A geomagnetic slow-varying region positioning method based on double least squares estimation

Abstract

The present invention discloses a geomagnetic slow-varying region positioning method based on double least squares estimation, belonging to the field of geomagnetic navigation. In the present invention, an approximate partial derivative matrix of a vector matching reference map is fitted by the first least squares method, and then the position difference between the true position of the carrier and the center point of the vector matching reference map is solved by the second least squares method, so as to obtain the true position of the carrier, and the matching accuracy can be improved in the geomagnetic slow-varying region.

Description

Technical Field

[0001] The invention relates to the field of geomagnetic navigation, and in particular to a geomagnetic slowly varying area positioning method based on double least squares estimation. Background Art

[0002] With the advancement of aircraft technology, the demand for autonomous navigation of aircraft is getting higher and higher. The geomagnetic field is distributed all over the world, widely distributed in the ocean, land, near-Earth space and high altitude, and is the natural physical field inherent in the earth. Geomagnetic navigation has the advantage of not being restricted by region or season. At present, geomagnetic navigation technology has been widely studied in multiple application objects and application scenarios. The geomagnetic field has been used in navigation systems in ancient China, and people determine the heading by the characteristics of the geomagnetic field pointing north. In modern times, with the advancement and development of geomagnetic measurement technology, the technology of geomagnetic field navigation is not limited to indicating the heading, but has developed the use of geomagnetic vector information for navigation. At present, geomagnetic navigation has a variety of application scenarios. However, positioning using the geomagnetic field is essentially obtained by matching the geomagnetic field information measured in advance with the geomagnetic field information measured in real time by the carrier, but in the slowly changing area of ​​the geomagnetic field (i.e., the area where the geomagnetic field changes slowly, such as the high altitude far away from the earth's crust), the geomagnetic matching algorithm is prone to mismatching or mismatching problems, so the present invention is a geomagnetic slowly changing area positioning method based on double least squares estimation to improve the matching accuracy in the geomagnetic slowly changing area. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for positioning in a geomagnetic slowly varying area based on double least squares estimation.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A method for locating a geomagnetic slowly varying region based on double least squares estimation comprises the following steps:

[0006] S1. In the navigation phase, the inertial navigation system provides the reference position of the current carrier to the geomagnetic navigation system. The geomagnetic navigation system defines the range of the vector matching reference map according to the current reference position, extracts the vector matching reference map from the geomagnetic vector database, and selects multiple geomagnetic vectors therein;

[0007] S2. Calculating an approximate partial derivative matrix according to the selected multiple geomagnetic vectors;

[0008] S3, obtaining the measurement vector of the current geomagnetic sensor, and calculating the position difference between the real position of the carrier and the center point of the vector matching reference map;

[0009] S4. Calculate the real position of the carrier according to the position of the center point of the vector matching reference image and the position difference calculated in S3.

[0010] Furthermore, the calculation method of the approximate partial derivative matrix in S2 is:

[0011]

[0012] In the formula, η φ and η λ The local magnetic field vector is φ and λ Partial derivatives of direction; are respectively the latitude and longitude of the selected geomagnetic vector; f Represents the mapping relationship from latitude and longitude to the geomagnetic field vector; R λ and R φ are the grid resolutions in longitude and latitude respectively; m and n are the numbers of the selected geomagnetic vectors; M and N are the number of grids in the longitude and latitude directions of the vector matching reference map, w n and w m is the symbol coefficient.

[0013] Furthermore, the specific calculation method of calculating the position difference between the real position of the carrier and the center point of the vector matching reference image in S3 is:

[0014]

[0015] In the formula, U is the position difference between the real position of the carrier and the center point of the vector matching reference image, K is the approximate partial derivative matrix of the vector matching reference graph, Y is the difference between the measured value and the geomagnetic vector of the center point of the vector matching reference map, and T is the matrix transpose.

[0016] Furthermore, the real position of the carrier in S4 is expressed as:

[0017]

[0018] In the formula, is the real coordinate of the carrier, U is the position difference between the real position of the carrier and the center point of the vector matching reference image, The position coordinates of the center point of the vector matching reference image.

[0019] The present invention has the following beneficial effects:

[0020] The present invention proposes a geomagnetic slowly varying region positioning method based on double least squares estimation, which can improve the matching accuracy in the geomagnetic slowly varying region and solve the problem that the traditional geomagnetic matching algorithm is prone to cause mismatching in the region where the geomagnetic field changes slowly. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The figure is a flow chart of the method for positioning in a slowly varying geomagnetic region based on double least squares estimation according to the present invention.

[0022] Figure 2 Schematic diagram of three orthogonal intensity components according to an embodiment of the present invention.

[0023] Figure 3 It is a schematic diagram of the total magnetic field intensity scalar, magnetic inclination and magnetic declination according to an embodiment of the present invention.

[0024] Figure 4 Schematic diagram of horizontal component, vertical component and magnetic declination according to an embodiment of the present invention.

[0025] Figure 5 A vector matching reference map and a point selection diagram according to an embodiment of the present invention. DETAILED DESCRIPTION

[0026] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0027] A method for locating geomagnetic slowly varying regions based on double least squares estimation, such as Figure 1 As shown, the following steps are included:

[0028] S1. In the navigation phase, the inertial navigation system provides the reference position of the current carrier to the geomagnetic navigation system. The geomagnetic navigation system defines the range of the vector matching reference map according to the current reference position, extracts the vector matching reference map from the geomagnetic vector database, and selects multiple geomagnetic vectors therein;

[0029] The geomagnetic field is a vector field. In order to fully describe the geomagnetic vector at a certain point, its direction and magnitude need to be described. There are usually three ways to fully represent the geomagnetic field vector:

[0030] 1) Three orthogonal intensity components, such as north-east-ground components (X, Y and Z components), such as Figure 2 As shown;

[0031] 2) Magnetic field total intensity scalar, magnetic inclination and magnetic declination (F, I and D), such as Figure 3 As shown;

[0032] 3) Two intensity components and an angle value, such as horizontal component, vertical component and magnetic declination (H, Z and D), such as Figure 4 shown.

[0033] Usually, the direct measurement information of the geomagnetic vector sensor is the three intensity components of the geomagnetic field, namely ( X , Y and Z Therefore, the "vector" in the geomagnetic vector database, vector matching benchmark map and measurement vector described later in this article refers to the geomagnetic field. X , Y and Z A vector composed of components. In this paper, the geomagnetic vector database and the vector matching reference map are both composed of grids. Therefore, the geomagnetic field vector at a point on the horizontal plane can be expressed as:

[0034] (1)

[0035] In the formula b m is the geomagnetic field vector, φ and λ denote latitude and longitude respectively, and f The mapping relationship from latitude and longitude to the geomagnetic field vector, that is, the relationship between the geomagnetic field vector and the horizontal position on a plane can be represented by the mapping f Indicates. Assume that at position ( ) is used to perform Taylor expansion on equation (1), and we have

[0036] (2)

[0037] in ε represents a high-order term. The smoother the change of the geomagnetic field, ε The smaller the value is. During geomagnetic navigation, the geomagnetic navigation system can obtain the vector matching reference map from the geomagnetic vector database according to the reference position provided by the inertial navigation system. However, the distribution of the vector matching reference map is not a continuous function, but a discrete grid. The vector matching reference maps in different regions have different characteristics. Therefore, the mapping f It cannot be described by a fixed formula, nor can it be obtained f right φ or λ However, due to the slow change of the geomagnetic slow-changing zone, the vector matching reference map can be used to approximate the local area geomagnetic field vector in φ and λ The partial derivative of the direction, the approximate partial derivative is recorded as η φ and η λ . Take 9 points in the vector matching benchmark image P 1 , P 2 , …, P 9 , the corresponding coordinates are ( φ 1 , λ 1 ), ( φ 2 , λ 2 ),…,( φ 9 , λ 9 The distribution of these points is as follows. Figure 5 shown.

[0038] P 5 Located at the center of the matching reference image, the grid resolutions in longitude and latitude are R λ and R φ At the same time, the number of grids in the longitude and latitude directions are M and N According to formula (1), P 1 arrive P 9 The geomagnetic field vector can be expressed as:

[0039] (3)

[0040] Introduce the function symbol diag( x ):

[0041] (4)

[0042] in x Represents any constant or variable. The difference between longitude and latitude is converted into the product of grid resolution and grid number, and equation (3) can be rewritten as:

[0043] (5)

[0044] In the formula, E 1 ~ E 9 is the unit matrix. Convert the above equation into matrix form and mark the dimension of the matrix in the lower right corner, we have:

[0045] (6)

[0046] S2. Calculating an approximate partial derivative matrix according to the selected multiple geomagnetic vectors;

[0047] Formula (5) is By the least squares method , which can be solved η φ and η λ :

[0048] (7)

[0049] In the formula, η φ and η λ The local area geomagnetic field vector is φ and λ Partial derivatives of direction; are respectively the latitude and longitude of the selected geomagnetic vector; f Represents the mapping relationship from latitude and longitude to the geomagnetic field vector; R λ and R φ are the grid resolutions in longitude and latitude respectively; m and n are the numbers of the selected geomagnetic vectors.

[0050] S3, obtaining the measurement vector of the current geomagnetic sensor, and calculating the position difference between the real position of the carrier and the center point of the vector matching reference map;

[0051] In the process of geomagnetic navigation, the real position of the current carrier is assumed to be ( ), the geomagnetic vector measured by the magnetic sensor at this location is ,Will Recorded as According to formula (5), we can get:

[0052] (8)

[0053] In the formula, It is still the position of the center point of the vector matching reference image. Equation (8) can be transformed into:

[0054] (9)

[0055] Right now:

[0056] (10)

[0057] Formula (10) contains three equations and two unknowns ( ), so formula (10) belongs to an overdetermined system of equations, and the solution of the overdetermined system of equations can be obtained by the least squares method. Formula (10) is written in matrix form:

[0058] (11)

[0059] In the formula, K is the approximate partial derivative matrix of the vector matching reference graph, Y is the difference between the measured value and the geomagnetic vector of the center point of the vector matching reference map, U is the position difference between the real position of the carrier and the center point of the vector matching reference image. Therefore, the least squares method can be used to obtain:

[0060] (12)

[0061] S4. Calculate the real position of the carrier according to the position of the center point of the vector matching reference image and the position difference calculated in S3.

[0062] Finally, the center point position of the reference image is matched according to the vector ( φ 5 , λ 5 )as well as U The result is used to calculate the real position of the carrier, as shown in formula (13):

[0063] (13)

[0064] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0065] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0066] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0067] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0068] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for positioning geomagnetic slowly varying regions based on double least squares estimation, characterized in that: The steps include: S1. In the navigation phase, the inertial navigation system provides the reference position of the current carrier to the geomagnetic navigation system. The geomagnetic navigation system defines the range of the vector matching reference map according to the current reference position, extracts the vector matching reference map from the geomagnetic vector database, and selects multiple geomagnetic vectors therein; S2. Based on the selected multiple geomagnetic vectors, the equation is constructed by the first least squares method Compute the approximate partial derivative matrix, where The local magnetic field vector is φ and λ Partial derivatives of direction η φ and η λ The matrix of is a matrix containing multiple identity matrices, is a matrix containing mapping relationships between multiple latitudes and longitudes and geomagnetic field vectors; S3. Get the measurement vector of the current geomagnetic sensor The position difference between the real position of the carrier and the center point of the vector matching reference map is calculated by the second least squares method. , specifically: in, K is the approximate partial derivative matrix of the vector matching reference graph, Y It is the difference between the measured value and the geomagnetic vector of the center point of the vector matching reference map; S4. Calculate the real position of the carrier according to the position of the center point of the vector matching reference image and the position difference calculated in S3.

2. The method for positioning a geomagnetic slowly varying region based on double least squares estimation according to claim 1, characterized in that: The calculation method of the approximate partial derivative matrix in S2 is: In the formula, η φ and η λ The local magnetic field vector is φ and λ Partial derivatives of direction; are respectively the latitude and longitude of the selected geomagnetic vector; f Represents the mapping relationship from latitude and longitude to the geomagnetic field vector; R λ and R φ The grid resolutions in longitude and latitude, respectively; m and n are the numbers of the selected geomagnetic vectors; M and N are the number of grids in the longitude and latitude directions of the vector matching reference map, w n and w m is the symbol coefficient.

3. The method for positioning a geomagnetic slowly varying region based on double least squares estimation according to claim 1, characterized in that: The actual position of the vector in S4 is expressed as: In the formula, is the real coordinate of the carrier, U is the position difference between the real position of the carrier and the center point of the vector matching reference image, The position coordinates of the center point of the vector matching reference image.

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