CN106096787B - A kind of earth rotation parameter (ERP) forecasting procedure of Adaptive matching - Google Patents
A kind of earth rotation parameter (ERP) forecasting procedure of Adaptive matching Download PDFInfo
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Abstract
The invention discloses a kind of earth rotation parameter (ERP) forecasting procedures of Adaptive matching.The Adaptive matching that can be realized a few class key parameters needed for ERP is forecast using the present invention, improves ERP forecast precision.The present invention carries out ERP forecast using LS+AR method, and gives ERP forecast time series training length experience design standard；The stationarity of ERP residual error is improved using difference method, and introduces Chi-square Test method, by calculating chi-square value, the distribution character of PMX, PMY and UT1-UTC residual error is quantitatively evaluated, and give the corresponding relationship Experience norms of chi-square value Yu difference order；Finally in the AR forecast of ERP residual error, the model order for giving AR model determines method, to realize the ERP forecast of Adaptive matching, and improves forecast precision.
Description
Technical field
The present invention relates to space telemetry and control technology fields, and in particular to a kind of earth rotation parameter (ERP) forecast side of Adaptive matching
Method.
Background technique
Earth rotation parameter (ERP) (ERP) is to realize that international Celestial Reference System (ICRS) and International Geophysical referential (ITRS) is converted
Necessary parameter, be indispensable important in the space missions such as deep-space spacecraft track navigation, terrestrial space spacecraft observing and controlling
State parameter.Since spacecraft orbit determination usually carries out in international Celestial Reference System, and the final purpose of navigation positioning system
It is position and speed of the determining spacecraft in terrestrial reference system, the almanac data of publication is in International Geophysical referential,
Therefore, it is necessary to carry out the mutual conversion of ICRS and ITRS.ERP mutually converts for realizing ICRS and ITRS, the direct shadow of precision
Two referential conversion accuracies are rung, and then the navigation of the high-precision of spacecraft, positioning result are directly had an impact.In addition, ERP conduct
One of most important parameter is studied by geodesy, astrometry and geophysics, with the core of the earth, curtain, the earth's crust, sea
Ocean, the motion of matter of each ring layer of atmosphere and interaction have close relationship.
Navigator fix task be unable to do without ERP data and supports when high-precision real, but due to passing from ERP observation process to data
Defeated, treatment process needs take a significant amount of time, and data handling procedure is more complex, when the publication of ERP product being caused to have certain
Between lag.On the one hand in order to quasi real time with real-time navigational tasks requirement, it is necessary to using ERP forecast model products for supporting task real
Applying, while being related to the advanced mission planning of spacecraft observing and controlling track etc. also needs ERP forecast model products to support；On the other hand, work as spacecraft
Into after autonomous orbit determination mode, ground control system cannot upload newest ERP data again to complete the conversion of ITRS and ICRS,
And it can only guarantee conversion between the two by ERP forecast model products.Therefore, carry out the forecasting procedure research of ERP for space flight
Device observing and controlling has a very important role.In addition, ERP forecast has important answer in terms of the dynamic analysis of geophysical phenomena
With value.
So far, domestic and international different researchers and academic institution have made intensive studies ERP forecast, and there are many forecast sides
Method is applied in the forecast of ERP, such as least square (LS) extrapolation, least square joint auto-regressive analysis method (LS+AR), nerve
Network method of prediction, least square Kalman filtering forecasting procedure, wavelet decomposition and auto-regressive analysis method etc..It is pre- in numerous ERP
In reporting method, one of most effective ERP forecasting procedure is known as based on LS+AR forecasting procedure in the world, at present ERP in the world
The main offer mechanism of forecast model products, International Earth Rotation and frame of reference Servers Organization (IERS) and USNO-US Naval Observatory
(USNO), it is based primarily upon LS+AR method and carries out ERP forecast.
In the ERP forecasting procedure of traditional LS+AR, there are also following problems: (1) smooth performance of ERP time series is commented
Estimating, the present invention proposes to improve ERP time series stationarity using difference processing, but current not specific difference order
Determine method；(2) although AR model has good predictor characteristic to stationary time series, current there is no specific AR
The optimal order of model determines method, and difference ERP characteristic corresponds to different AR model orders, and the optimal order of AR model is true
It is scheduled on particularly critical in AR model；(3) ERP gives the correct time in advance needs to utilize the ERP time series of certain length for training, thus real
Existing ERP Extrapotated prediction, for trained ERP length is directly related with ERP forecast precision and ERP is forecast critical issue it
One, but the choosing method of current not relevant ERP time series training length.
Summary of the invention
In view of this, can be realized ERP the present invention provides a kind of earth rotation parameter (ERP) forecasting procedure of Adaptive matching
The Adaptive matching of a few class key parameters needed for forecast, improves ERP forecast precision.
The earth rotation parameter (ERP) forecasting procedure of Adaptive matching of the invention, includes the following steps:
Step 1, PMX, PMY and UT1-UTC data of given training length are chosen respectively；Wherein, PMX, PMY of selection and
UT1-UTC is referred to as original ERP data；
Step 2, three kinds of original ERP data step 1 obtained carry out the minimum of periodic function and quadratic polynomial respectively
Two multiply fitting, obtain ERP match value；ERP match value is subtracted with the original ERP data of step 1, obtains ERP residual error；
Step 3, the ERP match value of step 2 is carried out using the periodic function of original ERP data and quadratic polynomial function
Extrapolation, wherein ERP extrapolation length is consistent with desired forecast length；
Step 4, chi-square value calculating is carried out to the ERP residual error that step 2 obtains, according to the chi-square value χ of ERP residual error2With formula (1)
Determine difference order:
Step 5, the difference order determined according to step 4 carries out calculus of differences to ERP residual error, it is residual to obtain differentiated ERP
Difference；
Step 6, the differentiated ERP residual error obtained for step 5 is forecast using the AR that AR model carries out ERP residual error, is obtained
Obtain the predicted value of ERP residual error；
Step 7, the predicted value that step 6 obtains ERP residual error is subjected to inverse difference processing, and divides unfavourable balance to processing result and step
Rapid 3 extrapolating results obtained are overlapped, that is, obtain the predictive initial value of ERP；
Step 8, the PMX predictive initial value and PMY predictive initial value that step 7 obtains are the final forecast for being respectively PMX and PMY
Value；UT1-UTC predictive initial value obtains final UT1-UTC after restoring with the forecast addition of humorous solid tide item with jump second and forecasts
Value.
Further, in the step 1, the training length of PMX, PMY and UT1-UTC data is chosen according to following formula:
Unit in formula is year, and length (PMX_N) is the training length of PMX, and length (PMY_N) is the training of PMY
Length, length (UT1-UTC_N) are the training length of UT1-UTC.
Further, in the step 6, the model order of the AR model determines that method is as follows:
Step 6.1, AR model are as follows:
Wherein,For AR model parameter；atFor white noise；P is AR model order；xt,xt-1,
xt-2,…,xt-pFor t, t-1, t-2 ..., the quantity of state of the stationary time series at t-p moment；
The search space that AR model order p is arranged is [1, P]；The P value of model order p is substituted into respectively in formula (4),
Obtain P AR model；
Step 6.2, the P AR model obtained for step 6.1 estimates each using solution Yule-Walker equation method
The corresponding model parameter of model order pThen in the model parameter estimated generation, is returned in formula (4), calculating obtains
The model value for obtaining stationary time series, then subtracts model value with the state value of stationary time series and obtains noise residual sequence；
Step 6.3, judgment criterion coefficient ξ corresponding to each AR order p is determined using whole pre-error criterionp:
Wherein, N is sample length,For the variance of noise residual sequence；
Step 6.4, the corresponding judgment criterion coefficient of P AR model order p is judged, minimum judgment criterion coefficient pair
The model order answered is the AR model order of determining AR model.
The utility model has the advantages that
The present invention proposes ERP forecast difference Experience norms, the AR order of Adaptive matching searches for the method for determination and gives the correct time in advance
Between sequence training length Experience norms, combine the least square smoothing method of multinomial and periodic function, Chi-square Test method with
AR forecasting procedure, it is comprehensive to determine ERP forecast result, and ERP forecast precision is evaluated, realize the ERP forecast of Adaptive matching.
Detailed description of the invention
Fig. 1 is the ERP forecast data process flow diagram of Adaptive matching.
Fig. 2 is for forecasting trained PMX original time domain waveform.
Fig. 3 is the least square fitting and residual plot of PMX.
Fig. 4 is for forecasting trained PMY original time domain waveform.
Fig. 5 is the least square fitting and residual plot of PMY.
The jump second that Fig. 6 is UT1-UTC is rejected to be eliminated with to humorous solid tide item.
Fig. 7 is the least square fitting and residual plot of UT1-UTC.
Fig. 8 is the forecast result and international comparison of PMX.
Fig. 9 is the forecast result and international comparison of PMY.
Figure 10 is the forecast result and international comparison of UT1-UTC.
Figure 11 is ERP prediction error statistical chart.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
The present invention provides a kind of earth rotation parameter (ERP) forecasting procedures of Adaptive matching, give the ERP forecast of LS+AR
The determination method of key parameter in method:
(1) in order to realize that ERP is forecast using AR model method, ERP time series to be processed need to meet stationarity and want
It asks.For ERP time series, original PMX (Ghandler motion X-component), PMY (Ghandler motion Y-component) and UT1-UTC (universal time and the world
Coordinate time difference value) stationarity requirement is not satisfied in time series, exist in one side PMX, PMY and UT1-UTC time series
The periodic component known, these periodic components must be deducted in advance before carrying out AR forecast, obtain PMX, PMY and UT1-
UTC residual error；Then, the stationarity of PMX, PMY and UT1-UTC residual error can be provided by way of difference.It is rationally poor in order to select
Sublevel, while difference order shortcoming or excessive difference are avoided, it need to be according to different PMX, PMY and UT1-UTC to be analyzed
The stationarity of residual error selects suitable difference order.Present invention introduces Chi-square Test methods quantitatively to be commented by calculating chi-square value
Estimate the distribution character of PMX, PMY and UT1-UTC residual error, and proposes the corresponding relationship criterion (formula of chi-square value Yu difference order
(1)), to realize the difference order Adaptive matching of PMX, PMY and UT1-UTC.
(2) in order to realize that the Adaptive matching of AR model order, the present invention propose that the AR order search of Adaptive matching is true
Determine method.For AR model, in a specified AR order search space, using solution Yule-Walker equation method for estimating
The corresponding AR model parameter of each model order p is counted, is then judged using whole pre-error criterion (FPE), is chosen optimal
AR model order.
(3) in order to select reasonable ERP forecast time series training length, effective forecast of ERP is realized, the present invention is big
It is as follows to give the ERP trained length Experience norms that call time in advance on analysis foundation for amount test:
Unit in formula is year (year), and PMX_N is the training length of PMX, and PMY_N is the training length of PMY, UT1-
UTC_N is the training length of UT1-UTC.
It is illustrated combined with specific embodiments below.
The present invention for forecast ERP initial data from the EOP 08C04 of the website IERS plus 1 month USNO's
ERP resolving value.The present invention is forecast 90 days backward by taking the forecast since on 2 19th, 2016 (corresponding MJD is 57437) as an example
ERP value.
The specific data handling procedure of the ERP forecasting procedure of Adaptive matching of the invention is as follows:
Step 1, middle ERP forecast time series training length Experience norms (formula (2)) proposed according to the present invention, determines
The training length of PMX/PMY/UT1-UTC.
According to the training length of ERP proposed by the present invention forecast time series training length Experience norms setting PMX, PMY
It is 1300 days (3.56), the training length of UT1-UTC is 7700 days (21.08).
Step 2, the least square fitting of ERP is carried out, ERP residual error is obtained.
PMX, PMY that step 1 is chosen directly are carried out least square according to its known periods function and quadratic polynomial to intend
It closes and obtains match value；UT1-UTC is after jump second detection, jump second are eliminated and are rejected with humorous solid tide item according to its known periods
Function and quadratic polynomial directly carry out least square fitting, obtain match value.ERP match value is subtracted with original ERP data, is obtained
Take ERP residual error.
The original waveform of PMX is as shown in Fig. 2, residual plot of the PMX after least square fitting is as shown in Figure 3.PMY's is original
Waveform is as shown in figure 4, residual plot of the PMY after least square fitting is as shown in Figure 5.The original waveform of UT1-UTC passes through jump second
Detection is with rejecting, with the figure after the rejecting of humorous solid tide item as shown in fig. 6, residual error of the UT1-UTC after least square fitting
Figure is as shown in Figure 7.
Step 3, ERP extrapolation is carried out using known periodic function and quadratic polynomial function.
Using periodic function known to PMX, PMY, UT1-UTC and quadratic polynomial function respectively to PMX, PMY and rejecting
Jump second carries out Extrapotated prediction with the UT1-UTC with humorous solid tide item.The known periods item of PMX, PMY are the Chandler period
(435 days), 1 annual period, 1/2 annual period and 1/3 annual period；The known periods item of UT1-UTC be 18.6,9.3 years,
1 year and 1/2 year；The quadratic polynomial coefficient of ERP is determined by least-square fitting approach.ERP extrapolation length with it is desired pre-
It reports length consistent, can be previously set, the extrapolation length in the present invention is 90 days, i.e., three months.
Step 4, the chi-square value that Chi-square Test method calculates ERP residual error is introduced.
In order to realize that ERP is forecast using AR model method, ERP time series to be processed need to meet stationarity requirement.
For ERP time series, original PMX, PMY and UT1-UTC time series is not satisfied stationarity and requires, one side PMX,
There are known periodic component in PMY and UT1-UTC time series, these periodic components must shift to an earlier date before carrying out AR forecast
It is deducted, obtains PMX, PMY and UT1-UTC residual error；On the other hand, PMX, PMY and UT1- can be provided by way of difference
The stationarity of UTC residual error in order to select reasonable difference order, while avoiding difference order shortcoming or excessive, need to be according to difference
The stationarity of PMX, PMY and UT1-UTC residual error to be analyzed selects suitable difference order.By introducing card side in the present invention
The distribution character of PMX, PMY and UT1-UTC residual error is quantitatively evaluated by calculating chi-square value in the method for inspection.The wherein meter of chi-square value
It calculates shown in formula such as formula (3).
Wherein, AiFor the observed frequency of i level, EiFor the expecterd frequency of i level, n is total frequency, piFor the expectation of i level
Frequency.The expecterd frequency E of i leveliEqual to the expected probability p of total frequency n × i leveli, k is cell number.When n is bigger,
χ2Statistic approximation obeys k-1 and (calculates EiWhen the number of parameters used) a freedom degree chi square distribution.
Based on above method, chi-square value calculating is carried out to the regression criterion of PMX, PMY, UT1-UTC respectively, as a result
χ2 pmx=0.41, χ2 pmy=0.36, χ2 ut1-utc=0.83.
Step 6, ERP difference Experience norms are proposed, determine the difference order of ERP residual error, and carry out the difference fortune of ERP residual error
It calculates.
The present invention proposes the corresponding relationship Experience norms of chi-square value and difference order, to realize PMX, PMY and UT1-UTC
Difference order Adaptive matching.The present invention proposes that ERP forecasts difference Experience norms, carries out difference to ERP sequence for determining
Order.ERP is forecast shown in difference Experience norms such as formula (1):
Therefore, ERP difference Experience norms proposed according to the present invention pass through 1 difference to PMX residual error, pass through to PMY residual error
1 difference is crossed, 2 difference are passed through to UT1-UTC residual error.
Step 7, it proposes that AR model order Adaptive matching searches for the method for determination, obtains AR model order, carry out ERP residual error
AR forecast.
In order to realize that the Adaptive matching of AR model order, the present invention propose that the AR order of Adaptive matching searches for determination side
Method.Its basic thought is to carry out optimum search to AR order in a specified AR order section, and look for according to judgment criterion
Optimal AR model order out.Concrete methods of realizing is as follows:
Shown in the mathematic(al) representation such as formula (4) for introducing AR model first.
In formulaFor AR model parameter；atFor white noise；P is AR model order；xt,xt-1,
xt-2,…,xt-pFor t, t-1, t-2 ..., the quantity of state of the stationary time series (i.e. differentiated ERP residual error) at t-p moment；Claim
Formula (4) is p rank autoregression model, is abbreviated as AR (p)；atMeet normal distribution, at~N (0, σ2), σ2For the variance of white noise.
It can be seen that AR model order directly affects AR forecast result from formula (4).
Then the method and step that AR model order of the invention determines is introduced are as follows: the search that AR model order is arranged in (a) is empty
Between be 1 to 200, i.e. p=1:200, at this moment p is brought into formula (4) respectively, obtains 200 AR models；(b) in order to solve formula (4)
AR model parameterHere estimate that every 1 model order p is corresponding using solution Yule-Walker equation method
Model parameterThen the model parameter estimated is brought into formula (4), calculates and obtains stationary time series
Model value, the model value of stationary time series is then subtracted with the state value of stationary time series, obtains noise residual sequence；
(c) using whole pre-error criterion (FPE), as shown in formula (5), for determining judgment criterion system corresponding to each AR order p
Number ξp；(d) compare ξp, p=1:200, as ξ (min)=ξpP be optimal AR model order.
N is sample length in formula, and p is model order,For the variance of noise residual sequence.
AR forecast is carried out to the difference value of ERP residual error, wherein AR model order is according to Adaptive matching proposed by the present invention
AR order is searched for the method for determination and is obtained.The AR order of PMX residual error forecast is that the AR order of 54, PMY residual error forecast is 54,
The AR order of UT1-UTC residual error forecast is 82.
Step 8, the inverse difference processing of ERP residual error forecast.
Inverse difference processing is carried out to the predicted value of ERP residual error, the order of unfavourable balance point is equal to the difference rank in previous step 5
It is secondary.
Step 9, joint least-squares extrapolation forecasts predicted value with AR, obtains ERP predictive initial value.
ERP residual error unfavourable balance divides ERP periodic function and the outer knot of quadratic polynomial function in forecast result combination step 3
Fruit, the two are added, and obtain the predictive initial value of ERP.
Step 10, ERP forecasts that end value determines.
The forecast result of PMX, PMY at this time is its final forecast result, and UT1-UTC predictive initial value passes through with humorous earth tide
Nighttide item forecast addition and jump second obtain UT1-UTC predicted value after restoring, based on this final acquisition ERP predicted value.
In order to intuitively illustrate the ERP value of forecasting of the invention, ERP predicted value and International Earth Rotation that the present invention is obtained
With the ERP predicted value of frame of reference Servers Organization (IERS), USNO-US Naval Observatory (USNO) international comparison is carried out, wherein IERS
Forecast that span is 180 days, the forecast span of USNO is 90 days, and forecast number of days of the invention is 90 days, the code name shown in figure
For BACC (abbreviation of Beijing Space flight control center).Fig. 8 be PMX forecast result with international comparison as a result, Fig. 9 is PMY pre-
Result and international comparison are reported as a result, Figure 10 is UT1-UTC forecast result and international comparison result.
The forecast result of the ERP (comprising PMX, PMY and UT1-UTC) shown from Fig. 8~Figure 10 intuitively can be seen that this hair
Bright PMX, PMY forecast result and the consistency of IERS, USNO is preferable, wherein in Figure 10, due to ERP used in the present invention
Nearest one month UT1-UTC value of forecast is the resolving value using USNO, so UT1-UTC forecast result and USNO's is consistent
Property is preferable.
Step 11, mean absolute error (MAE) criteria evaluation ERP forecast precision is utilized.
For quantitative description ERP forecast precision of the invention, using MAE criterion, as shown in formula (6), count here
Using the ERP prediction error situation of 2015 annual (totally 365 days) that the method for the present invention calculates, the forecast span of statistics is 30
It.Its prediction error is as shown in figure 11, and specific prediction error numerical value is as shown in table 1, it can be seen that ERP of the invention is forecast
With good precision, this ERP forecast precision is reached advanced world standards.
O is actual observed value in formula；P is predicted value；I is forecast span；N is forecast issue.
1 ERP prediction error statistical form of table
| Pre Day | PMX Pre Error(mas) | PMY Pre Error(mas) | UT1-UTC Pre Error(ms) |
| 1 | 0.205 | 0.179 | 0.046 |
| 5 | 1.71 | 0.967 | 0.291 |
| 10 | 2.28 | 1.52 | 0.818 |
| 20 | 2.35 | 2.47 | 2.13 |
| 30 | 3.14 | 3.18 | 3.58 |
The present invention proposes problem-solving approach, and integrated data processing side for the problems in three above ERP forecast
Method realizes the high accuracy prediction of ERP.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (1)
1. a kind of earth rotation parameter (ERP) forecasting procedure of Adaptive matching, which comprises the steps of:
Step 1, PMX, PMY and UT1-UTC data of given training length are chosen respectively；Wherein, PMX, PMY and UT1- of selection
UTC is referred to as original ERP data；The training length of PMX, PMY and UT1-UTC data is chosen according to following formula:
Unit in formula is year, and length (PMX_N) is the training length of PMX, and length (PMY_N) is the training length of PMY,
Length (UT1-UTC_N) is the training length of UT1-UTC；
Step 2, three kinds of original ERP data step 1 obtained carry out the least square of periodic function and quadratic polynomial respectively
Fitting obtains ERP match value；ERP match value is subtracted with the original ERP data of step 1, obtains ERP residual error；
Step 3, the ERP match value of step 2 is carried out using the periodic function of original ERP data and quadratic polynomial function outer
It pushes away, wherein ERP extrapolation length is consistent with desired forecast length；
Step 4, chi-square value calculating is carried out to the ERP residual error that step 2 obtains, according to the chi-square value χ of ERP residual error2It is determined with formula (1)
Difference order:
Step 5, the difference order determined according to step 4 carries out calculus of differences to ERP residual error, obtains differentiated ERP residual error；
Step 6, the differentiated ERP residual error obtained for step 5 is forecast using the AR that AR model carries out ERP residual error, is obtained
The predicted value of ERP residual error, the model order of AR model determine that method is as follows:
Step 6.1, AR model are as follows:
Wherein,For AR model parameter；atFor white noise；P is AR model order；xt,xt-1,xt-2,…,
xt-pFor t, t-1, t-2 ..., the quantity of state of the stationary time series at t-p moment；
The search space that AR model order p is arranged is [1, P]；The P value of model order p is substituted into respectively in formula (4), is obtained
P AR model；
Step 6.2, the P AR model obtained for step 6.1 estimates each model using solution Yule-Walker equation method
The corresponding model parameter of order pThen in the model parameter estimated generation, is returned in formula (4), calculating is put down
The model value of steady time series, then subtracts model value with the state value of stationary time series and obtains noise residual sequence；
Step 6.3, judgment criterion coefficient ξ corresponding to each AR order p is determined using whole pre-error criterionp:
Wherein, N is sample length,For the variance of noise residual sequence；
Step 6.4, minimum judgment criterion coefficient is corresponding to be judged to the corresponding judgment criterion coefficient of P AR model order p
Model order is the AR model order of determining AR model；
Step 7, the predicted value that step 6 obtains ERP residual error is subjected to inverse difference processing, and divides unfavourable balance to processing result and step 3
The extrapolating results of acquisition are overlapped, that is, obtain the predictive initial value of ERP；
Step 8, the PMX predictive initial value and PMY predictive initial value that step 7 obtains are the final predicted value for being respectively PMX and PMY；
UT1-UTC predictive initial value obtains final UT1-UTC predicted value after restoring with the forecast addition of humorous solid tide item with jump second.
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| 基于LS+AR模型的三种方式预报地球自转参数的比较;雷雨等;《时间频率学报》;20150131;第38卷(第1期);第52-60页 |
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