CN103793765A - Satellite telemetering data predicting method based on Kalman smoothing - Google Patents

Abstract

The invention relates to a satellite telemetering data predicting method based on Kalman smoothing. The satellite telemetering data predicting method based on Kalman smoothing solves the problems that the satellite telemetering data size is massive, the signal types are complicated, the requirements for the real-time performance, the consistency and the reliability of data are high, the data change rapidly along with the environment and a traditional manual data interpretation method can not meet the requirements of a satellite test. The telemetering data of the current moment of a satellite are used for predicting the telemetering data of the next moment in real time and abnormal changes of the data can be found in advance. In practical testing and applying, if the satellite telemetering data go abnormal, a certain telemetering value increases or decreases abnormally; at the initial stage, as the certain telemetering value does not exceed the preset threshold value, a tester can not find a test abnormality. By means of the data predicting method, the data of the next cycle can be accurately predicted, actions can be rapidly taken in terms of a zone with the abnormal data, the data abnormality can be found and predicted in time, and the tester is reminded to pay close attention to the data abnormality. In addition, the algorithm executing efficiency is high, the real-time performance requirement for the satellite test can be well met and the satellite telemetering data predicting method based on Kalman smoothing is suitable for long-term data interpretation and abnormal data detection.

Description

A kind of satellite telemetering data Forecasting Methodology based on Kalman filtering

Technical field

The present invention relates to a kind of satellite telemetering data Forecasting Methodology based on Kalman filtering, belong to satellite test technical field.

Background technology

Satellite telemetering data interpretation refers to that satellite is in floor synthetic test process, according to interpretation criterion, satellite steering order, descending telemetry are carried out to correlativity inspection, judge that whether the each equipment work of satellite is normal, whether interface is correct, the whether normal process of satellite transit.In order accurately to hold the duty of satellite, pinpoint the problems in time, tester must carry out continual supervision and interpretation to these data.

At present, most of satellite data interpretation work is still artificially to have led, and this not only needs to have in a large number the tester who enriches one's knowledge with experience, also exists the hidden danger of failing to judge and judging by accident.Satellite test process need monitors, detects real time data and the state of hundreds of parts (as load, sensor and topworks etc.).Amount of test data is huge, signal type is complicated, real-time property, consistance and reliability requirement is high, data are fast with environmental change, therefore data interpretation and processing speed etc. in satellite test system are all proposed to very high request, traditional-handwork data interpretation method cannot meet satellite test demand.For addressing the above problem, the main telemetry parameter automated surveillance tool software that uses, can carry out data interpretation according to the parameter area of definition automatically at present, sends alarm when parameter is crossed the border, but the definition for abnormal parameters scope is accurate not, and seriously rely on tester's experience.Under the situation that model task is increasingly heavy, satellite structure is increasingly sophisticated at present, find a kind of active data Forecasting Methodology, and finally realize computing machine automatic interpretation, seem more and more important.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of satellite telemetering data Forecasting Methodology based on Kalman filtering is provided, utilize the telemetry of satellite current time, the telemetry in next moment of real-time estimate, find that in time also forecast data is abnormal, remind tester to pay close attention to, and algorithm execution efficiency is high, can meet well the requirement of real-time of satellite test, be applicable to long term data interpretation and abnormal data and detect.

Technical solution of the present invention is: a kind of satellite telemetering data Forecasting Methodology based on Kalman filtering, and prediction steps is as follows:

(1) Kalman filter parameter initialization, comprises telemetry initial value to be predicted and predicated error variance battle array initial value; The initial value of telemetry optimal estimation value in using telemetry initial value to be predicted as step (2), the initial value of middle predicated error variance battle array using predicated error variance battle array initial value as step (2);

(2) by Kalman filter status renewal equation, according to the optimal estimation value of current k moment telemetry, the telemetry in prediction k+1 moment, i.e. the telemetry predicted value in k+1 moment, for carrying out satellite telemetering data interpretation; By Kalman filter status renewal equation, according to the predicated error variance battle array in current k moment, calculate the error covariance matrix of telemetry prediction, i.e. the predicated error variance battle array in k+1 moment, k=1,2 ..., n, n is observed reading number;

(3) utilize the error covariance matrix of the telemetry prediction that step (2) tries to achieve, calculating K alman filter gain matrix, step (4) and step (5) carry out with Kalman filter gain matrix telemetry predicted value and the predicated error variance battle array that aligning step (2) is tried to achieve;

(4) utilize the actual observed value of satellite k+1 moment telemetry and Kalman filter gain matrix that step (3) is tried to achieve to carry out the telemetry predicted value in the k+1 moment that aligning step (2) tries to achieve, try to achieve the telemetry optimal estimation value in k+1 moment;

(5) utilize Kalman filter gain Matrix Calculating that step (3) is tried to achieve to obtain the error covariance matrix of the optimal estimation in k+1 moment;

(6) utilize the telemetry optimal estimation value in k+1 moment and the error covariance matrix of the optimal estimation in the k+1 moment that step (5) is tried to achieve that step (4) is tried to achieve to carry out the telemetry prediction in k+2 moment;

(7) repeat (2) to (6) step.

The present invention's advantage is compared with prior art:

(1) change current telemetry parameter automated surveillance tool software and only carried out the present situation of data interpretation according to the parameter area of definition, in actual Test Application, as satellite telemetering data occurs abnormal, the abnormal soaring or decline of certain remote measurement value, initial stage, tester cannot find that test is abnormal because do not exceed predefined threshold value.Apply this data predication method, through data accumulation after a while, system can provide the warning that parameter is crossed the border after a period of time fast, reminds tester to pay close attention to, and is convenient to find telemetry ANOMALOUS VARIATIONS trend;

(2) by rationally setting up the setting of correlation parameter in the state equation of telemetry and observation equation and equation, Forecasting Methodology is swift in response to data abnormal area, algorithm execution efficiency is high, and be easy to realize computing machine automatic interpretation, meet well the requirement of real-time of satellite test, be applicable to long term data interpretation and abnormal data and detect.

Accompanying drawing explanation

Fig. 1 is the inventive method workflow diagram.

Embodiment

Kalman filtering is that the optimum linear take least mean-square error as criterion is estimated, it carrys out the currency of estimated signal according to previous estimated value and a nearest observed reading, utilize state equation and recurrence method to estimate, and the solution obtaining is also to provide with the form of estimated value, can be advantageously applied to the optimum filtering etc. of processing multi-variable system, time-varying linear systems and nonlinear system.Below in conjunction with accompanying drawing, the present invention is described in further detail:

If realize the prediction of telemetry, first to set up state equation and the observation equation of telemetry.

Telemetry is represented with X, without loss of generality, establishes this parameter and time t can be expressed as with nonlinear function:

X=X(t) (1)

According to telemetry feature, in finite time, consider the impact that is also subject to environmental change in stationary process, telemetry is launched approximate with times 2 rank Taylor, and establishing telemetry sampling time interval is Δ t, can obtain:

$X_{k+1}=X_k+{\stackrel{g}{X}}_k\mathrm{\Δt}+{\stackrel{\mathrm{gg}}{X}}_k\frac{{\mathrm{\Δt}}^2}{2}+O\left({\mathrm{\Δt}}^3\right)---\left(2\right)$

In formula (2), X _krepresent telemetry,

represent telemetry rate over time,

represent the time dependent acceleration of telemetry; K represents k sampling instant when k star (i.e., Δ t=1); O (Δ t ³) be the Pei Yanuo remainder that 2 rank Taylor launch, represent the error of 2 rank polynomial approximations.Formula (2) is the CA(Constant Acceleration of telemetry) model, this formula is in fact the regression model of telemetry about the time.

The state equation that can be obtained telemetry by formula (2) is described:

$\left[\begin{array}{c}{X}_{k+1}^0\\ X_{k+1}^1\\ X_{k+1}^2\end{array}\right]=\left[\begin{array}{ccc}1& \mathrm{\Δt}& \frac{{\mathrm{\Δt}}^2}{2}\\ 0& 1& \mathrm{\Δt}\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{X}_k^0\\ X_k^1\\ X_k^2\end{array}\right]+W_k---\left(3\right)$

In formula (3), ${\left[\begin{array}{ccc}{X}_k^0& X_k^1& X_k^2\end{array}\right]}^T$ The state vector in k moment, represent respectively the X in formula (2) _k,

with

$W_k={\left[\begin{array}{ccc}{W}_k^0& W_k^1& W_k^2\end{array}\right]}^T$ Represent respectively their error, i.e. the plant noise of system, is the normal white noise (being Q=1) that average is zero, covariance matrix is Q.When the middle telemetry k of formula (3), be carved into the state-transition matrix in k+1 moment as follows:

$\mathrm{\Φ}=\left[\begin{array}{ccc}1& \mathrm{\Δt}& \frac{{\mathrm{\Δt}}^2}{2}\\ 0& 1& \mathrm{\Δt}\\ 0& 0& 1\\ & & \end{array}\right].$

Observation equation is designated as:

$Z_{k+1}=H{\left[\begin{array}{ccc}{X}_{k+1}^0& X_{k+1}^1& X_{k+1}^2\end{array}\right]}^T+V_{k+1}---\left(4\right)$

In formula (4), V _k+1representing observational error, is the normal white noise (being R=1) that average is zero, covariance matrix is R, and and W _kuncorrelated mutually, Z _k+1represent observation vector.According to the state equation of formula (3), because observation vector is telemetry

therefore design observation matrix H is 1 × 3 dimension: H=[1 0 0].

Setting up on the basis of telemetry state equation (3) and observation equation (4) telemetry X _k+1best estimate can be provided by Kalman filtering equations group below.

The state renewal equation of Kalman wave filter is as follows:

${\tilde{X}}_{k+1}=\mathrm{\Φ}{\hat{X}}_k---\left(5\right)$

${\tilde{P}}_{k+1}=\mathrm{\Φ}{\hat{P}}_k{\mathrm{\Φ}}^T+Q---\left(6\right)$

Correction equation is as follows:

$K_{k+1}={\tilde{P}}_{k+1}{H}^T{(H+{\tilde{P}}_{k+1}{H}^T+R)}^{-1}---\left(7\right)$

${\hat{X}}_{k+1}={\hat{X}}_{k+1}+K_{k+1}[Z_{k+1}-{H\tilde{X}}_{k+1}]---\left(8\right)$

${\hat{P}}_{k+1}=(I-K_{k+1}H){\tilde{P}}_{k+1}---\left(9\right)$

Formula (5) to formula (9),

while representing by k, be carved into the telemetry predicted value in k+1 moment,

while representing by k, be carved into the error covariance matrix of the telemetry prediction in k+1 moment,

represent the telemetry optimal estimation value after proofreading and correct,

represent the error covariance matrix of the optimal estimation after proofreading and correct, K _k+1represent filter gain matrix.

As shown in Figure 1, a kind of satellite telemetering data Forecasting Methodology step based on Kalman filtering is as follows:

(1) Kalman filter parameter initialization, comprises telemetry initial value to be predicted

with predicated error variance battle array initial value

this initialization initial value can be used as the initial value of telemetry optimal estimation value and the initial value of predicated error variance battle array in step (2);

(2) by Kalman filter status renewal equation, utilize formula (5) according to the optimal estimation value of current k moment telemetry, the telemetry in prediction k+1 moment, i.e. the telemetry predicted value in k+1 moment

be used for carrying out satellite telemetering data interpretation; By Kalman filter status renewal equation, utilize formula (6) according to the predicated error variance battle array in current k moment, calculate the error covariance matrix of telemetry prediction, i.e. the predicated error variance battle array in k+1 moment k=1,2 ..., n, n is observed reading number;

(3) utilize the error covariance matrix of the telemetry prediction that step (2) tries to achieve utilize formula (7) calculating K alman filter gain matrix K _k+1, step (4) and step (5) are used Kalman filter gain matrix K _k+1carry out the k+1 moment telemetry predicted value that aligning step (2) is tried to achieve

with k+1 moment predicated error variance battle array

(4) utilize the actual observed value Z of k+1 moment telemetry _k+1and step (3) the Kalman filter gain matrix K of trying to achieve _k+1, carry out the telemetry predicted value in the k+1 moment that aligning step (2) tries to achieve by formula (8) try to achieve the telemetry optimal estimation value in k+1 moment

(5) the Kalman filter gain matrix K of utilizing step (3) to try to achieve _k+1, try to achieve the error covariance matrix of optimal estimation by formula (9)

(6) the k+1 moment telemetry optimal estimation value of utilizing step (4) to try to achieve

and the error covariance matrix of the optimal estimation in step (5) k+1 moment of trying to achieve

carry out telemetry prediction and the interpretation in k+2 moment;

(7) repeat (2) to (6) step.

The inventive method can dope next cycle data exactly, data abnormal area is swift in response, can find in time that also forecast data is abnormal, and algorithm execution efficiency is high, can meet well the requirement of real-time of satellite test, be applicable to long term data interpretation and abnormal data and detect.

The content not being described in detail in instructions of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1. the satellite telemetering data Forecasting Methodology based on Kalman filtering, is characterized in that prediction steps is as follows:

(1) Kalman filter parameter initialization, comprises telemetry initial value to be predicted and predicated error variance battle array initial value; The initial value of telemetry optimal estimation value in using telemetry initial value to be predicted as step (2), the initial value of middle predicated error variance battle array using predicated error variance battle array initial value as step (2);

(2) by Kalman filter status renewal equation, according to the optimal estimation value of current k moment telemetry, the telemetry in prediction k+1 moment, i.e. the telemetry predicted value in k+1 moment, for carrying out satellite telemetering data interpretation; By Kalman filter status renewal equation, according to the predicated error variance battle array in current k moment, calculate the error covariance matrix of telemetry prediction, i.e. the predicated error variance battle array in k+1 moment, k=1,2 ..., n, n is observed reading number;

(3) utilize the error covariance matrix of the telemetry prediction that step (2) tries to achieve, calculating K alman filter gain matrix, step (4) and step (5) carry out with Kalman filter gain matrix telemetry predicted value and the predicated error variance battle array that aligning step (2) is tried to achieve;

(4) utilize the actual observed value of satellite k+1 moment telemetry and Kalman filter gain matrix that step (3) is tried to achieve to carry out the telemetry predicted value in the k+1 moment that aligning step (2) tries to achieve, try to achieve the telemetry optimal estimation value in k+1 moment;

(5) utilize Kalman filter gain Matrix Calculating that step (3) is tried to achieve to obtain the error covariance matrix of the optimal estimation in k+1 moment;

(6) utilize the telemetry optimal estimation value in k+1 moment and the error covariance matrix of the optimal estimation in the k+1 moment that step (5) is tried to achieve that step (4) is tried to achieve to carry out the telemetry prediction in k+2 moment;

(7) repeat (2) to (6) step.

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