Inter-satellite optimal relative navigation method based on phase compensation and micron-level measurement

Abstract

An inter-satellite optimal relative navigation method based on phase compensation and micron-level measurement, according to the space relative state x r|k‑1 The main star and the secondary star state x c|k‑1 , x d|k‑1 Respectively, the orbit numerical recursion is converted to obtain the relative state prediction at k time, the relative dynamics model is constructed, the relative state equation Jacobian matrix is calculated, the linearization Jacobian matrix of the measurement model is constructed to correct the filter error covariance, and simultaneously after obtaining the real measurement at k time, the fitting residual and gain matrix are calculated, the state update and state covariance matrix update value are calculated. After the state update, the relative position and relative velocity information of the main star and the secondary star are obtained, and since there is a deviation in the antenna phase center, further calculation and compensation are still needed, and finally the corrected space relative navigation information is obtained. Through online estimation and compensation of the phase center, the output precision of the space precision measurement load is significantly improved.

Description

Technical Field

[0001] This invention relates to a technology in the field of satellite navigation, specifically an inter-satellite optimized relative navigation method based on phase compensation and micrometer-level measurement. Background Technology

[0002] In the field of space micrometer-level measurement, the measurement payload devices are affected by space interference, such as phase center jitter and random disturbances of high-precision microwave ranging antennas, which will cause relative measurement errors, thus causing output errors in relative navigation. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies for on-orbit micrometer-level measurement payloads due to space disturbances and the resulting relative navigation output errors. It proposes an inter-satellite optimized relative navigation method based on phase compensation and micrometer-level measurement. Through online estimation and compensation of the phase center, the output accuracy of space precision measurement payloads is significantly improved.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to an inter-satellite optimized relative navigation method based on phase compensation and micrometer-level measurements, comprising:

[0006] Step 1: Based on the spatial relative state x at time k-1 r|k-1 The primary and secondary star states involved x c|k-1 x d|k-1 By performing numerical recursion on the orbits, the relative state prediction at time k can be obtained.

[0007] Step 2: Construct a relative dynamic model based on the orbital dynamic equations of the primary and secondary stars, that is, from the state-space variables x of the continuous system. c x d Construct the relative state x r The mathematical expression for .

[0008] Step 3: Calculate the Jacobian matrix of the relative state equations, 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 actual measurement at time k, calculate the fitting residual, gain matrix, state update, and state covariance matrix update values.

[0010] Step 5: After the status update, the relative position and relative velocity information of the primary and secondary satellites are obtained. Since there is a deviation in the antenna phase center, further calculation and compensation are still required to finally obtain the corrected space relative navigation information.

[0011] Technical effects

[0012] The present application is directed to the online nonlinear estimation compensation of the spatial disturbance of the micron-level microwave precise measurement antenna phase center and the direct measurement error problem caused thereby, and improves the output accuracy of relative navigation. Compared with the prior art, the present application can significantly improve the output accuracy of relative navigation in the disturbance environment of the micron-level measurement load in space. Through the simulation of the example scenario, the root mean square of the relative navigation estimation error is analyzed, the relative distance RMS is reduced by 35%, the azimuth angle RMS is reduced by 28%, and the pitch angle RMS is reduced by 32%. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 The flowchart is for the example;

[0014] Figure 2 The schematic diagram is for the example relative distance estimation error;

[0015] Figure 3 The schematic diagram is for the example azimuth angle estimation error;

[0016] Figure 4 The schematic diagram is for the example pitch angle estimation error. DETAILED DESCRIPTION

[0017] As shown in Figure 1 , the present application relates to an inter-satellite optimized relative navigation system based on phase compensation and micron-level measurement, which comprises a numerical recursion module, a relative state construction module, a prediction error covariance matrix calculation module, a residual error and state update module, and a phase center compensation module. The numerical recursion module performs numerical integration from k-1 time to one step length according to the main and secondary satellite dynamics model, and the result is converted into a local horizontal coordinate system to construct a relative state vector. The relative state construction module constructs a relative state dynamics model from the perspective of analytical solution according to the main and secondary satellite orbit dynamics model, laying a foundation for subsequent navigation algorithms. The prediction recursion error covariance calculation module derives the Jacobian matrix according to the relative dynamics model, calculates the discretized state transition matrix, and obtains the state prediction error covariance matrix. The residual error and state update module calculates the measurement equation Jacobian matrix after obtaining the measurement value at time k, calculates the gain matrix, calculates the fitting residual error, and updates the relative state variable and state estimation error covariance matrix at time k. The phase center compensation module considers the problem that the reference phase center of the spatial relative precision measurement device does not coincide with the satellite center of mass, constructs a ranging model, constructs an estimation parameter vector of the phase compensation system, designs a spatial attitude maneuver type and obtains the corresponding residual value, constructs an observation state Jacobian matrix and performs multiple maneuver accumulation, and obtains the phase center estimation value by the least square algorithm and compensates the relative state estimation value.

[0018] This embodiment relates to an inter-satellite optimized relative navigation method based on phase compensation and micrometer-level measurements, including:

[0019] Step 1: Based on the spatial relative state x at time k-1 r|k-1 The status of the primary and secondary stars x c|k-1 x d|k-1 After performing numerical recursion on the orbits, the relative state prediction at time k is obtained. Where: subscript c represents the primary star, subscript d represents the secondary star, specifically including:

[0020] Step 1.1: Construct a continuous system orbital model, taking the primary star as an example: Where: the state variable x includes the three-dimensional position and three-dimensional velocity in the inertial frame, μ = Gm e =398600.436km 3 / s 2 Let f be the gravitational constant and f be the higher-order gravitational perturbation acceleration. The state-space expression is... Initial value of state space x c (t0)=x c (0)=x c0 .

[0021] Step 1.2: Perform numerical integration of the continuous system trajectory model within the step size: Transform the continuous system trajectory model into vector form: x c (t)=[x c1 (t),x c2 (t),...,x c6 (t)],F(t,x c ) = (f1, f2, ..., f6), 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 ),

[0022] z i2 =Lf i (t m +0.5L,x c1m +0.5z 11 ,x c2m +0.5z 21 ,...,x c6m +0.5z 61 ),

[0023] z i3 = Lf i (t m + 0.5L, x c1m + 0.5z 12 , x c2m + 0.5z 22 ,..., x c6m + 0.5z 62 ),

[0024] 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 recursion index, and L is the step size. The secondary numerical integration steps are not repeated here (replace the index c with d).

[0025] Step 1.3, numerical integration as discrete state variables Convert the relative state vector into the local horizontal coordinate system (LVLH), where: e z is perpendicular to the orbital plane, and e y forms a right-hand rule.

[0026] Step 2, based on the primary and secondary relative state step 1, one-step prediction in the relative coordinate system, and construct the relative dynamics model from the primary and secondary orbital dynamics equations, i.e., from the continuous system state space variables x c , x d , construct the relative state x r , which includes:

[0027] Step 2.1, difference processing based on the primary and secondary orbital dynamics equations , After rearrangement, we have

[0028] where: the secondary star relative to the primary star position x r = x d - x c , is the primary star orbital angular velocity vector, θ is the true anomaly, and f is the relative orbital perturbation acceleration.

[0029] Step 2.2, after first-order linearization of the expression in step 2.1, we get wherein:

[0030]

[0031] e is the orbit eccentricity, h is the orbit inertia.

[0032] Step 3, according to the relative orbit dynamics equation and the first-order linearization model obtained in step 2, the Jacobian matrix in the relative state is calculated, which is used for the linear model of the relative orbit dynamics system to predict the recursive error covariance matrix calculation, specifically including:

[0033] Step 3.1, the first-order linearization model obtained in step 2 is differentiated with respect to the state variable to obtain the system Jacobian matrix of the nonlinear state equation wherein: the relative state component x r = [x y z] T , the primary and secondary stars have the vectorial radius value r c , r d , 0 5×5 is a 5x5 zero matrix, I 5×5 is a 5x5 unit matrix,

[0034] Step 3.2, calculate the partial derivatives of each term in the matrix F 21 in step 3.1, including:

[0035] Step 3.3, calculate the partial derivatives of each term in the matrix F 22 in step 3.1, to get

[0036]

[0037] Step 3.4, according to the system Jacobian matrix F k-1 of the nonlinear state equation at time k-1 obtained in step 3.3, calculate the discrete state transition matrix Φ k-1 of the orbit recursion in step 1, according to Φ k-1 = exp(F k-1 Δt) is obtained, wherein: Δt = t k -t k-1 ; the relative state equation error matrix at time k is set to Q k in the discrete system description, then the one-step prediction of the relative state vector obtained in step 1 is the error covariance matrix is wherein:​ is the relative state estimation error covariance matrix at k-1 time.

[0038] Step 4, construct the linearized Jacobian matrix of the measurement model, after obtaining the real measurement at k time, substitute the relative state prediction value obtained in step 2 and the measurement value at k time to correct the filter error covariance, calculate the fitting residual, gain matrix, calculate the state update and state covariance matrix update value, which specifically includes:

[0039] Step 4.1, construct the Jacobian matrix of the measurement model, since the inter-satellite precise ranging has strong linear characteristics compared to the system state variable, the measurement model Jacobian matrix can be directly obtained as Wherein: is the measurement equation;

[0040] Step 4.2, according to the time sequence of the discrete system, after obtaining the measurement z k and the measurement model Jacobian matrix H k , the gain matrix K is obtained, wherein: R k is the measurement model error covariance matrix; then the fitting residual v can be calculated The state estimation at k time is updated as

[0041] Step 5, through step 4, the estimated output state of the relative navigation has been obtained, since the antenna reference phase center of the space relative precise measurement device does not coincide with the satellite center of mass, there is disturbance, which affects the actual relative navigation output precision, therefore, further on-orbit phase deviation estimation and compensation is needed, which specifically includes:

[0042] Step 5.1, construct the inter-satellite precise ranging model considering the phase center deviation, the main and secondary satellite attitude quaternions are q c , q d , the phase center deviation vector of the ranging sensor on the satellite in the body coordinate system is d pcc , d pcd , then the ranging model can be constructed as Wherein: r cd is the relative center of mass vector of the main and secondary satellites in the inertial system, * is the nominal value, is the attitude quaternion direction cosine matrix conversion operation, R br is the constant deviation value, R nr is the random deviation value, Poly(n) is the deviation term introduced by the orbit error, which is fitted by the n-order polynomial a n t n +…+a1t+a0;

[0043] Step 5.2, the estimation parameter of phase compensation is vector Where: the superscript MA is the attitude maneuver A, and MB, MC, MD are the attitude maneuvers B, C, D. After obtaining the measurement, the measurement residual of each maneuver is obtained as Where: M c , M d is the rotation matrix of the primary and secondary stars from the body system to the inertial system;

[0044] Step 5.3, construct the observation state Jacobian matrix

[0045] Where: each sub-maneuver MB, MC, MD is obtained as in step 5.2, that is, the Jacobian matrix of each observation and each sub-maneuver is accumulated to obtain The observation residual accumulation is Finally, the phase center estimation value is obtained by the least square method

[0046] Step 5.4, superimpose the phase center estimation value to the state estimation at time k in step 4 to obtain the relative navigation output result.

[0047] Through specific actual experiments, the space precise ranging system is generally deployed on a low earth orbit satellite for geophysical measurement. The embodiment is simulated in a virtual pendulum type space formation configuration located in a polar low earth orbit. The simulation parameters include: orbital height: 560 km; inclination: 89.2 deg; argument of perigee: 0 deg; longitude of ascending node: 0 deg; true anomaly: 0 deg. The secondary spacecraft flies in a pendulum relative to the primary spacecraft, with a longitudinal distance of about 80 km and an amplitude of 20 km. The preliminary design parameters of the primary and secondary spacecraft include: mass: 200 kg / 400 kg; reference area: 1.81 m 2 / 3.34 m 2 ; size drag coefficient: 1.29 / 1.5; size solar radiation, pressure coefficient: 1.2 / 3.27.

[0048] In order to better evaluate the performance of the relative navigation algorithm, the primary and secondary spacecraft are recursively calculated in the inertial system, and the relative position and velocity are calculated by difference and converted to the primary star relative orbit system, which is considered as the true value. In the dynamic model, four conservative force models are considered: 20-order earth gravity potential; earth-moon gravity DE405 / LE405; earth solid tide IERS1996; ocean tide Space Research 3.0; two non-conservative force models: atmospheric resistance NRLMSISE-00; solar radiation IERS1992.

[0049] Under the above specific simulation environment settings, the traditional relative navigation algorithm and the relative navigation output after the phase compensation algorithm in step 5 are compared. For example,Figure 2 、 Figure 3 、 Figure 4 As shown in Figs. 4, 5 and 6, the relative distance, azimuth angle and elevation angle estimation error diagrams given by different relative navigation algorithms in the four orbit period simulation process can be obviously seen, and the application has obvious precision advantage under the same condition.

[0050] Compared with the prior art, the method can effectively compensate the phase center jitter error of the precise ranging antenna under the space disturbance condition, and realize the output. Through the post-data statistical analysis, the root mean square (RMS) of the relative distance estimation error is reduced by 35%, the RMS of the azimuth angle estimation error is reduced by 28%, and the RMS of the elevation angle estimation error is reduced by 32%.

[0051] The above specific implementation can be adjusted in different ways by those skilled in the art without departing from the principles and purposes of the application, the protection scope of the application is subject to the claims and is not limited by the above specific implementation, and each implementation scheme within the scope is subject to the constraints of the application.

Claims

1. An inter-satellite optimized relative navigation method based on phase compensation and micron-level measurement, characterized in that, Comprise: Step 1, according to the spatial relative state x at k-1 time r|k-1 The main star and the secondary star state x involved c|k-1 , x d|k-1 Respectively, the orbit numerical recursion is obtained, and the relative state prediction at k time is obtained Step 2, construct the relative dynamics model according to the primary and secondary satellite orbit dynamics equations, i.e. from the continuous system state space variables x c , x d , construct the mathematical expression of the relative state x r ; Step 3, calculate the relative state equation Jacobian matrix, for the linear model of the relative orbit dynamics system to predict the recursive error covariance matrix calculation; Step 4, construct the linearization Jacobian matrix of the measurement model to correct the filter error covariance, while obtaining the true measurement at time k, calculate the fitting residual, gain matrix, calculate the state update and state covariance matrix update value; Step 5, after state update, obtain the relative position and relative velocity information of the primary star and the secondary star, since there is a deviation in the antenna phase center, further calculation compensation is still needed, and finally the modified space relative navigation information is obtained, which specifically includes: Step 5.1, construct the inter-satellite precise ranging model considering the phase center offset, the primary and secondary satellite attitude quaternions are q c , d , the phase center offset vector of the on-board ranging sensor in the body coordinate system is d pcc , pcd , then the ranging model can be constructed as where: r cd is the relative to the center of mass vector in the primary and secondary satellite inertial system, * is the nominal value, is the attitude quaternion to direction cosine matrix conversion operation, R br is the constant offset value, R nr is the random offset value, and Poly(n) is the offset term introduced due to orbit determination error, fitted by an n-order polynomial a n t n +...+a1t+a0. Step 5.2, the estimated parameters of phase compensation are vectors where the superscript MAis the attitude maneuver A, and so on… MD, after obtaining the measurements, the measurement residuals of each maneuver are obtained as where: M c M d is the rotation matrix of the primary and secondary stars from the body system to the inertial system; Step 5.3, Constructing the Observation State Jacobian Matrix where each submaneuver MB, MC, MD is similarly obtained, i.e., each observation and each submaneuver Jacobian matrix is accumulated The observation residual accumulation is The phase center estimate is finally obtained by least squares Step 5.4, superimpose the phase center estimation value to the state estimation at time k of step 4 to obtain the relative navigation output result.

2. The inter-satellite optimal relative navigation method based on phase compensation and micron-level measurement according to claim 1, characterized in that, The step 1 specifically comprises: Step 1.

1. Construct a continuous system orbit model, taking the primary star as an example: Where: the state variable x includes three-dimensional position in the inertial system, three-dimensional velocity, μ = Gm e = 398600.436 km 3 2 is the gravitational constant, f is the high-order gravitational perturbation acceleration, and the state space expression State space initial value x c (t0) = x c (0) = x c0 ;​ Step 1.2, Numerical integration of the continuous system orbit model in the step size: convert the continuous system orbit model into 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 index, and L is the step size. Step 1.

3. Numerical integration as a discrete state variable Convert the relative state vector to the local horizontal coordinate system (LVLH), where: e z is perpendicular to the orbital plane, e y constitutes the right-hand rule.

3. The inter-satellite optimal relative navigation method based on phase compensation and micron-level measurement according to claim 1, characterized in that, The step 2 specifically comprises: Step 2.1, according to the primary and secondary star orbit dynamics equation Difference processing is performed, After sorting Wherein: the secondary star position x relative to the primary star r = x d - x c , is the primary star orbit angular velocity vector, θ is the true anomaly, and f is the relative orbit perturbation acceleration; Step 2.

2. After first order linearization of the expression in step 2.1 wherein: e is the orbital eccentricity and h is the orbital moment of inertia.

4. The method according to claim 1, wherein the method is characterized by, The step 3 specifically comprises: Step 3.1, partial derivative of the first order linearized model obtained in step 2.2 with respect to state variables to obtain the system Jacobian matrix of the nonlinear state equation where: relative state component x r = [x y z] T , the main and secondary stars have the vectorial range value r c , r d , 0 5×5 is a 5x5 zero matrix, I 5×5 is a 5x5 unit matrix, To Step 3.

2. Calculate the matrix F from step 3.1 21 The partial derivatives of each term, including: Step 3.

3. Calculate the matrix F in step 3.1 22 The partial derivatives of each term are calculated to obtain Step 3.4: Based on the system Jacobian matrix F of the nonlinear state equation at time k-1 obtained in Step 3.

3. k-1 Calculate the discretized state transition matrix Φ of the orbit 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 description of the discrete system, the error matrix of the relative state equation at time k is set as Q. k Then the relative state vector obtained in step 1 can be predicted in one step. The error covariance matrix is in: Let be the relative state estimation error covariance matrix at time k-1.

5. The method according to claim 1, wherein the method is characterized by, The step 4 specifically comprises: Step 4.1, construct the measurement model Jacobian matrix, since the inter-satellite precise ranging has a strong linear characteristic compared to the system state variables, the measurement model Jacobian matrix is directly obtained as wherein: is the measurement equation; Step 4.2, obtain the measurement z at time k based on the time series of the discrete system k and the measurement model Jacobian H k and obtain the gain matrix K where R k is the measurement model error covariance matrix; then the fitting residual e can be calculated update the state estimation at time k update the state estimation error covariance matrix simultaneously 6. An inter-satellite optimized relative navigation system based on phase compensation and micron-level measurements implementing the method of any of claims 1-5, characterized in that, Comprise: The numerical recursion module, the relative state construction module, the prediction error covariance matrix calculation module, the residual and state update module and the phase center compensation module, wherein: the numerical recursion module carries out numerical integration from time k-1 to one step length according to the primary star and the secondary star dynamics model, and the result is converted into a local horizontal coordinate system to construct a relative state vector;The relative state construction module constructs the relative state dynamics model from the perspective of analytical solution according to the primary star and the secondary star orbit dynamics model, which lays a foundation for the subsequent navigation algorithm;The prediction recursive error covariance calculation module derives the Jacobian matrix according to the relative dynamics model, calculates the discretization state transition matrix, and obtains the state prediction error covariance matrix;The residual and state update module calculates the measurement equation Jacobian matrix after obtaining the measurement value at time k, calculates the gain matrix, calculates the fitting residual and updates the relative state variable and state estimation error covariance matrix at time k;The phase center compensation module considers 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 an estimation parameter vector of the phase compensation system, designs a space attitude maneuver type and obtains a corresponding residual value, constructs an observation state Jacobian matrix and accumulates multiple maneuvers, obtains a phase center estimation value by least square algorithm and compensates the relative state estimation value.

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