Method of correcting prediction errors of time-variable signals subjected to interference by various uncontrollable systematic effects

FIELD: radio engineering, communication.

SUBSTANCE: method comprises the following steps of correcting predictions of a parameter included in a received and time-variable signal: estimation of the prediction error based on a first set of values estimated during a determined time period by comparing these values with values previously predicted for the same determined time period; analysis of the predicted time series of prediction errors by a method of processing the signal and isolating the contributions of the systematic effects, extrapolation of the behaviour of the contributions of the systematic effects during the time period concerned and correction of the predictions using the duly extrapolated values.

EFFECT: correcting prediction of values of time-variable signals subjected to interference by various uncontrollable systematic effects without limitations to existing solutions.

3 cl, 3 dwg

 

The present invention relates to a method of correction of the prediction values of the time varying signals, vozmuschaemykh various uncontrolled systematic phenomena.

The navigation messages transmitted by global navigation satellite systems such as Galileo, GPS, ...) with additional systems that improve the integrity (EGNOS, WAAS, ...), also contain data for the prediction of the orbit of the satellites and the reference time. Using these predictions, the users of these navigation services calculates its position based on the dimensions of pseudoresistance.

Any error in these predictions entails an error in the value of the designated thus geographic location of the user. In the case of services for which security is a matter of life, provide for the segment integrity monitoring of users through the control of reliability of predictions and data transmission integrity (integrity indicators, such as SISA/SISMA for Galileo or UDRE for EGNOS/WAAS, which is a European sublayer for GPS). Users consider these indicators to assess the risk of exceeding the alarm threshold, the error affecting the specified position. At the present time there is standardization and certification of these indicators and algorithms for their application.

One of the basis of the data problems celebrated by all specialists in the field of satellite navigation, is the fact that in the modern standards of integrity measurements can be achieved only if required mathematical absence of accounting for systematic effects, in particular, shifts in the distribution of errors. Otherwise, even if individually to control the error of each satellite through the level majorization passed to users, the resulting error at the user level may not be verifiable.

Given that the bandwidth of the transmission channels of the navigation data is strictly limited, it is not possible to pass more than one parameter characteristics of the prediction errors of the orbit and synchronizer.

To solve this problem, an attempt was made to artificially inflate integrity indicators, in order to increase the level of majorization distribution of prediction errors. However, this artificial increase significantly affect the possibility of obtaining service integrity, because it entails increasing the number of false alarms. So there is a need to improve the quality of the data correction of the orbit and synchronizer.

Limitations associated with the quality of the predictions, not always clearly defined. The reason for this restriction can be many factors. In particular, you shall be specified:

- inaccuracy of the model of the field of attraction of the Earth,

- failure to take into account the influence of the tides-currents or the influence of multiple bodies (for example, other planets of the solar system)

- lack of reliability of extrapolation algorithms observations with predictions

- instability of onboard devices generating navigation signals,

- inaccurate modeling of the influence of solar radiation pressure,

- inaccuracy of data on the mass of the satellite, the position of its center of gravity, ...

and others not identified in the present time factors.

Most of the above factors or characteristic of the limitations of the known solutions (the first four), or connected with the deviation during the entire service life of the satellite (the last three). Currently, to reduce the influence of these factors basically apply the following resolutions:

- improving the accuracy of geophysical data, for example, improved models of the field of gravity or of the ebb-tides,

- increase the accuracy of the data associated with the current state of the satellite,

- improving the efficiency of computational schemes, so they can calculate more data with higher accuracy long iterative process of greater length,

- improved stability on-Board equipment (due to temperature to the control, improvements to electronic circuits, ...).

All these known solutions have limitations, in particular:

- accuracy geophysical data can only be improved with relatively slow implementation of research results,

- the accuracy of the data associated with equipment and components of the satellite, very limited due to the very limited possibilities of their observations after Sputnik. For example, this applies to parameters such as the optical reflectivity of the satellite in the inevitable deterioration of its external reflective coatings, which plays a decisive role in the influence of solar radiation pressure,

- effectiveness calculations cannot increase faster than the characteristics of the integrated circuits, which soon reached its limit, when the miniaturization reaches the scale of the atom.

The present invention aims to propose a correction method to predict the value of time-varying signals, vozmuschaemykh various uncontrolled systematic phenomena that is not bound by the foregoing limitations and is easy to use.

The method in accordance with the present invention differs in that it contains the following steps to correct the predictions of the parameter included in the received and changing savremeni signal:

the drafting history of the prediction error based on the first set of values, estimated aposteriori within a certain period of time with sufficient accuracy (which hereinafter will be referred to as "reproduced"values), comparing the reproduced values with a set of predicted values for the same certain period of time,

analysis of the predicted time series of prediction errors using the method of signal processing and allocation of share of systematic effects,

- extrapolation to a new period of time to predict the behaviour fractional systematic effects during the time interval under consideration and correction of predictions using extrapolated in this way values.

The present invention will be more apparent from the following description of the scenarios, presented as a non-restrictive example, with reference to the accompanying drawings, on which:

Fig. 1 is a timing diagram illustrating a simplified example of a set of values based on the received measurements, and the corresponding predicted values according to the claimed method.

Fig. 2 is a time chart of the change of the forecast errors of the predicted values shown in Fig. 1.

Fig. 3 - diagram in the plane is Urie, illustrating the systematic influence that lead to the error of the prediction.

Description the present invention relates to signals received from the radionavigation satellite, but, of course, it is not limited to this application and can be used for other applications, which are the signals that should change in time, at least partially random and can be distorted under the influence of various systematic reasons, and to have a chronology of changes to these distorting signals.

The present invention is based on the fact that the accurate prediction of the orbit is open in edit mode sets (process a large number of consecutive values in the time interval or "arc"), with the first stage necessarily an accurate estimation of the parameters of the position and orbit of the satellite along the arc of assessment, related to the previous period. Then the estimated position extrapolate for the period predictions, to obtain predictions of the orbital parameters.

In this case, the periods used to determine predictions, always overlap with one or more arcs of assessment used in the last arcs processing predictions. In addition, the accuracy of the reproduced value is higher than t the durability of the predicted values. Comparison (i.e. difference) of these two values is essential to detect errors of the predictive method. Known methods of signal processing can be applied to time series of these differences to make the extrapolation behavior of the errors and correct them until they began to exert influence.

The method in accordance with the present invention can significantly reduce potential systematic effects (like the above), due to their observation in the past that leads to the distribution of prediction errors, much more than the appropriate requirements of computing integrity.

The method in accordance with the present invention is used as follows.

Denote X(t) be any parameter, time-dependent, which may relate to the synchronizer or the orbit of the satellite. This parameter X can be any point of the orbit of the satellite at X=x, y, or z, which is a spatial coordinate X, or can be defined as X=δt, that is, the shift clock of the satellite. The method in accordance with the present invention includes the following three main stages:

- the assessment of prediction errors,

analysis of factors that systematically affect the forecast error,

- correction of the predictions.

What follows is a more detailed description of these stages. Sleep is Ala estimate the prediction error on the basis of two sets of values of the prediction.

And the first set of prediction values

The calculation of the satellite's orbit begins with measurements on relatively long (usually from several days to several weeks), arc grade E1=[tb,1,te,1]. This arc evaluation is used to assess reproduced values, such as values, reproduced classical numerical schemes appliances build orbits and synchronization parameter X. let Xr1(t) function, which allows to obtain reproduced the value of this parameter over the time interval t∈E1. Details of how to play are not essential to the present invention, and it only needs to be Xr1(t) over the duration of the arc E1. These reproduced values can, incidentally, be obtained from a source other than schemes for computing the predictions.

Reproduced values are associated with the assessment of some parameters (orbits, Earth rotation parameters, the model reflectivity of the satellite, ...)that can be used to calculate the values of X in the moments after te,1(te,1is the beginning of the P1). Let us assume Xp1(t) the values thus obtained for:

t∈P1=[te,1, tp,1]

In this expression, tp,1is the last time predictions. These values of Xp1 (t) give the first prediction of the parameter in question. It should also be noted that the invention of the implementation details of how the predictions are not significant, it only needs to be Xp1(t) over the duration of the arc P1.

In Fig. 1 shows the change with time of arcs evaluation (E1E2E3, ...) and the corresponding arcs of the prediction (P1, R2, R3, ...). This timing chart of the solid curve shows the reproduced values of X, whereas the segments dashed curves refer to the predicted values of X. In Fig. 2 points, forming a continuous curve, correspond to the error of the prediction X, obtained as the difference between the predicted values and the reproduced values of X in the same moments.

In a second set of prediction values

For the next set of values of the prediction of the orbit repeat the previous steps for the second arc of the evaluation of E2=[tb,1, te,2] at te,2≤tp,1. In addition, in most cases, tb,2≤te,1because the arc assessment should be longer than the arc prediction to provide the best quality predictions, and then we get R1⊂E2. Usually, but not restrictive in the present application these arc evaluation can last from 1 hour to 48 hours. Measurement produced during the time period of time E 2produce a set of replicated values of the orbital parameters or synchronization Xr,2(t)corresponding to the period of E2that can be spread over a period P2=[te,2, tp,2] and get to this age prediction orbit or synchronizer Xp,2(t).

It should be noted that for the time period P1available two values of X, since R1⊂E2, that is, Xp,1(t) and Xr,2(t) [te,1, tp,1]. Given that both values of Xp,1and Xr,2are approximations of the same parameter of the orbit or synchronizer in the same moments, but with higher accuracy for Xr,2than for Xp,1get the approximation of the prediction error for a period of time P1 using:

δX(t)=Xp,1(t)-Xr,2(t) [te,1, tp,1](1)

For the following sets of predictions as well as received δX(t), comparing the prediction of X in the first set with his play in the second set, we can estimate the prediction error for a set of n by comparing the prediction of Xp,n(t) for the set of n playback Xr,n+1(t):

δX(t)=Xp,n(t)-Xr,n+1(t) [te n , tp,n](2)

This sequence sets the evaluation and prediction, as well as the evaluation function of the prediction error δX(t) shown in Fig. 2.

Thus, the first main step of the method in accordance with the present invention comprises, for a set of n+1 values of the prediction, in constructing a time series δX(t) error of the prediction for each parameter X of the orbit or synchronizer by comparing the reproduced values available sets with the predicted values of the previous () set(s).

The next step of the method in accordance with the present invention consists in the allocation of systematic effects in the forecast error. Time series of prediction errors obtained by using the function δX(t) and simplistically shown in Fig. 2, contain all of the information about the prediction error. If this forecast error appeared only in the result of measurement errors, the curve describing δX(t), underwent random change. In most cases this isn't true, and, for example, by wavelet analysis or Fourier analysis of time series of prediction errors, as shown in Fig. 3, reveal the character is erotici these time series errors, which clearly shows that we are not talking about purely random change. These characteristics correspond to systematic errors that affect the process of prediction, and they are associated with the presence of errors in the models used to predict the orbit, or with the limitations of the prediction process.

In Fig. 3 shows a diagram of an example of a Fourier analysis, which presents the range of error in the exponentiation |δX(t)|2depending on the normalized frequency f. In this example, the components of the spectrum, the value of which is much greater than the average value of the spectrum (the diagram shows five narrow pulse), can be attributed to systematic influences. In the case of Fourier analysis, these components correspond to the fractions of δXS,i(t)=A(i)jωi(t)for different significant values ω(i) in the given range.

Thus, the second main step of the method in accordance with the present invention consists in the analysis of time series of prediction errors by using appropriate signal processing method (Fourier analysis, wavelet analysis, or other signal processing techniques) and in the allocation of a share of systematic effects δXS,t(t).

The next step is to implement the prediction and correction of systematic errors of prediction. After identifying the share of δXS,t(t) systematic effects can what about it is relatively easy to extrapolate their temporal behavior for the next time prediction P n+1. Thus, these shares can be used to correct predictions in the set of predictions n+1 by subtracting the different fractions of the values of the function δXS,t(t).

Thus, the third main step of the method in accordance with the present invention is to extrapolate the behavior of the fractional systematic effects δXS,t(t) in the considered interval of the prediction and correction of the predictions between the two values of the shares.

It should be noted that the method in accordance with the present invention can be applied to the adjusted or not adjusted predictions. On the other hand, arc prediction (corresponding to the intervals P1, P2, R3shown on Fig. 1) preferably overlap, although it is not necessary.

1. The correction method to predict the value of time-varying signals, vozmuschaemykh various uncontrolled systematic phenomena, characterized in that it contains the following steps to correct the predictions of the parameter included in the received and time-varying signal:
the drafting history of the prediction error based on the first set of values, estimated aposteriori (E1)within a certain period of time and called the reproduced values, comparing these FOTS the first value with a set of predicted values for the same certain period of time,
analysis of the predicted time series of prediction errors using the method of signal processing and allocation of share of systematic effects,
- extrapolation to a new period of time to predict the behaviour fractional systematic effects during the considered period of time (E1and correction of predictions using extrapolated thus values
when this method is used for signals received from the radionavigation-satellite correction data predicting the orbits of these satellites and their supporting synchronizer.

2. The method according to claim 1, characterized in that the method of signal processing is the Fourier transform or wavelet transform.

3. The method according to claim 1 or 2, characterized in that the time intervals of the prediction (P1P2P3) mutually overlap.



 

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