CN115841031A - Ephemeris prediction method and device based on fractional difference autoregression and moving average model - Google Patents
Ephemeris prediction method and device based on fractional difference autoregression and moving average model Download PDFInfo
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Abstract
The invention provides a method and a device for ephemeris prediction based on a fractional difference autoregression and a moving average model, wherein the method comprises the following steps: receiving an ephemeris prediction instruction, wherein the ephemeris prediction instruction comprises a specified satellite to be predicted, and receiving ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted; constructing an equation set of different satellites at the same historical time and an equation set of the same satellite at different historical times; calculating to obtain the historical ephemeris total error of the satellite to be predicted based on the equation sets of different satellites at the same time and the equation sets of the same satellite at different times; respectively sampling the historical ephemeris total error of the satellite to be predicted by adopting a plurality of different sampling frequencies, and outputting the predicted ephemeris total error based on a preset fraction difference autoregressive model and a moving average model; acquiring ephemeris parameters of the time to be predicted in the ephemeris data, and calculating predicted ephemeris parameters of the time to be predicted based on the ephemeris parameters of the time to be predicted and the predicted ephemeris total error.
Description
Technical Field
The invention relates to the technical field of satellite orbits, in particular to a method and a device for ephemeris prediction based on a fractional difference autoregression and a moving average model.
Background
An important vision of 6G mobile communication is to realize global wide-area high-speed coverage, so as to solve the problem that the requirement of high-speed communication service for users in mountainous areas, oceans, deserts, villages and other areas where base stations cannot cover or lack coverage is still not met after 5G commercial use. The ground mobile communication system mainly serves users through the base station, the network element position attribute is a mode of 'base station fixing-user movement', when the users move to the edge of a cell and need to carry out cell switching, the users can determine the next service cell needing to be selected by measuring the received base station signal power and quality. Unlike terrestrial mobile communication systems, the location attribute of a satellite network element is the "super-speed satellite motion-user motion" mode, which means that the satellite beam covering the user moves rapidly even if the user is stationary, and the user needs to frequently select and switch to the appropriate satellite beam to maintain continuous and reliable communication. Because the satellite is far away from the user, according to the geometric constraint relationship, the difference between the distance between the user at the center of the satellite beam and the user at the edge of the satellite is small, that is, the difference between the signal receiving power of the user at the center of the satellite beam and the signal receiving power of the user at the edge of the satellite is small, so that it is difficult to distinguish whether the user leaves or enters a satellite beam through the satellite signal receiving power and quality. Because the position of the satellite internet can be calculated according to the satellite constellation orbit position and the operation time, the user can calculate the satellite appearing in different time of the visual field above the current position, namely the satellite can be supported to select the next satellite and beam to be accessed. The satellite positions and velocities of the satellite constellation at different times can be represented in ephemeris. In a satellite mobile communication system, large-scale time and frequency deviation caused by rapid movement of a satellite transmitted by link physical layers such as time-frequency synchronization, doppler estimation and the like can be pre-compensated by ephemeris, and high-level signaling establishment and maintenance such as position attribution prediction, wireless resource management and control, beam selection, beam switching and the like can infer the service time of the current satellite through the ephemeris.
The existing satellite ephemeris prediction is mainly modeled based on a star motion law and describes the relevant influence factors of the orbit and the orbit position of a satellite, such as an orbit intersection angle, a rising point right ascension, eccentricity, an approach point angle and the like. However, because the influence of the gravity of the earth and the satellite, the influence of other satellite gravitations, the attitude deviation of the satellite, the transmission deviation of the ephemeris space and the like belong to uncertainty deviation, and the uncertainty deviation is difficult to be effectively represented by a model, actual satellite ephemeris data needs to be acquired and measured, and the satellite estimation ephemeris is fitted and revised. Therefore, the current optimization method for satellite ephemeris prediction mainly includes increasing the sending frequency of the satellite ephemeris measurement, or performing interpolation calculation on the ephemeris in a time domain, and the like. The method for increasing the sending frequency of the ephemeris of the measurement satellite is to realize that a link between the satellite and a user is established, otherwise, a terminal cannot receive the ephemeris to ensure link connection, that is, the user cannot effectively utilize the ephemeris when the user needs to be reconnected due to initial network access and rapid channel change. Meanwhile, the ephemeris is densely transmitted, and an extra channel needs to be divided in a broadcast channel, so that precious frequency resources are wasted. On the other hand, intensive measurement requires a large number of measurement and control systems on the ground to continuously observe satellites, but due to uncertainty of errors, when the measurement time is insufficient, the accuracy of the provided ephemeris is still to be improved.
Disclosure of Invention
In view of the above, embodiments of the present invention provide a method and an apparatus for ephemeris prediction based on a fractional difference autoregressive and moving average model, so as to obviate or mitigate one or more of the disadvantages in the prior art.
One aspect of the invention provides an ephemeris prediction method based on a fractional difference autoregressive model and a moving average model, which comprises the following steps:
receiving an ephemeris prediction instruction, wherein the ephemeris prediction instruction comprises a specified satellite to be predicted, and receiving ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted;
respectively constructing an equation set of different satellites at the same historical time and an equation set of the same satellite at different historical times based on ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted;
calculating to obtain the historical ephemeris total error of the satellite to be predicted based on the equation sets of different satellites at the same time and the equation sets of the same satellite at different times;
sampling the historical ephemeris total error of the satellite to be predicted by adopting a plurality of different sampling frequencies respectively, and outputting the predicted ephemeris total error based on a preset fraction difference autoregressive model and a moving average model;
acquiring ephemeris parameters of the time to be predicted in the ephemeris data, and calculating predicted ephemeris parameters of the time to be predicted based on the ephemeris parameters of the time to be predicted and the predicted ephemeris total error.
By adopting the scheme, the historical ephemeris total error of the satellite to be predicted is obtained by performing combined calculation through ephemeris data of adjacent satellites of the satellite to be predicted, the predicted ephemeris total error of the future time is obtained through fractional autoregressive and moving average model (ARIMA model), and the predicted ephemeris parameter of the time to be predicted is obtained by calculating based on the basic ephemeris parameter of the time to be predicted in the ephemeris data and the predicted ephemeris total error.
In some embodiments of the present invention, the historical ephemeris total errors include random errors and non-random errors, in the step of sampling the historical ephemeris total errors of the satellite to be predicted respectively by using a plurality of different sampling frequencies, and outputting the predicted ephemeris total errors based on the preset fraction differential autoregressive model and the moving average model, the predicted random errors and the non-random errors are calculated respectively based on the weight parameters set for the random errors and the non-random errors in each sampling and the preset fraction differential autoregressive model and the moving average model, and the predicted ephemeris total errors are calculated based on the predicted random errors and the non-random errors.
In some embodiments of the present invention, in the step of constructing the equation sets of different satellites at the same historical time and the equation set of the same satellite at different historical times based on the ephemeris data of the satellite to be predicted and the adjacent satellite of the satellite to be predicted, respectively, the equation sets of the different satellites at the same historical time are as follows:
eph t，k ephemeris data, eph, representing k satellites at time t t，k-1 Ephemeris data, Δ eph, at time t representing a neighbor k-1 satellite of the k-satellite t，k Total error of historical ephemeris, Δ eph, representing ephemeris data for k-satellites at time t t，k-1 Representing the historical ephemeris gross error, eph, of the ephemeris data of k-1 satellites at time t t，k+1 Ephemeris data, Δ eph, representing the satellites k +1 adjacent to the k satellite at time t t，k+1 The historical ephemeris total error of the ephemeris data of the k +1 satellite at the time t is shown, and G1 is a condition parameter of different satellite conditions at the same historical time.
In some embodiments of the present invention, in the step of constructing the equation sets of different satellites at the same historical time and the equation set of the same satellite at different historical times based on the ephemeris data of the satellite to be predicted and the adjacent satellite of the satellite to be predicted, respectively, the equation sets of the same satellite at different historical times are as follows:
eph t，k ephemeris data, eph, representing k satellites at time t t-1，k Ephemeris data, Δ eph, representing k-satellites at time t-1 t，k Total error of historical ephemeris, Δ eph, representing ephemeris data for k-satellites at time t t-1，k Historical satellites representing ephemeris data of k satellites at time t-1Calendar total error, eph t+1，k Ephemeris data, Δ eph, representing k satellites at time t +1 t+1，k Represents the historical ephemeris gross error for the ephemeris data for the k satellites at time t +1, and G2 represents the condition parameters for the same satellite case at different historical times.
In some embodiments of the present invention, in the step of calculating the predicted randomness error and the predicted non-randomness error respectively based on the weight parameters set for the randomness error and the non-randomness error for each sampling and the preset fractional difference auto-regression and moving average models, the predicted randomness error is calculated according to the following formula:
wherein F () represents the output parameters of the fractional difference autoregressive and moving average model with the parameters in (), N represents the number of the sampling frequencies, i represents the sampling at the ith sampling frequency, and R i Denotes the weighting parameter, Δ eph, corresponding to the sampling frequency at the ith time of the random error k，i Represents a curve, Δ eph, formed by a set of parameters obtained by sampling the total error of the historical ephemeris of k satellites at the ith sampling frequency t+Δt，k (rand) represents the curve formed by the random errors of the satellites for the predicted time period k t to Δ t.
In some embodiments of the present invention, the non-random errors include periodic errors and similarity errors, and in the step of calculating the predicted random errors and non-random errors respectively based on the weight parameters set for the random errors and the non-random errors in each sampling and a preset fractional difference auto-regression and moving average model, the predicted non-random errors are calculated according to the following formula:
wherein, Δ eph t+Δt，k (period) denotes the periodicity of the satellite for a time period k from t to Δ tCurve formed by error, Δ eph t+Δt，k (similar) represents a curve formed by similarity errors for the satellites over a time period k from t to Δ t, Δ eph t+Δt，k (period)+Δeph t+Δt，k (similar) represents a curve formed by periodic errors in a predicted time period from t to delta t and a superposed curve formed by similarity errors, F () represents an output parameter of a fractional difference autoregressive and moving average model which is input by a parameter in (), N represents the number of sampling frequencies, i represents sampling at the sampling frequency of the ith time, li represents a weight parameter corresponding to the sampling frequency of the ith time of non-random errors, and delta eph represents a weighted parameter corresponding to the sampling frequency of the ith time of non-random errors k，i The curve is formed by a parameter group obtained by sampling the historical ephemeris total error of the k satellites at the sampling frequency of the ith time.
In some embodiments of the invention, in the step of calculating the predicted total ephemeris error based on the predicted random error and the non-random error, the predicted total ephemeris error is calculated from the random error and the non-random error according to the following formula:
Δeph t+Δt，k ＝Δeph t+Δt，k (rand)+Δeph t+Δt，k (period)+Δeph t+Δt，k (similar)；
wherein, Δ eph t+Δt，k (period)+Δeph t+Δt，k (similar) represents a curve formed by the periodic error and a superimposed curve formed by the similarity error over the predicted time period t to Δ t, Δ eph t+Δt，k (rand) represents the curve formed by the stochastic error of the satellite for the predicted time period k t to Δ t, Δ eph t+Δt，k A curve of total error in ephemeris predicted over a time period t to Δ t.
In some embodiments of the present invention, the step of calculating the predicted ephemeris parameters at the time to be predicted based on the ephemeris parameters at the time to be predicted and the total ephemeris error to be predicted comprises:
acquiring the total error of ephemeris at the moment to be predicted in a curve formed by the total error of ephemeris within the predicted time period from t to delta t;
and receiving the basic ephemeris parameters at the time to be predicted sent by the ground base station, and calculating the predicted ephemeris parameters at the time to be predicted based on the ephemeris total errors at the time to be predicted in a curve formed by the basic ephemeris parameters at the time to be predicted and the ephemeris total errors in the predicted time period from t to delta t.
In some embodiments of the present invention, when the actual time reaches the time to be predicted, the weight parameter corresponding to the sampling frequency of the ith time of the non-random error and the weight parameter corresponding to the sampling frequency of the ith time of the random error are updated by using the actual value of the ephemeris parameter of the time to be predicted and the predicted ephemeris parameter based on the following formulas:
Δeph＝|eph1-eph2|
delta eph represents the parameter difference, eph1 represents the prediction ephemeris parameters at the time to be predicted, eph2 represents the actual values of the ephemeris parameters at the time to be predicted;
according to the simulated annealing algorithm, R is paired with a probability parameter P i And L i Updating, wherein the expression of the specific P is as follows:
wherein P represents a probability parameter, and T represents a preset temperature parameter;
L i ′＝L i ″*(1-P)；
R i ′＝R i ″*P；
wherein L is i "represents the weighting parameter corresponding to the sampling frequency of the ith time of the non-random error before updating, R i "represents a weight parameter corresponding to the sampling frequency of the i-th time of the random error before update, L i ' represents the updated weighting parameter corresponding to the sampling frequency of the ith time of the non-random error, R i ' indicates the updated weighting parameter corresponding to the sampling frequency at the ith time of the random error.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and drawings.
It will be appreciated by those skilled in the art that the objects and advantages that can be achieved with the present invention are not limited to what has been particularly described hereinabove, and that the above and other objects that can be achieved with the present invention will be more clearly understood from the following detailed description.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention.
FIG. 1 is a diagram of a method for ephemeris prediction based on a fractional difference autoregressive and moving average model according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and/or processing steps closely related to the scheme according to the present invention are shown in the drawings, and other details not so relevant to the present invention are omitted.
It should be emphasized that the term "comprises/comprising" when used herein, is taken to specify the presence of stated features, elements, steps or components, but does not preclude the presence or addition of one or more other features, elements, steps or components.
It is also noted that, unless otherwise specified, the term "coupled" is used herein to refer not only to a direct connection, but also to an indirect connection with an intermediate.
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the drawings, the same reference numerals denote the same or similar parts, or the same or similar steps.
Introduction of the prior art:
prior art 1:
interpolation is a method of predicting a function value between two points within a set, given a discrete set of data points. The commonly used interpolation methods at present mainly include Lagrange interpolation method, newton interpolation method, chebyshev polynomial fitting method and the like. The order of the same difference algorithm for achieving the optimal precision of different orbit satellites is different, and the optimal difference order of different difference algorithms for the same satellite is also different;
the interpolation results of linear interpolation, parabolic interpolation, newton interpolation and Lagrange interpolation in orbit prediction are compared through simulation experiments, and the conclusion that the characteristics of original data determine the selection of the interpolation method is obtained. The linear difference method and the parabolic interpolation method have a better effect on the difference of regular data, while the Newton interpolation method and the Lagrange interpolation method have a better effect on the difference of irregular data. Thus, like orbit predictions for spacecraft, the interpolation results of Newton interpolation and Lagrange interpolation are far superior to linear difference and parabolic interpolation;
the Lagrange interpolation method and the Chebyshev polynomial fitting method are obtained from the interpolation precision analysis results of the GEO satellite precise ephemeris, the IGSO satellite precise ephemeris and the MEO satellite precise ephemeris, and the selection of the order of the interpolation algorithm influences the conclusion of the interpolation algorithm on the precision of orbit prediction. In order to obtain a more accurate orbit prediction result, both interpolation orders should not be too low or too high in order selection. The interpolation results of the three satellites are analyzed, and the interpolation results of the two interpolation algorithms with the orders within the range of 9-15 orders are better. The orders of the same interpolation algorithm for achieving the optimal precision of different orbit satellites are different, and the optimal interpolation orders of different interpolation algorithms for the same satellite are also different. For the same interpolation algorithm, the selected orders are different when the difference precision of the three coordinate components of the satellite orbit reaches the best.
Disadvantages of prior art 1:
the order of the difference method affects the interpolation accuracy, and generally, the higher the order is, the higher the accuracy of the difference method prediction is, but as the order increases, the computational complexity of the difference method also increases.
Prior art 2:
and the dynamic model orbit prediction adopts a dynamic fitting method to estimate the position, the speed and the dynamic parameters under a group of satellite initial epochs according to the known satellite orbit as prior information, and utilizes the initial information of the group of satellites to carry out the orbit prediction. The influence of the selection of a dynamic fitting interval on GPS track prediction is researched by adopting an almost ideal state, and the predicted track precision is higher when the arc length of the observation track is selected for 40-45 hours; the influence of the GPS forecast orbit, obtained by studying the fitting arc length of different dynamic orbits, on the fixation of the precision single-point positioning ambiguity is researched, and the conclusion that the success rate of the 42-hour fitting arc length ambiguity fixation is higher is obtained; the orbit prediction is carried out on an HY-2 satellite by utilizing a dynamics fitting method, the influence of different fitting intervals on the accuracy of prediction of different arc lengths is analyzed, and the fact that the 3-dimensional root mean square value of the orbit in 1 day predicted by using the fitting intervals of 24 hours and 12 hours is superior to 1m is found, but a long-term prediction test is not carried out.
Disadvantages of prior art 2:
the divergence trend of the prediction error is intensified along with the extension of the prediction time, the magnitude of the prediction error is greatly different along with the difference of the initial epoch, and meanwhile, a continuous and periodic relationship exists between the prediction error and the initial epoch. The forecast error variation has a certain relation with the satellite orbit period.
Prior art 3:
ephemeris forecast in recent years uses a new modeling approach: a neural network. And a compensation model of the spacecraft dynamics model is established by utilizing the neural network, so that the orbit prediction precision is improved.
A neural network model is established on the basis of the dynamic model, errors obtained by prediction of the dynamic model are learned and trained through the neural network, and the obtained training model is used for compensating and improving the forecast orbit at the current moment. Through simulation experiments, on the basis of the prediction of an original dynamic model, the results obtained by BP neural network prediction are used for compensation, and the improved amplitudes of the 15d and 30d tracks are 41-80% and 32-88% respectively. However, the data obtained in the experiment are not universal, and the improvement effect of different satellites at different initial moments is different. The time sequence prediction is directly used as a basis, the obtained time sequence is used as a training set of a neural network model, and a prediction result with the accuracy reaching hundreds of meters in one week is obtained under the condition of no dynamic model.
Disadvantages of prior art 3:
because the satellite position quantity is directly used as the output of the neural network, the dynamic range of the state quantity of the neural network is large, and the improvement of the forecasting precision is limited.
In the prior art, interpolation calculation of ephemeris estimation is mainly implemented by interpolating a continuous function to acquired discrete data, and the aim is to realize numerical estimation in a known point interval. In the satellite ephemeris prediction, algorithms such as Lagrange interpolation, newton interpolation, chebyshev polynomial fitting and the like can be used. The interpolation calculation method depends on the accuracy of the boundary point of the interpolation interval, if the error of the boundary point is small, the interpolation estimation precision is high, and if the error of the boundary point is large, the interpolation estimation precision is low. In recent years, with the development of artificial intelligence algorithms, prediction algorithms based on neural networks or deep learning have also gained wide attention. The method mainly learns or infers the uncertain errors in ephemeris prediction by constructing a model experience base or fuzzy logic judgment and the like, and improves the automatic adjustment capability and precision of ephemeris prediction.
By combining the analysis, ephemeris prediction of the satellite internet needs to meet the following requirements: the frequency of satellite ephemeris broadcast cannot be too large; too much channel resources cannot be occupied; the ephemeris can only reflect outdated ephemeris calibration. On the premise, the existing ephemeris prediction method has the following problems: the complex multi-factor errors are used as overall errors for prediction, and the overall ephemeris prediction influence caused by different errors is difficult to evaluate; on the premise of not increasing the broadcasting frequency, the single-satellite broadcast ephemeris is difficult to provide more reliable priori knowledge; the periodicity and similarity of ephemeris error over time need to be mined further.
Therefore, aiming at the problem of insufficient prediction precision under a sparse ephemeris broadcast period in the conventional ephemeris prediction algorithm, the invention decomposes and models errors of different influence factors in ephemeris prediction errors and analyzes the time-varying characteristics of the errors of the different influence factors. And then, based on the current broadcast ephemeris, the precise ephemeris, the ephemeris at the corresponding moment and the prediction ephemeris of the local satellite and the adjacent satellites, checking iteration and error cancellation of multiple data sources are carried out. And finally, analyzing and compensating the ephemeris error through a multi-stage iterative fraction difference autoregression and a moving average model, thereby obtaining more accurate ephemeris.
As shown in FIG. 1, one aspect of the present invention provides a method for ephemeris prediction based on a fractional differential autoregressive and moving average model, the method comprising the following steps:
step S100, receiving an ephemeris prediction instruction, wherein the ephemeris prediction instruction comprises a specified satellite to be predicted, and receiving ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted;
in a specific implementation process, the adjacent satellite is two adjacent satellites which are in the same satellite orbit with the satellite to be predicted.
In a specific implementation, the ephemeris data is velocity data or position data of the satellite.
Step S200, respectively constructing an equation set of different satellites at the same historical time and an equation set of the same satellite at different historical times based on ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted;
by adopting the scheme, the broadcast ephemeris of a plurality of satellites can be received at the same time above the visual field of the user position. However, the terminal usually only considers the ephemeris of the current service satellite during processing, but neglects the broadcast ephemeris of the adjacent satellite and the previous service satellite; according to the scheme, the influence factors of the ephemeris errors of the satellites and the characteristics of the satellites along with space-time distribution are considered, and the same orbital ephemeris at the same time and the same orbital ephemeris at different times can be subjected to feature extraction and association by utilizing the time and space correlation among the ephemeris.
Step S300, calculating to obtain the total error of the historical ephemeris of the satellite to be predicted based on the equation sets of different satellites at the same time and the equation sets of the same satellite at different times;
in a specific implementation process, the total ephemeris error at a plurality of historical times can be obtained by obtaining the total ephemeris error at the same historical time based on the two equation sets and obtaining the total ephemeris error at one historical time based on the two equation sets.
Step S400, sampling the historical ephemeris total error of the satellite to be predicted by adopting a plurality of different sampling frequencies respectively, and outputting the predicted ephemeris total error based on a preset fraction difference autoregressive model and a moving average model;
in some embodiments of the present invention, based on the above method for obtaining a total ephemeris error at a historical time by using two equation sets, a total ephemeris error at a historical time at each sampling time can be obtained, the total ephemeris error sampled at each sampling frequency is used as a parameter set, in a specific implementation process, a matlab image is drawn based on the total ephemeris error sampled at each sampling frequency as a parameter set, the matlab image corresponding to each sampling frequency is input into a fractional differential auto-regression and moving average model, a corresponding predicted matlab image is output, and the predicted matlab images output based on a plurality of sampling frequencies are superimposed based on weights pre-allocated to each sampling frequency, so as to obtain a matlab image corresponding to the predicted total ephemeris error, where the matlab image corresponding to the predicted total ephemeris error includes ephemeris parameters corresponding to a plurality of time points.
In a specific implementation process, in the step of inputting the matlab image corresponding to each sampling frequency into the fractional difference autoregressive and moving average model and outputting the corresponding predicted matlab image, sampling points in the matlab image corresponding to each sampling frequency, inputting a plurality of sampled data points into the fractional difference autoregressive and moving average model, outputting the predicted data points, and drawing the predicted data points into the matlab image.
Step S500, ephemeris parameters at the time to be predicted in the ephemeris data are obtained, and predicted ephemeris parameters at the time to be predicted are calculated based on the ephemeris parameters at the time to be predicted and the predicted ephemeris total error.
In a specific implementation process, the ephemeris parameters at the time to be predicted can be obtained from a ground base station, the ground base station calculates historical data by using an SGP4 algorithm to obtain the coarse ephemeris parameters at the time to be predicted, and the scheme adjusts the coarse ephemeris parameters at the time to be predicted according to the total error of the predicted ephemeris, so that the prediction precision is improved.
By adopting the scheme, the historical ephemeris total error of the satellite to be predicted is obtained by performing combined calculation through ephemeris data of adjacent satellites of the satellite to be predicted, the predicted ephemeris total error of the future time is obtained through fractional autoregressive and moving average model (ARIMA model), and the predicted ephemeris parameter of the time to be predicted is obtained by calculating based on the basic ephemeris parameter of the time to be predicted in the ephemeris data and the predicted ephemeris total error.
In some embodiments of the present invention, the historical ephemeris total error includes a random error and a non-random error, in the step of sampling the historical ephemeris total error of the satellite to be predicted by using a plurality of different sampling frequencies respectively, and outputting the predicted ephemeris total error based on a preset fraction difference autoregressive model and a moving average model, the predicted ephemeris total error is calculated based on a weight parameter set for the random error and the non-random error in each sampling and the preset fraction difference autoregressive model and the moving average model respectively, and the predicted ephemeris total error is calculated based on the predicted random error and the predicted non-random error.
In implementations, the non-random errors include periodic errors and similarity errors.
In a specific implementation process, the random errors comprise first-time data interference, star attitude deviation and ephemeris space transmission deviation; the similarity errors comprise transmission processing errors in similar geographic space and similar landform; the periodic error includes an error existing in a satellite periodic motion.
In some embodiments of the present invention, in the step of constructing the equation sets of different satellites at the same historical time and the equation sets of the same satellite at different historical times based on the ephemeris data of the satellite to be predicted and the adjacent satellites of the satellite to be predicted respectively, the equation sets of different satellites at the same historical time are as follows:
eph t，k ephemeris data, eph, representing k satellites at time t t，k-1 Ephemeris data, Δ eph, at time t representing a neighbor k-1 satellite of the k-satellite t，k Total error of historical ephemeris, Δ eph, representing ephemeris data for k-satellites at time t t，k-1 Representing the historical ephemeris gross error, eph, of the ephemeris data of k-1 satellites at time t t，k+1 Ephemeris data, Δ eph, at time t representing the satellites adjacent to k +1 of k satellites t，k+1 The historical ephemeris total error of the ephemeris data of the k +1 satellite at the time t is shown, and G1 is a condition parameter of different satellite conditions at the same historical time.
In the course of the specific implementation,
in some embodiments of the present invention, in the step of constructing the equation sets of different satellites at the same historical time and the equation set of the same satellite at different historical times based on the ephemeris data of the satellite to be predicted and the adjacent satellite of the satellite to be predicted, respectively, the equation sets of the same satellite at different historical times are as follows:
eph t，k ephemeris data, eph, representing k satellites at time t t-1，k Ephemeris data, Δ eph, representing k satellites at time t-1 t，k Historical ephemeris representing ephemeris data for k-satellites at time tTotal error, Δ eph t-1，k Representing the historical ephemeris gross error, eph, of the ephemeris data of the k-satellites at time t-1 t+1，k Ephemeris data, Δ eph, representing k satellites at time t +1 t+1，k Represents the historical ephemeris gross error for the ephemeris data for the k satellites at time t +1, and G2 represents the condition parameters for the same satellite case at different historical times.
By adopting the scheme, the two equation sets are combined for joint calculation, and the delta eph is obtained through calculation t，k The parameter value of (2).
In some embodiments of the present invention, in the step of calculating the predicted random error and the non-random error based on the weight parameters set for the random error and the non-random error for each sampling and the preset fractional difference autoregressive and moving average models, respectively, the predicted random error and the non-random error are calculated according to the following formulas:
wherein F () represents the output parameters of the fractional difference autoregressive and moving average model with the parameters in (), N represents the number of the sampling frequencies, i represents the sampling at the ith sampling frequency, and R i Denotes the weighting parameter, Δ eph, corresponding to the sampling frequency at the ith time of the random error k，i Δ eph, which is a curve formed by a parameter set obtained by sampling the total error of the historical ephemeris of k satellites at the ith sampling frequency t+Δt，k (rand) represents the curve formed by the randomness errors of the satellites for the predicted time period k t to Δ t.
In the specific implementation process, in the step of inputting a curve formed by a parameter group obtained by sampling the historical ephemeris gross error of a k-th satellite at the ith sampling frequency into a fractional difference autoregressive and moving average model, a plurality of curves corresponding to a plurality of sampling rates are sampled, each curve samples the same time point, in the formula, each sampled time point corresponds to a predicted value, the predicted values corresponding to the same time points in different curves are overlapped based on weight values to obtain the predicted randomness error of the time point, the ephemeris parameters predicted by the time points are drawn into matlab images, and the curve formed by the predicted randomness error of the k-th satellite in a time period from t to delta t is obtained.
In some embodiments of the present invention, the non-random errors include periodic errors and similarity errors, and in the step of calculating the predicted random errors and non-random errors respectively based on the weight parameters set for the random errors and the non-random errors in each sampling and a preset fractional difference auto-regression and moving average model, the predicted non-random errors are calculated according to the following formula:
wherein, Δ eph t+Δt，k (period) represents the curve formed by the periodic error of the satellite for a time period k from t to Δ t, Δ eph t+Δt，k (similar) represents a curve formed by similarity errors for the satellites over a time period k from t to Δ t, Δ eph t+Δt，k (period)+Δeph t+Δt，k (similar) represents a curve formed by periodic errors in a predicted time period from t to delta t and a superposed curve formed by similarity errors, F () represents an output parameter of a fractional difference autoregressive and moving average model which is input by a parameter in (), N represents the number of sampling frequencies, i represents sampling at the sampling frequency of the ith time, and L represents the sampling frequency of the ith time i Denotes the weighting parameter, Δ eph, corresponding to the sampling frequency of the ith time of the non-random error k，i The curve is formed by a parameter group obtained by sampling the historical ephemeris total error of the k satellites at the sampling frequency of the ith time.
In the specific implementation process, in the step of inputting a curve formed by a parameter group obtained by sampling the total error of the historical ephemeris of the k-th satellite at the ith sampling frequency into a fractional difference autoregressive and moving average model, sampling a plurality of curves corresponding to a plurality of sampling rates, wherein each curve samples the same time point, in the formula, each sampled time point corresponds to a predicted value, the predicted values corresponding to the same time points in different curves are overlapped based on weight values to obtain the non-random error predicted at the time point, drawing the ephemeris parameters predicted at the plurality of time points into a matlab image, and obtaining a curve formed by the non-random errors of the k-satellite at a predicted time period from t to delta t, namely a curve formed by overlapping the periodic error and the similarity error of the k-satellite at the time period from t to delta t.
In some embodiments of the invention, in the step of calculating the predicted total ephemeris error based on the predicted random error and the non-random error, the predicted total ephemeris error is calculated from the random error and the non-random error according to the following formula:
Δeph t+Δt，k ＝Δeph t+ Δ t，k (rand)+Δeph t+Δt，k (period)+Δeph t+Δt，k (similar)；
wherein, Δ eph t+Δt，k (period)+Δeph t+Δt，k (similar) represents a curve formed by the periodic error and a superimposed curve formed by the similarity error in the predicted time period from t to Δ t, Δ eph t+Δt，k (rand) represents the curve formed by the stochastic error of the satellite for the predicted time period k t to Δ t, Δ eph t+Δt，k A predicted total error in ephemeris for a time period t to Δ t.
In a specific implementation process, considering satellite ephemeris error influence factors and the characteristics of the satellite space-time distribution, the time and space correlation between the ephemeris can be utilized, and different sampling rates are adopted for the same orbital ephemeris at the same time and the same orbital ephemeris at different times to perform feature extraction and association.
In a specific implementation, the sampling rate may be set to 3.
By adopting the scheme, the two curves are superposed, namely the parameters of the corresponding time points are added to obtain a curve formed by the ephemeris total error in the predicted time period from t to delta t.
In the specific implementation process, a differential autoregressive and moving average method is modeled, and the key point is to determine an autoregressive term p of 6 groups of data with different characteristics, a moving average term q and a difference order d when a time sequence becomes stable. For 6 groups of data, 6 combinations of (p, d, q) can be obtained respectively, and the 6 groups of data are random error parameter sets and non-random error parameter sets sampled at three sampling frequencies;
setting the order d, calculating the value d corresponding to each group of parameters through multiple differential processing, and using an Aging Information Criterion (AIC) to rank p and q. Only when the value of AIC is minimal, the resulting p and q are the values we want; model parameters are fitted using Exact Maximum Likelihood (EML) estimation methods to obtain a prediction differencing autoregression and a moving average model (p, d, q).
And determining the parameters of the fractional difference autoregressive model and the mobile smooth model of the rest five groups of data by the same steps to finally obtain 6 prediction models.
In some embodiments of the present invention, the step of calculating the ephemeris parameters to be predicted based on the ephemeris parameters and the total ephemeris error to be predicted comprises:
acquiring the total error of ephemeris at the moment to be predicted in a curve formed by the total error of ephemeris within the predicted time period from t to delta t;
and receiving the basic ephemeris parameters at the time to be predicted sent by the ground base station, and calculating the predicted ephemeris parameters at the time to be predicted based on the ephemeris total errors at the time to be predicted in a curve formed by the basic ephemeris parameters at the time to be predicted and the ephemeris total errors in the predicted time period from t to delta t.
By adopting the scheme, the predicted ephemeris total error is compensated for the basic ephemeris parameters, and the ephemeris accuracy is improved.
In some embodiments of the present invention, when the actual time reaches the time to be predicted, the weight parameter corresponding to the sampling frequency of the ith time of the non-random error and the weight parameter corresponding to the sampling frequency of the ith time of the random error are updated by using the actual value of the ephemeris parameter of the time to be predicted and the predicted ephemeris parameter based on the following formulas:
Δeph＝|eph1-eph2|
delta eph represents the parameter difference, eph1 represents the prediction ephemeris parameters at the time to be predicted, eph2 represents the actual values of the ephemeris parameters at the time to be predicted;
according to the simulated annealing algorithm, R is paired with a probability parameter P i And L i Updating, wherein the expression of the specific P is as follows:
wherein, P represents a probability parameter, and T represents a preset temperature parameter;
L i ′＝L i ″*(1-P)；
R i ′＝R i ″*P；
wherein L is i "represents the weighting parameter corresponding to the sampling frequency of the ith time of the non-random error before updating, R i "represents a weight parameter corresponding to the sampling frequency of the ith random error before update, L i ' represents the updated weighting parameter corresponding to the sampling frequency of the ith time of the non-random error, R i ' denotes a weight parameter corresponding to the updated sampling frequency for the ith time of the random error.
In a specific implementation process, a weight parameter corresponding to the ith sampling frequency of the non-random error and a weight parameter corresponding to the ith sampling frequency of the random error satisfy the following relation:
in the prior art, an ephemeris prediction method without increasing satellite ephemeris broadcast ephemeris has great technical advantages in satellite internet application. In order to improve the prediction precision, the existing method mainly calculates the fitting ephemeris estimation value by constructing a finer satellite dynamics model or by interpolation, but the error caused by the influence of the satellite ephemeris has obvious uncertainty, so that a more accurate prediction model is difficult to construct, and the precision of the prediction value obtained by interpolation is difficult to guarantee if the precision of the reference value of the interpolation is insufficient. Therefore, the method mainly solves the problems of how to enlarge the dimension of the information observed by the user and analyze and improve the comprehensive prediction performance under different error influence factors on the premise of not increasing the frequency of broadcasting the satellite ephemeris. The main problems include:
problem 1: and (3) effective separation and analysis of ephemeris error multi-heterogeneous influence factors. The satellite broadcast ephemeris generally transmits three-dimensional coordinates and velocities of satellites at different time and regions, and errors of the satellite broadcast ephemeris include uncertainty deviations caused by the influence of gravity of the earth and the satellite, the influence of gravity of other satellites, attitude deviation of the satellite, transmission deviation of ephemeris space and the like. All of these biases will have an impact on the overall prediction bias of the satellite ephemeris. However, the broadcast ephemeris is obtained through observation, and can be analyzed only from two indexes, namely three-dimensional coordinates and speed. The influence of gravity on the satellite, the change of the satellite attitude and other heterogeneous data belonging to different dimensions and different values have certain difficulty in analyzing the corresponding error influence degree from the broadcast ephemeris prediction error. Therefore, the invention analyzes and models the errors with different change trends and characteristics such as similarity, periodicity and the like through time series error analysis, and provides support for further analyzing ephemeris error sources.
Problem 2: and (3) performing fusion analysis and compensation on various ephemeris data errors in different time and space. Broadcast ephemeris for multiple satellites may be received simultaneously over the field of view of the user's location. However, the terminal usually only considers the ephemeris of the current serving satellite and ignores the broadcast ephemeris of the neighboring satellite and the previous serving satellite. The gravity errors of the satellites in the same orbit at the same time are similar, the transmission errors of the satellites in the same orbit at different times are similar, and more error source combinations can be obtained to realize better error compensation. There are certain challenges in how to evaluate different data combinations to obtain a prediction accuracy gain.
Therefore, the method sets the estimated threshold value of ephemeris prediction, sets different data combinations as the input of multiple iterations, and improves the satellite internet ephemeris prediction precision by designing the fast optimization of scene threshold value optimization time sequence prediction.
The method decomposes and models the errors of different influence factors in ephemeris prediction errors, and analyzes the time-varying characteristics of the errors of the different influence factors. And then, based on the current broadcast ephemeris, the precise ephemeris, the ephemeris at the corresponding moment and the prediction ephemeris of the local satellite and the adjacent satellites, checking iteration and error cancellation of multiple data sources are carried out. And finally, analyzing and compensating the ephemeris error through a multi-stage iterative fraction difference autoregression and a moving average model, thereby obtaining more accurate ephemeris.
The beneficial effects of the invention include:
1. the technology of the invention can obviously improve the time length of prediction on the premise of meeting the prediction precision.
2. The invention can reduce the frequency of receiving the ephemeris data by the ground user, thereby reducing the load data volume of the ground user.
The invention also provides an ephemeris prediction apparatus based on a fractional difference autoregressive and moving average model, comprising a computer device including a processor and a memory, the memory having stored therein computer instructions for executing the computer instructions stored in the memory, the apparatus implementing the steps as described above when the computer instructions are executed by the processor.
Embodiments of the present invention also provide a computer-readable storage medium, on which a computer program is stored, where the computer program is executed by a processor to implement the steps implemented by the foregoing metadata-based railroad engineering ECM management method. The computer readable storage medium may be a tangible storage medium such as Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, floppy disks, hard disks, removable storage disks, CD-ROMs, or any other form of storage medium known in the art.
Those of ordinary skill in the art will appreciate that the various illustrative components, systems, and methods described in connection with the embodiments disclosed herein may be implemented as hardware, software, or combinations of both. Whether this is done in hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention. When implemented in hardware, it may be, for example, an electronic circuit, an Application Specific Integrated Circuit (ASIC), suitable firmware, plug-in, function card, or the like. When implemented in software, the elements of the invention are the programs or code segments used to perform the required tasks. The program or code segments may be stored in a machine-readable medium or transmitted by a data signal carried in a carrier wave over a transmission medium or a communication link.
It is to be understood that the invention is not limited to the precise arrangements and instrumentalities shown. A detailed description of known methods is omitted herein for the sake of brevity. In the above embodiments, several specific steps are described and shown as examples. However, the method processes of the present invention are not limited to the specific steps described and illustrated, and those skilled in the art can make various changes, modifications and additions or change the order between the steps after comprehending the spirit of the present invention.
Features that are described and/or illustrated with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments and/or in combination with or instead of the features of the other embodiments in the present invention.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A method and a device for ephemeris prediction based on a fractional difference autoregression and a moving average model are characterized in that the method comprises the following steps:
receiving an ephemeris prediction instruction, wherein the ephemeris prediction instruction comprises a specified satellite to be predicted, and receiving ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted;
respectively constructing an equation set of different satellites at the same historical moment and an equation set of the same satellite at different historical moments based on ephemeris data of the satellite to be predicted and an adjacent satellite of the satellite to be predicted;
calculating to obtain the historical ephemeris total error of the satellite to be predicted based on the equation sets of different satellites at the same time and the equation sets of the same satellite at different times;
sampling the historical ephemeris total error of the satellite to be predicted by adopting a plurality of different sampling frequencies respectively, and outputting the predicted ephemeris total error based on a preset fraction difference autoregressive model and a moving average model;
acquiring ephemeris parameters of the time to be predicted in the ephemeris data, and calculating predicted ephemeris parameters of the time to be predicted based on the ephemeris parameters of the time to be predicted and the predicted ephemeris total error.
2. The method according to claim 1, wherein the historical ephemeris total errors include random errors and non-random errors, and in the step of sampling the historical ephemeris total errors of the satellite to be predicted respectively by using a plurality of different sampling frequencies and outputting the predicted ephemeris total errors based on a preset fraction difference autoregressive model and a moving average model, the predicted random errors and the predicted non-random errors are calculated respectively based on weight parameters set for the random errors and the non-random errors in each sampling and the preset fraction difference autoregressive model and the moving average model, and the predicted ephemeris total errors are calculated based on the predicted random errors and the predicted non-random errors.
3. The method according to claim 1, wherein in the step of constructing the equation sets of different satellites at the same historical time and the equation sets of the same satellite at different historical times based on the ephemeris data of the satellite to be predicted and the adjacent satellites of the satellite to be predicted respectively, the equation sets of the different satellites at the same historical time are as follows:
eph t,k ephemeris data, eph, representing k satellites at time t t,k-1 Ephemeris data, Δ eph, at time t representing a neighbor k-1 satellite of the k-satellite t,k Total error of historical ephemeris, Δ eph, representing ephemeris data for k-satellites at time t t,k-1 Total error of historical ephemeris, eph, representing ephemeris data of k-1 satellites at time t t,k+1 Ephemeris data, Δ eph, representing the satellites k +1 adjacent to the k satellite at time t t,k+1 The historical ephemeris total error of the ephemeris data of the k +1 satellite at the time t is shown, and G1 is a condition parameter of different satellite conditions at the same historical time.
4. The method according to claim 1, wherein in the step of constructing the equation sets of different satellites at the same historical time and the equation set of the same satellite at different historical times based on the ephemeris data of the satellite to be predicted and the adjacent satellite of the satellite to be predicted respectively, the equation sets of the same satellite at different historical times are as follows:
eph t,k ephemeris data, eph, representing k satellites at time t t-1,k Ephemeris data, Δ eph, representing k satellites at time t-1 t,k Total error of historical ephemeris, Δ eph, representing ephemeris data for k-satellites at time t t-1,k Representing the historical ephemeris gross error, eph, of the ephemeris data of the k-satellites at time t-1 t+1,k Ephemeris data, Δ eph, representing k satellites at time t +1 t+1,k Represents the historical ephemeris gross error for the ephemeris data for the k satellites at time t +1, and G2 represents the condition parameters for the same satellite case at different historical times.
5. The method of claim 2, wherein in the step of calculating the predicted random error and the non-random error based on the weight parameters set for the random error and the non-random error for each sampling and a preset fractional difference autoregressive and moving average model, respectively, the predicted random error and the non-random error are calculated according to the following formulas:
wherein F () represents the output parameters of the fractional difference autoregressive and moving average model with the parameters in (), N represents the number of the sampling frequencies, i represents the sampling at the ith sampling frequency, and R i Denotes the weighting parameter, Δ eph, corresponding to the sampling frequency at the ith time of the random error k,i Δ eph, which is a curve formed by a parameter set obtained by sampling the total error of the historical ephemeris of k satellites at the ith sampling frequency t+Δt,k (rand) represents the curve formed by the randomness errors of the satellites for the predicted time period k t to Δ t.
6. The method according to claim 2, wherein the non-random errors include periodic errors and similarity errors, and the predicted non-random errors are calculated according to the following formulas in the step of calculating the predicted random errors and non-random errors respectively based on the weight parameters set for the random errors and the non-random errors for each sampling and a preset fractional differential autoregressive and moving average model:
wherein, Δ eph t+Δt,k (period) represents the curve formed by the periodic error of the satellite for a time period k from t to Δ t, Δ eph t+Δt,k (similar) represents a curve formed by similarity errors for the satellites over a time period k from t to Δ t, Δ eph t+Δt,k (period)+Δeph t+Δt,k (similar) represents a curve formed by periodic errors in a predicted time period from t to delta t and a superposed curve formed by similarity errors, F () represents an output parameter of a fractional difference autoregressive and moving average model which is input by a parameter in (), N represents the number of sampling frequencies, i represents sampling at the sampling frequency of the ith time, and L represents the sampling frequency of the ith time i Denotes the weighting parameter, Δ eph, corresponding to the sampling frequency of the ith time of the non-random error k,i The curve is formed by a parameter group obtained by sampling the historical ephemeris total error of the k satellites at the sampling frequency of the ith time.
7. The method of claim 2, wherein in the step of calculating the predicted total ephemeris error based on the predicted random and non-random errors, the predicted total ephemeris error is calculated from the random and non-random errors according to the following equation:
Δeph t+Δt,k ＝Δeph t+Δt,k (rand)+Δeph t+Δt,k (period)+Δeph t+Δt,k (similar)；
wherein, Δ eph t+Δt,k (period)+Δeph t+Δt,k (silar) represents a curve formed by the periodic error and a superimposed curve formed by the similarity error over the predicted time period t to Δ t, Δ eph t+Δt,k (rand) represents the curve formed by the stochastic errors of the satellites for the predicted t to Δ t time period k, Δ eph t+Δt,k A predicted total error in ephemeris for a time period t to Δ t.
8. The method of claim 1, wherein the step of calculating predicted ephemeris parameters for the time to be predicted based on the ephemeris parameters for the time to be predicted and the predicted total ephemeris error comprises:
acquiring the total error of ephemeris at the moment to be predicted in a curve formed by the total error of ephemeris within the predicted time period from t to delta t;
and receiving the basic ephemeris parameters at the time to be predicted sent by the ground base station, and calculating the predicted ephemeris parameters at the time to be predicted based on the ephemeris total errors at the time to be predicted in a curve formed by the basic ephemeris parameters at the time to be predicted and the ephemeris total errors in the predicted time period from t to delta t.
9. The method according to claim 1, wherein when the actual time reaches the time to be predicted, the weight parameters corresponding to the sampling frequency of the ith time of the non-random error and the weight parameters corresponding to the sampling frequency of the ith time of the random error are updated by using the actual value of the ephemeris parameters of the time to be predicted and the predicted ephemeris parameters based on the following formula:
Δeph＝|eph1-eph2|
delta eph represents the parameter difference, eph1 represents the prediction ephemeris parameters at the time to be predicted, eph2 represents the actual values of the ephemeris parameters at the time to be predicted;
according to the simulated annealing algorithm, R is paired with a probability parameter P i And L i Updating, wherein the expression of the specific P is as follows:
wherein P represents a probability parameter, and T represents a preset temperature parameter;
L i ’＝L i ”*(1-P)；
R i ’＝R i ”*P；
wherein L is i "represents a weight parameter R corresponding to the sampling frequency of the ith time of the non-random error before update i "represents a weight parameter L corresponding to the sampling frequency of the ith random error before update i ' represents the updated weighting parameter corresponding to the sampling frequency of the ith time of the non-random error, R i ' denotes a weight parameter corresponding to the updated sampling frequency for the ith time of the random error.
10. An apparatus for ephemeris prediction based on a fractional differential autoregressive and moving average model, the apparatus comprising a computer device comprising a processor and a memory, the memory having stored therein computer instructions for executing computer instructions stored in the memory, the apparatus when executed by the processor performing the steps as recited in any of claims 1-9.
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| CN117312760A (en) * | 2023-11-28 | 2023-12-29 | 中国电子科技集团公司第五十四研究所 | Space grid-based space-time distribution prediction method for moving target |
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| CN116774255B (en) * | 2023-03-28 | 2024-01-30 | 南京信息工程大学 | Daily reproduction period forecasting method for IGSO navigation satellite |
| CN117312760A (en) * | 2023-11-28 | 2023-12-29 | 中国电子科技集团公司第五十四研究所 | Space grid-based space-time distribution prediction method for moving target |
| CN117312760B (en) * | 2023-11-28 | 2024-01-30 | 中国电子科技集团公司第五十四研究所 | Space grid-based space-time distribution prediction method for moving target |
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