An event-triggered unscented Kalman filter spacecraft orbit estimator

Abstract

This invention discloses an event-triggered unscented Kalman filter spacecraft orbit estimator, comprising: a spacecraft orbit system module for establishing the state equation and measurement equation of the spacecraft's motion along its orbit; an event triggering module for determining whether an event triggering condition is met, and based on the determination result, determining whether to transmit the current ground station measurement information to the unscented Kalman filter estimation module; and an unscented Kalman filter estimation module for estimating the orbit at the current moment based on the spacecraft's state equation and measurement equation, combined with the current ground station measurement information transmitted from the event triggering module, and determining whether the current orbit deviates from the spacecraft's predetermined orbit based on the current orbit estimation result. The estimator described in this invention can reduce the communication rate while ensuring estimation effectiveness, thus solving the problem of limited communication resources during information transmission between the spacecraft and the ground station.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft orbit estimation technology, and particularly relates to an event-triggered unscented Kalman filter spacecraft orbit estimator. Background Technology

[0002] With the development of communication, space, and computer technologies, human space activities are becoming increasingly frequent. Spacecraft are devices used to perform specific space missions. During operation, spacecraft need to maintain timely and effective communication with the ground to obtain attitude, velocity, and orbital information, and react quickly to ensure their safe operation. Spacecraft orbit estimation is one of the most crucial tasks in its operation and control. Orbit estimation, based on the initial orbit, uses real-time orbital information acquired from ground stations to predict the spacecraft's orbital state at future moments, providing timely feedback and taking appropriate adjustments to keep the spacecraft within the required orbital range and successfully and safely complete its mission.

[0003] Spacecraft orbital information can be obtained by ground stations tracking and measuring the spacecraft's distance, velocity, azimuth, and elevation relative to the ground station. The ground station receives spacecraft telemetry data and transmits it to the space tracking and control center. It then receives plans, instructions, and data from the control center and, as required, sends instructions and data to the spacecraft, completing various spacecraft operations. The operating frequency band selected for spacecraft communication affects the system's transmission capacity and communication quality; suitable frequency bands are limited. To reduce the burden on ground stations, lower the cost of space engineering, and improve satellite survivability, an event-triggered state estimation method is proposed.

[0004] Event-triggered state estimation adds event triggering to the spacecraft estimator. The system can adjust the sampling time based on the estimation effect of orbital information, thereby avoiding unnecessary communication. During communication between the ground station and the spacecraft, if a certain data transmission triggering mechanism can determine whether to send measurement values ​​to the estimator, communication resources will be saved, latency and packet loss will be reduced, and the performance of the estimator will be improved. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide an event-triggered unscented Kalman filter spacecraft orbit estimator. This estimator can reduce the communication rate while ensuring the estimation effect, thus solving the problem of limited communication resources when transmitting information between spacecraft and ground stations.

[0006] To address the aforementioned technical problems, this invention discloses an event-triggered unscented Kalman filter spacecraft orbit estimator, comprising:

[0007] The spacecraft orbital system module is used to establish the state equations and measurement equations for the spacecraft's motion along its orbit.

[0008] The event triggering module is used to determine whether the event triggering conditions are met, and based on the determination result, to determine whether to transmit the ground station measurement information at the current moment to the unscented Kalman filter estimation module.

[0009] The unscented Kalman filter estimation module is used to estimate the orbit at the current moment based on the state equation and measurement equation of the spacecraft's motion along the orbit, combined with the ground station measurement information transmitted from the event triggering module. Based on the orbit estimation result at the current moment, it determines whether the current orbit deviates from the spacecraft's predetermined orbit.

[0010] In the aforementioned event-triggered unscented Kalman filter spacecraft orbit estimator, the unscented Kalman filter estimation module, when estimating the orbit at the current moment based on the spacecraft's state equation and measurement equation along its orbit, combined with the ground station measurement information transmitted from the event-triggered module, includes:

[0011] Based on the state equation and measurement equation of the spacecraft's motion along the orbit, the orbital state at the current moment is predicted using the estimated orbital state at the previous moment, thus obtaining the predicted value of the orbital state at the current moment.

[0012] When the event triggering condition is met, and the ground station measurement information at the current moment is obtained from the event triggering module, the measured value of the orbital state at the current moment is obtained from the ground station measurement information at the current moment, and the predicted value of the orbital state at the current moment is corrected using the measured value of the orbital state at the current moment to obtain the final estimated value of the orbital state and output it.

[0013] When the event triggering conditions are not met and the ground station measurement information for the current moment is not obtained from the event triggering module, the orbital state for the next moment is estimated based on the measured values ​​of the orbital state at historical moments.

[0014] In the aforementioned event-triggered unscented Kalman filter spacecraft orbit estimator, the unscented Kalman filter estimation module is also used to: issue a command signal when it is determined that the current orbit deviates from the spacecraft's predetermined orbit, so that the onboard equipment can act according to the command.

[0015] In the event-triggered unscented Kalman filter spacecraft orbit estimator described above, the state equations and measurement equations for the spacecraft's motion along the orbit are expressed as follows:

[0016]

[0017] y t =h(x t )+v t

[0018] Wherein, system state x t Contains the spacecraft position vector r = [r x r y r z ] and velocity vector v = [v x v y v z The function f(·) is used to describe the state model of the spacecraft orbital system; h(x) t ) represents the measurement process function, which is determined by the azimuth, elevation angle, and range measured by the ground station.

[0019] In the aforementioned event-triggered unscented Kalman filter spacecraft orbit estimator, for f(x) t ),have:

[0020]

[0021] Where μ is the Earth's gravitational constant, J2 is the J2 perturbation, r=||r|| represents the distance from the spacecraft to the central celestial body, and R e This is the radius of the Earth's equator.

[0022] In the aforementioned event-triggered unscented Kalman filter spacecraft orbit estimator, the event triggering module is used for:

[0023] The determination of whether the event triggering condition is met is based on the following formula (1):

[0024]

[0025] in, This represents the measurement information of sensor i at time k. This represents the measurement information from the previous measurement by sensor i; δ i This represents the trigger threshold corresponding to sensor i;

[0026] Ground station measurement information Includes: measurement information obtained from several sensors Right now M represents the number of sensors;

[0027] when At that time, the measurement information of sensor i is At this point, the measurement information of sensor i is transmitted to the unscented Kalman filter estimation module;

[0028] when At that time, the measurement information of sensor i is At this point, no new measurement information is transmitted to the unscented Kalman filter estimation module.

[0029] In the event-triggered unscented Kalman filter spacecraft orbit estimator described above, the unscented Kalman filter estimation module is specifically used to estimate the orbit at the current moment in the following manner:

[0030] Obtain all information up to the (i+1)th sensor information.

[0031]

[0032] in,

[0033] According to Bayes' theorem, the minimum mean square error estimate of the process state is calculated.

[0034]

[0035]

[0036] when The true state of sensor i at time k The estimated value can then be updated to the orbital state estimate for the next time step as follows:

[0037] 1) Select the Sigma point:

[0038]

[0039]

[0040]

[0041] Where n represents the system state dimension;

[0042] 2) Map the Sigma points to a new set of Sigma points:

[0043]

[0044] 3) The weighted new Sigma point set is used to predict the estimated values ​​and covariance of the orbital state:

[0045]

[0046]

[0047] The weighting formula is as follows:

[0048]

[0049]

[0050] λ=α2 (n+κ)-n

[0051] In the formula, α represents the i-th column of the matrix, which is the scaling function of the distribution; α represents the distance from the mean point of the Sigma point set, and α and κ are used to control the distribution of the Sigma point set; β is related to the distribution of x, and β is used to adjust the accuracy of the variance. If the distribution of x is Gaussian, then β = 2 is the optimal choice.

[0052] 4) Map the Sigma point set to a new Sigma point set using the orbital observation function:

[0053]

[0054] 5) The weighted new Sigma point set is used to predict the estimates and covariance of spacecraft orbit observations:

[0055]

[0056]

[0057] 6) The track state measurement covariance matrix is ​​used to calculate the filter gain:

[0058]

[0059]

[0060] 7) Orbit status update

[0061] Define auxiliary variables So when When the event triggering conditions are met, the estimated orbital state and covariance matrix are:

[0062]

[0063]

[0064] And when That is, when the event triggering condition is not met:

[0065]

[0066]

[0067] in,

[0068] This completes the estimation of the spacecraft's orbital state triggered by the event.

[0069] In the aforementioned event-triggered unscented Kalman filter spacecraft orbit estimator, when measuring spacecraft orbit information, a radio pulse signal is sent to the spacecraft via ground radar. After receiving the radio pulse signal, the transponder on the spacecraft amplifies it and immediately sends a radio pulse response signal back to the ground. Based on the propagation time of the transmitted radio pulse signal and the returned radio pulse response signal, the distance between the spacecraft and the ground station is calculated, and the position of the spacecraft is determined based on the azimuth of the radar antenna elevation angle.

[0070] The present invention has the following advantages:

[0071] This invention proposes an event-triggered unscented Kalman filter spacecraft orbit estimator. Unscented Kalman filtering is an estimation method for nonlinear systems; it approximates the probability density distribution. Because it does not ignore higher-order terms, it has high accuracy in solving nonlinear problems. Its core transformation idea is that approximating a probability distribution is easier than approximating any nonlinear function or nonlinear transformation. Unscented Kalman filtering exhibits superior performance under highly nonlinear conditions because it is based on unscented transformations and does not include any traditional linearization processes or assumptions. Furthermore, when a spacecraft is in orbit and is not subjected to external disturbances or is in an ideal motion state, periodic data transmission from the ground not only wastes limited computing and communication resources but may also cause data transmission delays and communication congestion. Considering the event-triggered mechanism, measurement data is transmitted only when the event trigger condition is met, and the estimator updates the measurement to complete the orbit state estimation; when the event trigger condition is not met, orbit state estimation is performed by combining historical information. Therefore, this event-triggered unscented Kalman filter spacecraft orbit estimator can achieve similar or better estimation performance while reducing the data transmission rate. Attached Figure Description

[0072] Figure 1 This is a structural diagram of an event-triggered unscented Kalman filter spacecraft orbit estimator according to an embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of the geometric relationship between a spacecraft and a ground station in an embodiment of the present invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0075] One of the core ideas of this invention is the disclosure of an event-triggered unscented Kalman filter spacecraft orbit estimator, comprising: a spacecraft orbit system module, an event triggering module, and an unscented Kalman filter estimation module. The spacecraft orbit observation data is not obtained by directly measuring orbital elements, but by measuring parameters related to spacecraft motion. Based on orbital dynamics principles, orbital elements are calculated using a specific algorithm. The ground station can observe the spacecraft's distance, azimuth, and elevation angles, and use this data and the specific algorithm for spacecraft orbital dynamics to obtain the spacecraft's position and velocity information at a given moment. Since the spacecraft's motion state is relatively stable, an event triggering module is designed to conserve communication resources. When the event triggering conditions are met, the ground station obtains the orbital information at that moment through measurement; when the event triggering conditions are not met, the ground station does not perform measurements. After judgment by the event triggering module, the acquired information is transmitted to the unscented Kalman filter estimation module, which performs orbit estimation based on whether data input is available. When the orbit estimation deviates from the spacecraft's predetermined orbit, a command signal is issued, causing the onboard equipment to act accordingly.

[0076] like Figure 1 In this embodiment, the event triggers an unscented Kalman filter spacecraft orbit estimator, including:

[0077] The spacecraft orbital system module is used to establish the state equations and measurement equations for the spacecraft's motion along its orbit.

[0078] In this embodiment, the state equation and measurement equation for the spacecraft's motion along the orbit are expressed as follows:

[0079]

[0080] y t =h(x t )+v t

[0081] Wherein, system state x t Contains the spacecraft position vector r = [r x r y r z ] and velocity vector v = [v x v y v z The function f(·) is used to describe the state model of the spacecraft orbital system; h(x) t ) represents the measurement process function, which is determined by the azimuth, elevation angle, and range measured by the ground station.

[0082] For f(x) t ),have:

[0083]

[0084] Where μ is the Earth's gravitational constant, J2 is the J2 perturbation, r=||r|| represents the distance from the spacecraft to the central celestial body, and R e This is the radius of the Earth's equator.

[0085] The event triggering module is used to determine whether the event triggering conditions are met, and based on the determination result, to determine whether to transmit the ground station measurement information at the current moment to the unscented Kalman filter estimation module.

[0086] In this embodiment, as Figure 2 When measuring spacecraft orbital information, a radio pulse signal is sent to the spacecraft via ground radar. After receiving the radio pulse signal, the transponder on the spacecraft amplifies it and immediately sends a radio pulse response signal back to the ground. Based on the propagation time of the transmitted radio pulse signal and the returned radio pulse response signal, the distance between the spacecraft and the ground station is calculated, and the position of the spacecraft is determined based on the azimuth of the radar antenna elevation angle. Figure 2 In this context, ρ represents the distance between the ground station and the spacecraft, r represents the radius vector of the spacecraft, and R s α represents the radius vector of the ground tracking station. s and δ s These are the right ascension and declination of aerospace, θ s For the stellar time of ground tracking stations, λ s φ is the latitude of the ground tracking station. s From the ground tracking station to the spacecraft's east longitude.

[0087] The basic orbit measurement model is as follows:

[0088] r = R s +ρ

[0089] The distance vector ρ between the spacecraft and the ground station is expressed as:

[0090]

[0091] Ground station coordinates (up, east, and north) are as follows Figure 2 As shown, the conversion from the inertial coordinate system to the ground station coordinate system is as follows:

[0092]

[0093] Ground stations measure the spacecraft's azimuth (az), elevation (el), and distance (ρ) to determine its orbital information. The corresponding measurement information is as follows:

[0094]

[0095] Typically, ground stations determine spacecraft orbits using various measurement data. This embodiment sets trigger conditions for each type of measurement data, and determines whether the measurement data needs updating by judging whether the event trigger conditions are met. The designed event trigger conditions are as follows:

[0096]

[0097] in, This represents the measurement information of sensor i at time k. This represents the measurement information from the previous measurement by sensor i; δ i This represents the trigger threshold corresponding to sensor i.

[0098] Ground station measurement information Includes: measurement information obtained from several sensors Right now M represents the number of sensors.

[0099] when At that time, the measurement information of sensor i is At this point, the measurement information of sensor i is transmitted to the unscented Kalman filter estimation module.

[0100] when At that time, the measurement information of sensor i is At this point, no new measurement information is transmitted to the unscented Kalman filter estimation module.

[0101] The unscented Kalman filter estimation module is used to estimate the orbit at the current moment based on the state equation and measurement equation of the spacecraft's motion along the orbit, combined with the ground station measurement information transmitted from the event triggering module. Based on the orbit estimation result at the current moment, it determines whether the current orbit deviates from the spacecraft's predetermined orbit. When it is determined that the current orbit deviates from the spacecraft's predetermined orbit, a command signal is issued to cause the on-board equipment to act according to the command.

[0102] In this embodiment, the unscented Kalman filter estimation module, when estimating the orbit at the current moment based on the state equation and measurement equation of the spacecraft's orbital motion, combined with the ground station measurement information transmitted from the event triggering module, includes: predicting the orbital state at the current moment using the orbital estimation state from the previous moment, based on the state equation and measurement equation of the spacecraft's orbital motion, to obtain a predicted value of the orbital state at the current moment; when the event triggering condition is met and the ground station measurement information at the current moment is obtained from the event triggering module, obtaining the measured value of the orbital state at the current moment from the ground station measurement information, and using the measured value of the orbital state at the current moment to correct the predicted value of the orbital state at the current moment, to obtain the final estimated value of the orbital state and output it; when the event triggering condition is not met and the ground station measurement information at the current moment is not obtained from the event triggering module, estimating the orbital state at the next moment based on the measured values ​​of the orbital state at historical moments. Specifically:

[0103] Obtain all information up to the (i+1)th sensor information.

[0104]

[0105] in,

[0106] According to Bayes' theorem, the minimum mean square error estimate of the process state is calculated.

[0107]

[0108]

[0109] when The true state of sensor i at time k The estimated value can then be updated to the orbital state estimate for the next time step as follows:

[0110] 1) Select the Sigma point:

[0111]

[0112]

[0113]

[0114] Where n represents the system state dimension.

[0115] 2) Map the Sigma points to a new set of Sigma points:

[0116]

[0117] 3) The weighted new Sigma point set is used to predict the estimated values ​​and covariance of the orbital state:

[0118]

[0119]

[0120] The weighting formula is as follows:

[0121]

[0122]

[0123] λ=α 2 (n+κ)-n

[0124] In the formula, α represents the i-th column of the matrix, which is the scaling function of the distribution; α represents the distance from the mean point of the Sigma point set, and α and κ are used to control the distribution of the Sigma point set; β is related to the distribution of x, and β is used to adjust the accuracy of the variance. If the distribution of x is Gaussian, then β = 2 is the optimal choice.

[0125] 4) Map the Sigma point set to a new Sigma point set using the orbital observation function:

[0126]

[0127] 5) The weighted new Sigma point set is used to predict the estimates and covariance of spacecraft orbit observations:

[0128]

[0129]

[0130] 6) The track state measurement covariance matrix is ​​used to calculate the filter gain:

[0131]

[0132]

[0133] 7) Orbit status update

[0134] Define auxiliary variables So when When the event triggering conditions are met, the estimated orbital state and covariance matrix are:

[0135]

[0136]

[0137] And when That is, when the event triggering condition is not met:

[0138]

[0139]

[0140] in,

[0141] This completes the estimation of the spacecraft's orbital state triggered by the event.

[0142] As the system implementation is in contrast to the method implementation, it is described in a simpler way. For relevant details, please refer to the description in the method implementation section.

[0143] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0144] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. An event-triggered unscented Kalman filter spacecraft orbit estimator, characterized in that, include: The spacecraft orbital system module is used to establish the state equations and measurement equations for the spacecraft's motion along its orbit. The event triggering module is used to determine whether the event triggering conditions are met, and based on the determination result, to determine whether to transmit the ground station measurement information at the current moment to the unscented Kalman filter estimation module. The unscented Kalman filter estimation module is used to estimate the orbit at the current moment based on the state equation and measurement equation of the spacecraft's motion along the orbit, combined with the ground station measurement information transmitted from the event triggering module at the current moment. Based on the orbit estimation result at the current moment, it is determined whether the current orbit deviates from the spacecraft's predetermined orbit. The event triggering module is specifically used for: The determination of whether the event triggering condition is met is based on the following formula (1): in, This represents the measurement information of sensor i at time k. This represents the measurement information from the previous measurement by sensor i; δ i This represents the trigger threshold corresponding to sensor i; Ground station measurement information Includes: measurement information obtained from several sensors Right now M represents the number of sensors; when At that time, the measurement information of sensor i is At this point, the measurement information of sensor i is transmitted to the unscented Kalman filter estimation module; when At that time, the measurement information of sensor i is At this point, no new measurement information is transmitted to the unscented Kalman filter estimation module; The unscented Kalman filter estimation module is specifically used to estimate the trajectory at the current moment in the following way: Obtain all information up to the (i+1)th sensor information. in, According to Bayes' theorem, the minimum mean square error estimate of the process state is calculated. when The true state of sensor i at time k The estimated value can then be updated to the orbital state estimate for the next time step as follows: 1) Select the Sigma point: Where n represents the system state dimension; 2) Map the Sigma points to a new set of Sigma points: 3) The weighted new Sigma point set is used to predict the estimated values ​​and covariance of the orbital state: The weighting formula is as follows: λ=a 2 (n+k)-n In the formula, α represents the i-th column of the matrix, which is the scaling function of the distribution; α represents the distance from the mean point of the Sigma point set, and α and κ are used to control the distribution of the Sigma point set; β is related to the distribution of x, and β is used to adjust the accuracy of the variance. If the distribution of x is Gaussian, then β = 2 is the optimal choice. 4) Map the Sigma point set to a new Sigma point set using the orbital observation function: 5) The weighted new Sigma point set is used to predict the estimates and covariance of spacecraft orbit observations: 6) The track state measurement covariance matrix is ​​used to calculate the filter gain: 7) Orbit status update Define auxiliary variables So when When the event triggering conditions are met, the estimated orbital state and covariance matrix are: And when That is, when the event triggering condition is not met: in, This completes the estimation of the spacecraft's orbital state triggered by the event.

2. The event-triggered unscented Kalman filter spacecraft orbit estimator according to claim 1, characterized in that, The unscented Kalman filter estimation module, based on the spacecraft's state equations and measurement equations along its orbit, and in conjunction with ground station measurement information transmitted from the event triggering module, estimates the orbit at the current moment, including: Based on the state equation and measurement equation of the spacecraft's motion along the orbit, the orbital state at the current moment is predicted using the estimated orbital state at the previous moment, thus obtaining the predicted value of the orbital state at the current moment. When the event triggering condition is met, and the ground station measurement information at the current moment is obtained from the event triggering module, the measured value of the orbital state at the current moment is obtained from the ground station measurement information at the current moment, and the predicted value of the orbital state at the current moment is corrected using the measured value of the orbital state at the current moment to obtain the final estimated value of the orbital state and output it. When the event triggering conditions are not met and the ground station measurement information for the current moment is not obtained from the event triggering module, the orbital state for the next moment is estimated based on the measured values ​​of the orbital state at historical moments.

3. The event-triggered unscented Kalman filter spacecraft orbit estimator according to claim 2, characterized in that, The unscented Kalman filter estimation module is also used to: issue command signals when it is determined that the current orbit deviates from the spacecraft's predetermined orbit, so that the on-board equipment can act according to the command.

4. The event-triggered unscented Kalman filter spacecraft orbit estimator according to claim 1, characterized in that, The state equations and measurement equations for the spacecraft's motion along its orbit are expressed as follows: y t =h(x t )+v t Wherein, system state x t Contains the spacecraft position vector r = [r x r y r z ] and velocity vector v = [v x v y v z The function f(·) is used to describe the state model of the spacecraft orbital system; h(x) t ) represents the measurement process function, which is determined by the azimuth, elevation angle, and range measured by the ground station.

5. The event-triggered unscented Kalman filter spacecraft orbit estimator according to claim 4, characterized in that, For f(x) t ),have: Where μ is the Earth's gravitational constant, J2 is the J2 perturbation, r=||r|| represents the distance from the spacecraft to the central celestial body, and R e This is the radius of the Earth's equator.

6. The event-triggered unscented Kalman filter spacecraft orbit estimator according to claim 1, characterized in that, When measuring spacecraft orbital information, a radio pulse signal is sent to the spacecraft via ground radar. After receiving the radio pulse signal, the transponder on the spacecraft amplifies it and immediately sends a radio pulse response signal back to the ground. Based on the propagation time of the transmitted radio pulse signal and the returned radio pulse response signal, the distance between the spacecraft and the ground station is calculated, and the position of the spacecraft is determined based on the azimuth of the radar antenna elevation angle.

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