A method for determining satellite gravity measurement errors based on accelerometer radial observation noise

Abstract

The present invention belongs to the technical field of satellite gravity measurement and discloses a method for determining satellite gravity measurement error based on accelerometer radial observation noise, comprising: obtaining a radial observation noise time series of an accelerometer under an observation time length T; performing time-domain windowing on the radial observation noise time series to obtain a radial observation noise time series after time-domain windowing; wherein the window function used is 1 during a satellite orbit-descending period and is -1 during a satellite orbit-ascending period; calculating a discrete-time Fourier transform of the radial observation noise time series after time-domain windowing; substituting the discrete-time Fourier transform into a relationship satisfied between the accelerometer radial observation noise and a gravity field potential coefficient error to obtain a gravity field potential coefficient error; the gravity field potential coefficient error is used to reflect the satellite gravity measurement error; the present invention clarifies the propagation mechanism between the accelerometer radial observation noise and the gravity measurement error, which is of great significance for the payload design and error analysis of gravity satellites.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite gravity measurement, and more specifically, relates to a method for determining satellite gravity measurement error based on accelerometer radial observation noise. Background Art

[0002] In gravity satellite missions, accelerometers measure the non-conservative forces acting on the satellite. However, due to the accelerometer's inherent structural design and the influence of the on-orbit environment, its on-orbit observation data (accelerometer observations) are inevitably contaminated with various noises. As the core payload of gravity satellites, the accelerometer's observation noise is closely related to gravity measurement errors. Clearly and accurately understanding the mapping between accelerometer observation noise (the error between the accelerometer's observed value and the true value is called observation noise, or observation error) and gravity measurement errors is crucial for the design of gravity satellite payload accuracy specifications and the propagation mechanism of gravity measurement errors. Among these, radial accelerometer observation noise has the greatest impact on gravity measurement errors.

[0003] In the prior art, numerical methods have been used to study the mapping relationship between accelerometer observation errors and gravity measurement errors. However, these methods cannot obtain universal laws, and the calculation process is complex and computationally intensive. Another approach is to study the mapping relationship between accelerometer observation errors and gravity measurement errors using a semi-analytical method. This method expresses the intersatellite distance using a Fourier series under the linear Hill equation approximation and the nominal orbit approximation, and establishes a relationship between the gravity potential coefficient and the Fourier coefficient. While this method reduces the computational complexity to some extent compared to numerical methods, it still cannot directly reflect the relationship between payload error (accelerometer observation error) and gravity measurement error. This also leads to the problem of high computational complexity when designing the accuracy specifications of gravity satellite payloads. Furthermore, the propagation mechanism of payload error to gravity measurement error remains unclear. Summary of the Invention

[0004] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for determining satellite gravity measurement error based on accelerometer radial observation noise, the purpose of which is to quickly determine the contribution of accelerometer radial observation noise to satellite gravity measurement error based on accelerometer radial observation noise, improve computational efficiency, and clarify the propagation mechanism between accelerometer observation noise and gravity measurement error.

[0005] To achieve the above object, according to a first aspect of the present invention, a method for determining satellite gravity measurement error based on accelerometer radial observation noise is provided, comprising:

[0006] Under the observation time length T, obtain the radial observation noise time series f(n) of the accelerometer;

[0007] Performing time domain windowing on the radial observation noise time series f(n) to obtain a radial observation noise time series after time domain windowing; wherein the window function used for time domain windowing is w(n), and during the satellite orbit descending period, the window function w(n)=1, and during the satellite orbit ascending period, the window function w(n)=-1;

[0008] Calculate the discrete-time Fourier transform F of the radial observation noise time series after time domain windowing;

[0009] Substituting the discrete-time Fourier transform F into the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error, the gravity field potential coefficient error δk is obtained. lm ; Wherein, the gravity field coefficient error δk lm Used to reflect satellite gravity measurement errors;

[0010] The relationship between the accelerometer radial observation noise and the gravity field potential coefficient error is:

[0011]

[0012] Where l and m are the order and degree of the preset gravity field potential coefficient; g lm (z) is the Fourier coefficient determined based on the associated Legendre function; ω θ is the angular velocity of the satellite, ω λ is the angular velocity of the Earth's rotation, G is the gravitational constant, M is the mass of the Earth, R is the average radius of the Earth, and H is the altitude of the satellite's orbit.

[0013] Furthermore, determining the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error includes:

[0014] Establish the gravity field potential coefficient error δk lm The spatial distribution of the radial observation noise of the accelerometer δg z The relationship S1 between (θ, λ) is:

[0015]

[0016] in, Y lm The conjugate of (θ, λ), Y lm (θ, λ) is the complex spherical function Y of the gravitational potential lm (θ, λ); θ and λ represent the latitude and longitude of the satellite in spherical coordinates, respectively; Ω represents the solid angle integrated over the spherical surface;

[0017] Integrate the solid angle ∫δg in the relation S1 z (θ, λ)·Y lm (θ,λ)dΩ is converted into a double integral

[0018] Under the satellite polar circular orbit approximation, the sub-satellite point trajectory of the satellite descending or ascending orbit is projected into a plane rectangular coordinate system, and the projection plane is divided into K parallelograms; the double integral Expressed as The sum of the definite integrals in K parallelograms, and then the double integral in the process of satellite orbit descending or ascending, is obtained. The time-dependent form of the radial observation noise of the accelerometer δg z (t); where δg z (t) The discrete form of the observation time length T is the radial observation noise time series f(n);

[0019] Double integration during satellite orbit lowering and orbit raising The time-dependent form of the radial observation noise of the accelerometer δg z (t), we get the double integral The time-dependent form of the radial observation noise of the accelerometer δg z (t) the relationship between S2;

[0020] Substituting the relationship S2 and the discrete time Fourier transform F of the radial observation noise time series after time domain windowing into the relationship S1, a satisfied relationship between the accelerometer radial observation noise and the gravity field potential coefficient error is obtained.

[0021] Furthermore, the double integral during the satellite orbit reduction process The time-dependent form of the radial observation noise of the accelerometer δg z The relationship between (t) is:

[0022]

[0023] Among them, t i represents the time when the satellite is at the starting position of the ith sub-satellite point track when descending, and Δt is the time it takes for the satellite to fly through the entire sub-satellite point track from the starting moment;

[0024] Double integration during satellite orbit raising The time-dependent form of the radial observation noise of the accelerometer δg z The relationship between (t) is:

[0025]

[0026] Among them, t i ′ represents the time when the satellite is at the starting position of the ith sub-satellite point trajectory during orbit raising.

[0027] Furthermore, the relationship S2 is:

[0028]

[0029] Wherein, w(t) is the time-dependent form of the window function w(n).

[0030] Furthermore, the Fourier coefficient g lm (z) is determined by the following formula:

[0031]

[0032] Among them, P lm (cosθ) is the associated Legendre function, θ represents the latitude of the satellite in spherical coordinates; where f lm (z) is the associated Legendre function P lm The trigonometric expansion coefficient of (cosθ);

[0033] f lm (z) and g lm (z) satisfies:

[0034] g lm (z) = f lm (z-1)-f lm (z+1)z∈[-l+1:2:l-1]

[0035] g lm (-l-1)=-f lm (-l)

[0036] g lm (l+1)=f lm (l).

[0037] According to a second aspect of the present invention, a method for determining a design accuracy index of a gravity satellite payload is provided, comprising:

[0038] The method for determining satellite gravity measurement error based on accelerometer radial observation noise according to any one of the first aspects is used to obtain the gravity field potential coefficient error δk lm ;

[0039] Based on the gravity field potential coefficient error δk lm Compared with known gravity measurement requirements Satisfying relationship between: Solve the values ​​of the accelerometer radial observation noise at different frequencies to determine the amplitude-frequency characteristics and phase-frequency characteristics of the accelerometer radial observation noise;

[0040] The accuracy index of gravity satellite payload design is determined based on the amplitude-frequency characteristic and the phase-frequency characteristic.

[0041] According to a third aspect of the present invention, there is provided an electronic device comprising a computer-readable storage medium and a processor;

[0042] The computer-readable storage medium is used to store executable instructions;

[0043] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for determining satellite gravity measurement error based on accelerometer radial observation noise as described in any one of the first aspects, or / and, to execute the method for determining the gravity satellite payload design accuracy index as described in the second aspect.

[0044] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the program is executed by a processor, it implements the method for determining the satellite gravity measurement error based on the accelerometer radial observation noise as described in any one of the first aspects, or / and, when executed, it implements the method for determining the gravity satellite payload design accuracy index as described in the second aspect.

[0045] According to a fifth aspect of the present invention, a computer program product is provided. When the computer program product is run on a computer, the computer is caused to execute the method for determining the satellite gravity measurement error based on the accelerometer radial observation noise as described in any one of the first aspects, or / and execute the method for determining the gravity satellite payload design accuracy index as described in the second aspect.

[0046] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0047] (1) The method of determining satellite gravity measurement error based on accelerometer radial observation noise of the present invention directly establishes the gravity field potential coefficient error δk of different orders and suborders. lm The relationship between the radial observation noise spectrum of the accelerometer directly reflects the relationship between the payload error (accelerometer radial observation error) and the gravity measurement error. Based on this relationship, the contribution of the accelerometer radial observation noise to the satellite gravity measurement error can be quickly determined, which improves the calculation efficiency and clarifies the propagation mechanism between the accelerometer observation noise and the gravity measurement error. In addition, based on the gravity field potential coefficient error δk lm The computational complexity is also greatly reduced when determining the accuracy indicators of gravity satellite payload design.

[0048] (2) Furthermore, the present invention provides a method for establishing a relationship between the accelerometer radial observation noise and the gravity field potential coefficient error, by first establishing the gravity field potential coefficient error δk lm The spatial distribution of the radial observation noise of the accelerometer δg zThe relationship S1 between (θ, λ) is satisfied. The solid angle integral in relationship 1 is converted into a double integral. Under the satellite polar circular orbit approximation, considering that the sub-satellite trajectory of the satellite descending or ascending orbit is projected into a cluster of parallel lines in the plane, the projection plane is divided into several parallelograms. By calculating the sum of the definite integrals of the double integral in multiple parallelograms, the double integral and the time-dependent form of the accelerometer radial observation noise δg are established. z (t), and substitute the relationship S2 and the discrete time Fourier transform F of the radial observation noise time series after time domain windowing into the relationship S1 to obtain the gravity field potential coefficient error δk at different orders and suborders. lm The relationship between the frequency domain noise of the accelerometer and the radial observation noise spectrum can be used to intuitively analyze the impact mechanism of the accelerometer frequency domain noise on the gravity field potential coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a method for determining satellite gravity measurement error based on accelerometer radial observation noise in an embodiment of the present invention.

[0050] Figure 2 It is the sub-satellite point trajectory of the satellite in the polar circular orbit during the orbit descending period in the embodiment of the present invention.

[0051] Figure 3 is the i-th parallelogram in the embodiment of the present invention.

[0052] Figure 4 This is a comparison diagram of the order error of the gravity field potential coefficient determined when the accelerometer white noise is input in an embodiment of the present invention and the result of the existing numerical method.

[0053] Figure 5 This is a comparison diagram of the order error of the gravity field potential coefficient determined when the accelerometer has colored noise as input in an embodiment of the present invention and the result of the existing numerical method. DETAILED DESCRIPTION

[0054] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0055] Example 1

[0056] like Figure 1 As shown, the method for determining satellite gravity measurement error based on accelerometer radial observation noise in an embodiment of the present invention includes:

[0057] Under the observation time length T, obtain the radial observation noise time series f(n) of the accelerometer;

[0058] The radial observation noise time series f(n) is windowed in the time domain to obtain the windowed radial observation noise time series. The window function w(n) used is:

[0059]

[0060] Perform discrete time Fourier transform DTFT on the windowed radial observation noise time series to obtain the corresponding Fourier transform F;

[0061] Substituting the Fourier transform F into the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error, the gravity field potential coefficient error δk is obtained. lm ; The gravity field potential coefficient error δk lm It is used to reflect the satellite gravity measurement error. Based on the satellite gravity measurement error, it can be used to determine the accuracy index of the gravity satellite payload design. Among them, the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error is:

[0062]

[0063] Where, δk lm is the gravity field potential coefficient error, l and m are the order and degree of the preset gravity field potential coefficient; F is the Fourier transform of the accelerometer radial observation noise time series f(n) after time domain windowing; g lm (z) is the Fourier coefficient determined based on the associated Legendre function; ω θ is the angular velocity of the satellite, ω λ is the angular velocity of the Earth's rotation, G is the gravitational constant, M is the mass of the Earth, R is the average radius of the Earth, and H is the altitude of the satellite's orbit.

[0064] This relationship reflects the contribution of the accelerometer radial observation noise to the satellite gravity measurement error.

[0065] Specifically, in the embodiment of the present invention, the Fourier transform F of the accelerometer radial observation noise time series f(n) after time domain windowing is:

[0066]

[0067] Among them, δg z (t) is the continuous expression of the accelerometer radial observation noise time series f(n); w(t) is the continuous expression of the window function w(n), that is:

[0068]

[0069] glm (z) is the Fourier coefficient determined based on the associated Legendre function and is determined according to the following formula:

[0070]

[0071] Among them, P lm (cosθ) is the associated Legendre function, θ represents the latitude of the satellite in spherical coordinates; where f lm (z) is the associated Legendre function P lm The trigonometric expansion coefficient of (cosθ) is:

[0072]

[0073] f lm (z) and g lm (z) satisfies:

[0074] g lm (z) = f lm (z-1)-f lm (z+1)z∈[-l+1:2:l-1]

[0075] g lm (-l-1)=-f lm (-l)

[0076] g lm (l+1)=f lm (l)

[0077] Where i represents the imaginary unit, the symbol ! represents the factorial, k1, k2, and s are summation variables, and set A is the set of all (k1, k2, s) that satisfy the following equation:

[0078]

[0079] 0≤k1≤m

[0080]

[0081] 0≤k2≤lm-2s

[0082] The following specifically describes a method for obtaining a relationship between the accelerometer radial observation noise and the gravity field potential coefficient error.

[0083] Newton's second law states that the satellite's motion function (position, velocity, acceleration) is a functional of conservative and non-conservative force information. The primary contribution of conservative forces comes from Earth's gravitational field, while non-conservative forces can be measured by onboard accelerometers. Information about the satellite's motion function can be obtained from GNSS satellite navigation systems and onboard GNSS receivers. Treating the gravity field as an unknown quantity allows the establishment of observation equations, which can be solved to determine the gravity field. This is the fundamental principle behind the inversion of the gravity field from high and low SST.

[0084] Due to the gravitational pull of the earth Outside the Earth, the Laplace equation is satisfied, so it can be expanded into a spherical function series of gravitational potential:

[0085]

[0086] in, is the normalized associated Legendre function, C lm 、S lm is the gravity field potential coefficient, which is the gravity field potential coefficient expressed in real number form; (r, λ, θ) is the coordinate of the satellite in spherical coordinates.

[0087] Express formula (1) in another form:

[0088]

[0089] Among them, Y lm (θ, λ) is the complex spherical function of the Earth's gravitational potential, and its expression is:

[0090] Y lm (θ,λ)=P lm (cosθ)e imλ (3)

[0091] Among them, P lm (cosθ) is the associated Legendre function; when m<0, we have:

[0092] P lm (cosθ)=(-1) m ·P l，-m (cosθ) (4)

[0093] Among them, P l，-m (cosθ) is the associated Legendre function when m<0.

[0094] It can be seen that the complex sphere function Y of the gravity potential in formula (2) is lm The gravitational field potential coefficient k in the expression of (θ, λ) lm Also plural.

[0095] Complex form of gravitational field potential coefficient klm and the gravitational field potential coefficient C in real form lm 、S lm The conversion relationship between them is as follows:

[0096]

[0097] Here, i represents the imaginary unit.

[0098] Taking the radial direction of the accelerometer as an example, the expression of the radial component of gravity acceleration is:

[0099]

[0100] Radial acceleration of gravity observed value g z The above equation is satisfied at any time during the satellite flight. The radial observation error (observation noise) of the accelerometer is now recorded as δg z , wherein, in the embodiment of the present invention, δg z (θ, λ) is the spatial representation of the radial observation error of the accelerometer, δg z (t) is the time-dependent form of the radial observation error of the accelerometer, and f(n) is δg z (t) is a discrete form; the corresponding bit coefficient error is recorded as δk lm , then the relationship between the two is:

[0101]

[0102] Considering the complex spherical function Y lm To ensure the orthogonality of (θ, λ), multiply both sides of formula (7) by Y lm (θ, λ), and perform full space integration to establish the spatial distribution of the accelerometer radial observation noise and the gravity field potential coefficient error δk lm Satisfying relationship between:

[0103]

[0104] in, Y lm The conjugate of (θ, λ); Ω represents the solid angle integral over the sphere;

[0105] Based on dΩ=sinθdθdλ, the integral of the solid angle ∫δg in the numerator of formula (8) is z (θ, λ)·Y lm (θ, λ)dΩ is converted into a double integral and the following formula is obtained:

[0106]

[0107] The main task below is to transform the spatial distribution of the accelerometer radial observation noise δgz (θ, λ) is converted to the time-dependent form δg z (t), and then δg z (t) discretization, the coefficient error δk can be established lm The relationship between the radial observation noise time series f(n) of the accelerometer.

[0108] Specifically, if Figure 2 As shown in the figure, under the polar circular orbit approximation, the sub-satellite trajectory of the satellite in the descending or ascending orbit is projected into a plane as a cluster of parallel lines. The projected plane area is divided into several parallelograms according to these parallel lines. By calculating Indirect evaluation of definite integrals in a single parallelogram Then establish the bit coefficient error δk lm The relationship between the radial observation noise time series f(n) of the accelerometer.

[0109] The following analysis takes the satellite orbit descent as an example. Under the polar circular orbit, the sub-satellite point trajectory of the satellite orbit descent is projected into the plane rectangular coordinate system, and the projection plane is divided into several parallelograms. When the observation time T is long enough, each parallelogram will become narrow enough, and the angular velocity of the satellite flight is recorded as ω θ , the angular velocity of the Earth's rotation is denoted as ω λ , assuming that at t = 0, the spherical coordinates of the satellite are (0, 0), the spherical coordinates of the satellite at any time can be expressed as follows:

[0110] θ=ω θ tλ=ω λ t (10)

[0111] Then the double integral It can be expressed as The sum of the definite integrals in each parallelogram, and The definite integral within each parallelogram can be expressed as the line integral along the trajectory of the subsatellite point and the width Δx of a single parallelogram along the latitude θ. i The product of Figure 3 As shown; where the line integral along the subsatellite point trajectory can be expressed as:

[0112]

[0113] Where dl represents the length of the line element, l i represents the length of the i-th sub-satellite point trajectory.

[0114] According to the relationship between dl and time t, formula (11) can be written as a time-dependent expression:

[0115]

[0116] Formula (12) is the line integral along the subsatellite point trajectory.

[0117] but The definite integral in the i-th parallelogram can be expressed as:

[0118]

[0119] Among them, S i represents the i-th parallelogram; t i represents the moment when the satellite is at the starting position of the i-th parallel line when descending the orbit, Δt is the time it takes for the satellite to fly across the entire parallel line from the starting moment; Δx i represents the width of the i-th parallelogram (along the latitude θ direction).

[0120] Therefore, the integral over the entire space (projection plane) can be expressed as:

[0121]

[0122]

[0123] In the formula, is Δx i The average value of the observation time is T. The number of circles the satellite flies in time T is equal to the number of roots of parallel lines.

[0124]

[0125] The following formulas (16)-(20) are used to convert Expand into triangular form:

[0126] The explicit expression for the associated Legendre function is as follows:

[0127]

[0128] Where [n] represents the largest integer not exceeding n, and for any 0≤θ<π:

[0129]

[0130] sinθ and cosθ can be expressed as complex numbers:

[0131]

[0132] After substituting sinθ and cosθ in complex form and careful calculation, we get the following form:

[0133]

[0134] A is the set of all (k1, k2, s) that satisfies the following equation:

[0135]

[0136] 0≤k1≤m

[0137]

[0138] 0≤k2≤lm-2s

[0139] After the above deduction, the present invention found that P lm (cosθ) can be expanded into a form similar to the "Fourier series". Substituting this expansion into the spherical function and further processing formula (14) is:

[0140]

[0141] Substitute the time-dependent expressions of θ and λ and simplify further:

[0142]

[0143] When the satellite is raising its orbit, similar derivation can be used to obtain:

[0144]

[0145] Among them, t i ' represents the moment when the satellite is at the starting position of the i-th parallel line during orbit raising.

[0146] It should be noted that for satellite orbit raising, formula (10) is different, but the other formulas have the same expression.

[0147] By adding formula (22) and formula (23), we can get the integral within the observation time T:

[0148]

[0149] w(t) in formula (24) can be regarded as a window function:

[0150]

[0151] Formula (24) can be transformed into:

[0152]

[0153] The function w(t)·δg z (t) is defined to extend to (-∞, +∞). When t is outside the observation time period [0, T], the default function value is 0. It can be seen that the definite integral on the right side of the above equation is exactly w(t)·δgz (t) is the Fourier transform of w(t)·δg z The Fourier transform of (t) is denoted as F(ω), then the above formula can be expressed as:

[0154]

[0155] Substituting formula (26) and formula (9) into formula (8), we obtain:

[0156]

[0157] Thus, the relationship between the gravity field potential coefficient error of any order and the spectrum of the accelerometer single-axis observation noise (radial observation noise) is obtained.

[0158] Based on the above analysis, in the embodiment of the present invention, the method of obtaining the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error includes:

[0159] Establish the gravity field potential coefficient error δk lm The spatial distribution of the radial observation noise of the accelerometer δg z The relationship between (θ, λ) is as shown in formula (8);

[0160] The integral of the solid angle ∫δg in the above relationship is z (θ, λ)·Y lm (θ,λ)dΩ is converted into a double integral

[0161] Under the satellite polar circular orbit approximation, the sub-satellite point trajectory of the satellite descending or ascending orbit is projected into the plane rectangular coordinate system, and the projection plane is divided into K parallelograms; the double integral Expressed as The sum of the definite integrals in K parallelograms, and then the double integral in the process of satellite orbit descending or ascending, is obtained. The time-dependent form of the radial observation noise of the accelerometer δg z (t); where δg z (t) The discrete form of the observation time length T is the radial observation noise time series f(n);

[0162] Double integration during satellite orbit lowering and orbit raising The time-dependent form of the radial observation noise of the accelerometer δg z (t), we can get the double integral under the whole space The time-dependent form of the radial observation noise of the accelerometer δg z (t), see formula (25) for details;

[0163] Substitute this relationship into the gravity field potential coefficient error δk lm The spatial distribution of the radial observation noise of the accelerometer δg z (θ, λ), and based on Fourier transform, the relationship between the gravity field potential coefficient error of any order and the accelerometer radial observation noise spectrum is obtained; among them, the gravity field potential coefficient error of any order is used to reflect the satellite gravity measurement error.

[0164] In an embodiment of the present invention, based on the polar circular orbit approximation, the satellite gravity acceleration observation value is extended from the flight orbit to the entire sphere, and the orthogonality of spherical functions is used to establish a relationship between the accelerometer spatial noise and the gravity field potential coefficient error. Then, the accelerometer spatial noise and time domain noise are linked by replacing the integral variable. Finally, an analytical relationship between the gravity field potential coefficient error of any order and the accelerometer radial observation noise spectrum is obtained. Through this analytical relationship, the influence mechanism of the accelerometer frequency domain noise on the gravity field potential coefficient can be intuitively analyzed, which is of great significance for the payload design and error analysis of gravity satellites.

[0165] To further illustrate the accuracy of the method of the present invention, white noise and colored noise of the accelerometer are input respectively. The error of the gravity field potential coefficient is determined based on the method of the present invention and the existing relatively reliable least square method (numerical method). The observation time length T is one month and the sampling frequency of the accelerometer is 1Hz. The experimental results are as follows: Figure 4 and Figure 5 As shown, Figure 4 and Figure 5 The order error in is the sum of the squares of all potential coefficient errors of the same order. The analytical method refers to the gravity field potential coefficient error determined by the relationship between the gravity field potential coefficient error of any order constructed by the present invention and the radial observation noise spectrum of the accelerometer. It can be seen that the results of the two are relatively close, reflecting the high accuracy of the method of the present invention.

[0166] Example 2

[0167] An embodiment of the present invention provides a method for determining a design accuracy index of a gravity satellite payload, comprising:

[0168] Based on the gravity field potential coefficient error δk lm Compared with known gravity measurement requirements Satisfying relationship between: Solve the value of the accelerometer radial observation noise at different frequencies to determine the amplitude-frequency characteristics and phase-frequency characteristics of the accelerometer radial observation noise; among them, the gravity field potential coefficient error δk lm Determined by the method for determining satellite gravity measurement error based on accelerometer radial observation noise in Example 1; related technical solutions refer to the description in Example 1;

[0169] The accuracy index of gravity satellite payload design is determined based on the amplitude-frequency and phase-frequency characteristics of the accelerometer radial observation noise.

[0170] Example 3

[0171] An embodiment of the present invention provides an electronic device, including a computer-readable storage medium and a processor;

[0172] Computer-readable storage media for storing executable instructions;

[0173] The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for determining the satellite gravity measurement error based on the accelerometer radial observation noise in Example 1, or / and, to execute the method for determining the gravity satellite payload design accuracy index in Example 2.

[0174] Example 4

[0175] An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the method for determining satellite gravity measurement errors based on accelerometer radial observation noise as in Example 1 is implemented, or / and, when executed, the method for determining the design accuracy index of a gravity satellite payload as in Example 2 is implemented.

[0176] Example 5

[0177] An embodiment of the present invention provides a computer program product. When the computer program product runs on a computer, it enables the computer to execute the method for determining satellite gravity measurement errors based on accelerometer radial observation noise in Example 1, or / and, execute the method for determining the design accuracy index of the gravity satellite payload in Example 2.

[0178] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining satellite gravity measurement error based on accelerometer radial observation noise, characterized in that: include: Length of observation time Next, obtain the radial observation noise time series f(n) of the accelerometer; The radial observation noise time series f(n) is windowed in the time domain to obtain the radial observation noise time series after time domain windowing; wherein the window function used for time domain windowing is , during the satellite orbit reduction period, the window function , during the satellite orbit raising period, the window function ; Compute the discrete-time Fourier transform of the time series of radially observed noise after windowing in the time domain ; The discrete-time Fourier transform Substituting the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error into the relationship between the gravity field potential coefficient error is obtained ; Wherein, the gravity field coefficient error Used to reflect satellite gravity measurement errors; The relationship between the accelerometer radial observation noise and the gravity field potential coefficient error is: Where, is the order and degree of the preset gravity field potential coefficient; are the Fourier coefficients determined based on the associated Legendre function; is the angular velocity of the satellite, is the angular velocity of the Earth's rotation, G is the gravitational constant, M is the mass of the Earth, R is the average radius of the Earth, and H is the altitude of the satellite's orbit.

2. The method for determining satellite gravity measurement error based on accelerometer radial observation noise according to claim 1, characterized in that: Determining a relationship between the accelerometer radial observation noise and the gravity field potential coefficient error includes: Establishing gravity field potential coefficient error Spatial distribution of radial observation noise of accelerometer The relationship S1 is satisfied between: in, for The conjugate of is the complex spherical function of the gravitational potential; and Respectively represent the latitude and longitude of the satellite in spherical coordinates; represents the solid angle integrated over the sphere; Integrate the solid angle in the relation S1 Convert to double integral ; Under the satellite polar circular orbit approximation, the sub-satellite point trajectory of the satellite descending or ascending orbit is projected into a plane rectangular coordinate system, and the projection plane is divided into K parallelograms; the double integral Expressed as The sum of the definite integrals in K parallelograms, and then the double integral in the process of satellite orbit descending or ascending, is obtained. The time-dependent form of the accelerometer radial observation noise is The relationship between Length of observation time The discrete form of the radial observation noise time series f(n) is as follows; Double integration during satellite orbit lowering and orbit raising The time-dependent form of the accelerometer radial observation noise is The relationship between the two gives the double integral The time-dependent form of the accelerometer radial observation noise is The relationship between S2; The discrete time Fourier transform of the relationship S2 and the radial observation noise time series after time domain windowing is Substituting into the relationship S1, the relationship between the accelerometer radial observation noise and the gravity field potential coefficient error is obtained.

3. The method for determining satellite gravity measurement error based on accelerometer radial observation noise according to claim 2, characterized in that: Double integration during satellite orbit reduction The time-dependent form of the accelerometer radial observation noise is The relationship between them is: in, It represents the time when the satellite starts at the i-th sub-satellite point trajectory when descending the orbit. The time it takes for the satellite to fly through the entire sub-satellite point track from the starting moment; Double integral during satellite orbit raising The time-dependent form of the accelerometer radial observation noise is The relationship between them is: in, It represents the time when the satellite reaches the starting position of the ith sub-satellite point trajectory during orbit raising.

4. The method for determining satellite gravity measurement error based on accelerometer radial observation noise according to claim 3, characterized in that: The relationship S2 is: in, is the window function The timed form of .

5. The method for determining satellite gravity measurement error based on accelerometer radial observation noise according to claim 1, characterized in that: The Fourier coefficients Determined by the following formula: in, is the associated Legendre function, represents the latitude of the satellite in spherical coordinates; where, is the associated Legendre function The trigonometric expansion coefficient of ; and Satisfy between: 。 6. A method for determining the design accuracy index of a gravity satellite payload, characterized in that: include: The method for determining satellite gravity measurement error based on accelerometer radial observation noise according to any one of claims 1 to 5 is used to obtain the gravity field potential coefficient error. ; Based on the gravity field potential coefficient error Compared with known gravity measurement requirements Satisfying relationship between: ≤ , solve the value of the accelerometer radial observation noise at different frequencies to determine the amplitude-frequency characteristic and phase-frequency characteristic of the accelerometer radial observation noise; The accuracy index of gravity satellite payload design is determined based on the amplitude-frequency characteristic and the phase-frequency characteristic.

7. An electronic device, characterized in that: comprising a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium to execute the method for determining satellite gravity measurement error based on accelerometer radial observation noise as described in any one of claims 1-5, or / and, to execute the method for determining the gravity satellite payload design accuracy index as described in claim 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, it implements the method for determining satellite gravity measurement error based on accelerometer radial observation noise as described in any one of claims 1 to 5, or / and, when executed, it implements the method for determining the design accuracy index of gravity satellite payload as described in claim 6.

9. A computer program product, characterized in that When the computer program product runs on a computer, the computer executes the method for determining satellite gravity measurement error based on accelerometer radial observation noise as described in any one of claims 1 to 5, or / and executes the method for determining the design accuracy index of gravity satellite payload as described in claim 6.

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