Space-based space target orbit determination method considering observation platform position error

Abstract

The application provides a space-based space target orbit determination method considering observation platform position error. The method respectively establishes observation platform position error models according to different orbit determination means of the space-based observation platform and provides a space-based space target orbit determination algorithm. When the space-based observation platform uses a global navigation satellite system (GNSS) for real-time positioning, the observation platform position error at each observation time is modeled as a Gaussian white noise sequence in a measurement equation, and an extended Kalman filter (EKF) is used for filtering estimation of the space target position and velocity. When the space-based observation platform is orbit-determined by using the tracking results of a ground station to inject values, the observation platform position and velocity error and the space target position and velocity are simultaneously used as state variables to be estimated between adjacent injection time points, an EKF is used for filtering estimation, and the filter is reinitialized at each injection time point, so that high-precision orbit determination of the space-based space target is realized.

Description

Technical Field

[0001] This invention provides a method for orbit determination of a space target based on a space-based observation platform, taking into account its positional errors. The method involves using the position of the space-based observation platform obtained through various means such as GNSS or ground station tracking, as well as observation data of the space target from the space-based observation platform, to determine the target's orbit. This belongs to the field of navigation technology. Background Technology

[0002] With increasingly frequent space activities worldwide, the types and numbers of space objects, including satellites and space debris, have also increased dramatically. As of 2023, there were more than 9,000 operational satellites of various types in space, and approximately 35,150 pieces of space debris that were regularly tracked and cataloged by Space Surveillance Networks (SSNs). Therefore, maintaining space order and environmental protection are under severe pressure, and the future development of space urgently requires the improvement of space situational awareness capabilities.

[0003] Space situational awareness refers to the perception of events, threats, activities, and states occurring in space. It involves the recognition and analysis of factors influencing space activities and is the foundation for conducting spaceflight activities. Based on the location of the observation platform, space situational awareness can be divided into ground-based situational awareness and space-based situational awareness. Compared with ground-based observation equipment, space-based platforms overcome constraints such as weather, environment, and geographical conditions, enabling long-term continuous observation of space targets, thus possessing significant advantages. Therefore, space-based situational awareness, as an important component of space situational awareness, has received widespread attention.

[0004] Orbit determination of space targets based on space-based observation platforms is an upstream link and key technology in the construction of space-based situational awareness capabilities. In the field of situational awareness, space-based space target orbit determination mainly refers to the orbit determination of non-cooperative space targets on space-based platforms, which can be traced back to the Space-based Visible (SBV) program initiated by the United States in 1996. This program launched the Midcourse Space Experiment (MSX) satellite, developed by MIT Lincoln Laboratory and carrying SBV optical sensors, into a near-sun-synchronous orbit, marking the world's first demonstration and verification of space-based space surveillance. Since then, space-based space target orbit determination has received increasing attention, and researchers both domestically and internationally have conducted numerous related studies.

[0005] The main error sources affecting the orbit determination accuracy of space-based targets include measurement system errors, dynamic model errors, and observation platform position errors. Some typical studies at home and abroad have considered these error sources to varying degrees.

[0006] Domestic research on orbit determination of space-based non-cooperative space targets began after the launch of the MSX satellite. In 2005, Guo Fucheng et al. studied the problem of passive tracking of a reconnaissance satellite by intercepting the radiated signals of the reconnaissance satellite through an electronic reconnaissance aircraft, considering the observation errors of azimuth and elevation angles. In 2011, Zhao Bo et al. proposed a joint orbit determination method for space targets based on ground-based telemetry and control, which integrates the angular observation information of the ground-based station on the space-based platform and the optical angular observation information of the target from the space-based platform in the batch processing algorithm, improving the target orbit determination accuracy while correcting the position and velocity errors of the observation platform. In 2021, Song Yezhi et al. studied the problem of tracking non-cooperative geosynchronous orbit (GEO) satellites by a low-Earth orbit optical observation platform, adding the harmonic position error with a 3m amplitude to the ephemeris of the low-Earth orbit (LEO) observation platform to obtain the ephemeris model of the observation platform. In 2023, further research was conducted on the effectiveness of the LEO optical observation platform in tracking non-cooperative Medium Earth Orbit (MEO) and GEO satellites. The study analyzed the orbit determination performance of non-cooperative space targets with an orbital error of 20m and pointed out that the required ephemeris accuracy for the observation platform could be provided by GNSS orbit determination technology. However, no corresponding processing of the observation platform's ephemeris error was performed during the orbit determination process.

[0007] Research on space-based non-cooperative target orbit determination began earlier abroad, but publicly published research results were roughly synchronous with domestic research in this area. In 2006, Ossama Abdelkhalik et al. proposed a space-based non-cooperative target orbit determination technique using star sensor observation data, but did not model or analyze observation errors. In 2015, Gioacchino Scire et al. proposed a space-based electro-optical angle target orbit determination method based on batch estimators, which only considered angle measurement noise. In 2019, Samuel Hilton et al. integrated the navigation uncertainty of the space-based platform and the radar measurement uncertainty and gave a quantitative expression for the target orbit determination uncertainty. In 2022, Blythe A. Andrews et al. proposed a GEO target orbit determination technique based on space-ground hybrid angle observation and EKF, considering the random noise and constant bias of angle observations as well as the orbit determination noise of the space-based platform, and modeling all noise as zero-mean Gaussian white noise.

[0008] In summary, current research on space-based target orbit determination mainly focuses on the fusion of multi-source measurements and the improvement of filtering methods. A small portion of research focuses on handling ephemeris errors of space-based platforms, primarily employing batch processing methods. However, space-based observation data requires the use of surveillance satellite ephemeris to establish measurement equations between target state and observations for orbit determination. Therefore, surveillance satellite ephemeris errors significantly impact the tracking performance of space-based targets, and space-based situational awareness demands high real-time performance. This invention addresses this issue by proposing suitable platform position and velocity error modeling methods based on two different space-based observation platform orbit determination methods: GNSS real-time positioning and intermittent ground station tracking. It also presents a real-time space-based target orbit determination algorithm based on the established error models, providing high-precision space target orbit determination results. Summary of the Invention

[0009] To address the need for high-precision orbit determination of space targets based on space-based observation platforms, this invention presents a space-based space target orbit determination method that considers the position and velocity errors of the observation platform. The advantages of this invention are: when determining the orbit of a space target based on a space-based observation platform, it considers not only the measurement uncertainty caused by measurement system noise, but also the influence of the platform's own position and velocity errors on the orbit determination results. Furthermore, it provides modeling and processing methods based on the characteristics of two different space-based observation platform orbit determination methods: real-time positioning based on GNSS and orbit determination based on ground station tracking results. This supports the realization of high-precision orbit determination of space targets.

[0010] The main technical solution of this invention is as follows: When the space-based observation platform uses GNSS for autonomous real-time positioning, the position and velocity errors of the observation platform at each observation time are modeled as a Gaussian white noise sequence in the measurement equation. The position and velocity of the space target are filtered and estimated using EKF to achieve high-precision orbit determination of the space-based target. When the space-based observation platform relies on the orbit determination results uploaded by the ground station for orbit determination, between two adjacent upload times, the position and velocity errors of the observation platform and the position and velocity of the space target are simultaneously used as state variables to be estimated. The state equation is given by orbit dynamics, and EKF is used to filter and estimate it. The filter is re-initialized at each upload time to achieve high-precision orbit determination of the space-based target.

[0011] When a space-based observation platform performs real-time positioning by receiving GNSS signals in real time using an onboard GNSS receiver, the positioning error at each moment can be modeled as random noise. Considering that positioning results at different times do not affect each other in real-time positioning, the positioning error can be modeled as a white noise sequence. When a space-based observation platform performs orbit determination by tracking the orbit determination results from ground-based observation stations, the observation platform determines its own position and velocity at each epoch using the above-mentioned values ​​and uses an orbit propagator for prediction. In this case, the platform's position and velocity errors can be modeled as state equations evolving based on orbit dynamics. Here, taking the orbit determination of a space target by a single space-based observation platform as an example, the main steps of the space-based space target orbit determination method considering the state error of the observation platform described in this invention are explained according to two different orbit determination methods of the space-based observation platform.

[0012] (I) Space-based observation platform performs real-time positioning based on GNSS

[0013] 1. State equation model:

[0014] The position r and velocity v of the spatial target in the ECI coordinate system constitute the state variable x, i.e.

[0015] x = [r T v T ] T =[xyzv x v y v z ] T (1)

[0016] It satisfies the following continuous nonlinear time-varying state equation with random input terms:

[0017]

[0018] Among them, a m For the modeled acceleration, w t This represents unmodeled acceleration, typically represented by zero-mean Gaussian white noise.

[0019] Due to the discreteness of the observation time, equation (2) needs to be discretized to obtain the following discrete nonlinear time-varying state equation:

[0020] x k =f(x) k-1 ,t k ,t k-1 )+w k-1 (3)

[0021] Where, x k Indicates t k The state variable of the time-space target, w k-1For discretized process noise, f(·) generally does not have an explicit expression.

[0022] 2. Measurement equation model:

[0023] Let the measurement equation be as follows:

[0024] z = h(x, x O ,p)+υ (4)

[0025] Where z is the observation, x O To observe the platform state, p represents other random parameters, and h(x,x) O p) represents the state variable x and the state of the space-based observation platform x. O And other linear / nonlinear functions of the randomness parameter p, where υ is the measurement noise, and its covariance matrix is ​​R. υ .

[0026] 3. The main steps for determining the orbit of a space target using EKF:

[0027] (1) Filter initialization at time t0

[0028] Initialize the state estimate and its error covariance by setting k=1, and then proceed to step (2).

[0029] (2)t k One-step prediction of time and state

[0030] In order to estimate the target state from the observations using the extended Kalman filter, the state error transition matrix Φ needs to be given. k-1 =Φ(t) k ,t k-1 ) and process noise covariance matrix Q k-1 =Q(t) k ,t k-1 Both satisfy the following matrix differential equations:

[0031]

[0032] Let t k-1 The state estimate after the time measurement update is The state estimation error covariance matrix is Based on EKF, t can be obtained. k One-step prediction equation for time:

[0033]

[0034] Then proceed to step (3).

[0035] (3)t k Time-state measurement update

[0036] Let t k The platform status obtained by the time observation platform based on GNSS orbit determination is as follows: The error is The covariance matrix is The observed values ​​of other randomness parameter p are Its error is The covariance matrix is Then t k The time measurement equation can be written as:

[0037]

[0038] Linearizing equation (8) using Taylor expansion yields:

[0039]

[0040] Wherein, the Jacobian matrix is

[0041]

[0042] The equivalent measurement noise covariance matrix considering the noise from the observation platform location measurement is:

[0043]

[0044] Therefore, the measurement update equation is:

[0045]

[0046] Therefore, t can be obtained. k The state estimation of the spatial target at time and its error covariance are then performed, and then proceed to step (4).

[0047] (4) If the space target orbit determination mission is completed, the algorithm stops; otherwise, let k = k + 1 and proceed to step (2).

[0048] (II) The space-based observation platform performs orbit determination based on the annotated values ​​of the tracking and orbit determination results from the ground station.

[0049] 1. State equation model:

[0050] Let the true position and velocity of the space-based observation platform be r, respectively. O With v O Its nominal position and velocity are respectively and Let x O and These represent the actual state and nominal state of the space-based observation platform, respectively.

[0051]

[0052] Using the position r and velocity v of the space target in the ECI coordinate system and the position error of the space-based observation platform With speed error The state variable y is constituted, that is

[0053] y = [x T ε T ] T (14)

[0054] Where x represents the state of the space target, and ε represents the state error of the space-based observation platform, i.e.

[0055]

[0056] x、x O as well as The state equations that are satisfied can all be characterized by equation (2), therefore

[0057]

[0058] The state equation satisfied by the state variable y is:

[0059]

[0060] Due to the discreteness of the observation time, equation (18) needs to be discretized to obtain the following discrete nonlinear time-varying state equation:

[0061]

[0062] Where, x k With ε k They represent t respectively k Error between the state variables of the spatial target and the state variables of the space-based observation platform at any given time. and The noise is the discretized process noise and the two are unrelated.

[0063] 2. Measurement equation model:

[0064] Let the measurement equation be as follows:

[0065]

[0066] Where z is the observation and y is the state variable. Let p represent the nominal state of the observation platform, and p represent other randomness parameters. For the state variable y, the nominal state of the space-based observation platform A linear / nonlinear function of other randomness parameters p, where υ is measurement noise, and its covariance matrix is ​​R. υ .

[0067] 3. Symbol Conventions:

[0068] Let t n (n = 0, 1, 2…) represents the (n+1)th observation time. The j-th and (j+1)th consecutive upload times of the ground station's tracking and orbit determination results of the space-based observation platform are respectively the (k+1)th observation time t. k and the k+mth j +1 observation time Where m j Let be the number of observations of the space target by the space-based observation platform between the j-th and j+1-th uploading times. The following notation conventions shall be used:

[0069]

[0070] In this context, (·) represents any symbol.

[0071] In the following technical solutions, assuming that time t0 is also the time when the first tracking and orbit determination result of the space-based observation platform is uploaded, the following relationship holds:

[0072]

[0073] This establishes a one-to-one mapping between k and j.

[0074] 4. The main steps for determining the orbit of a space target using EKF:

[0075] (1) Timing filter initialization

[0076] The state estimate and its error covariance are initialized at this time, k=0, i=0, j=1, and then proceed to step (4).

[0077] (2) Time filter reinitialization

[0078] State error transition matrix of space targets and space-based observation platforms and The satisfied matrix differential equation can be given by equation (5), and the process noise matrix of both is... and The satisfied matrix differential equation is given by equation (6), where the coefficient matrix is ​​calculated along the nominal orbits of the space target and the space-based observation platform, respectively. The state error transition matrix Φ of the state variable y... k-1 =Φ(t) k ,t k-1 ) and process noise matrix Q k-1 =Q(t) k ,t k-1 )for:

[0079]

[0080] set up The state variable estimate after the time measurement update is: The state estimation error covariance matrix is State error transition matrix Process noise matrix Based on EKF, we can obtain One-step prediction equation for time:

[0081]

[0082] From this we can obtain One-step prediction result of the time-space target state and

[0083] set up The orbit determination results from the space-based observation platform, constantly uploaded by the ground station, are its nominal state. The error estimate of the nominal state and its error covariance are respectively and make Then the filter can be reinitialized, that is, let

[0084]

[0085] As the initial value for the filter, the time is noted from the orbit determination result of the j-th space-based observation platform. Restart the filtering process, which means proceeding to step (4).

[0086] (3) One-step prediction of time and state

[0087] set up The state variable estimate after the time measurement update is: The state estimation error covariance matrix is State error transition matrix Process noise matrix Based on EKF, we can obtain One-step prediction equation for time:

[0088]

[0089] Then proceed to step (4).

[0090] (4) Time-state measurement update

[0091] set up At time t, the observed values ​​of other randomness parameters p are Its error is The covariance matrix is but The time measurement equation can be written as

[0092]

[0093] Linearizing equation (27) using Taylor expansion yields:

[0094]

[0095] Wherein, the Jacobian matrix is

[0096]

[0097] The equivalent measurement noise covariance matrix is ​​then...

[0098]

[0099] Therefore, the measurement update equation is:

[0100]

[0101] This is how you can obtain Estimate the state variable y at time t and its error covariance, and then proceed to step (5).

[0102] (5) If the space target orbit determination mission is completed, the algorithm stops; if the mission is not completed, then if i = m j -1, then let i = 0, k = k + m j If j = j + 1, proceed to step (2); otherwise, let i = i + 1 and proceed to step (3). Attached Figure Description

[0103] Figure 1 This is a flowchart of the orbit determination process for space targets when the space-based observation platform performs orbit determination based on GNSS.

[0104] Figure 2 This is a flowchart of the orbit determination process for space targets when the space-based observation platform determines the orbit based on the tracking results uploaded from the ground station. Detailed Implementation

[0105] The specific implementation of the algorithm described in this invention will now be described in detail with reference to the accompanying drawings.

[0106] (I) Space-based observation platform performs real-time positioning based on GNSS

[0107] 1. Let k = 0. The state variables are the position and velocity of the spatial target. At the initial time t0, the state variable estimates and their error covariance are initialized to obtain... and Let k = k + 1 and proceed to step 2.

[0108] 2. From t k-1 Perform numerical integration up to t k One-step prediction results of state estimation and its error covariance are obtained using EKF.

[0109]

[0110] Next, proceed to step 3.

[0111] 3. Calculate the Jacobian matrix of the measurement equation based on the one-step prediction results, the orbit determination results of the space-based observation platform, and other stochastic parameter observations.

[0112]

[0113] Next, proceed to step 4.

[0114] 4. Calculate the equivalent measurement noise covariance matrix, taking into account the noise from the observation platform's location.

[0115]

[0116] Next, proceed to step 5.

[0117] 5. Based on the current time t k The observations are updated using EKF to measure the state estimate and its error covariance.

[0118]

[0119] Next, proceed to step 6.

[0120] 6. If the space target orbit determination mission is completed, the algorithm ends; otherwise, let k = k + 1 and proceed to step 2.

[0121] (II) The space-based observation platform performs orbit determination based on the tracking results uploaded from the ground station.

[0122] 1. Let k = 0, i = 0, j = 1. The state variables are the position and velocity of the space target and the position and velocity errors of the space-based observation platform. At the initial time t0, the state variable estimates and their error covariance are initialized to obtain... and Then proceed to step 4.

[0123] 2. From the state equation, the state error transition matrix differential equation, and the process noise differential equation... Perform numerical integration to One-step prediction results of state estimation and its error covariance are obtained using EKF.

[0124]

[0125] Next, if i == m j Let i = 0 and k = k + m j If i, k, and j are equal to j+1, proceed to step 3; otherwise, keep i, k, and j unchanged and proceed directly to step 4.

[0126] 3. Obtain the orbit determination results of the space-based observation platform and calculate the platform's orbit determination error. and its covariance and combined

[0127] Time to The time-space target state estimation and its error covariance are the one-step prediction results constituting the initial estimation of state variables and their error covariance.

[0128]

[0129] The filter is reinitialized with this initial value, and then proceed to step 4.

[0130] 4. Calculate the Jacobian matrix of the measurement equation based on the state variable estimates, their initial values ​​of error covariance or one-step prediction results, and other observed values ​​of stochastic parameters.

[0131]

[0132] Next, proceed to step 5.

[0133] 5. Calculate the equivalent measurement noise covariance matrix.

[0134]

[0135] Next, proceed to step 6.

[0136] 6. Based on the current time t k The observations are updated using EKF to measure the state estimate and its error covariance.

[0137]

[0138] Next, proceed to step 7.

[0139] 7. If the space target orbit determination mission is completed, the algorithm ends; otherwise, let i = i + 1 and proceed to step 2.

Claims

1. An orbit determination algorithm for space-based targets based on ground station tracking results when a space-based observation platform performs orbit determination, characterized in that: Step 1: Establish notation conventions, let t n (n = 0, 1, 2…) represents the (n+1)th observation time. The j-th and (j+1)th consecutive upload times of the ground station's tracking and orbit determination results of the space-based observation platform are respectively the (k+1)th observation time t. k and the k+mth j +1 observation time Where m j The number of observations of a space target by a space-based observation platform between the j-th and j+1-th uploading times is notated as follows: Where (·) represents any symbol, Assuming that time t0 is also the time when the first tracking and orbit determination result from the space-based observation platform is uploaded, then the following relationship holds: This establishes a one-to-one mapping between k and j. Step 2: State initialization. Let k = 0, i = 0, j = 1. The state variables are the position and velocity of the space target and the position and velocity errors of the space-based observation platform. At the initial time t0, the state variable estimates and their error covariance are initialized, resulting in... and Then proceed to step 5. Step 3: From the differential equations of the state equation, the state error transition matrix, and the process noise, ... Perform numerical integration to One-step prediction results of state estimation and its error covariance are obtained using EKF. Next, if i == m j Let i = 0 and k = k + m j If j = j + 1, proceed to step 4; otherwise, keep i, k, and j unchanged and proceed directly to step 5. Step 4: Obtain the orbit determination results of the space-based observation platform and obtain the platform's orbit determination error. and its covariance and combined Time to The time-space target state estimation and its error covariance are the one-step prediction results that constitute the initial estimation of the state variables and their error covariance. Reinitialize the filter with the initial values, and then proceed to step 5. Step 5: Calculate the Jacobian matrix of the measurement equation based on the state variable estimates, their initial error covariance values ​​or one-step prediction results, and other observed values ​​of stochastic parameters. Then calculate the equivalent measurement noise covariance matrix. Then based on the current time t k The observations are updated using EKF to measure the state estimate and its error covariance. If the space target orbit determination mission is not completed, let i = i + 1 and proceed to step 3.

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