CN103793765B - A kind of satellite telemetering data Forecasting Methodology based on Kalman filter - Google Patents
A kind of satellite telemetering data Forecasting Methodology based on Kalman filter Download PDFInfo
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Abstract
A kind of satellite telemetering data Forecasting Methodology based on Kalman filter, for satellite telemetering data amount is huge, signal type is complicated, real-time property, uniformity and reliability requirement is high, data are with the problem of environmental change is fast, traditional-handwork data interpretation method can not meet satellite test demand, utilize the telemetry at satellite current time, the telemetry of real-time estimate subsequent time, the anomalous variation of data can be found in advance.In actual test application, exception occurs for such as satellite telemetering data, and some telemetry value is extremely soaring or declines, and initial stage, tester can not have found that test is abnormal because being not above threshold value set in advance.Using this data predication method, energy Accurate Prediction goes out next cycle data, data abnormal area is swift in response, find in time and forecast data is abnormal, tester is reminded to pay close attention to, and algorithm performs efficiency high, the requirement of real-time of satellite test can be met well, it is adaptable to long term data interpretation and anomaly data detection.
Description
Technical field
The present invention relates to a kind of satellite telemetering data Forecasting Methodology based on Kalman filter, belong to satellite test technology neck
Domain.
Background technology
Satellite telemetering data interpretation refers to satellite in floor synthetic test process, according to interpretation criterion, to satellite control
Instruction, downlink telemetry data carry out correlation inspection, judge the work of each equipment of satellite whether normal, interface whether correctly, satellite
Operation whether normal process.In order to accurately hold the working condition of satellite, pinpoint the problems in time, tester must be to these
Data carry out continual monitoring and interpretation.
At present, most of satellite data interpretation work is still completed taking human as main, and this, which not only needs largely to have, enriches one's knowledge
With the tester of experience, the hidden danger failed to judge and judged by accident is also there is.Satellite test process needs to monitor, detects hundreds of parts
The real time data and state of (such as load, sensor and executing agency).Amount of test data is huge, signal type is complicated, data
Real-time, uniformity and reliability requirement are high, data are fast with environmental change, therefore to data interpretation and place in satellite test system
Reason speed etc. proposes very high request, and traditional-handwork data interpretation method can not meet satellite test demand.To solve above-mentioned ask
Topic, is currently mainly used telemetry parameter automated surveillance tool software, can carry out data automatically according to the parameter area of definition
Interpretation, sends alarm when parameter is crossed the border, but the definition for abnormal parameters scope is not accurate enough, and heavy dependence is tested
The experience of personnel.Under the current situation that model task is increasingly heavy, satellite structure is increasingly sophisticated, a kind of effective data are found
Forecasting Methodology, and finally realize computer automatic interpretation, it appears it is more and more important.
The content of the invention
The technology of the present invention solves problem：Overcoming the deficiencies in the prior art, there is provided a kind of defending based on Kalman filter
Star telemetry Forecasting Methodology, using the telemetry at satellite current time, the telemetry of real-time estimate subsequent time, in time
It was found that simultaneously forecast data is abnormal, tester is reminded to pay close attention to, and algorithm performs efficiency high, satellite can be met well
The requirement of real-time of test, it is adaptable to long term data interpretation and anomaly data detection.
The present invention technical solution be：A kind of satellite telemetering data Forecasting Methodology based on Kalman filter, prediction
Step is as follows：
（1）Kalman filter parameter initialization, including telemetry initial value to be predicted and predicated error variance matrix initial value；
It regard telemetry initial value to be predicted as step（2）The initial value of middle telemetry optimal estimation value, by predicated error variance matrix
Initial value is used as step（2）The initial value of middle predicated error variance matrix；
（2）By Kalman filter state renewal equation, according to the optimal estimation value of current k moment telemetry, in advance
The telemetry predicted value of the telemetry, i.e. k+1 moment at k+1 moment is surveyed, for carrying out satellite telemetering data interpretation；Pass through
Kalman filter state renewal equation, according to the predicated error variance matrix at current k moment, calculates the error of telemetry prediction
The predicated error variance matrix of variance matrix, i.e. k+1 moment, k=1,2 ..., n, n is observation number；
（3）Utilize step（2）The error covariance matrix for the telemetry prediction tried to achieve, calculates Kalman filter gain square
Battle array, step（4）And step（5）Carry out aligning step using Kalman filter gain matrix（2）The telemetry predicted value tried to achieve
With predicated error variance matrix；
（4）Utilize the actual observed value and step of the moment of satellite k+1 telemetry（3）The Kalman filter gain tried to achieve
Matrix carrys out aligning step（2）The telemetry predicted value at the k+1 moment tried to achieve, tries to achieve the telemetry optimal estimation at k+1 moment
Value；
（5）Utilize step（3）The Kalman filter gain matrix tried to achieve tries to achieve the error side of the optimal estimation at k+1 moment
Poor battle array；
（6）Utilize step（4）The telemetry optimal estimation value and step at the k+1 moment tried to achieve（5）The k+1 moment tried to achieve
Optimal estimation error covariance matrix carry out the k+2 moment telemetry prediction；
（7）Repeat（2）Extremely（6）Step.
Present invention advantage compared with prior art is：
（1）The parameter area progress data that current telemetry parameter automated surveillance tool software is changed according only to definition are sentenced
The present situation of reading, in actual test application, exception occurs for such as satellite telemetering data, and some telemetry value is extremely soaring or declines, initial stage
Because being not above threshold value set in advance, tester can not have found that test is abnormal.Using this data predication method, pass through
The data accumulation of a period of time, system can quickly provide the alarm that parameter after a period of time is crossed the border, and remind tester's emphasis
Concern, is easy to find telemetry anomalous variation trend；
（2）The setting of relevant parameter, makes in state equation and observational equation and equation by rationally setting up telemetry
Obtain Forecasting Methodology to be swift in response to data abnormal area, algorithm performs efficiency high, and be easily achieved computer automatic interpretation, very well
Ground meets the requirement of real-time of satellite test, it is adaptable to long term data interpretation and anomaly data detection.
Brief description of the drawings
Fig. 1 is the inventive method workflow diagram.
Embodiment
Kalman filter is the optimum linear estimation using least mean-square error as criterion, and it is according to previous estimate and most
A nearly observation estimates the currency of signal, and utilization state equation and recurrence method are estimated, and obtained solution
It is to be provided in the form of estimate, processing multi-variable system, time-varying linear systems and nonlinear system can be advantageously applied to
Optimum filtering etc..The present invention is described in further detail below in conjunction with the accompanying drawings：
If realizing the prediction of telemetry, first have to set up the state equation and observational equation of telemetry.
Telemetry is represented with X, without loss of generality, if the parameter can be expressed as with time t with nonlinear function：
X=X(t) (1)
According to telemetry feature, in finite time, it is contemplated that also influenceed in stationary process by environmental change, remote measurement
The data rank Taylor of time 2 deploys approximate, if telemetry sampling time interval is Δ t, then can obtain：
Formula（2）In, XkRepresent telemetry,Represent that telemetry changes with time rate,Represent telemetry
The acceleration changed over time；K represents k-th of sampling instant（That is during k-th of star, then Δ t=1）；O(Δt3) it is 2 rank Taylor
The Pei Yanuo remainders of expansion, represent the approximate error of 2 rank multinomials.Formula（2）The as CA of telemetry（Constant
Acceleration）Model, the formula is substantially regression model of the telemetry on the time.
By formula（2）The state equation description of telemetry can be obtained：
Formula（3）In,It is the state vector at k moment,Difference representative formula
（2）In Xk,With The plant noise of their error, i.e. system is represented respectively,
It is that average is the normal white noise that zero, covariance matrix is Q（That is Q=1）.Formula（3）The shape at middle telemetry k moment to k+1 moment
State transfer matrix is as follows：
Observational equation is designated as：
Formula（4）In, Vk+1Observation error is represented, is that average is the normal white noise that zero, covariance matrix is R（That is R=1）,
And and WkIt is orthogonal, Zk+1Represent observation vector.According to formula（3）State equation, because observation vector is telemetryTherefore design observation matrix H is 1 × 3-dimensional：H=[1 0 0].
Establishing telemetry state equation（3）And observational equation（4）On the basis of, telemetry Xk+1Optimal estimate
Evaluation can be provided by following Kalman filter equation group.
The state renewal equation of Kalman filter is as follows：
Correction equation is as follows：
Formula（5）To formula（9）In,The telemetry predicted value by the k moment to k+1 moment is represented,Represent by k when
The error covariance matrix of the telemetry prediction at k+1 moment is carved into,The telemetry optimal estimation value after correction is represented,Represent the error covariance matrix of the optimal estimation after correction, Kk+1Represent filter gain matrix.
As shown in figure 1, a kind of satellite telemetering data Forecasting Methodology step based on Kalman filter is as follows：
（1）Kalman filter parameter initialization, including telemetry initial value to be predictedWith at the beginning of predicated error variance matrix
ValueThe initialization initial value can be used as step（2）The initial value of middle telemetry optimal estimation value and predicated error variance matrix
Initial value；
（2）By Kalman filter state renewal equation, formula is utilized（5）According to current k moment telemetry most
Excellent estimate, predicts the telemetry predicted value of the telemetry, i.e. k+1 moment at k+1 momentIt is distant for carrying out satellite
Survey data interpretation；By Kalman filter state renewal equation, formula is utilized（6）According to the predicated error side at current k moment
Poor battle array, calculates the predicated error variance matrix of the error covariance matrix, i.e. k+1 moment of telemetry predictionK=1,2 ..., n, n
For observation number；
（3）Utilize step（2）The error covariance matrix for the telemetry prediction tried to achieveUtilize formula（7）Calculate
Kalman filter gain matrix Kk+1, step（4）And step（5）Use Kalman filter gain matrix Kk+1Carry out aligning step
（2）The k+1 moment telemetry predicted values tried to achieveWith k+1 moment predicated error variance matrixes
（4）Utilize the actual observed value Z of k+1 moment telemetriesk+1And step（3）The Kalman filter gain tried to achieve
Matrix Kk+1, pass through formula（8）Carry out aligning step（2）The telemetry predicted value at the k+1 moment tried to achieveWhen trying to achieve k+1
The telemetry optimal estimation value at quarter
（5）Utilize step（3）The Kalman filter gain matrix K tried to achievek+1, pass through formula（9）Try to achieve optimal estimation
Error covariance matrix
（6）Utilize step（4）The k+1 moment telemetry optimal estimation values tried to achieveAnd step（5）During the k+1 tried to achieve
The error covariance matrix of the optimal estimation at quarterCarry out the telemetry prediction and interpretation at k+2 moment；
（7）Repeat（2）Extremely（6）Step.
The inventive method can predict next cycle data exactly, and data abnormal area is swift in response, and can send out in time
Now simultaneously forecast data is abnormal, and algorithm performs efficiency high, and the requirement of real-time of satellite test can be met well, it is adaptable to
Long term data interpretation and anomaly data detection.
The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.
Claims (1)
1. a kind of satellite telemetering data Forecasting Methodology based on Kalman filter, it is characterised in that step is as follows：
(1) according to telemetry feature, in finite time, it is contemplated that influenceed in stationary process by environmental change, remote measurement number
Deploy approximate according to the rank Taylor of time 2, if telemetry sampling time interval is Δ t, then obtain the remote measurement number at k+1 moment
According to：
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Wherein, XkRepresent telemetry,Represent that telemetry changes with time rate,Represent that telemetry is changed over time
Acceleration；K represents k-th of sampling instant, i.e. during k-th of star, then Δ t=1；O(Δt3) it is the Pei Ya that 2 rank Taylor deploy
Promise remainder, represents the approximate error of 2 rank multinomials；
(2) state equation and observational equation of telemetry are set up；
The state equation of telemetry：
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Wherein,It is the state vector at k moment,Represent respectively in step (1)
Xk,WithWk=[Wk 0 Wk 1 Wk 2]TThe plant noise of their error, i.e. system is represented respectively, is that average is zero, association
Variance matrix is Q normal white noise, i.e. Q=1；
The observational equation of telemetry：
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Wherein, Vk+1Observation error is represented, is that average is the normal white noise (i.e. R=1) that zero, covariance matrix is R, and and WkMutually
It is uncorrelated, Zk+1Observation vector is represented, design observation matrix H is 1 × 3-dimensional：H=[1 0 0]；
(3) Kalman filter parameter initialization, including telemetry initial value to be predicted and predicated error variance matrix initial value；It will treat
Telemetry initial value is predicted as the initial value of telemetry optimal estimation value in step (4), by predicated error variance matrix initial value
It is used as the initial value of predicated error variance matrix in step (4)；
(4) by Kalman filter state renewal equation, according to the optimal estimation value of current k moment telemetry, k+1 is predicted
The telemetry predicted value of the telemetry at moment, i.e. k+1 moment, for carrying out satellite telemetering data interpretation；Pass through Kalman
Filter status renewal equation, according to the predicated error variance matrix at current k moment, calculates the error variance of telemetry prediction
Battle array, i.e. the predicated error variance matrix at k+1 moment, k=1,2 ..., n, n is observation number；
(5) error covariance matrix for the telemetry prediction tried to achieve using step (4), calculates Kalman filter gain matrix, step
Suddenly (6) and step (7) carry out telemetry predicted value and the prediction that aligning step (4) is tried to achieve using Kalman filter gain matrix
Error covariance matrix；
(6) Kalman filter gain matrix tried to achieve using the actual observed value and step (5) of the moment of satellite k+1 telemetry
Carry out the telemetry predicted value at the k+1 moment that aligning step (4) is tried to achieve, try to achieve the telemetry optimal estimation value at k+1 moment；
(7) Kalman filter gain matrix tried to achieve using step (5) tries to achieve the error variance of the optimal estimation at k+1 moment
Battle array；
(8) the k+1 moment that the telemetry optimal estimation value at k+1 moment and step (7) tried to achieve using step (6) are tried to achieve is most
The error covariance matrix of excellent estimation carries out the telemetry prediction at k+2 moment；
(9) (4) to (8) step is repeated.
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| 章辉等.《Kalman滤波预测的多小区子载波分配方法》.《北京邮电大学学报》.2009,第32卷(第3期), * |
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