A method and device for determining the osculating azimuth of gravity lines for assisting instrument leveling

Abstract

The present invention relates to the field of geodetic technology, and in particular to a method and device for determining the osculating azimuth of gravity lines for assisting instrument leveling, the method comprising: calculating the gravity eastward gradient based on the earth's gravity field model; calculating the gravity northward gradient based on the gravity field model; and calculating the gravity osculating azimuth based on the obtained gravity eastward gradient and gravity northward gradient. The present invention calculates the gravity line osculating azimuth through the earth's gravity field model, describes the distribution characteristics of the global gravity line osculating azimuth, and then provides the osculating azimuth adjustment parameters for assisting instrument leveling, which can quantitatively characterize and describe the gravity line osculating azimuth parameters during instrument leveling, and provides a theoretical and technical basis for enriching the theoretical connotation of the measurement and leveling module and improving the efficiency of instrument measurement work preparation.

Description

Technical Field

[0001] The present invention relates to the field of geodetic measurement technology, and in particular to a method and device for determining the osculating azimuth of a gravity line for assisting instrument leveling. Background Art

[0002] Before surveying, one of the necessary tasks for surveying instruments and equipment (total station, theodolite, level, etc.) is to level the instrument, that is, to adjust the instrument so that its horizontal disk is in the orthogonal direction of the plumb line (gravity direction), so as to achieve the observation state, which is intuitively presented as the centering of the circular level bubble of the instrument. In essence, the level surface is the reference surface for geodetic measurement, and the instrument is leveled by adjusting the instrument foot screw and other devices to make the horizontal direction of the instrument coincide with the corresponding level surface. In the physical level, the level surface is a gravity equipotential surface, which is orthogonal to the gravity line everywhere. The gravity line is a spatial curve. When the horizontal direction of the instrument coincides with the corresponding level surface, the osculating azimuth (angle between the gravity line curvature vector and the north direction) of the corresponding gravity line at the measuring point is also uniquely determined. However, the current instrument leveling practice and simulation process do not take into account the auxiliary role of the gravity line osculating azimuth parameter in leveling and its theoretical guidance connotation. Summary of the invention

[0003] The present invention aims at the problem that the current practical operation and simulation process of surveying and mapping instrument leveling does not take into account the auxiliary leveling effect of the gravity line osculating azimuth parameter and its theoretical guidance connotation. By utilizing the connection between the gravity line osculating azimuth and the level surface, the present invention provides a method and device for determining the gravity line osculating azimuth for auxiliary instrument leveling. The gravity line osculating azimuth is calculated by the earth's gravity field model, the distribution characteristics of the global gravity line osculating azimuth are described, and then the osculating azimuth adjustment parameters for auxiliary instrument leveling are given. The present invention can quantitatively characterize and describe the gravity line osculating azimuth parameter during instrument leveling, and provide a theoretical and technical basis for enriching the theoretical connotation of the measurement and leveling module and improving the efficiency of instrument measurement work preparation.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] The present invention discloses a method for determining the osculating azimuth of a gravity line for assisting instrument leveling, comprising:

[0006] Step 1: Calculate the eastward gravity gradient based on the Earth's gravity field model;

[0007] Step 2: Calculate the northward gravity gradient based on the gravity field model;

[0008] Step 3: Calculate the osculating azimuth of the gravity line based on the obtained gravity easting gradient and gravity northing gradient.

[0009] Furthermore, the step 1 comprises:

[0010] Under the local north-east coordinate system, the eastward gradient of gravity at any point P on the level surface is expressed as

[0011]

[0012] In the formula, g y represents the eastward gradient of gravity; g is gravity;

[0013] g y The relationship with gravity potential is

[0014]

[0015] Where W is the gravity potential, W yz represents the second-order gradient of the gravity potential in the yz direction. The gravity potential is equal to the sum of the corresponding gravitational potential and the centrifugal force, that is,

[0016] W=V+Q (3)

[0017] In the formula, V and Q represent the gravitational potential and centrifugal potential respectively. Under the conditions of the geocentric coordinate system, the expressions of V and Q are:

[0018]

[0019] Where ρ is the geocentric radial of the research point; θ and λ represent the geocentric colatitude and geocentric longitude of the research point respectively; GM is the gravitational constant; n and m represent the order and degree of the spherical harmonic coefficients respectively, Nmax represents the highest order of the spherical harmonic coefficients; a represents the major semi-axis of the ellipsoid; and represents the fully normalized spherical harmonic coefficients; is the nth order and mth order completely normalized associated Legendre function; ω represents the angular velocity of the earth's rotation;

[0020] Finally, the Earth's gravitational gradient V in the local north-pointing coordinate system yz It can be expressed as

[0021]

[0022] Among them, V yz represents the second-order gradient of the gravitational potential in the yz direction,

[0023]

[0024] Among them, the recursive formula of the fully normalized associated Legendre function is

[0025]

[0026] in, represents the nth-order nth-order fully normalized associated Legendre function, represents the n-1th order and n-1th degree completely normalized associated Legendre function, represents the nth order n-1th order completely normalized associated Legendre function, represents the nth order and mth order completely normalized associated Legendre function, represents the n-2 order mth completely normalized associated Legendre function;

[0027] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0028] Q yz =0 (9)

[0029] Then we get W yz =V yz +Q yz ;

[0030] Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Q yz It represents the second-order gradient of centrifugal force in the yz direction;

[0031] Finally based on W yz Formula (2) can be used to obtain the eastward gradient of gravity at any point P on the level surface under the local north-east coordinate system.

[0032] Furthermore, the step 2 comprises:

[0033] Under the local north-east coordinate system, the northward gradient of gravity at any point P on the level surface is expressed as

[0034]

[0035] In the formula, g x is the northward gradient of gravity;

[0036] g x The relationship with gravity potential is

[0037]

[0038] Among them, W xz Represents the second-order gradient of the gravitational potential in the xz direction

[0039] W xz =V xz +Q xz (12)

[0040] Among them, V xz represents the second-order gradient of the gravitational potential in the xz direction, Q xz It represents the second-order gradient of centrifugal force in the xz direction;

[0041]

[0042] In the formula,

[0043]

[0044] in, represents the nth order m+1th order completely normalized associated Legendre function;

[0045] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0046]

[0047] in,

[0048]

[0049] Furthermore, the step 3 comprises:

[0050] When the angle between the gravity line curvature vector and the north direction, that is, the osculating azimuth of the gravity line, is α, it is related to the horizontal gravity gradient, that is,

[0051]

[0052] The final gravity line osculating azimuth α is

[0053]

[0054] Another aspect of the present invention provides a device for determining the osculating azimuth of a gravity line for assisting instrument leveling, comprising:

[0055] The gravity eastward gradient calculation module is used to calculate the gravity eastward gradient based on the earth's gravity field model;

[0056] Gravity north gradient calculation module, used to calculate the gravity north gradient based on the gravity field model;

[0057] The gravity line osculating azimuth calculation module is used to calculate the gravity line osculating azimuth based on the obtained gravity eastward gradient and gravity northward gradient.

[0058] Furthermore, the gravity eastward gradient calculation module is specifically used for:

[0059] Under the local north-east coordinate system, the eastward gradient of gravity at any point P on the level surface is expressed as

[0060]

[0061] In the formula, g y represents the eastward gradient of gravity; g is gravity;

[0062] g y The relationship with gravity potential is

[0063]

[0064] Where W is the gravity potential, W yz represents the second-order gradient of the gravity potential in the yz direction. The gravity potential is equal to the sum of the corresponding gravitational potential and the centrifugal force, that is,

[0065] W=V+Q (3)

[0066] In the formula, V and Q represent the gravitational potential and centrifugal potential respectively. Under the conditions of the geocentric coordinate system, the expressions of V and Q are:

[0067]

[0068] Where ρ is the geocentric radial of the research point; θ and λ represent the geocentric colatitude and geocentric longitude of the research point respectively; GM is the gravitational constant; n and m represent the order and degree of the spherical harmonic coefficients respectively, Nmax represents the highest order of the spherical harmonic coefficients; a represents the major semi-axis of the ellipsoid; and represents the fully normalized spherical harmonic coefficients; is the nth order and mth order completely normalized associated Legendre function; ω represents the angular velocity of the earth's rotation;

[0069] Finally, the Earth's gravitational gradient V in the local north-pointing coordinate system yz It can be expressed as

[0070]

[0071] Among them, V yz represents the second-order gradient of the gravitational potential in the yz direction,

[0072]

[0073] Among them, the recursive formula of the fully normalized associated Legendre function is

[0074]

[0075] in, represents the nth-order nth-order fully normalized associated Legendre function, represents the n-1th order and n-1th degree completely normalized associated Legendre function, represents the nth order n-1th order completely normalized associated Legendre function, represents the nth order and mth order completely normalized associated Legendre function, represents the n-2 order mth completely normalized associated Legendre function;

[0076] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0077] Q yz =0 (9)

[0078] Then we get W yz =V yz +Q yz ;

[0079] Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Q yz It represents the second-order gradient of centrifugal force in the yz direction;

[0080] Finally based on W yz Formula (2) can be used to obtain the eastward gradient of gravity at any point P on the level surface under the local north-east coordinate system.

[0081] Furthermore, the gravity north gradient calculation module is specifically used for:

[0082] Under the local north-east coordinate system, the northward gradient of gravity at any point P on the level surface is expressed as

[0083]

[0084] In the formula, g x is the northward gradient of gravity;

[0085] g x The relationship with gravity potential is

[0086]

[0087] Among them, W xz Represents the second-order gradient of the gravitational potential in the xz direction

[0088] W xz =V xz +Q xz (12)

[0089] Among them, V xz represents the second-order gradient of the gravitational potential in the xz direction, Q xz It represents the second-order gradient of centrifugal force in the xz direction;

[0090]

[0091] In the formula,

[0092]

[0093] in, represents the nth order m+1th degree completely normalized associated Legendre function.

[0094] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0095]

[0096] in,

[0097]

[0098] Furthermore, the gravity line osculating azimuth calculation module is specifically used for:

[0099] When the angle between the gravity line curvature vector and the north direction, that is, the osculating azimuth of the gravity line, is α, it is related to the horizontal gravity gradient, that is,

[0100]

[0101] The final gravity line osculating azimuth α is

[0102]

[0103] Compared with the prior art, the present invention has the following beneficial effects:

[0104] The present invention utilizes the connection between the osculating azimuth of gravity lines and the level surface, proposes a method and device for determining the osculating azimuth of gravity lines for assisting instrument leveling, calculates the osculating azimuth of gravity lines through the earth's gravity field model, describes the distribution characteristics of the global osculating azimuth of gravity lines, and thus provides osculating azimuth adjustment parameters for assisting instrument leveling. The present invention can quantitatively characterize and describe the osculating azimuth parameters of gravity lines during instrument leveling, and provides a theoretical and technical basis for improving the efficiency of instrument measurement work preparation. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 A basic flow chart of a method for determining the osculating azimuth of a gravity line for assisting instrument leveling according to an embodiment of the present invention;

[0106] Figure 2 This is a distribution diagram of the eastward gravity gradient of an embodiment of the present invention;

[0107] Figure 3 This is a north-direction gravity gradient distribution diagram of an embodiment of the present invention;

[0108] Figure 4 This is a distribution diagram of the osculating azimuth angles of gravity lines according to an embodiment of the present invention;

[0109] Figure 5 The present invention is a schematic structural diagram of a device for determining the osculating azimuth of gravity lines for assisting instrument leveling according to an embodiment of the present invention. DETAILED DESCRIPTION

[0110] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0111] like Figure 1 As shown, a method for determining the osculating azimuth of a gravity line for assisting instrument leveling comprises:

[0112] Step S101: Calculate the eastward gravity gradient based on the earth's gravity field model.

[0113] Under the local northeast coordinate assumption (x-axis points to the north, y-axis points to the east, and z-axis is the gravity direction), the eastward gradient of gravity at any point P on the level surface can be expressed as

[0114]

[0115] In the formula, g y Represents the eastward gradient of gravity; g is gravity.

[0116] g y The relationship with gravity potential is

[0117]

[0118] Where W is the gravity potential, W yz Represents the second-order gradient of the gravity potential in the yz direction.

[0119] The gravitational potential is equal to the sum of the corresponding gravitational potential and the centrifugal force, that is,

[0120] W=V+Q (3)

[0121] In the formula, V and Q represent gravitational potential and centrifugal potential respectively. Under the condition of geocentric coordinate system, the expressions of V and Q are:

[0122]

[0123] Where ρ is the geocentric radial of the research point; θ and λ represent the geocentric colatitude and geocentric longitude of the research point, respectively; GM is the gravitational constant; n and m represent the order and degree of the spherical harmonic coefficients, respectively; Nmax represents the highest order of the spherical harmonic series; a represents the major semi-axis of the ellipsoid; and represents the fully normalized spherical harmonic coefficients (obtained through the gravity field model); is the nth order and mth order completely normalized associated Legendre function; ω represents the angular velocity of the Earth's rotation.

[0124] Finally, the Earth's gravitational gradient V in the local north-pointing coordinate system yz It can be expressed as

[0125]

[0126] Among them, V yz represents the second-order gradient of the gravitational potential in the yz direction,

[0127]

[0128] Among them, the recursive formula of the fully normalized associated Legendre function is

[0129]

[0130] in, represents the nth-order nth-order fully normalized associated Legendre function, represents the n-1th order and n-1th degree completely normalized associated Legendre function, represents the nth order n-1th order completely normalized associated Legendre function, represents the nth order and mth order completely normalized associated Legendre function, represents the n-2 order mth completely normalized associated Legendre function.

[0131] The initial value of the fully normalized associated Legendre function is

[0132]

[0133] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0134] Q yz =0 (9)

[0135] Then we get W yz =V yz +Q yz ;

[0136] Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Q yz It represents the second-order gradient of centrifugal force in the yz direction;

[0137] Finally based on W yz Formula (2) can be used to obtain the eastward gradient of gravity at any point P on the level surface under the local north-east coordinate system.

[0138] Step S102: Calculate the northward gravity gradient based on the gravity field model.

[0139] Under the assumption of local north-east coordinates, the northward gravity gradient of any point P on the level surface can be expressed as

[0140]

[0141] In the formula, g x is the northward gradient of gravity; the other parameters have the same meanings as above.

[0142] g x The relationship with gravity potential is

[0143]

[0144] The parameters in the formula have the same meaning as above. xzRepresents the second-order gradient of the gravitational potential in the xz direction

[0145] W xz =V xz +Q xz (12)

[0146] Among them, V xz represents the second-order gradient of the gravitational potential in the xz direction, Q xz It indicates the second-order gradient of centrifugal force in the xz direction.

[0147]

[0148] In the formula,

[0149]

[0150] in, represents the nth order m+1th degree completely normalized associated Legendre function.

[0151] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0152]

[0153] in,

[0154]

[0155] The parameters in the formula have the same meaning as above.

[0156] Step S103: Calculate the osculating azimuth of the gravity line.

[0157] Assume that the angle between the gravity line curvature vector and the north direction (x axis) is α, which is the osculating azimuth of the gravity line, which is related to the horizontal gradient of gravity, that is,

[0158]

[0159] Wherein, the parameters have the same meaning as above.

[0160] The final gravity line osculating azimuth α is

[0161]

[0162] Using the eastward gravity gradient obtained in step S101 and the northward gravity gradient obtained in step S102 as input, α can be obtained using equation (18), thereby obtaining the osculating azimuth adjustment parameter for assisting instrument leveling.

[0163] As a specific implementable method, the EIGEN6C4 earth gravity field model is used as calculation input to calculate the eastward gravity gradient and the northward gravity gradient respectively, and then obtain the osculating azimuth at any point of the gravity line.

[0164] Step 1: Use the EIGEN6C4 gravity field model to calculate the global 5′×5′ resolution gravity eastward gradient. The results are as follows: Figure 2 As shown, the influence of actual terrain undulation is ignored when calculating the geocentric coordinates.

[0165] Step 2: Use the EIGEN6C4 gravity field model to calculate the global 5′×5′ resolution gravity north gradient. The results are as follows: Figure 3 As shown, the influence of actual terrain undulation is ignored when calculating the geocentric coordinates.

[0166] Step 3: Use the global 5′×5′ resolution gravity easting gradient obtained in step 1 and the global 5′×5′ resolution gravity northing gradient obtained in step 2 to calculate the global 5′×5′ resolution gravity line osculating azimuth. The result is as follows: Figure 4 shown.

[0167] Figure 4 It shows that the maximum value of the osculating azimuth of gravity lines in the global range is close to 180°, and the average value and standard deviation are about 90° and 59° respectively. At the same time, the osculating azimuth of gravity lines varies with different points and is not a fixed value. In other words, after the instrument is leveled, the osculating azimuth of gravity lines at the center of the instrument is uniquely determined. In other words, the determination of the osculating azimuth of gravity lines at the center of the instrument can provide an empirical reference for instrument leveling. In addition, taking the 5′×5′ grid size as a reference, about 49.86% of the regions in the world have osculating azimuths less than 90°, that is, the global gravity lines are concave to the north and concave to the south, accounting for half of the area.

[0168] Based on the above embodiments, Figure 5 As shown, another aspect of the present invention provides a device for determining the osculating azimuth of a gravity line for assisting instrument leveling, comprising:

[0169] The gravity eastward gradient calculation module is used to calculate the gravity eastward gradient based on the earth's gravity field model;

[0170] Gravity north gradient calculation module, used to calculate the gravity north gradient based on the gravity field model;

[0171] The gravity line osculating azimuth calculation module is used to calculate the gravity line osculating azimuth based on the obtained gravity eastward gradient and gravity northward gradient.

[0172] Furthermore, the gravity eastward gradient calculation module is specifically used for:

[0173] Under the local north-east coordinate system, the eastward gradient of gravity at any point P on the level surface is expressed as

[0174]

[0175] In the formula, g y represents the eastward gradient of gravity; g is gravity;

[0176] g y The relationship with gravity potential is

[0177]

[0178] Where W is the gravity potential, W yz represents the second-order gradient of the gravity potential in the yz direction. The gravity potential is equal to the sum of the corresponding gravitational potential and the centrifugal force, that is,

[0179] W=V+Q (3)

[0180] In the formula, V and Q represent the gravitational potential and centrifugal potential respectively. Under the conditions of the geocentric coordinate system, the expressions of V and Q are:

[0181]

[0182] Where ρ is the geocentric radial of the research point; θ and λ represent the geocentric colatitude and geocentric longitude of the research point respectively; GM is the gravitational constant; n and m represent the order and degree of the spherical harmonic coefficients respectively, Nmax represents the highest order of the spherical harmonic coefficients; a represents the major semi-axis of the ellipsoid; and represents the fully normalized spherical harmonic coefficients; is the nth order and mth order completely normalized associated Legendre function; ω represents the angular velocity of the earth's rotation;

[0183] Finally, the Earth's gravitational gradient V in the local north-pointing coordinate system yz It can be expressed as

[0184]

[0185] Among them, V yz represents the second-order gradient of the gravitational potential in the yz direction,

[0186]

[0187] Among them, the recursive formula of the fully normalized associated Legendre function is

[0188]

[0189] in, represents the nth-order nth-order fully normalized associated Legendre function, represents the n-1th order and n-1th degree completely normalized associated Legendre function, represents the nth order n-1th order completely normalized associated Legendre function, represents the nth order and mth order completely normalized associated Legendre function, represents the n-2 order mth completely normalized associated Legendre function.

[0190] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0191] Q yz =0 (9)

[0192] Then we get W yz =V yz +Q yz ;

[0193] Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Q yz It indicates the second-order gradient of centrifugal force in the yz direction.

[0194] Finally based on W yz Formula (2) can be used to obtain the eastward gradient of gravity at any point P on the level surface under the local north-east coordinate system.

[0195] Furthermore, the gravity north gradient calculation module is specifically used for:

[0196] Under the local north-east coordinate system, the northward gradient of gravity at any point P on the level surface is expressed as

[0197]

[0198] In the formula, g x is the northward gradient of gravity;

[0199] g x The relationship with gravity potential is

[0200]

[0201] Among them, W xz Represents the second-order gradient of the gravitational potential in the xz direction

[0202] W xz =V xz +Q xz (12)

[0203] Among them, V xz represents the second-order gradient of the gravitational potential in the xz direction, Q xz It indicates the second-order gradient of centrifugal force in the xz direction.

[0204]

[0205] In the formula,

[0206]

[0207] in, represents the nth order m+1th order completely normalized associated Legendre function;

[0208] The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as

[0209]

[0210] in,

[0211]

[0212] Furthermore, the gravity line osculating azimuth calculation module is specifically used for:

[0213] When the angle between the gravity line curvature vector and the north direction, that is, the osculating azimuth of the gravity line, is α, it is related to the horizontal gravity gradient, that is,

[0214]

[0215] The final gravity line osculating azimuth α is

[0216]

[0217] In summary, the present invention utilizes the connection between the osculating azimuth of gravity lines and the level surface, proposes a method and device for determining the osculating azimuth of gravity lines for auxiliary instrument leveling, calculates the osculating azimuth of gravity lines through the earth's gravity field model, and describes the distribution characteristics of the osculating azimuth of global gravity lines, thereby providing osculating azimuth adjustment parameters for auxiliary instrument leveling. The present invention can quantitatively characterize and describe the osculating azimuth parameters of gravity lines during instrument leveling, and provide a theoretical and technical basis for improving the efficiency of instrument measurement work preparation.

[0218] The above is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for determining the osculating azimuth of gravity lines for assisting instrument leveling, characterized in that: include: Step 1: Calculate the eastward gravity gradient based on the Earth's gravity field model; The step 1 comprises: Under the local north-east coordinate system, the eastward gradient of gravity at any point P on the level surface is expressed as In the formula, g y represents the eastward gradient of gravity; g is gravity; g y The relationship with gravity potential is Where W is the gravity potential, W yz represents the second-order gradient of the gravity potential in the yz direction. The gravity potential is equal to the sum of the corresponding gravitational potential and the centrifugal force, that is, W=V+Q (3) In the formula, V and Q represent the gravitational potential and centrifugal potential respectively. Under the conditions of the geocentric coordinate system, the expressions of V and Q are: Where ρ is the geocentric radial of the research point; θ and λ represent the geocentric colatitude and geocentric longitude of the research point respectively; GM is the gravitational constant; n and m represent the order and degree of the spherical harmonic coefficients respectively, Nmax represents the highest order of the spherical harmonic coefficients; a represents the major semi-axis of the ellipsoid; and represents the fully normalized spherical harmonic coefficients; is the nth order and mth order completely normalized associated Legendre function; ω represents the angular velocity of the earth's rotation; Finally, the Earth's gravitational gradient V in the local north-pointing coordinate system yz It can be expressed as Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Among them, the recursive formula of the fully normalized associated Legendre function is in, represents the nth-order nth-order fully normalized associated Legendre function, represents the n-1th order and n-1th degree completely normalized associated Legendre function, represents the nth order n-1th order completely normalized associated Legendre function, represents the nth order and mth order completely normalized associated Legendre function, represents the n-2 order mth completely normalized associated Legendre function; The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as Q yz ＝0 (9) Then we get W yz =V yz +Q yz ; Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Q yz It represents the second-order gradient of centrifugal force in the yz direction; Finally based on W yz , formula (2) obtains the eastward gradient of gravity at any point P on the level surface under the local north-east coordinate system; Step 2: Calculate the northward gravity gradient based on the gravity field model; The step 2 comprises: Under the local north-east coordinate system, the northward gradient of gravity at any point P on the level surface is expressed as In the formula, g x is the northward gradient of gravity; g x The relationship with gravity potential is Among them, W xz represents the second-order gradient of gravity potential in the xz direction; W xz =V xz +Q xz (12) Among them, V xz represents the second-order gradient of the gravitational potential in the xz direction, Q xz It represents the second-order gradient of centrifugal force in the xz direction; In the formula, in, represents the nth order m+1th order completely normalized associated Legendre function; The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as in, Step 3: Calculate the osculating azimuth of the gravity line based on the obtained gravity eastward gradient and gravity northward gradient; The step 3 comprises: When the angle between the gravity line curvature vector and the north direction, that is, the osculating azimuth of the gravity line, is α, it is related to the horizontal gravity gradient, that is, The final gravity line osculating azimuth α is 2. A device for determining the osculating azimuth of gravity lines for assisting instrument leveling, characterized in that: include: The gravity eastward gradient calculation module is used to calculate the gravity eastward gradient based on the earth's gravity field model; The gravity eastward gradient calculation module is specifically used for: Under the local north-east coordinate system, the eastward gradient of gravity at any point P on the level surface is expressed as In the formula, g y represents the eastward gradient of gravity; g is gravity; g y The relationship with gravity potential is Where W is the gravity potential, W yz represents the second-order gradient of the gravity potential in the yz direction. The gravity potential is equal to the sum of the corresponding gravitational potential and the centrifugal force, that is, W=V+Q (3) In the formula, V and Q represent the gravitational potential and centrifugal potential respectively. Under the conditions of the geocentric coordinate system, the expressions of V and Q are: Where ρ is the geocentric radial of the research point; θ and λ represent the geocentric colatitude and geocentric longitude of the research point respectively; GM is the gravitational constant; n and m represent the order and degree of the spherical harmonic coefficients respectively, Nmax represents the highest order of the spherical harmonic coefficients; a represents the major semi-axis of the ellipsoid; and represents the fully normalized spherical harmonic coefficients; is the nth order and mth order completely normalized associated Legendre function; ω represents the angular velocity of the earth's rotation; Finally, the Earth's gravitational gradient V in the local north-pointing coordinate system yz It can be expressed as Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Among them, the recursive formula of the fully normalized associated Legendre function is in, represents the nth-order nth-order fully normalized associated Legendre function, represents the n-1th order and n-1th degree completely normalized associated Legendre function, represents the nth order n-1th order completely normalized associated Legendre function, represents the nth order and mth order completely normalized associated Legendre function, represents the n-2 order mth completely normalized associated Legendre function; The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as Q yz ＝0 (9) Then we get W yz =V yz +Q yz ; Among them, V yz represents the second-order gradient of gravitational potential in the yz direction, Q yz It represents the second-order gradient of centrifugal force in the yz direction; Finally based on W yz , formula (2) obtains the eastward gradient of gravity at any point P on the level surface under the local north-east coordinate system; Gravity north gradient calculation module, used to calculate the gravity north gradient based on the gravity field model; The gravity north gradient calculation module is specifically used for: Under the local north-east coordinate system, the northward gradient of gravity at any point P on the level surface is expressed as In the formula, g x is the northward gradient of gravity; g x The relationship with gravity potential is Among them, W xz Represents the second-order gradient of the gravitational potential in the xz direction W xz =V xz +Q xz (12) Among them, V xz represents the second-order gradient of the gravitational potential in the xz direction, Q xz It represents the second-order gradient of centrifugal force in the xz direction; In the formula, in, represents the nth order m+1th order completely normalized associated Legendre function; The centrifugal force gradient at the research point is expressed in the local north-pointing coordinate system as in, A gravity line osculating azimuth calculation module is used to calculate the gravity line osculating azimuth based on the obtained gravity eastward gradient and gravity northward gradient; The gravity line osculating azimuth calculation module is specifically used for: When the angle between the gravity line curvature vector and the north direction, that is, the osculating azimuth of the gravity line, is α, it is related to the horizontal gravity gradient, that is, The final gravity line osculating azimuth α is

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