Relativistic navigation filter optimization design method

Abstract

The invention belongs to the technical field of spaceflight control, and discloses a relativistic navigation filter optimization design method, which comprises the following steps: configuring a sub-millisecond star angular distance measuring device and a star sensor, and providing star angular distance and sight line direction measurement information for spacecraft positioning and attitude determination; based on the estimation capability of a multi-model unscented Kalman filter and a data-driven self-learning navigation strategy, full-autonomous navigation of the position, speed and attitude of the spacecraft is realized. According to the optimization design method for the relativistic navigation filter, the estimation capability of a traditional filter and the decision-making capability of a self-learning method are utilized, reasonable filtering model structures and parameters are selected in a self-adaptive mode through interaction between the filter and the environment, the state estimation precision is gradually improved in the actual application process, and the filtering efficiency is improved. The restriction of the uncertainty of the model on the navigation precision is weakened, and the task capability of the navigation system is enhanced, so that a wider application prospect is developed.

Description

Technical Field

[0001] The invention relates to the field of aerospace control technology, and in particular to a relativistic navigation filter optimization design method. Background Art

[0002] Traditional spacecraft autonomous celestial navigation algorithms are constrained by factors such as the conservatism of uncertain system models, the stability of state and statistical parameter estimation, and the complexity of model set implementation, which partially limits their on-orbit application. Therefore, technical requirements are put forward for long-term, high-precision, and fully autonomous navigation of spacecraft, and accurate navigation information plays an important role in the realization of space missions.

[0003] In order to improve the performance of autonomous navigation, most state estimation methods mainly improve the accuracy of state estimation by improving the filtering algorithm. The improvement methods mainly include filtering methods based on adaptive approximation of system models and robust filtering methods for system error suppression. With the changes in mission requirements, the autonomous navigation system model is becoming more and more complex, and there are more and more uncertain factors in the on-orbit operating environment. The accuracy of existing model approximation algorithms is limited, making it difficult to achieve high-precision state estimation of the navigation system on board.

[0004] Therefore, in view of the above problems, the present invention proposes a relativistic navigation filter optimization design method. Summary of the invention

[0005] The purpose of the present invention is to provide a relativistic navigation filter optimization design method, which utilizes the estimation ability of traditional filters and the decision-making ability of self-learning methods, and through the interaction between itself and the environment, adaptively selects reasonable filter model structures and parameters, gradually improves the state estimation accuracy in the actual application process, weakens the constraints of model uncertainty on navigation accuracy, and enhances the mission capability of the navigation system, thereby opening up a broader application prospect.

[0006] To achieve the above object, the present invention provides a relativistic navigation filter optimization design method, comprising the following steps:

[0007] Step S1, selecting the position vector, velocity vector and sensor reference deviation of the spacecraft as the state vector of the navigation and positioning dynamics model, and selecting the unit attitude quaternion and gyro zero bias of the spacecraft as the state vector of the spacecraft attitude determination system;

[0008] Step S2, configuring a sub-milliarcsecond star angular distance measurement device and a star sensor to provide star angular distance and line-of-sight direction measurement information for spacecraft positioning and attitude determination;

[0009] Step S3: Based on the unscented Kalman filter, a multi-model unscented Kalman filter is designed to improve the accuracy and robustness of state estimation; wherein the final output of the multi-model unscented Kalman filter is a weighted sum of state estimation results of multiple unscented Kalman filters;

[0010] Step S4: Based on the unscented Kalman filter and the Q-learning method, a data-driven self-learning navigation strategy is designed, which integrates the estimation capability of the nonlinear Kalman filter and the decision-making capability of the intelligent learning method to achieve fully autonomous navigation of the position, velocity and attitude of the spacecraft.

[0011] Preferably, in step S1, the position vector, velocity vector and sensor reference deviation of the spacecraft are selected as the state vector of the navigation and positioning dynamics model, and the spacecraft navigation and positioning model is established. The state vector is as follows:

[0012]

[0013] Among them, r k =[r xk r yk r zk ] T is the position vector of the spacecraft in the Earth-centered inertial coordinate system; v k =[v xk v yk v zk ] T is the velocity vector of the spacecraft in the geocentric inertial coordinate system; κ k =[… κ ijk …] T is the sensor reference deviation, the subscript k represents discrete time, and is the kth calculation cycle.

[0014] Preferably, in step S1, the unit attitude quaternion and gyro bias of the spacecraft are selected as the state vector of the spacecraft attitude determination system, and a spacecraft navigation attitude determination model is established. The state vector is as follows:

[0015]

[0016] Where, d represents the gyro bias, Represents the unit attitude quaternion, satisfy:

[0017]

[0018] Where ω=[ω x ,ω y ,ω z ] T Represents the angular velocity vector of the spacecraft relative to its body coordinate system; Represents the cross product operator for the unit quaternion.

[0019] Preferably, in step S3, based on the multi-model unscented Kalman filter developed by the unscented Kalman filter, the weight calculation formula is:

[0020]

[0021] Among them, Ω k is an adjustable positive definite matrix, represents the measurement residual, is the weight of the i-th unscented Kalman filter at time k-1, is the target weight at time k.

[0022] Preferably, in step S4, a multi-model unscented Kalman filter designed based on an unscented Kalman filter is used to estimate the position vector, the velocity vector and the attitude of the spacecraft respectively through the unscented Kalman filter;

[0023] The spacecraft navigation and positioning model is as follows:

[0024] f(x k )=x k +Φ(x k )Δ t ;

[0025]

[0026] Among them, Δ t is the state prediction time step; p(r k ) includes the effects of other orbital perturbations besides the gravity of the Earth's center;

[0027] The estimation strategy of decoupling the spacecraft position and attitude is adopted to simplify the influence of external force rejection. Therefore, the state equation of the spacecraft attitude determination system is as follows:

[0028]

[0029] Where w represents the system noise of the spacecraft attitude determination system.

[0030] Therefore, the present invention adopts the above-mentioned relativistic navigation filter optimization design method, utilizes the estimation ability of traditional filters and the decision-making ability of self-learning methods, and adaptively selects reasonable filter model structures and parameters through the interaction between itself and the environment. In the actual application process, the state estimation accuracy is gradually improved, the constraints of model uncertainty on navigation accuracy are weakened, and the mission capability of the navigation system is enhanced, thereby opening up a broader application prospect.

[0031] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A flow chart of a relativistic navigation filter optimization design method of the present invention;

[0033] Figure 2 This is a schematic diagram of stellar aberration of the present invention;

[0034] Figure 3 This is a schematic diagram of the light gravitational deflection effect of the present invention;

[0035] Figure 4 A schematic diagram of position comparison of a navigation and positioning algorithm in an embodiment of the present invention;

[0036] Figure 5 A schematic diagram of speed comparison of navigation and positioning algorithms in an embodiment of the present invention;

[0037] Figure 6 Schematic diagram of comparison of navigation attitude determination algorithms in embodiments of the present invention. DETAILED DESCRIPTION

[0038] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0039] like Figure 1 As shown, the present invention provides a relativistic navigation filter optimization design method, comprising the following steps:

[0040] Step S1, selecting the position vector, velocity vector and sensor reference deviation of the spacecraft as the state vector of the navigation and positioning dynamics model, and selecting the unit attitude quaternion and gyro zero bias of the spacecraft as the state vector of the spacecraft attitude determination system;

[0041] Step S2, configuring a sub-milliarcsecond star angular distance measurement device and a star sensor to provide star angular distance and line-of-sight direction measurement information for spacecraft positioning and attitude determination;

[0042] Step S3: Based on the unscented Kalman filter, a multi-model unscented Kalman filter is designed to improve the accuracy and robustness of state estimation; wherein the final output of the multi-model unscented Kalman filter is a weighted sum of state estimation results of multiple unscented Kalman filters;

[0043] Step S4: Based on the unscented Kalman filter and the Q-learning method, a data-driven self-learning navigation strategy is designed, which integrates the estimation capability of the nonlinear Kalman filter and the decision-making capability of the intelligent learning method to achieve fully autonomous navigation of the position, velocity and attitude of the spacecraft.

[0044] Example 1

[0045] Since the relativistic effect was proposed, its impact has always been of concern to researchers. For the problem of spacecraft navigation, the apparent direction of stars observed by its sensors is the result of the influence of the relativistic effect. By establishing the observation equation of the relativistic navigation system, the influence of the two relativistic effects of stellar aberration and gravitational deflection of light on the observed direction of the star line of sight is studied.

[0046] Stellar aberration is the difference in the direction of sight to the same star measured by an observer in motion and a stationary observer at the same moment. Figure 2 As shown, the spacecraft in the figure is the observer, u' Iik is the line of sight of the star obtained by a stationary observer under the influence of the earth's gravitational field, u″ Iik When an observer moves at a speed v under the influence of the gravitational field obs,k The line of sight to the star obtained during motion.

[0047] Due to the gravitational field of celestial bodies, star light will be deflected when passing near celestial bodies. The gravitational deflection effect of light is as follows: Figure 3 As shown, u I1k and u I2k is the line of sight of the star observed without the effect of the gravitational field. Under the effect of the earth's gravitational field, the line of sight of the star observed becomes u′ I1k and u′ I2k .

[0048] Stellar aberration reflects the speed of the spacecraft in the direction perpendicular to the line of sight of the star, while the gravitational deflection effect of light reflects the relative position of the spacecraft and the main gravitational body. Therefore, the correlation between stellar aberration and the gravitational deflection effect of light and the state of the spacecraft can be established, and the motion state of the carrier can be accurately estimated based on the extremely high-precision measurement of starlight.

[0049] The sub-milliarcsecond stellar angular distance measurement device is an optical navigation sensor that uses stars as signal sources and provides high-precision stellar angular distance measurement information for spacecraft positioning. The observation function of the stellar angular distance observation is as follows:

[0050] y k =h(x k )+v k,p ;

[0051]

[0052] Among them, y k is the observed value obtained using the milliarcsecond sidereal angular distance measurement device, v k,p represents the measurement noise ξ ijk The variance matrix is ​​a symmetric positive definite matrix R k Observation yijk and the observation function h(x k ) in each component h ij (x k ) are:

[0053] y ijk =(u″ Iik ) T u″ Ijk +κ ijk +ξ ijk ;

[0054]

[0055] Among them, κ ijk is the reference deviation of the milliarcsecond sidereal angular distance measuring device, ξ ijk is the measurement noise. (u″ Iik ) T u″ Ijk is the angular distance between the i-th star and the j-th star after the line of sight is affected by the stellar aberration and the gravitational deflection effect of light, v k is the velocity of the spacecraft relative to the center of the earth; v M,k is the speed of the Earth relative to the center of mass of the solar system; c is the speed of light.

[0056] Considering the influence of the relativistic effect on the line of sight of stars, the coordinates of the two non-parallel unit star vectors in the space output by the sensor in the body coordinate system are recorded as b1 and b2, and the angular velocity of the spacecraft observed by the gyroscope device is added to obtain the observation equation of the spacecraft attitude determination system, as shown below:

[0057]

[0058] Where y represents the observation vector of the spacecraft attitude determination system; v represents the observation noise of the spacecraft attitude determination system, ω represents the angular velocity vector of the spacecraft relative to its body coordinate system, d represents the gyro zero bias, and C br Represents the direction cosine matrix from the ground inertial reference coordinate system to the spacecraft body coordinate system. r1” and r2” represent the coordinates of the two unit star vectors in the ground reference inertial coordinate system under the influence of the relativistic effect on the star line of sight.

[0059] Based on the above principle, the present invention proposes a relativistic navigation filter optimization design method, the specific steps are as follows:

[0060] Step S1, selecting the position vector, velocity vector and sensor reference deviation of the spacecraft as the state vector of the navigation and positioning dynamics model, and selecting the unit attitude quaternion and gyro zero bias of the spacecraft as the state vector of the spacecraft attitude determination system.

[0061] Step S11: Establish a spacecraft navigation and positioning model, and the state vector is as follows:

[0062]

[0063] Among them, r k =[r xk r yk r zk ] T is the position vector of the spacecraft in the Earth-centered inertial coordinate system; v k =[v xk v yk v zk ] T is the velocity vector of the spacecraft in the geocentric inertial coordinate system; κ k =[… κ ijk …] T is the sensor reference deviation, the subscript k represents discrete time, and is the kth calculation cycle.

[0064] Step S12: Establish a spacecraft navigation attitude model, and the state vector is as follows:

[0065]

[0066] Where, d represents the gyro bias, Represents the unit attitude quaternion, satisfy:

[0067]

[0068] Where ω=[ω x ,ω y ,ω z ] T Represents the angular velocity vector of the spacecraft relative to its body coordinate system; Represents the cross product operator for the unit quaternion.

[0069] Step S2: configuring a sub-milliarcsecond star angular distance measurement device and a star sensor to provide high-precision star angular distance and line-of-sight direction measurement information for spacecraft positioning and attitude determination.

[0070] Step S3: Based on the unscented Kalman filter (UKF), a multi-model unscented Kalman filter (MMUKF) is developed. The final output of the filter is the weighted sum of multiple UKF state estimation results, thereby improving the accuracy and robustness of the state estimation.

[0071] The weight calculation formula of the multi-model unscented Kalman filter developed based on the unscented Kalman filter is:

[0072]

[0073] Among them, Ω k is an adjustable positive definite matrix, represents the measurement residual, is the weight of the i-th unscented Kalman filter at time k-1, is the target weight at time k.

[0074] Step S4: Based on the unscented Kalman filter and the Q-learning method, a data-driven self-learning navigation algorithm is developed. The algorithm integrates the estimation capability of the nonlinear Kalman filter and the decision-making capability of the intelligent learning method, and realizes fully autonomous navigation of the position, velocity and attitude of the spacecraft.

[0075] Combining the unscented Kalman filter estimation and the decision-making ability of the Q-learning method, a Q-learning unscented Kalman filter is designed, and the recursive solution process is as follows:

[0076]

[0077] In the above algorithm flow, and P k denote the state estimate of the navigation filter and the corresponding estimation error variance matrix, respectively. and Respectively represent the state estimate and the corresponding estimation error variance matrix in the exploration filter, and denote the measurement innovations of the navigation filter and the exploration filter respectively, represents the optional system noise variance matrix, represents the system noise variance matrix selected by the Q learning method, Q(s,a) represents the state action value function (or cumulative reward) of state s and action a in the Q learning algorithm, which can be written in the form of a table, where s represents the currently selected system noise variance matrix, and a represents the Select different system noise variance matrix actions in, R(s,a) represents the reward obtained by performing action a in state s, T represents the time period used to calculate the reward R(s,a); in the recursive calculation formula of Q(s,a), 0≤α<1 represents the learning rate, 0<γ≤1 represents the discount factor, both of which are adjustable parameters; the QLUKF estimation result is the output of the navigation filter and {P k}.

[0078] The spacecraft navigation and positioning model is as follows:

[0079] f(x k )=x k +Φ(x k )Δ t;

[0080]

[0081] Among them, Δ t is the state prediction time step; p(r k ) includes the effects of other orbital perturbations besides the Earth's central gravity.

[0082] In the attitude estimation problem, the estimation strategy of decoupling the spacecraft position and attitude is adopted to simplify the influence of external forces. Therefore, the state equation of the spacecraft attitude determination system is as follows:

[0083]

[0084] Where w represents the system noise of the spacecraft attitude determination system.

[0085] Example 2

[0086] Taking the spacecraft in the cis-lunar space as an example, the effectiveness of the self-learning relativistic navigation method is demonstrated through numerical simulation. In the process of simulating the nominal orbit data of the spacecraft and the simulated values ​​of the observations of the measurement sensor, the semi-major axis is taken as 39842 kilometers, the eccentricity is taken as 0.0051, the orbit inclination is taken as 10.11°, the right ascension of the ascending node is taken as 330.92°, the argument of perigee is taken as 177.7°, and the mean anomaly is taken as 121.27°.

[0087] A sub-milliarcsecond stellar angular distance measurement device is configured on the spacecraft in the Earth-Moon space to observe three stars and form three angular distance observations. The stellar angular distance measurement noise standard deviation is 1mas, the data update rate is 1Hz, and the simulation time is 96h.

[0088] like Figure 4 and Figure 5 As shown in Figure 1, the state estimation error of the navigation system using UKF, MMUKF and QLUKF changes over time. The simulation lasts 96 hours, and the estimated state includes position and velocity. The solid line represents the state estimation error of QLUKF, the dashed line represents the state estimation error of UKF, and the dotted line represents the state estimation error of MMUKF.

[0089] Depend on Figure 4 and Figure 5 It can be seen that the traditional UKF algorithm performs poorly due to the uncertainty of the statistical characteristics of the system noise; QLUKF can select the system noise variance matrix that helps to improve the navigation performance based on the measurement information, thereby achieving state estimation accuracy that is better than traditional UKF and other algorithms.

[0090] Assuming that the sampling period of the sub-milliarcsecond star angular distance measurement device is 1 second, the variance of the sensor's observation error for the unit star vector coordinate is 1×10 -9Assume that the spacecraft is not equipped with an offset momentum wheel and has no control force resistance, and moves only under the action of environmental disturbance torque. The environmental disturbance torque on the three coordinate axes of the spacecraft is set as:

[0091]

[0092] Among them, T dx0 , T dy0 , T dz0 represents the amplitude of the environmental disturbance torque,

[0093] T dx0 =T dy0 =T dz0 =1×10 -5 N·m; ω θ ,ω ψ represents the frequency of the environmental disturbance torque, ω θ =4ω e ,ω ψ =8ω e ,ω e is the angular velocity of the spacecraft’s revolution around the earth. The initial value of the spacecraft’s unit attitude quaternion is set to q0=q1=q2=q3=0.5, and the simulation time is set to 96h.

[0094] like Figure 6 As shown in Figure 1, the simulation results of the attitude error of the navigation system using UKF, MMUKF and QLUKF over time are shown. The solid line represents the attitude estimation error of QLUKF, the dotted line represents the attitude estimation error of UKF, and the dotted line represents the attitude estimation error of MMUKF.

[0095] according to Figure 6 It can be seen that the attitude estimation curve of the algorithm has a slight oscillation in the initial short period of simulation, and then quickly approaches the actual value of the spacecraft attitude, and always follows the real-time changes of the actual value, realizing its function of determining the attitude of the spacecraft.

[0096] Depend on Figure 6 It can be seen that the traditional UKF algorithm performs poorly due to the uncertainty of the statistical characteristics of the system noise; QLUKF can select the system noise variance matrix that helps to improve the navigation performance based on the measurement information, thereby achieving state estimation accuracy that is better than traditional UKF and other algorithms.

[0097] From the above simulation, we can see that the difference between QLUKF and MMUKF in design concept is that the selection of Q array in MMUKF depends on the cognitive level of engineering and technical personnel and the processing power of onboard computers, and the performance is affected by subjective cognition; while QLUKF drives the Q learning algorithm through observation data to select reasonable filter parameters, and its filtering stability is easier to guarantee.

[0098] The main technical content of the present invention is used for spacecraft navigation in the Earth-Moon space. When the angle measurement accuracy of the sensor reaches the mas level, the steady-state positioning accuracy of the spacecraft can be achieved at the hundred-meter level.

[0099] Therefore, the present invention adopts the above-mentioned relativistic navigation filter optimization design method, utilizes the estimation ability of traditional filters and the decision-making ability of self-learning methods, and adaptively selects reasonable filter model structures and parameters through the interaction between itself and the environment. In the actual application process, the state estimation accuracy is gradually improved, the constraints of model uncertainty on navigation accuracy are weakened, and the mission capability of the navigation system is enhanced, thereby opening up a broader application prospect.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A relativistic navigation filter optimization design method, characterized in that: The following steps are involved: Step S1, selecting the position vector, velocity vector and sensor reference deviation of the spacecraft as the state vector of the navigation and positioning dynamics model, and selecting the unit attitude quaternion and gyro zero bias of the spacecraft as the state vector of the spacecraft attitude determination system; Step S2, configuring a sub-milliarcsecond star angular distance measurement device and a star sensor to provide star angular distance and line-of-sight direction measurement information for spacecraft positioning and attitude determination; Step S3: Based on the unscented Kalman filter, a multi-model unscented Kalman filter is designed to improve the accuracy and robustness of state estimation; wherein the final output of the multi-model unscented Kalman filter is a weighted sum of state estimation results of multiple unscented Kalman filters; Step S4: Based on the unscented Kalman filter and the Q-learning method, a data-driven self-learning navigation strategy is designed, which integrates the estimation capability of the nonlinear Kalman filter and the decision-making capability of the intelligent learning method to achieve fully autonomous navigation of the position, velocity and attitude of the spacecraft.

2. A relativistic navigation filter optimization design method according to claim 1, characterized in that: In step S1, the position vector, velocity vector and sensor reference deviation of the spacecraft are selected as the state vector of the navigation and positioning dynamics model, and the spacecraft navigation and positioning model is established. The state vector is as follows: Among them, r k =[r xk r yk r zk ] T is the position vector of the spacecraft in the Earth-centered inertial coordinate system; v k =[v xk v yk v zk ] T is the velocity vector of the spacecraft in the geocentric inertial coordinate system; κ k =[… κ ijk …] T is the sensor reference deviation, the subscript k represents discrete time, and is the kth calculation cycle.

3. The method for optimizing the design of a relativistic navigation filter according to claim 1, characterized in that: In step S1, the unit attitude quaternion and gyro bias of the spacecraft are selected as the state vector of the spacecraft attitude determination system, and the spacecraft navigation attitude determination model is established. The state vector is as follows: Where, d represents the gyro bias, Represents the unit attitude quaternion, satisfy: Where ω=[ω x ,ω y ,ω z ] T Represents the angular velocity vector of the spacecraft relative to its body coordinate system; Represents the cross product operator for the unit quaternion.

4. The method for optimizing the design of a relativistic navigation filter according to claim 1, characterized in that: In step S3, the weight calculation formula of the multi-model unscented Kalman filter developed based on the unscented Kalman filter is: Among them, Ω k is an adjustable positive definite matrix, represents the measurement residual, is the weight of the i-th unscented Kalman filter at time k-1, is the target weight at time k.

5. The method for optimizing the design of a relativistic navigation filter according to claim 1, characterized in that: In step S4, a multi-model unscented Kalman filter designed based on the unscented Kalman filter is used to estimate the position vector, velocity vector and attitude of the spacecraft respectively through the unscented Kalman filter; The spacecraft navigation and positioning model is as follows: f(x k )=x k +Φ(x k )D t ; Among them, Δ t is the state prediction time step; p(r k ) includes the effects of other orbital perturbations besides the gravity of the Earth's center; The estimation strategy of decoupling the spacecraft position and attitude is adopted to simplify the influence of external force rejection. Therefore, the state equation of the spacecraft attitude determination system is as follows: Where w represents the system noise of the spacecraft attitude determination system.

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