Inter-satellite optimization relative navigation method based on phase compensation and micron-order measurement

Abstract

The invention relates to an inter-satellite optimization relative navigation method based on phase compensation and micron-order measurement, which comprises the following steps: respectively carrying out orbit numerical recursion according to states xck-1 and xdk-1 of a primary satellite and an auxiliary satellite involved in a space relative state xrk-1 at a k-1 moment, carrying out conversion to obtain a relative state prediction # imgabs0 # at a k moment, constructing a relative kinetic model, and calculating a Jacobian matrix of a relative state equation; constructing a linear Jacobian matrix of the measurement model to correct filtering error covariance, and after real measurement at the moment k is obtained, calculating a fitting residual error and a gain matrix, and calculating state update and a state covariance matrix update value; after the state is updated, the relative position and relative speed information of the primary satellite and the secondary satellite are obtained, further calculation compensation still needs to be carried out due to deviation of the antenna phase center, and finally corrected space relative navigation information is obtained. According to the invention, through on-line estimation and compensation of the phase center, the output precision of the space precision measurement load is obviously improved.

Description

Technical Field

[0001] The present invention relates to a technology in the field of satellite navigation, in particular to an inter-satellite optimized relative navigation method based on phase compensation and micron-level measurement. Background Art

[0002] In the field of space micron-level measurement, since the measurement payload devices are affected by space interference, such as phase center jitter of high-precision microwave ranging antennas, random disturbances and other factors, relative measurement errors will occur, thereby causing output errors of relative navigation. Summary of the invention

[0003] In view of the spatial disturbance problem of on-orbit micron-level measurement payloads in the prior art and the resulting relative navigation output error, the present invention proposes an inter-satellite optimized relative navigation method based on phase compensation and micron-level measurement. Through online estimation and compensation of the phase center, the output accuracy of the space precision measurement payload is significantly improved.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to an inter-satellite optimized relative navigation method based on phase compensation and micron-level measurement, comprising:

[0006] Step 1: According to the relative state x of space at time k-1 r|k-1 Status of the primary and secondary stars involved x c|k-1 、x d|k-1 Perform orbit numerical recursion respectively to obtain the relative state prediction at time k

[0007] Step 2: Construct a relative dynamics model based on the orbital dynamics equations of the primary and secondary satellites, that is, from the continuous system state space variable x c , x d , construct the relative state x r The mathematical expression of .

[0008] Step 3: Calculate the Jacobian matrix of the relative state equation, which is used in the linear model of the relative orbital dynamics system to predict the recursive error covariance matrix calculation.

[0009] Step 4: Construct the linearized Jacobian matrix of the measurement model to correct the filter error covariance. At the same time, after obtaining the real measurement at time k, calculate the fitting residual, gain matrix, state update and state covariance matrix update value.

[0010] Step 5: After the status is updated, the relative position and relative speed information of the primary and secondary satellites are obtained. Due to the deviation of the antenna phase center, further calculation and compensation are still required to finally obtain the corrected space relative navigation information. Technical Effects

[0011] The present invention performs online nonlinear estimation compensation for the spatial disturbance of the phase center of the micron-level microwave precision measurement antenna and the direct measurement error problem caused by it, thereby improving the output accuracy of relative navigation. Compared with the prior art, the present invention can significantly improve the relative navigation output accuracy in the environment of micron-level measurement payload disturbance in orbit. Through the simulation of the embodiment scenario, the root mean square of the relative navigation estimation error is analyzed, and the relative distance RMS is reduced by 35%, the azimuth RMS is reduced by 28%, and the pitch angle RMS is reduced by 32%. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a flow chart of an embodiment;

[0013] Figure 2 is a schematic diagram of relative distance estimation error in an embodiment;

[0014] Figure 3 Schematic diagram of azimuth estimation error in the embodiment;

[0015] Figure 4 Schematic diagram of pitch angle estimation error in an embodiment. DETAILED DESCRIPTION

[0016] like Figure 1 As shown, this embodiment relates to an inter-satellite optimized relative navigation system based on phase compensation and micron-level measurement, including: a numerical recursion module, a relative state construction module, a prediction error covariance matrix calculation module, a residual and state update module and a phase center compensation module, wherein: the numerical recursion module performs numerical integration from the k-1 moment to a step length in the state space according to the dynamic model of the primary and secondary satellites, and the result is converted into a local horizontal coordinate system to construct a relative state vector; the relative state construction module constructs a dynamic model of the relative state from the perspective of analytical solution according to the orbital dynamic model of the primary and secondary satellites, laying a foundation for the subsequent navigation algorithm; the prediction recursion error covariance calculation module performs numerical integration from the k-1 moment to a step length according to the relative dynamic model The Jacobian matrix is ​​derived from the model, the discretized state transfer matrix is ​​calculated, and the state prediction error covariance matrix is ​​obtained; after obtaining the measurement value at time k, the residual and state update module calculates the Jacobian matrix of the measurement equation, the gain matrix, the fitting residual, and updates the relative state variable at time k and the state estimation error covariance matrix; the phase center compensation module considers the problem that the reference phase center of the space relative precision measurement device does not coincide with the satellite center of mass, constructs a ranging model, constructs the estimated parameter vector of the phase compensation system, designs the space attitude maneuver type and obtains the corresponding residual value, constructs the observation state Jacobian matrix and performs multi-maneuver accumulation, obtains the phase center estimate through the least squares algorithm and compensates it to the relative state estimate.

[0017] This embodiment relates to an inter-satellite optimized relative navigation method based on phase compensation and micron-level measurement, including:

[0018] Step 1: According to the relative state x of space at time k-1 r|k-1 Status of main star and secondary star x c|k-1 、x d|k-1 After recursive orbital numerical calculation, the relative state prediction at time k is obtained. Among them: subscript c represents the primary star, subscript d represents the secondary star, specifically including:

[0019] Step 1.1: Construct a continuous system orbit model, taking the primary star as an example: Among them: the state variable x contains the three-dimensional position and three-dimensional velocity in the inertial system, μ = Gm e =398600.436km 3 / s 2 is the gravitational constant, f is the high-order gravitational perturbation acceleration, and the state space expression is Initial value x in state space c (t0) = x c (0) = x c0 .

[0020] Step 1.2: Numerically integrate the continuous system orbit model within the step size: Convert the continuous system orbit model into vector form: x c (t) = [x c1 (t),x c2 (t),...,x c6 (t)],F(t,x c )=(f1,f2...,f6), and then perform numerical integration: x ci,m+1 =x ci,m+1 +(z i1 +2z i2 +2z i3 +z i4 ) / 6,z i1 =Lf i (t m ,x c1m ,x c2m ,...,x c6m ), z i2 =Lf i (t m +0.5L,x c1m +0.5z 11 ,x c2m +0.5z 21 ,...,x c6m +0.5z 61 ), zi3 =Lf i (t m +0.5L,x c1m +0.5z 12 ,x c2m +0.5z 22 ,...,x c6m +0.5z 62 ), z i4 =Lf i (t m +L,x c1m +z 13 ,x c2m +z 23 ,...,x c6m +z 63 ), where: i = 1, 2, ..., 6 is the system order, m is the recursive subscript, and L is the step size. The steps of the secondary star numerical integration are as above and will not be repeated (replace the subscript c with d).

[0021] Step 1.3: Numerical integration as discrete state variables The relative state vector Transformed to the local horizontal coordinate system (LVLH), where: e z Perpendicular to the orbital plane, e y Constitute the right-hand rule.

[0022] Step 2: According to the recursive orbits of the primary and secondary satellites obtained in step 1, the relative states in the relative coordinate system are converted into a one-step prediction. At the same time, the relative dynamics model is constructed from the orbital dynamics equations of the primary and secondary satellites, that is, from the continuous system state space variable x c , x d , construct the relative state x r , specifically including:

[0023] Step 2.1: Based on the orbital dynamics equations of the primary and secondary stars To make a difference, After sorting out Where: The position of the secondary star relative to the primary star is x r =x d -x c , is the orbital angular velocity vector of the main star, θ is the true anomaly angle, and f is the relative orbital perturbation acceleration.

[0024] Step 2.2: Linearize the expression in step 2.1 to get in: e is the orbital eccentricity and h is the orbital inertia.

[0025] Step 3: Based on the relative orbital dynamics equation obtained in step 2 and the first-order linearized model, the Jacobian matrix in the relative state is calculated for the linear model of the relative orbital dynamics system to predict the recursive error covariance matrix calculation, specifically including:

[0026] Step 3.1: Take the partial derivative of the first-order linearized model obtained in step 2.2 with respect to the state variable to obtain the system Jacobian matrix of the nonlinear state equation: Where: relative state component x r =[xyz] T , the radius vector value of the primary and secondary satellites in the inertial system is r c ,r d , 0 5×5 is a 5×5 zero matrix, I 5×5 is a 5×5 identity matrix, for

[0027] Step 3.2: Calculate the matrix F in step 3.1 21 The partial differentials in include:

[0028] Step 3.3: Calculate the matrix F in step 3.1 22 Taking partial derivatives of each term, we get

[0029] Step 3.4: The Jacobian matrix F of the nonlinear state equation at time k-1 obtained according to step 3.3 k-1 , calculate the discretized state transfer matrix Φ of the orbital recursion in step 1 k-1 , according to Φ k-1 =exp(F k-1 Δt) is obtained, where: Δt = t k -t k-1 ; In the discrete system description, the relative state equation error matrix at time k is set to Q k , then the relative state vector obtained in step 1 is predicted in one step The error covariance matrix is in: is the relative state estimation error covariance matrix at time k-1.

[0030] Step 4: Construct the linearized Jacobian matrix of the measurement model. After obtaining the real measurement at time k, substitute the relative state prediction value obtained in step 2 and the measurement value at time k to correct the filter error covariance, calculate the fitting residual, gain matrix, and calculate the state update and state covariance matrix update value, which specifically includes:

[0031] Step 4.1: Construct the Jacobian matrix of the measurement model. Since the intersatellite precise ranging has a strong linear characteristic compared with the system state variables, the Jacobian matrix of the measurement model can be directly obtained as in: is the measurement equation;

[0032] Step 4.2: According to the discrete system time series, measure z at the time k k and the measurement model Jacobian matrix H k Then, we get the gain matrix Where: R k is the measurement model error covariance matrix; the fitted residuals can then be calculated Update the state estimate at time k At the same time, update the state estimation error covariance matrix

[0033] Step 5: Through step 4, the estimated output state of relative navigation has been obtained. Since the antenna reference phase center of the space relative precision measurement device does not coincide with the satellite mass center, there is a disturbance, which affects the actual relative navigation output accuracy. Therefore, it is necessary to further estimate and compensate the on-orbit phase deviation, which includes:

[0034] Step 5.1: Construct an intersatellite precise ranging model that takes into account the phase center deviation. The attitude quaternions of the primary and secondary satellites are q c ,q d The deviation vector of the phase center of the onboard ranging sensor in the satellite coordinate system is d pcc ,d pcd , then the distance measurement model can be constructed as Where: r cd is the relative center of mass vector of the primary and secondary satellites in the inertial system, * is the nominal value, is the conversion operation from attitude quaternion to direction cosine matrix, R br is the constant deviation value, R nr is the random deviation value, Poly(n) is the deviation term introduced by orbit determination error, and is expressed by n-order polynomial a n t n +…+a1t+a0 fitting;

[0035] Step 5.2: The estimated parameters of phase compensation are vector Where: superscript MA is attitude maneuver A, MB, MC, MD are attitude maneuvers B, C, D. After obtaining the measurement values, the measurement residual of each maneuver can be obtained as Where: M c ,M d is the rotation matrix of the primary and secondary stars from their own system to the inertial system;

[0036] Step 5.3: Construct the Jacobian matrix of the observed state Where: MB, MC, MD of each sub-maneuver are obtained as in step 5.2, that is, the Jacobian matrix of each observation and each sub-maneuver is accumulated to obtain The observation residuals are accumulated as Finally, the phase center estimate is obtained by the least squares method.

[0037] Step 5.4: Superimpose the phase center estimate value onto the state estimate at time k in step 4 to obtain the relative navigation output result.

[0038] After specific actual experiments, it was found that the space precision ranging system is generally deployed on low-orbit satellites for geophysical measurements. This embodiment is simulated in a virtual pendulum-type space formation configuration located in the polar low-earth orbit. The simulation parameters include: orbit altitude: 560km; inclination: 89.2deg; perigee angle: 0deg; ascending node right ascension: 0deg; true anomaly: 0deg. The auxiliary spacecraft flies as a pendulum relative to the main spacecraft, with a longitudinal distance of about 80km and a swing amplitude of 20km. The preliminary design parameters of the main and auxiliary spacecraft include: mass: 200kg / 400kg; reference area: 1.81m 2 / 3.34m 2 ; Dimensional drag coefficient: 1.29 / 1.5; Dimensional solar radiation, pressure coefficient: 1.2 / 3.27.

[0039] In order to better evaluate the performance of the relative navigation algorithm, the main and auxiliary spacecraft are recursively calculated in the inertial system in the dynamic calculation, and the relative positions and velocities are calculated by difference and converted to the relative orbit system of the main spacecraft, which are considered to be true values. In the dynamic model, four conservative force models are considered: Earth gravity potential 20th order; Earth-Moon gravity DE405 / LE405; Earth solid tide IERS1996; Ocean tide Space Research 3.0; Two non-conservative force models: atmospheric drag NRLMSISE-00; Solar pressure IERS1992.

[0040] Under the above specific simulation environment settings, the relative navigation outputs of the traditional relative navigation algorithm and the relative navigation output after the phase compensation algorithm in step 5 are compared. Figure 2 , Figure 3 , Figure 4As shown, the relative distance, azimuth and pitch angle estimation error diagrams obtained by using different relative navigation algorithms during the simulation of four orbital cycles. It can be clearly seen that under the same conditions, the present invention has obvious accuracy advantages.

[0041] Compared with the existing technology, this method can effectively compensate for the phase center jitter error of the precision ranging antenna under spatial disturbance conditions and achieve output. Through post-data statistical analysis, the root mean square (RMS) of the relative distance estimation error is reduced by 35%, the azimuth estimation error RMS is reduced by 28%, and the elevation angle estimation error RMS is reduced by 32%.

[0042] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. An intersatellite optimized relative navigation method based on phase compensation and micron-level measurement, characterized in that: include: Step 1: According to the relative state x of space at time k-1 r|k-1 Status of the primary and secondary stars involved x c|k-1 、x d|k-1 Perform orbit numerical recursion respectively to obtain the relative state prediction at time k Step 2: Construct a relative dynamics model based on the orbital dynamics equations of the primary and secondary satellites, that is, from the continuous system state space variable x c , x d , construct the relative state x r The mathematical expression of Step 3, calculate the Jacobian matrix of the relative state equation, which is used in the linear model of the relative orbital dynamics system to predict the recursive error covariance matrix calculation; Step 4: construct the linearized Jacobian matrix of the measurement model to correct the filter error covariance. At the same time, after obtaining the real measurement at time k, calculate the fitting residual, gain matrix, state update and state covariance matrix update value; Step 5: After the status is updated, the relative position and relative speed information of the primary and secondary satellites are obtained. Due to the deviation of the antenna phase center, further calculation and compensation are still required to finally obtain the corrected space relative navigation information.

2. The intersatellite optimized relative navigation method based on phase compensation and micron-level measurement according to claim 1 is characterized in that: The step 1 specifically includes: Step 1.1: Construct a continuous system orbit model, taking the primary star as an example: Among them: the state variable x contains the three-dimensional position and three-dimensional velocity in the inertial system, μ = Gm e =398600.436km 3 / s 2 is the gravitational constant, f is the high-order gravitational perturbation acceleration, and the state space expression is Initial value x in state space c (t0) = x c (0) = x c0 ; Step 1.2: Numerically integrate the continuous system orbit model within the step size: Convert the continuous system orbit model into a vector form: x(t) = [x1(t), x2(t), ..., x6(t)], F(t, x) = (f1, f2..., f6), and then perform numerical integration: x i,m+1 =x i,m+1 +(z i1 +2z i2 +2z i3 +z i4 ) / 6,z i1 =Lf i (t m ,x 1m ,x 2m ,...,x 6m ), z i2 =Lf i (t m +0.5L,x 1m +0.5z 11 ,x 2m +0.5z 21 ,...,x 6m +0.5z 61 ), z i3 =Lf i (t m +0.5L,x 1m +0.5z 12 ,x 2m +0.5z 22 ,...,x 6m +0.5z 62 ), z i4 =Lf i (t m +L,x 1m +z 13 ,x 2m +z 23 ,...,x 6m +z 63 ), where: i = 1, 2, ..., 6 is the system order, m is the recursive subscript, and L is the step size; Step 1.3: Numerical integration as discrete state variables The relative state vector Transformed to the local horizontal coordinate system (LVLH), where: e z Perpendicular to the orbital plane, e y Constitute the right-hand rule.

3. The intersatellite optimized relative navigation method based on phase compensation and micron-level measurement according to claim 1 is characterized in that: The step 2 specifically includes: Step 2.1: Based on the orbital dynamics equations of the primary and secondary stars To make a difference, After sorting out Where: The position of the secondary star relative to the primary star is x r =x d -x c , is the orbital angular velocity vector of the main star, θ is the true anomaly angle, and f is the relative orbital perturbation acceleration; Step 2.2: Linearize the expression in step 2.1 to get in: e is the orbital eccentricity and h is the orbital inertia.

4. The intersatellite optimized relative navigation method based on phase compensation and micron-level measurement according to claim 1 is characterized in that: The step 3 specifically includes: Step 3.1: Take the partial derivative of the first-order linearized model obtained in step 2.2 with respect to the state variable to obtain the system Jacobian matrix of the nonlinear state equation: Where: relative state component x r =[xyz] T , the radius vector value of the primary and secondary satellites in the inertial system is r c ,r d , 0 5×5 is a 5×5 zero matrix, I 5×5 is a 5×5 identity matrix, Step 3.2: Calculate the matrix F in step 3.1 21 The partial differentials in include: Step 3.3: Calculate the matrix F in step 3.1 22 Taking partial derivatives of each term, we get Step 3.4: The Jacobian matrix F of the nonlinear state equation at time k-1 obtained according to step 3.3 k-1 , calculate the discretized state transfer matrix Φ of the orbital recursion in step 1 k-1 , according to Φ k-1 =exp(F k-1 Δt) is obtained, where: Δt = t k -t k-1 ; In the discrete system description, the relative state equation error matrix at time k is set to Q k , then the relative state vector obtained in step 1 is predicted in one step The error covariance matrix is in: is the relative state estimation error covariance matrix at time k-1.

5. The intersatellite optimized relative navigation method based on phase compensation and micron-level measurement according to claim 1 is characterized in that: The step 4 specifically includes: Step 4.1: Construct the Jacobian matrix of the measurement model. Since the intersatellite precise ranging has a strong linear characteristic compared with the system state variables, the Jacobian matrix of the measurement model is directly obtained as in: is the measurement equation; Step 4.2: According to the discrete system time series, measure z at the time k k and the measurement model Jacobian matrix H k Then, we get the gain matrix Where: R k is the measurement model error covariance matrix; the fitted residuals can then be calculated Update the state estimate at time k At the same time, update the state estimation error covariance matrix 6. The intersatellite optimized relative navigation method based on phase compensation and micron-level measurement according to claim 1 is characterized in that: The step 5 specifically includes: Step 5.1: Construct an intersatellite precise ranging model that takes into account the phase center deviation. The attitude quaternions of the primary and secondary satellites are q c ,q d The deviation vector of the phase center of the onboard ranging sensor in the satellite coordinate system is d pcc ,d pcd , then the distance measurement model can be constructed as Where: r cd is the relative center of mass vector of the primary and secondary satellites in the inertial system, * is the nominal value, is the conversion operation from attitude quaternion to direction cosine matrix, R br is the constant deviation value, R nr is the random deviation value, Poly(n) is the deviation term introduced by orbit determination error, and is expressed by n-order polynomial a n t n +…+a1t+a0 fitting; Step 5.2: The estimated parameters of phase compensation are vector Where: The superscript MA is the attitude maneuver A, and so on... MD. After obtaining the measurement value, the measurement residual of each maneuver can be obtained as Where: M c ,M d is the rotation matrix of the primary and secondary stars from their own system to the inertial system; Step 5.3: Construct the Jacobian matrix of the observed state Among them: MB, MC, MD of each sub-maneuver are obtained similarly, that is, the Jacobian matrix of each observation and each sub-maneuver is accumulated to obtain The observation residuals are accumulated as Finally, the phase center estimate is obtained by the least squares method. Step 5.4: Superimpose the phase center estimate value onto the state estimate at time k in step 4 to obtain the relative navigation output result.

7. An intersatellite optimized relative navigation system based on phase compensation and micron-level measurement for implementing any of the methods described in claims 1-6, characterized in that: include: Numerical recursion module, relative state construction module, prediction error covariance matrix calculation module, residual and state update module and phase center compensation module, among which: the numerical recursion module performs numerical integration from k-1 moment to one step length in the state space according to the dynamic model of the main and secondary satellites, and constructs the relative state vector after the result is converted into the local horizontal coordinate system; the relative state construction module constructs the dynamic model of the relative state from the perspective of analytical solution based on the orbital dynamics model of the main and secondary satellites, laying the foundation for the subsequent navigation algorithm; the prediction recursion error covariance calculation module derives the Jacobian matrix according to the relative dynamics model and calculates the discretized state transfer matrix, and obtain the state prediction error covariance matrix; after obtaining the measurement value at time k, the residual and state update module calculates the measurement equation Jacobian matrix, calculates the gain matrix, calculates the fitting residual and updates the relative state variable at time k and the state estimation error covariance matrix; the phase center compensation module considers the problem that the reference phase center of the space relative precision measurement device does not coincide with the satellite center of mass, constructs a ranging model, constructs the estimated parameter vector of the phase compensation system, designs the space attitude maneuver type and obtains the corresponding residual value, constructs the observation state Jacobian matrix and performs multi-maneuver accumulation, obtains the phase center estimate through the least squares algorithm and compensates it to the relative state estimate.

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