A fast error decomposition method for celestial navigation system with small field of view

Abstract

The present invention relates to a method for rapid decomposition of errors of a small-field-of-view celestial navigation system, which respectively constructs an inertial reference error model, an installation axis system error model, an attitude angle error model caused by a time error, and an altitude angle error and an azimuth angle error model caused by a time error; the four error models are used to decompose the errors of the small-field-of-view celestial navigation system into an inertial reference error, an installation axis system error, an attitude angle error caused by a time error, an altitude angle error and an azimuth angle error caused by a time error. By establishing an inertial reference error model, an installation axis system error model, an altitude angle and an azimuth angle error model directly introduced by a time error, and an altitude angle and an azimuth angle error model indirectly introduced by a time error, the quantitative influence of each error source on the altitude angle and the azimuth angle can be quickly obtained.

Description

Technical Field

[0001] The invention relates to the technical field of celestial navigation, and in particular to a method for fast error decomposition of a small-field-of-view celestial navigation system. Background Art

[0002] According to the field of view of the star sensor, the celestial navigation system can be divided into a large field of view celestial navigation system and a small field of view celestial navigation system. The small field of view celestial navigation system consists of an inertial reference and a star tracker. When the small field of view celestial navigation system is working, the inertial reference provides horizontal attitude information. The star tracker obtains the position error angle by observing the stars based on the horizontal attitude information provided by the inertial reference and the servo axis system, and then corrects the longitude and latitude information output by the inertial reference based on the position error angle to obtain the attitude, longitude and latitude values ​​output by the small field of view celestial navigation system.

[0003] When the star tracker in the small field of view celestial navigation system is measuring stars, in theory, the starlight vector should be projected at the center of the star tracker's visual axis. However, in addition to the inertial reference error and the installation axis error in the system, when the carrier moves with high dynamics, the attitude angle error, altitude angle error and azimuth angle error caused by the time error will also be stimulated. The projection of starlight in the star tracker actually deviates from the center of the visual axis, and the star tracker outputs the miss amount information. Further calculation based on the miss amount output by the star tracker can obtain the estimated value of the inertial reference error, and use the estimated value of the inertial reference error to correct the inertial reference, ultimately achieving the effect of suppressing the error divergence of the celestial navigation system.

[0004] At present, there are theoretical studies on inertial reference error, installation axis error, star catalog error, star point extraction error, etc. in small-field-of-view astronomical navigation systems. However, there are few theoretical studies on attitude angle error caused by time error and altitude and azimuth angle errors caused by time error. Summary of the invention

[0005] The present invention aims at the technical problems existing in the prior art and provides a method for rapid decomposition of errors of a small-field-of-view celestial navigation system. Based on the inertial reference error and the installation axis system error, the attitude angle error, altitude angle error and azimuth angle error of the small-field-of-view celestial navigation are stimulated by the time error in the high dynamic motion and large pitch angle motion environment, and the attitude angle error, altitude angle error and azimuth angle error models caused by the time error are derived; the inertial reference error source, the installation axis system error source and the time error source are difficult to quantify and decompose in the theoretical demonstration and design stage of the small-field-of-view celestial navigation system, and a method for rapid decomposition of errors of the small-field-of-view celestial navigation system is established.

[0006] The technical solution of the present invention to solve the above technical problems is as follows: a method for rapid error decomposition of a small field of view celestial navigation system, comprising:

[0007] The inertial reference error model, the installation axis error model, the attitude angle error model caused by time error, the altitude angle error and the azimuth angle error model caused by time error are constructed respectively; the error of the small field of view celestial navigation system is decomposed into the inertial reference error, the installation axis error, the attitude angle error caused by time error, the altitude angle error and the azimuth angle error caused by time error by using the four error models;

[0008] The input of the inertial reference error model is the inertial navigation latitude error, longitude error and attitude error angle, the direct output of the inertial reference error model is the pitch angle error and heading angle error, and the indirect output is the altitude angle error and azimuth angle error;

[0009] The input of the installation axis error model is the azimuth axis installation error angle, the pitch axis installation error angle, and the boresight installation error angle, and the output is the altitude error and the azimuth error;

[0010] The input of the attitude angle error model caused by the time error is the UTC time error, the direct output is the pitch angle error and the heading angle error, and the indirect output is the altitude angle error and the azimuth angle error;

[0011] The input of the altitude angle error and azimuth angle error model caused by the time error is the UTC time error, and the output is the pitch angle error and the heading angle error.

[0012] Furthermore, the attitude angle error model caused by the time error is shown in the following formula:

[0013]

[0014] Where Δθ is the pitch angle error, Δγ is the roll angle error, Δψ is the heading angle error, θ is the ideal output pitch angle of the system, L is the ideal output latitude of the system, ψ is the ideal output heading angle of the system, Δt UTC is the UTC time error, ω ie is the angular velocity of the Earth's rotation;

[0015] is the pitch angle actually output by the system, is the heading angle actually output by the system, is the latitude actually output by the system, and ΔL is the latitude error.

[0016] Furthermore, the altitude error and azimuth error model caused by the time error is shown in the following formula:

[0017]

[0018] In the formula,

[0019] a 1=-cos(ζ)-tan(α)sin(ζ)+cot(L)tan(δ)sec(α)

[0020] a 2 =-csc(L)sin(ζ)+csc(L)tan(α)cos(ζ)

[0021] b 1 = sin(ζ)-cos(ζ)tan(α)

[0022] b 2 =-csc(L)cos(ζ)-csc(L)tan(α)sin(ζ)

[0023] α is the star right ascension, δ is the star declination, ζ = λ-λ 0 +ω ie ·t UTC , λ is the ideal output longitude of the system, is the actual output longitude of the system, Δλ is the longitude error, λ 0 is the initial longitude, ω ie is the angular velocity of the Earth’s rotation, t UTC is UTC time, L is the ideal output latitude of the system, is the latitude actually output by the system, ΔL is the latitude error, Δt UTC is the UTC time error, ΔH is the altitude error, ΔA z is the azimuth error, A z is the azimuth.

[0024] Furthermore, the inertial reference error model is as follows:

[0025]

[0026]

[0027] Where Δθ is the pitch angle error, Δγ is the roll angle error, Δψ is the heading angle error, Δλ is the longitude error, ΔL is the latitude error, Δh is the altitude difference, γ is the ideal output roll angle of the system, θ is the ideal output pitch angle of the system, L is the ideal output latitude of the system, ψ is the ideal output heading angle of the system, and Δt UTC is the UTC time error, is the pitch angle actually output by the system, is the heading angle actually output by the system, is the latitude actually output by the system, ΔH is the altitude error, ΔA z is the azimuth error, H is the altitude angle, φ E is the eastward attitude angle error, φ N is the north attitude angle error, φU is the celestial attitude angle error.

[0028] Furthermore, the installation axis error model is as follows:

[0029]

[0030] In the formula, η=[η x η y η z ] T is the axis error vector of system b, μ=[μ x μ y μ z ] T is the axis error vector of the B system, τ=[τ x τ y τ z ] T is the axis error vector of m system, K μ , K η , K τ are the constant error coefficient matrices of μ, η, and τ respectively, m is the coordinate system of the star measuring lens, B is the ideal pitch axis coordinate system, b is the ideal base coordinate system, and ΔH is the altitude angle error.

[0031] The beneficial effects of the present invention are as follows: (1) The present invention systematically derives the quantitative formulas between time error and attitude angle error, altitude angle error and azimuth angle error for the first time. The influence of time error on altitude angle error and azimuth angle error in high dynamic and large pitch angle environment cannot be ignored. Therefore, studying the influence of time error on altitude angle error and azimuth angle error is helpful to establish an accurate time error compensation model.

[0032] (2) Improve the error decomposition efficiency of the small field of view celestial navigation system. Inertial reference error sources, installation axis error sources, and time error sources are difficult to quantify and decompose during the theoretical demonstration and design stages of the small field of view celestial navigation system, and the calculation of each indicator is scattered and has not formed a system. By establishing an inertial reference error model, an installation axis error model, an altitude angle and azimuth angle error model directly introduced by time error, and an altitude angle and azimuth angle error model indirectly introduced by time error, the quantitative impact of each error source on the altitude angle and azimuth angle can be quickly obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A schematic diagram of the overall scheme of a method for rapid error decomposition of a small-field-of-view celestial navigation system provided by an embodiment of the present invention;

[0034] Figure 2 A schematic diagram of an altitude angle and azimuth angle error model indirectly introduced by a time error provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0035] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0036] Figure 1 The figure shows the overall scheme for the rapid decomposition of the small field of view celestial navigation system errors. The premise of this overall scheme is that the inertial reference error, installation axis error, attitude angle error caused by time error, altitude angle error and azimuth angle error caused by time error are independent of each other. In the demonstration and design stage of the small field of view celestial navigation system, the comprehensive error index of the small field of view celestial navigation system is given according to the application scenario. Considering the time error factor, the overall error of the small field of view celestial navigation system is decomposed into four error models: inertial reference error model, installation axis error model, altitude angle and azimuth angle error model directly introduced by time error, and altitude angle and azimuth angle error model indirectly introduced by time error.

[0037] The input of the inertial reference error model is the inertial navigation latitude error, longitude error and attitude error angle. The direct output of the inertial reference error model is the pitch angle error and heading angle error, and the indirect output is the altitude angle error and azimuth angle error.

[0038] The input of the installation axis error model is the azimuth axis installation error angle, the pitch axis installation error angle, and the boresight installation error angle, and the output is the altitude angle error and the azimuth angle error.

[0039] The input of the attitude angle error model caused by time error is the UTC time error, the direct output is the pitch angle error and the heading angle error, and the indirect output is the altitude angle error and the azimuth angle error.

[0040] The input of the altitude error and azimuth error model caused by time error is the UTC time error, and the output is the pitch angle error and heading angle error.

[0041] Constructing an Inertial Reference Error Model

[0042] Inertial reference error refers to the height error and azimuth error of the star tracker output caused by the inertial position error and attitude error. The derivation process of the inertial reference error model meets the assumption that when the inertial reference is error-free, the star tracker can accurately track the starlight vector, that is, the projection point of the starlight vector on the target surface of the star tracker detector is located at the center of the visual axis. The construction of the inertial reference error model is divided into three processes, namely, the separation process of position error and attitude error, the process of establishing the quantitative relationship between the Euler error angle and the position error and attitude error, and the process of establishing the quantitative relationship between the Euler error angle and the height error angle and the azimuth error angle.

[0043] ①Separation of position error and attitude error

[0044] The ideal attitude matrix output by the star tracker when the inertial reference has only position error The actual position matrix of the inertial navigation output Actual measurement attitude matrix with small field of view celestial navigation The relationship between them is as follows:

[0045]

[0046] Position Matrix Longitude provided by inertial navigation latitude get, Obtained from the precession-nutation matrix, the Earth rotation matrix and the polar motion matrix.

[0047] In addition to the position error, the inertial reference also considers the attitude error

[0048]

[0049] In formula (2) Only the inertial navigation attitude error is included, is the chain multiplication expression of the attitude matrix output by the star tracker caused by the combined effect of the inertial navigation attitude error and the position error. The actual output longitude of the celestial navigation system is latitude Pitch Angle Roll Angle and heading angle The relationship between the ideal output λ, L, θ, γ, and ψ is shown in equation (3):

[0050]

[0051] Where Δθ, Δγ, Δψ are attitude error angles, and ΔL, Δλ are longitude and latitude errors.

[0052] ② Quantitative relationship between Euler error angle and position error and attitude error

[0053] Combining both sides of the equation (2) with equation (3) to simplify, we can get the quantitative relationship between the Euler error angle and the position error and attitude error, as shown in (4):

[0054]

[0055] ③ Quantitative relationship between Euler error angle, altitude error angle and azimuth error angle

[0056] Considering only the base pitch angle error and azimuth angle error, the quantitative relationship between the Euler error angle and the height error angle and azimuth error angle is shown in (5):

[0057]

[0058] Equations (4) and (5) are the inertial reference error models.

[0059] Constructing the installation shaft error model

[0060] When there is an error angle in the installation axis system, the projection vector u of the starlight vector on the carrier system b and the projection vector u on the detector plane m Between (6):

[0061]

[0062] Where m′ is the conversion coordinate system of the star measuring lens, m is the coordinate system of the star measuring lens, B1 is the actual pitch axis coordinate system, B is the ideal pitch axis coordinate system, b1 is the actual base coordinate system, and b is the ideal base coordinate system; They represent the transformation matrices between m to m′, B1, B to B1, b1, and b to b1 respectively. They are the measured altitude angle and azimuth angle, which are different from the ideal altitude angle H and the ideal azimuth angle A. z , altitude error ΔH and azimuth error ΔA z The relationship between them can be seen in (7):

[0063]

[0064] Combining equations (6) and (7), the installation shaft error model is shown in (8):

[0065]

[0066] Where η=[η x η y η z ] T is the axis error vector of system b, μ=[μ x μ y μ z ] T is the axis error vector of the B system, τ=[τ x τ y τ z ] T is the axis error vector of m system, K μ , K η , K τ are the constant error coefficient matrices of μ, η, and τ respectively.

[0067] Constructing the attitude angle error model caused by time error

[0068] Assume that there is only UTC time error Δt UTC , the attitude matrix from navigation system n to carrier system b See formula (9):

[0069]

[0070] Combining formula (2), simplifying both sides of the equation (9) yields (10):

[0071]

[0072] Formula (10) can be further simplified to obtain the attitude angle error model caused by time error (11):

[0073]

[0074] Constructing the model of altitude error and azimuth error caused by time error

[0075] Stellar right ascension α, declination δ and the measured altitude angle of the star Azimuth The relationship between them can be seen in (12):

[0076]

[0077] Where ζ=λ-λ 0 +ω ie ·t UTC .

[0078] Assume that the UTC time error Δt UTC Causes altitude error ΔH and azimuth error ΔA z , the position of the observer L, λ, α, δ are known, then the altitude error and azimuth error model caused by the time error is as follows (13):

[0079]

[0080] In formula (13):

[0081]

[0082] Before evaluating the error of the small field of view celestial navigation system, the accuracy index of the inertial navigation system is given first, and then the position error and attitude error of the inertial navigation are calculated. The position error and attitude error of the inertial navigation are used as the input of the inertial reference error model. After being processed by the inertial reference error model, the error index 1 is output. Index 1 represents the quantified value of the altitude error and azimuth error.

[0083] In the small field of view astronomical navigation system, the star tracker has two servo tracking axis systems, namely the pitch tracking axis and the azimuth tracking axis. Due to the problems of inaccurate axis processing and installation, installation errors are inevitable. Therefore, by establishing a mathematical model between the installation error angle and the altitude error and azimuth error, the quantized value between the calibrated axis installation error angle and the altitude error and azimuth error is given, and the output index 2 is the quantized value.

[0084] There are two situations of altitude error and azimuth error caused by time error: time error causes attitude error, and attitude error further causes altitude and azimuth measurement errors; time error directly causes altitude error and azimuth error. With time error as input, after the altitude and azimuth error model directly introduced by time error, index 3 is output, which is the altitude error and azimuth error; with time error as input, after the altitude and azimuth error model indirectly introduced by time error, index 4 is output, which is the altitude error and azimuth error.

[0085] Figure 2 This is a schematic diagram of the altitude and azimuth error model indirectly introduced by the time error. The time error will first introduce the attitude error, which is converted into the attitude error, altitude error, and azimuth error to output the final altitude and azimuth errors.

[0086] The fast error decomposition method of small field of view celestial navigation system proposed by the present invention is Figure 1 and Figure 2 After execution, the error can be quickly decomposed.

[0087] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0088] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A fast error decomposition method for astronomical navigation systems with small field of view, It is characterized in that include: Construct the inertial reference error model, the installation axis error model, the attitude angle error model caused by time error, and the altitude angle error and azimuth angle error models caused by time error respectively; Four error models are used to decompose the small field of view celestial navigation system error into inertial reference error, installation axis error, attitude angle error caused by time error, altitude angle error caused by time error, and azimuth angle error. The input of the inertial reference error model is the inertial navigation latitude error, longitude error and attitude error angle, the direct output of the inertial reference error model is the pitch angle error and heading angle error, and the indirect output is the altitude angle error and azimuth angle error; The input of the installation axis error model is the azimuth axis installation error angle, the pitch axis installation error angle, and the boresight installation error angle, and the output is the altitude error and the azimuth error; The input of the attitude angle error model caused by the time error is the UTC time error, the direct output is the pitch angle error and the heading angle error, and the indirect output is the altitude angle error and the azimuth angle error; The input of the altitude error and azimuth error model caused by the time error is the UTC time error, and the output is the altitude error and the azimuth error; The altitude error and azimuth error model caused by the time error are shown in the following formula: In the formula, is the sidereal right ascension, is the stellar declination, , is the ideal output longitude of the system, , is the actual output longitude of the system, is the longitude error, is the initial longitude, is the Earth's rotation angular velocity, is UTC time, is the ideal output latitude of the system, , is the latitude actually output by the system, is the latitude error, is the UTC time error, is the altitude angle, is the altitude angle error, is the azimuth error, is the azimuth.

2. The method according to claim 1, It is characterized in that The attitude angle error model caused by the time error is shown in the following formula: In the formula, is the pitch angle error, is the roll angle error, is the heading angle error, is the ideal output pitch angle of the system, is the ideal output latitude of the system, is the ideal output heading angle of the system, is the UTC time error, is the angular velocity of the Earth's rotation; , is the pitch angle actually output by the system, is the heading angle actually output by the system, is the latitude actually output by the system, is the latitude error.

3. The method according to claim 1, It is characterized in that The inertial reference error model is as follows: In the formula, is the pitch angle error, is the roll angle error, is the heading angle error, is the longitude error, is the latitude error, is the altitude difference, is the ideal output roll angle of the system, is the ideal output pitch angle of the system, is the ideal output latitude of the system, is the ideal output heading angle of the system, is the UTC time error, , is the pitch angle actually output by the system, is the heading angle actually output by the system, is the latitude actually output by the system, is the altitude angle error, is the azimuth error, is the altitude angle, is the eastward attitude angle error, is the north attitude angle error, is the celestial attitude angle error.

4. The method according to claim 1, It is characterized in that The installation axis error model is as follows: In the formula, for The axis error vector, for The axis error vector, for The axis error vector, They are The constant error coefficient matrix of is the coordinate system of the star measuring lens, is the ideal pitch axis coordinate system, is the ideal base coordinate system, is the altitude angle error, is the azimuth error.

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