A relative navigation method based on differential GNSS

Abstract

The application discloses a relative navigation method based on differential GNSS, which utilizes the inertial measurement device installed on a spacecraft to estimate the relative maneuvering acceleration of two stars caused by external force in real time, compensates the relative position information output by GNSS according to the time difference between system time and GNSS time, obtains the measurement value at the current time, simultaneously utilizes the absolute attitude determination output relative body four-element number in the inertial system and the orbit information of the target star to solve the conversion relationship among the body system, the inertial system and the orbit system of the target star, unifies the acceleration and the relative position information to the orbit system of the target star, finally solves the relative position of the two stars by using Kalman filtering, designs a data jump fault processing mechanism, limits the correction amount of the navigation filtering according to the size of the correction value after the convergence of the Kalman filtering, reduces the influence of the measurement jump on the navigation and closed-loop orbit control, eliminates the measurement value lag problem caused by the output frequency of the differential GNSS single machine, and obtains high-precision positioning data.

Description

Technical Field

[0001] This invention relates to the problem of relative navigation of cooperative targets, and more particularly to a relative navigation method based on differential GNSS. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) offer all-weather, all-day coverage and have mature application technologies in low Earth orbit (LEO). While single-point GPS positioning accuracy is limited to meter-level accuracy due to ionospheric and tropospheric errors, differential GPS technology utilizes the temporal and spatial correlations of these errors to reduce or eliminate their impact on positioning accuracy, significantly improving it. Compared to traditional microwave and optical relative measurement sensors, differential GNSS is smaller, lighter, and free from the limitations of optical tracking caused by space illumination, making it increasingly widely used in LEO satellite formation and space rendezvous and docking missions. With the increasing application of space relative positioning, differential GNSS measurement systems are less constrained by the relative distance between two satellites and space environmental factors, resulting in higher measurement accuracy and gradually distinguishing itself from relative measurement sensors. However, GNSS outputs measurements in whole seconds, and the measurement information is based on a single-unit measurement system; information lag can lead to increased navigation algorithm errors. Summary of the Invention

[0003] The purpose of this invention is to provide a relative navigation method based on differential GNSS, which eliminates the measurement lag problem caused by the output frequency of a single differential GNSS unit, and obtains high-precision positioning data.

[0004] To achieve the above objectives, the present invention provides a relative navigation method based on differential GNSS, comprising the following steps:

[0005] Step S1: GNSS data alignment. The whole-second measurement information output by GNSS is pushed back to the current time to ensure that it is aligned with the input of other systems at the same time point.

[0006] Step S2: Coordinate system alignment, converting the position and velocity from the GNSS measurement system to the target star orbit system;

[0007] Step S3: Establish the relative motion equations and observation equations;

[0008] Step S4: Use the Kalman filter algorithm to calculate the relative position of the two stars, and limit the correction amount of the navigation filter according to the magnitude of the correction value after the Kalman filter converges.

[0009] Step S1 includes:

[0010] Calculate the time difference: Δt2 = t gnc -t rel ;

[0011] Among them, t gnc For system time, t rel The timescale is the same as the position and velocity output by the GNSS.

[0012] From the previous three-axis position Call the module that calculates Earth's gravity from position and velocity to calculate gravitational acceleration g:

[0013]

[0014] Among them, R e The Earth's average radius is 6,378,137 m; J² = 1082.63607e⁻⁶, and μ = 398,600 km / s is the geocentric gravitational constant.

[0015] At the current moment, determine the relative position and relative velocity between the two antennas of the J2000 series:

[0016]

[0017]

[0018] v rel1 =v rel +a i ·Δt2

[0019] in, Let f be the transformation matrix from the system to the inertial frame. b For the acceleration in this system, r rel and v rel These represent the position and velocity of the GNSS, respectively, r rel1 and v rel1 These represent the position and velocity at the current moment.

[0020] Step S2 includes:

[0021] Convert the relative position output from the differential GNSS to the target orbital system:

[0022]

[0023] in, The transformation matrix from the inertial frame to the target star's orbital frame is obtained from the target orbital elements. The calculation process is as follows:

[0024]

[0025]

[0026]

[0027] Where Ω, i, and u are the right ascension of the ascending node, the orbital inclination, and the latitudinal argument of the target, respectively.

[0028] Step S3 includes:

[0029] Step S3.1: Relative motion dynamics modeling and establishment of state equations:

[0030] In a near-circular orbit, the dynamic equations of the relative motion between the two stars are as follows, abbreviated as the CW equations:

[0031]

[0032]

[0033]

[0034] With relative position and relative velocity As the system state, the relative motion dynamics equations can be expressed in state-space form;

[0035] Transforming the relative kinematic equations of the target spacecraft in the first orbital coordinate system to the second orbital coordinate system of the target spacecraft, the relative kinematic equations become as follows:

[0036]

[0037]

[0038]

[0039] Generally, replacing n with ω, f x f y f z Replace each with 'a' x a y a z ;Bundle As state variables, the equations of relative motion can be written in state-space form as follows:

[0040]

[0041] The abbreviation is as follows:

[0042]

[0043] In the formula: A 11 =[0 3×3 A 12 =I 3×3 ,

[0044] B1 = [0 3×3 ],B2=I 3×3

[0045] Let be the average orbital angular velocity of the target spacecraft, μ be the geocentric gravitational constant, and a be the orbital radius of the target spacecraft. x a y a z The relative acceleration of the two spacecraft along their three orbital control axes in the orbital coordinate system;

[0046] In each guidance and control cycle, assume U(t) = [a x a y a z ] T Given constant values, the analytical solution of the state equation is obtained using the Laplace transform:

[0047]

[0048] In the formula:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] t0 is the current time, t f For the final time, τ = t f -t0;

[0056] Discretizing the state equations yields:

[0057] X k,k-1 =Φ k,k-1 X k-1 +Q k,k-1 U k-1 Step S3.2: Establish the observation equation:

[0058]

[0059] H k =[I 3×3 0 3×3 ].

[0060] Step S4 includes:

[0061] Step S4.1: Calculate the relative positions of the two stars using the Kalman filter algorithm.

[0062] State estimation:

[0063]

[0064] Among them, the predicted value is:

[0065]

[0066] Filter gain:

[0067]

[0068] Filtering error covariance:

[0069]

[0070] Forecast error covariance:

[0071] P k =[IK k H k ]P k,k-1

[0072] Step S4.2: Limit the amplitude of the correction amount Δz for the navigation filter;

[0073] in,

[0074] The amplitude limit for Δz is as follows:

[0075] Δz max =0.12m, 5m≤R<140m;

[0076] 0.25m, 140m≤R<5km;

[0077] 1.5m, 5km≤R≤10km.

[0078] This invention utilizes inertial measurement units (IMUs) installed on the aircraft to estimate the relative maneuvering acceleration between two satellites caused by external forces in real time. It compensates for the relative position information output by the GNSS based on the time difference between the system time and the GNSS time, obtaining the measurement value at the current moment. Simultaneously, it uses the absolute attitude to determine the quaternion of the output inertial frame relative to the home frame, and the target satellite's orbital information to calculate the conversion relationship between the home frame, the inertial frame, and the target satellite's orbital frame. This unifies the acceleration and relative position information under the target satellite's orbital frame. Finally, Kalman filtering is used to calculate the relative position of the two satellites, and a data jump fault handling mechanism is designed. Based on the magnitude of the correction value after Kalman filtering convergence, the correction amount of the navigation filter is limited to reduce the impact of measurement jumps on navigation and closed-loop orbit control. This eliminates the measurement value lag problem caused by the differential GNSS single-unit output frequency, obtaining high-precision positioning data. Attached Figure Description

[0079] Figure 1 This is a flowchart of a relative navigation method based on differential GNSS provided by the present invention.

[0080] Figure 2 It refers to the relative navigation position error in the 5km to 10km distance range before and after the amplitude limit.

[0081] Figure 3 It refers to the relative navigation speed error before and after the amplitude limit in the 5km to 10km distance range.

[0082] Figure 4 It refers to the relative navigation position error in the 5m to 140m distance range before and after the amplitude limit.

[0083] Figure 5 It refers to the relative navigation speed error before and after the amplitude limit in the distance range of 5m to 140m. Detailed Implementation

[0084] The following is based on Figures 1-5 The preferred embodiments of the present invention will be described in detail below.

[0085] like Figure 1 As shown, this invention provides a relative navigation method based on differential GNSS, comprising the following steps:

[0086] Step S1: GNSS data alignment;

[0087] The whole-second measurement information output by GNSS is recursively pushed to the current time to ensure that it is aligned with the input of other systems at the same time point;

[0088] Calculate the time difference: Δt2 = t gnc -t rel ;

[0089] Among them, tgnc For system time, t rel The timescale is the same as the position and velocity output by the GNSS.

[0090] Depend on (Based on the previous three-axis position), call the module to calculate Earth's gravity from position and velocity, and calculate the gravitational acceleration g:

[0091]

[0092] Among them, R e The average radius of the Earth is 6,378,137 m; J² = 1082.63607e⁻⁶, μ

[0093] =398600km / s is the gravitational constant of the Earth's core.

[0094] At the current moment, determine the relative position and relative velocity between the two antennas of the J2000 series:

[0095]

[0096]

[0097] v rel1 =v rel +a i ·Δt2

[0098] in, Let f be the transformation matrix from the system to the inertial frame. b For the acceleration in this system, r rel and v rel These represent the position and velocity of the GNSS, respectively, r rel1 and v rel1 These represent the current position and velocity, respectively.

[0099] Step S2: Coordinate system alignment, converting the position and velocity from the GNSS measurement system to the target star orbit system;

[0100] Convert the relative position output from the differential GNSS to the target orbital system (system time):

[0101]

[0102] in, The transformation matrix from the inertial frame to the target star's orbital frame is obtained from the target orbital elements. The calculation process is as follows:

[0103]

[0104]

[0105]

[0106] Where Ω, i, and u are the right ascension of the ascending node, the orbital inclination, and the latitudinal argument of the target, respectively;

[0107] Step S3: Establish the relative motion equations and observation equations;

[0108] Step S3.1: Relative motion dynamics modeling and establishment of state equations:

[0109] In a near-circular orbit, the dynamic equations of the relative motion between the two stars are as follows, abbreviated as the CW equations:

[0110]

[0111]

[0112]

[0113] Where x, y, and z are the positions on the three axes. For three-axis velocity, The acceleration is triaxial, and n is the orbital angular velocity, with relative position and relative velocity. As the system state, the relative motion dynamics equations can be expressed in state-space form;

[0114] Transforming the relative kinematic equations of the target spacecraft in the first orbital coordinate system to the second orbital coordinate system of the target spacecraft, the relative kinematic equations become as follows:

[0115]

[0116]

[0117]

[0118] Among them, f x f y f z For triaxial acceleration; generally, replace n with ω, f x f y f z Replace each with 'a' x a y a z ;Bundle As state variables, the equations of relative motion can be written in state-space form as follows:

[0119]

[0120] The abbreviation is as follows:

[0121]

[0122] In the formula: A 11 =[0 3×3 A 12 =I 3×3 ,

[0123] B1 = [0 3×3 ],B2=I 3×3

[0124] Let be the average orbital angular velocity of the target spacecraft, μ be the geocentric gravitational constant, and a be the orbital radius of the target spacecraft. x a y a z The relative acceleration of the two spacecraft along their three orbital control axes in the orbital coordinate system;

[0125] The state equations under near-circular orbits are relatively simple in form. Analytical solutions can be obtained by using the Laplace transform, assuming the thrust is constant. The analytical solutions are simple in form and easy to use.

[0126] In each guidance and control cycle, assume U(t) = [a x a y a z ] T Given constant values, we obtain the analytical solution to the state equation:

[0127]

[0128] In the formula:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] t0 is the current time, t f For the final time, τ = t f -t0;

[0136] Discretizing the state equations yields:

[0137] X k,k-1=Φ k,k-1 X k-1 +Q k,k-1 U k-1 ;

[0138] Step S3.2: Establish the observation equation:

[0139]

[0140] H k =[I 3×3 0 3×3 ];

[0141] Step S4: Use the Kalman filter algorithm to calculate the relative position of the two satellites, and limit the correction amount of the navigation filter according to the magnitude of the correction value after the Kalman filter converges, so as to reduce the impact of measurement jumps on navigation and closed-loop orbit control.

[0142] Step S4.1: Calculate the relative positions of the two stars using the Kalman filter algorithm.

[0143] State estimation:

[0144]

[0145] Among them, the predicted value is:

[0146]

[0147] Filter gain:

[0148]

[0149] Filtering error covariance:

[0150]

[0151] Forecast error covariance:

[0152] P k =[IK k H k ]P k,k-1

[0153] Step S4.2: Limit the amplitude of the correction amount Δz for the navigation filter;

[0154] in,

[0155] The GNSS carrier phase differential positioning error is as follows:

[0156] Relative position accuracy: better than 0.1m (single axis) (5m≤R<140m); better than 0.2m (single axis) (140m≤R<5km); better than 1m (single axis) (5km≤R≤10km);

[0157] Relative speed accuracy: better than 0.05 m / s (single axis) (5 km ≤ R ≤ 10 km); better than 0.03 m / s (single axis) (5 m ≤ R ≤ 5 km);

[0158] Based on the above accuracy indicators, the amplitude limit for Δz is as follows:

[0159] Δz max =0.12m (5m≤R<140m);

[0160] 0.25m (140m≤R<5km);

[0161] 1.5m (5km≤R≤10km).

[0162] Figure 2 It refers to the relative navigation position error before and after the amplitude limit in the 5km to 10km distance range. Figure 3 It is the relative navigation speed error before and after the amplitude limit in the 5km to 10km distance range, caused by Figure 2 and Figure 3 It can be seen that after the amplitude limiter, the navigation position error of the 3m jump is less than 0.5m and the speed error is less than 0.1m / s (the error before the amplitude limiter is 3m and 0.5m / s), which meets the track control requirements.

[0163] Figure 4 It refers to the relative navigation position error in the 5m to 140m distance range before and after the amplitude limit. Figure 5 It is the relative navigation speed error before and after the amplitude limit in the distance range of 5m to 140m, caused by Figure 4 and Figure 5 It can be seen that after amplitude limiting processing, the navigation position error of a jump with an amplitude of 0.5m is less than 0.1m and the speed error is less than 0.02m / s, which meets the system requirements.

[0164] This invention utilizes inertial measurement units (IMUs) installed on the aircraft to estimate the relative maneuvering acceleration between two satellites caused by external forces in real time. It compensates for the relative position information output by the GNSS based on the time difference between the system time and the GNSS time, obtaining the measurement value at the current moment. Simultaneously, it uses the absolute attitude to determine the quaternion of the output inertial frame relative to the home frame, and the target satellite's orbital information to calculate the conversion relationship between the home frame, the inertial frame, and the target satellite's orbital frame. This unifies the acceleration and relative position information under the target satellite's orbital frame. Finally, Kalman filtering is used to calculate the relative position of the two satellites, and a data jump fault handling mechanism is designed. Based on the magnitude of the correction value after Kalman filtering convergence, the correction amount of the navigation filter is limited to reduce the impact of measurement jumps on navigation and closed-loop orbit control. This eliminates the measurement value lag problem caused by the differential GNSS single-unit output frequency, obtaining high-precision positioning data.

[0165] It should be noted that, in the embodiments of the present invention, the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the embodiments and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0166] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A relative navigation method based on differential GNSS, characterized in that, Includes the following steps: Step S1: GNSS data alignment. The whole-second measurement information output by GNSS is pushed back to the current time to ensure that it is aligned with the input of other systems at the same time point. Calculate the time difference: ; in, For system time, The timescale is the same as the position and velocity output by the GNSS. From the previous three-axis position Call the module that calculates Earth's gravity from position and velocity to calculate gravitational acceleration. : in, The average radius of the Earth is 6,378,137 m. J 2 =1082.63607e-6, =398600km / s is the gravitational constant of the Earth's core. ; At the current moment, determine the relative position and relative velocity between the two antennas of the J2000 series: in, This is the transformation matrix from the system to the inertial frame. For acceleration under this system, and These are the GNSS position and velocity, respectively. and These represent the current position and velocity, respectively. Step S2: Coordinate system alignment, converting the position and velocity from the GNSS measurement system to the target star orbit system; Step S3: Establish the relative motion equations and observation equations; Step S4: Use the Kalman filter algorithm to calculate the relative position of the two stars, and limit the correction amount of the navigation filter according to the magnitude of the correction value after the Kalman filter converges. Step S4.1: Calculate the relative positions of the two stars using the Kalman filter algorithm. State estimation: Among them, the predicted value is: Filter gain: Filtering error covariance: Forecast error covariance: Step S4.2: Adjustment of navigation filter Limit the amplitude; in, ; right The limits are as follows: =0.12m,5m≤R<140m; 0.25m, 140m≤R<5km; 1.5m, 5km≤R≤10km.

2. The relative navigation method based on differential GNSS as described in claim 1, characterized in that, Step S2 includes: Convert the relative position output from the differential GNSS to the target orbital system: in, The transformation matrix from the inertial frame to the target star's orbital frame is obtained from the target orbital elements. The calculation process is as follows: in, , , These are the target's right ascension of the ascending node, orbital inclination, and latitudinal argument, respectively.

3. The relative navigation method based on differential GNSS as described in claim 2, characterized in that, Step S3 includes: Step S3.1: Relative motion dynamics modeling and establishment of state equations: In a near-circular orbit, the dynamic equations of the relative motion between the two stars are as follows, abbreviated as the CW equations: in, x , y , z For three-axis positions, , , For three-axis velocity, , , The acceleration is triaxial, and 'n' is the orbital angular velocity, with relative position and relative velocity as the coordinates. As the system state, the relative motion dynamics equations can be expressed in state-space form; Transforming the relative kinematic equations of the target spacecraft in the first orbital coordinate system to the second orbital coordinate system of the target spacecraft, the relative kinematic equations become as follows: in, , , For triaxial acceleration; generally, Replace with , , , Replace with , , ;Bundle As state variables, the equations of relative motion can be written in state-space form as follows: The abbreviation is as follows: In the formula: , , , , , , , The average orbital angular velocity of the target spacecraft. The gravitational constant is the constant of gravity. The orbital radius of the target spacecraft. The relative acceleration of the two spacecraft along their three orbital control axes in the orbital coordinate system; In each guidance control cycle, assuming Given constant values, the analytical solution of the state equation is obtained using the Laplace transform: In the formula: ； ； ； ； ； ； For the current moment, For the final moment, ; Discretizing the state equations yields: ； Step S3.2: Establish the observation equation: 。

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