CN103793765A

CN103793765A - Satellite telemetering data predicting method based on Kalman smoothing

Info

Publication number: CN103793765A
Application number: CN201410048805.3A
Authority: CN
Inventors: 吴婧; 陆春玲; 苏振华; 常武军; 刘鸣鹤
Original assignee: Aerospace Dongfanghong Satellite Co Ltd
Current assignee: Aerospace Dongfanghong Satellite Co Ltd
Priority date: 2014-02-12
Filing date: 2014-02-12
Publication date: 2014-05-14
Anticipated expiration: 2034-02-12
Also published as: CN103793765B

Abstract

A satellite telemetry data prediction method based on Kalman filter, aiming at the large amount of satellite telemetry data, complex signal types, high data real-time, consistency and reliability requirements, fast data change with the environment, and traditional manual data interpretation methods cannot meet satellite testing For the problem of demand, using the telemetry data at the current moment of the satellite to predict the telemetry data at the next moment in real time can detect abnormal changes in the data in advance. In the actual test application, if the satellite telemetry data is abnormal, and a certain telemetry value rises or falls abnormally, the tester cannot find the test abnormality because it does not exceed the preset threshold value in the initial stage. Applying this data prediction method can accurately predict the data of the next cycle, respond quickly to data abnormal areas, detect and predict data abnormalities in time, remind testers to focus on, and the algorithm execution efficiency is high, which can well meet the real-time requirements of satellite testing. It is suitable for long-term data interpretation and abnormal data detection.

Description

A Prediction Method of Satellite Telemetry Data Based on Kalman Filter

技术领域technical field

本发明涉及一种基于Kalman滤波的卫星遥测数据预测方法，属于卫星测试技术领域。The invention relates to a method for predicting satellite telemetry data based on Kalman filtering, and belongs to the technical field of satellite testing.

背景技术Background technique

卫星遥测数据判读是指卫星在地面综合测试过程中，依据判读准则，对卫星控制指令、下行遥测数据进行相关性检查，判断卫星各设备工作是否正常、接口是否正确、卫星运行是否正常的过程。为了准确把握卫星的工作状态，及时发现问题，测试人员必须对这些数据进行不间断的监视和判读。Interpretation of satellite telemetry data refers to the process of conducting a correlation check on satellite control commands and downlink telemetry data during the comprehensive ground test process of the satellite, and judging whether the satellite equipment is working normally, whether the interface is correct, and whether the satellite is operating normally. In order to accurately grasp the working status of the satellite and find problems in time, testers must continuously monitor and interpret these data.

目前，大部分卫星数据判读工作仍以人为主完成，这不但需要大量具有丰富知识和经验的测试人员，还存在着漏判和误判的隐患。卫星测试过程需要监视、检测数百个部件(如载荷、敏感器和执行机构等)的实时数据和状态。测试数据量庞大、信号类型复杂、数据实时性、一致性和可靠性要求高、数据随环境变化快，因此对卫星测试系统中数据判读和处理速度等均提出很高要求，传统手工数据判读方法无法满足卫星测试需求。为解决上述问题，目前主要使用遥测参数自动化监视工具软件，能够自动根据定义的参数范围进行数据判读，参数越界时发出报警提示，但是对于参数异常范围的定义不够精确，且严重依赖测试人员的经验。在目前型号任务日趋繁重、卫星结构日趋复杂的形势下，寻找一种有效的数据预测方法，并最终实现计算机自动判读，显得越来越重要。At present, most of the satellite data interpretation work is still done by humans, which not only requires a large number of testers with rich knowledge and experience, but also has hidden dangers of missed and misjudged. The satellite test process needs to monitor and detect the real-time data and status of hundreds of components (such as loads, sensors and actuators, etc.). The amount of test data is huge, the types of signals are complex, the requirements for real-time data, consistency and reliability are high, and the data changes rapidly with the environment. Therefore, high requirements are placed on data interpretation and processing speed in satellite test systems. Traditional manual data interpretation methods Unable to meet satellite testing needs. In order to solve the above problems, the telemetry parameter automatic monitoring tool software is mainly used at present, which can automatically perform data interpretation according to the defined parameter range, and send an alarm prompt when the parameter exceeds the limit, but the definition of the abnormal range of the parameter is not precise enough, and it relies heavily on the experience of the tester . In the current situation where model tasks are becoming more and more heavy and satellite structures are becoming more and more complex, it is becoming more and more important to find an effective data prediction method and finally realize automatic computer interpretation.

发明内容Contents of the invention

本发明的技术解决问题是：克服现有技术的不足，提供一种基于Kalman滤波的卫星遥测数据预测方法，利用卫星当前时刻的遥测数据，实时预测下一时刻的遥测数据，及时发现并预报数据异常，提醒测试人员重点关注，并且算法执行效率高，能够很好地满足卫星测试的实时性要求，适用于长期数据判读和异常数据检测。The technical solution problem of the present invention is: overcome the deficiency of prior art, provide a kind of satellite telemetry data prediction method based on Kalman filter, utilize the telemetry data of satellite current moment, real-time forecast the telemetry data of next moment, discover and forecast data in time Anomalies remind testers to focus on, and the algorithm has high execution efficiency, which can well meet the real-time requirements of satellite testing, and is suitable for long-term data interpretation and abnormal data detection.

本发明的技术解决方案是：一种基于Kalman滤波的卫星遥测数据预测方法，预测步骤如下：The technical solution of the present invention is: a kind of satellite telemetry data prediction method based on Kalman filter, and prediction step is as follows:

（1）Kalman滤波器参数初始化，包括待预测遥测数据初值和预测误差方差阵初值；将待预测遥测数据初值作为步骤（2）中遥测数据最优估计值的初始值，将预测误差方差阵初值作为步骤（2）中预测误差方差阵的初始值；(1) Kalman filter parameter initialization, including the initial value of the telemetry data to be predicted and the initial value of the variance matrix of the prediction error; the initial value of the telemetry data to be predicted is used as the initial value of the optimal estimated value of the telemetry data in step (2), and the prediction error The initial value of the variance matrix is used as the initial value of the forecast error variance matrix in step (2);

（2）通过Kalman滤波器状态更新方程，根据当前k时刻遥测数据的最优估计值，预测k+1时刻的遥测数据，即k+1时刻的遥测数据预测值，用于进行卫星遥测数据判读；通过Kalman滤波器状态更新方程，根据当前k时刻的预测误差方差阵，计算遥测数据预测的误差方差阵，即k+1时刻的预测误差方差阵，k=1,2,…,n，n为观测值个数；(2) Through the Kalman filter state update equation, according to the optimal estimated value of the telemetry data at the current time k, predict the telemetry data at time k+1, that is, the predicted value of the telemetry data at time k+1, which is used for satellite telemetry data interpretation ; Through the Kalman filter state update equation, calculate the error variance matrix of telemetry data prediction according to the current prediction error variance matrix at time k, that is, the prediction error variance matrix at k+1 time, k=1,2,...,n,n is the number of observations;

（3）利用步骤（2）求得的遥测数据预测的误差方差阵，计算Kalman滤波器增益矩阵，步骤（4）和步骤（5）使用Kalman滤波器增益矩阵来校正步骤（2）求得的遥测数据预测值和预测误差方差阵；(3) Use the error variance matrix of telemetry data prediction obtained in step (2) to calculate the Kalman filter gain matrix, and step (4) and step (5) use the Kalman filter gain matrix to correct the obtained in step (2) Telemetry data prediction value and prediction error variance matrix;

（4）利用卫星k+1时刻遥测数据的实际观测值和步骤（3）求得的Kalman滤波器增益矩阵来校正步骤（2）求得的k+1时刻的遥测数据预测值，求得k+1时刻的遥测数据最优估计值；(4) Use the actual observed value of satellite telemetry data at time k+1 and the Kalman filter gain matrix obtained in step (3) to correct the predicted value of telemetry data obtained in step (2) at time k+1, and obtain k The optimal estimated value of the telemetry data at the +1 moment;

（5）利用步骤（3）求得的Kalman滤波器增益矩阵求得k+1时刻的最优估计的误差方差阵；(5) Use the Kalman filter gain matrix obtained in step (3) to obtain the error variance matrix of the optimal estimate at time k+1;

（6）利用步骤（4）求得的k+1时刻的遥测数据最优估计值和步骤（5）求得的k+1时刻的最优估计的误差方差阵进行k+2时刻的遥测数据预测；(6) Use the optimal estimated value of the telemetry data at time k+1 obtained in step (4) and the error variance matrix of the optimal estimate at time k+1 obtained in step (5) to perform telemetry data at time k+2 predict;

（7）重复（2）至（6）步骤。(7) Repeat steps (2) to (6).

本发明与现有技术相比的优点是：The advantage of the present invention compared with prior art is:

（1）改变了目前遥测参数自动化监视工具软件仅根据定义的参数范围进行数据判读的现状，实际测试应用中，如卫星遥测数据发生异常，某个遥测值异常攀升或下降，初期因为没有超过预先设定的门限值，测试人员无法发现测试异常。应用此数据预测方法，经过一段时间的数据积累，系统能够快速给出一段时间后参数越界的报警，提醒测试人员重点关注，便于发现遥测数据异常变化趋势；(1) It has changed the status quo that the current telemetry parameter automatic monitoring tool software only performs data interpretation according to the defined parameter range. In the actual test application, if the satellite telemetry data is abnormal, and a certain telemetry value rises or falls abnormally, the initial stage is because it does not exceed the preset value. With the set threshold value, the tester cannot find the abnormality of the test. Applying this data prediction method, after a period of data accumulation, the system can quickly give an alarm that the parameters are out of bounds after a period of time, reminding the testers to focus on it, so as to find the abnormal trend of telemetry data;

（2）通过合理建立遥测数据的状态方程和观测方程及方程中相关参数的设置，使得预测方法对数据异常区域反应迅速，算法执行效率高，且易于实现计算机自动判读，很好地满足卫星测试的实时性要求，适用于长期数据判读和异常数据检测。(2) Through the reasonable establishment of the state equation and observation equation of telemetry data and the setting of relevant parameters in the equation, the prediction method can respond quickly to the abnormal area of the data, the algorithm execution efficiency is high, and it is easy to realize the automatic interpretation of the computer, which satisfies the satellite test well. It is suitable for long-term data interpretation and abnormal data detection.

附图说明Description of drawings

图1为本发明方法工作流程图。Fig. 1 is the working flow diagram of the method of the present invention.

具体实施方式Detailed ways

Kalman滤波是以最小均方误差为准则的最佳线性估计，它根据前一个估计值和最近一个观测值来估计信号的当前值，利用状态方程和递推方法进行估计，而且得到的解也是以估计值的形式给出的，能很好地应用于处理多变量系统、时变线性系统及非线性系统的最佳滤波等。下面结合附图对本发明作进一步详细地描述：Kalman filtering is the best linear estimation based on the minimum mean square error. It estimates the current value of the signal based on the previous estimated value and the latest observed value, and uses the state equation and recursive method to estimate, and the obtained solution is also based on Given in the form of estimated values, it can be well applied to the optimal filtering of multivariable systems, time-varying linear systems, and nonlinear systems. The present invention is described in further detail below in conjunction with accompanying drawing:

如果要实现遥测数据的预测，首先要建立遥测数据的状态方程和观测方程。If the prediction of telemetry data is to be realized, the state equation and observation equation of the telemetry data must first be established.

将遥测数据用X表示，不失一般性，设该参数与时间t可用非线性函数表示为：The telemetry data is represented by X, without loss of generality, the parameter and time t can be expressed as a nonlinear function:

X=X(t) (1)X=X(t) (1)

根据遥测数据特点，在有限时间内，考虑到平稳过程中还受环境变化的影响，遥测数据用时间2阶Taylor展开近似，设遥测数据采样时间间隔为Δt，则可得：According to the characteristics of telemetry data, within a limited time, considering the influence of environmental changes in the stationary process, the telemetry data is approximated by the second-order Taylor expansion of time, and the sampling time interval of telemetry data is Δt, then we can get:

${X x}_{k k + + 11} = = {X x}_{k k} + + {\overset{g g}{X x}}_{k k} Δt Δt + + {\overset{gg gg}{X x}}_{k k} \frac{{Δt Δt}^{22}}{22} + + O o (({Δt Δt}^{33})) - - - - - - ((22))$

式（2）中，X_k表示遥测数据，

表示遥测数据随时间的变化率，

表示遥测数据随时间变化的加速度；k代表第k个采样时刻（即第k个星时，则Δt=1）；O(Δt³)是2阶Taylor展开的佩亚诺余项，表示2阶多项式近似的误差。式（2）即为遥测数据的CA（Constant Acceleration）模型，该式实质上是遥测数据关于时间的回归模型。In formula (2), X _k represents telemetry data,

Indicates the rate of change of telemetry data over time,

Indicates the acceleration of the telemetry data over time; k represents the kth sampling moment (that is, the kth satellite time, then Δt=1); O(Δt ³ ) is the Peano remainder of the second-order Taylor expansion, which means The error of the polynomial approximation. Equation (2) is the CA (Constant Acceleration) model of telemetry data, which is essentially a regression model of telemetry data with respect to time.

由式（2）可得遥测数据的状态方程描述：The state equation description of the telemetry data can be obtained from formula (2):

$[\begin{matrix} {X x}_{k k + + 11}^{00} \\ {X x}_{k k + + 11}^{11} \\ {X x}_{k k + + 11}^{22} \end{matrix}] = = [\begin{matrix} 11 & Δt Δt & \frac{{Δt Δt}^{22}}{22} \\ 00 & 11 & Δt Δt \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} {X x}_{k k}^{00} \\ {X x}_{k k}^{11} \\ {X x}_{k k}^{22} \end{matrix}] + + {W W}_{k k} - - - - - - ((33))$

式（3）中， ${[\begin{matrix} X_{k}^{0} & X_{k}^{1} & X_{k}^{2} \end{matrix}]}^{T}$ 是k时刻的状态向量，分别代表式（2）中的X_k，

和

W_{k} = {[\begin{matrix} W_{k}^{0} & W_{k}^{1} & W_{k}^{2} \end{matrix}]}^{T}

分别代表它们的误差，即系统的模型噪声，是均值为零、协方差矩阵为Q的正态白噪声（即Q=1）。式（3）中遥测数据k时刻到k+1时刻的状态转移矩阵如下：In formula (3),

{[\begin{matrix} x_{k}^{0} & x_{k}^{1} & x_{k}^{2} \end{matrix}]}^{T}

is the state vector at time k, represent X _k in formula (2), respectively,

and

W_{k} = {[\begin{matrix} W_{k}^{0} & W_{k}^{1} & W_{k}^{2} \end{matrix}]}^{T}

Represent their errors respectively, that is, the model noise of the system, which is a normal white noise with a mean value of zero and a covariance matrix of Q (that is, Q=1). The state transition matrix of the telemetry data from time k to k+1 in formula (3) is as follows:

$Φ Φ = = [\begin{matrix} 11 & Δt Δt & \frac{{Δt Δt}^{22}}{22} \\ 00 & 11 & Δt Δt \\ 00 & 00 & 11 \end{matrix}] . .$

观测方程记为：The observation equation is written as:

${Z Z}_{k k + + 11} = = H h {[\begin{matrix} {X x}_{k k + + 11}^{00} & {X x}_{k k + + 11}^{11} & {X x}_{k k + + 11}^{22} \end{matrix}]}^{T T} + + {V V}_{k k + + 11} - - - - - - ((44))$

式（4）中，V_k+1表示观测误差，是均值为零、协方差矩阵为R的正态白噪声（即R=1），且与W_k互不相关，Z_k+1表示观测向量。根据式（3）的状态方程，由于观测向量即为遥测数据

故设计观测矩阵H为1×3维：H=[1 0 0]。In formula (4), V _k+1 represents the observation error, which is normal white noise with zero mean and covariance matrix R (that is, R=1), and is not correlated with W _k , and Z _k+1 represents the observed vector. According to the state equation of formula (3), since the observation vector is the telemetry data

Therefore, the design observation matrix H is 1×3 dimension: H=[1 0 0].

在建立了遥测数据状态方程（3）和观测方程（4）的基础上，遥测数据X_k+1的最佳估计值可以由下面的Kalman滤波方程组给出。On the basis of establishing telemetry data state equation (3) and observation equation (4), the best estimated value of telemetry data X _k+1 can be given by the following Kalman filter equations.

Kalman滤波器的状态更新方程如下：The state update equation of the Kalman filter is as follows:

${\overset{~ ~}{X x}}_{k k + + 11} = = Φ Φ {\overset{^^}{X x}}_{k k} - - - - - - ((55))$

${\overset{~ ~}{P P}}_{k k + + 11} = = Φ Φ {\overset{^^}{P P}}_{k k} {Φ Φ}^{T T} + + Q Q - - - - - - ((66))$

校正方程如下：The correction equation is as follows:

${K K}_{k k + + 11} = = {\overset{~ ~}{P P}}_{k k + + 11} {H h}^{T T} {((H h + + {\overset{~ ~}{P P}}_{k k + + 11} {H h}^{T T} + + R R))}^{- - 11} - - - - - - ((77))$

${\overset{^^}{X x}}_{k k + + 11} = = {\overset{^^}{X x}}_{k k + + 11} + + {K K}_{k k + + 11} [[{Z Z}_{k k + + 11} - - {H h \overset{~ ~}{X x}}_{k k + + 11}]] - - - - - - ((88))$

${\overset{^^}{P P}}_{k k + + 11} = = ((I I - - {K K}_{k k + + 11} H h)) {\overset{~ ~}{P P}}_{k k + + 11} - - - - - - ((99))$

式（5）至式（9）中，

表示由k时刻到k+1时刻的遥测数据预测值，

表示由k时刻到k+1时刻的遥测数据预测的误差方差阵，

表示校正后的遥测数据最优估计值，

表示校正后的最优估计的误差方差阵，K_k+1表示滤波器增益矩阵。In formula (5) to formula (9),

Indicates the predicted value of telemetry data from time k to time k+1,

Represents the error variance matrix predicted from telemetry data from time k to time k+1,

Indicates the optimal estimated value of the corrected telemetry data,

Represents the corrected optimal estimated error variance matrix, and K _k+1 represents the filter gain matrix.

如图1所示，一种基于Kalman滤波的卫星遥测数据预测方法步骤如下：As shown in Figure 1, the steps of a satellite telemetry data prediction method based on Kalman filtering are as follows:

（1）Kalman滤波器参数初始化，包括待预测遥测数据初值

和预测误差方差阵初值

该初始化初值可作为步骤（2）中遥测数据最优估计值的初始值和预测误差方差阵的初始值；(1) Kalman filter parameter initialization, including the initial value of the telemetry data to be predicted

and the initial value of the forecast error variance matrix

The initialization initial value can be used as the initial value of the optimal estimated value of the telemetry data and the initial value of the forecast error variance matrix in step (2);

（2）通过Kalman滤波器状态更新方程，利用公式（5）根据当前k时刻遥测数据的最优估计值，预测k+1时刻的遥测数据，即k+1时刻的遥测数据预测值

用于进行卫星遥测数据判读；通过Kalman滤波器状态更新方程，利用公式（6）根据当前k时刻的预测误差方差阵，计算遥测数据预测的误差方差阵，即k+1时刻的预测误差方差阵k=1,2,…,n，n为观测值个数；(2) Through the Kalman filter state update equation, use formula (5) to predict the telemetry data at time k+1 according to the optimal estimated value of telemetry data at time k+1, that is, the predicted value of telemetry data at time k+1

It is used to interpret satellite telemetry data; through the Kalman filter state update equation, use formula (6) to calculate the error variance matrix of telemetry data prediction according to the current prediction error variance matrix at time k, that is, the prediction error variance matrix at k+1 time k=1,2,...,n, n is the number of observations;

（3）利用步骤（2）求得的遥测数据预测的误差方差阵利用公式（7）计算Kalman滤波器增益矩阵K_k+1，步骤（4）和步骤（5）使用Kalman滤波器增益矩阵K_k+1来校正步骤（2）求得的k+1时刻遥测数据预测值

和k+1时刻预测误差方差阵

(3) The error variance matrix predicted by the telemetry data obtained in step (2) Use the formula (7) to calculate the Kalman filter gain matrix K _k+1 , step (4) and step (5) use the Kalman filter gain matrix K _k+1 to correct the telemetry data at time k+1 obtained in step (2) Predictive value

and forecast error variance matrix at time k+1

（4）利用k+1时刻遥测数据的实际观测值Z_k+1和步骤（3）求得的Kalman滤波器增益矩阵K_k+1，通过公式（8）来校正步骤（2）求得的k+1时刻的遥测数据预测值求得k+1时刻的遥测数据最优估计值

(4) Use the actual observation value Z _{k+1 of the telemetry data at time k+1} and the Kalman filter gain matrix K _k+1 obtained in step (3), and use the formula (8) to correct the obtained value in step (2) Predicted value of telemetry data at time k+1 Obtain the optimal estimated value of the telemetry data at time k+1

（5）利用步骤（3）求得的Kalman滤波器增益矩阵K_k+1，通过公式（9）求得最优估计的误差方差阵

(5) Using the Kalman filter gain matrix K _k+1 obtained in step (3), obtain the optimal estimated error variance matrix by formula (9)

（6）利用步骤（4）求得的k+1时刻遥测数据最优估计值

和步骤（5）求得的k+1时刻的最优估计的误差方差阵

进行k+2时刻的遥测数据预测和判读；(6) Using the optimal estimated value of the telemetry data at time k+1 obtained in step (4)

and the optimal estimated error variance matrix at time k+1 obtained in step (5)

Predict and interpret telemetry data at time k+2;

（7）重复（2）至（6）步骤。(7) Repeat steps (2) to (6).

本发明方法能准确地预测出下一周期数据，对数据异常区域反应迅速，能及时发现并预报数据异常，并且算法执行效率高，能够很好地满足卫星测试的实时性要求，适用于长期数据判读和异常数据检测。The method of the invention can accurately predict the data of the next cycle, respond quickly to data abnormal areas, and can detect and predict data abnormalities in time, and the algorithm execution efficiency is high, which can well meet the real-time requirements of satellite testing and is suitable for long-term data Interpretation and outlier data detection.

本发明说明书中未作详细描述的内容属于本领域技术人员的公知技术。The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

Claims

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.