecting a "signal" and in the field T is calculated by the formula:

$$p\left(a/T\right)=\frac{{\lambda }_{\mathrm{one}}}{\mathrm{one}+{\lambda }_{\mathrm{one}}}\left(10\right)$$

Among all the theoretical models considered, one is selected for which the coefficient µ is maximum. If μ> 0, then p> 0.5. For sections, µ (x, h), λ ₁ (x, h), p (x, h) can be used. As anomalies, α (x) are the effects of magnetically disturbing objects of the type: balls, thin layers, rods, etc.

Since for the geological interpretation and navigation we are interested in the shape of the perturbing object and the area of its location, in the quantitative interpretation the magnitude of the selection error is not so much significant as the similarity of the selected “signal” with the anomaly in the observed field.

, и строится карта µ(х, h). Если по µ(x, h) построены карты по наблюденным и эталонным аномалиям, соответственно µ_н и µ_э, то их можно сравнивать путем корреляции.Thus, in the absence of a priori geological information, we have the right to assume the presence of an object at any point in the lower half-space. Covering the lower half-space with a network of nodes with a step along the x axis equal to the distance between adjacent observation points, and vertically with a step that would satisfy the interpreter with the detail of the section, we calculate the likelihood coefficient for all nodes of this network. As a result of the calculations, zones with a likelihood coefficient indicator greater than zero, i.e. $$p\left(\frac{\alpha }{5}\right)>0.5$$

, and a map µ (x, h) is constructed. If, based on μ (x, h), maps are constructed from the observed and reference anomalies, respectively, μ _n and μ _e, then they can be compared by correlation.

The effects of the most reliably selected objects can be subtracted from the observed field, and the search for new objects can be continued by residual anomalies, i.e. the method of subtracting theoretical effects is used [4].

Interpretation results in this way will have mixed decisions. This one ambiguity in the field on both routes (real and reference) will be the same. This allows them to be compared with high reliability.

In the obtained sections, both standard and actually measured, interfering (false - detection probability less than 0.5; very weak; obtained by anomalies whose intensity is less than three shooting errors (maps)) objects located to certain depths h can be eliminated ₁ and deeper than h ₂ . Then, sections are compared in the depth interval from h ₁ to h ₂ .

Thus, a comparison of the sections can be performed not only by μ (x, h) (or λ, λ ₁ , etc.), but also by the position in the section of the maxima μ, where the centers of magnetically disturbing objects are located, and their magnetization and the shape of the bodies, which increases the reliability of decision-making during navigation of the carrier, according to anomalies of the magnetic field and / or geomagnetic sections.

Thus, the following sequence of actions is proposed, which leads to an estimate of the coordinates of the carrier in a certain period of time and / or space.

The method of magnetic navigation along geomagnetic sections contains a reference map of the Earth’s magnetic field of the studied area, provides for measuring the Earth’s magnetic field from the carrier, and it is required to have the coordinates of the starting point and a regular system for approximate coordination of the carrier. For example, speed and heading sensors. Geomagnetic sections are constructed from the reference and measured fields. The construction of geomagnetic sections should be carried out in a way that allows us to give estimates at all points of the lower half-space. In principle, it can be recounting the field down. But the authors give another (author's) more reliable way. This method gives the position of objects of a certain shape that can be changed, magnetic masses and the like at all points for the presence of objects in them.

In addition, in a given interval of the observed field and a given interval of depths, false (for example, at the noise level of measurements) and partially falling into the section window, for example, shallow, lateral and deep objects, are excluded. In a given interval of the geomagnetic section obtained from the Earth’s magnetic field measured using the on-board system, it is compared with reference geomagnetic sections obtained from the reference field. By calculating a certain functional, such as a correlation function between sections, obtained from the field observed from the carrier and a number of sections obtained from the reference map, and searching for the extremum of this function, the position of the observed profile is found on the reference map and the exact coordinates of the carrier are determined.

Bibliography

1. The way to determine their place by ships on the topography of the seabed. - U.S. Pat. 33-1, No. 3.212.189, publ. 10/19/1965

2. Beloglazov I.N., Dzhanzhgava G.I., Chigin G.P. Fundamentals of navigation through geophysical fields. M: "Science." The main edition of the physical and mathematical literature, 1985. 328 p.

3. Timoshin Yu.V. Pulse seismic holography, M., NEDRA, 1978.

4. Palamarchuk V.K. Geology and Geophysics, Novosibirsk, SCIENCE, 1986.

5. Timoshin Yu.V. A method of constructing seismic sections. Description of the invention to copyright certificate 210395. Declared 23.IX.1963 (No. 858143 / 26-25).

6. Logachev A.A., Zakharov V.P. Magnetic exploration, Leningrad, NEDRA, 1979.

Claims (1)

A method of magnetic navigation through geomagnetic sections, containing a reference map of the Earth’s magnetic field of the studied area, measuring the Earth’s magnetic field from the carrier, coordinates of the starting point and a regular system for approximate coordination of the carrier, characterized in that geomagnetic sections are constructed from the reference and measured fields, according to the selected parameters of the section (coordinates of objects, magnetic masses) in a given observation interval and a given interval of depths, exclude false and interfering objects in given intervals, compared was obtained from the measured sections and magnetic fields of the Earth reference by calculating a functional type of correlation function and the search for an extremum of the function, and determine the exact coordinates of the carrier.