**4. Detection of changes in FOG bias using SVM**

It has been needed to find any weak sign of event that would link to some system troubles. Such demand called failure detection, a sub category of system monitoring, has been researched for ground systems as well as onboard systems in many fields. Having experience of working for years as an operator of REIMEI, the author also has felt such for failure detection only for system failure but also for detection of degrade of performance: signs of changes in specification that there is no error but something seems to be wrong. In this section, an example of such failure detection is shown using a problem of degrade of FOG bias drifting in REMEI.

## **4.1 Signs of changes in bias**

Figure 12 shows time history plots of the angular difference of propagation and the angular difference of the STT over 2 years, which are plotted over different time spans such as one month, ten days, and one day.

From the statistics for these time spans, it is easy to observe the level of fitness of the EKF parameters. By taking statistics over a longer time span, randomness can be reduced. For example, there is no sign of parameter mismatch before Oct. 2006, but an event occurred in Oct. 2006; the difference between the median and mode of the distribution of the angular difference of propagation has been increasing since Nov. 2006. The median indicates the accuracy of bias estimation, while the mode indicates the random-walk error of bias drift.

According to these time history plots over 2 years, it can be concluded that the EKF parameters have been mismatched with the actual state of the FOGs since Oct. 2006. This means that the characteristics of the FOG bias changed at that time. The most probable reason for the bias error is that the degradation of fibre transparency due to radiation became sufficiently large to cause bias instability. However, this degradation is still considered to have a limited effect according to the results of radiation tests performed before the launch; there must be another factor causing this degradation.

From the operator's viewpoint, one month is a too long period to take any measures to prevent the degradation of accuracy of attitude determination. Any parameter mismatch must be noticed as soon as possible rather from the analysis of monthly statistics.

Telemetry Data Mining with SVM for Satellite Monitoring 109

support vectors, the entire telemetry data set (test data set) can be classified as an OK data set or an NG data set, i.e., it can be established whether or not the current parameters are

The angular difference of propagation and the DOP of stars shown in Fig. 14 were selected as the training data set to test the performance of the SVM technique. Even though the SVM was generated using one month of statistical data, it detected a change in bias for ten days of statistical data as well as one month of statistical data. A summary of this detection is shown in Fig. 15. Since Mar. 2007, the parameters have been changed several times to reduce the angular difference of propagation to a sufficiently small value to meet the mission

Fig. 14. Two plots of propagation error angle vs DOP starts calculated using deferent statistics. These plots show the discrimination performance how the SVM generated using

tuned appropriately.

Fig. 13. The 4 steps to make up a SVM

requirements. All these changes were detected in the results.

training data can judge the state of FOG bias using test data.

#### **4.2 Support vector machine**

The easiest way to rapidly detect signs of bias change is to shorten the time span of statistics to ten days or one day. However, the shorter the time span, the less accurate the statistical results. Thus, it is necessary to define a threshold for determining whether or not the level of fitness of parameters is acceptable before calculating short-time-span statistics using the telemetry data.

Fig. 12. Trend plots of the angular difference for two years time span

The support vector machine (SVM) technique is one of the most practical methods of detecting such signs from telemetry data. It is a popular discrimination scheme used in many fields. The SVM technique is a type of supervisory learning method (Cristianini & Shawer-Tylor, 2000). It is thus necessary to carry out a training process before using it for discrimination, which is shown in Fig. 13. The SVM technique is as follows: in Step 1, a telemetry data set that was obtained before the change in bias is prepared. This data set is treated as a no-error (OK) data set. In Step 2, a telemetry data set is prepared that contains some signs indicating that the parameters are unsuitable. This data set is treated as an erroneous (NG) data set. In Step 3, using these data sets as training data sets, support vectors are calculated. The kernel function is a simple linear function for this case. Using the

The easiest way to rapidly detect signs of bias change is to shorten the time span of statistics to ten days or one day. However, the shorter the time span, the less accurate the statistical results. Thus, it is necessary to define a threshold for determining whether or not the level of fitness of parameters is acceptable before calculating short-time-span statistics using the

Fig. 12. Trend plots of the angular difference for two years time span

The support vector machine (SVM) technique is one of the most practical methods of detecting such signs from telemetry data. It is a popular discrimination scheme used in many fields. The SVM technique is a type of supervisory learning method (Cristianini & Shawer-Tylor, 2000). It is thus necessary to carry out a training process before using it for discrimination, which is shown in Fig. 13. The SVM technique is as follows: in Step 1, a telemetry data set that was obtained before the change in bias is prepared. This data set is treated as a no-error (OK) data set. In Step 2, a telemetry data set is prepared that contains some signs indicating that the parameters are unsuitable. This data set is treated as an erroneous (NG) data set. In Step 3, using these data sets as training data sets, support vectors are calculated. The kernel function is a simple linear function for this case. Using the

**4.2 Support vector machine** 

telemetry data.

support vectors, the entire telemetry data set (test data set) can be classified as an OK data set or an NG data set, i.e., it can be established whether or not the current parameters are tuned appropriately.

Fig. 13. The 4 steps to make up a SVM

The angular difference of propagation and the DOP of stars shown in Fig. 14 were selected as the training data set to test the performance of the SVM technique. Even though the SVM was generated using one month of statistical data, it detected a change in bias for ten days of statistical data as well as one month of statistical data. A summary of this detection is shown in Fig. 15. Since Mar. 2007, the parameters have been changed several times to reduce the angular difference of propagation to a sufficiently small value to meet the mission requirements. All these changes were detected in the results.

Fig. 14. Two plots of propagation error angle vs DOP starts calculated using deferent statistics. These plots show the discrimination performance how the SVM generated using training data can judge the state of FOG bias using test data.

Telemetry Data Mining with SVM for Satellite Monitoring 111

on a real-time OS. The deliberator layer processes all the input data such as environment measurement data, hardware status data, and operation commands and determines the next action to be taken. The executor layer connects input and output data between the executor and driver layers by interpreting the stream of abstract data such as operator commands (for examples GO or STOP) into the hardware data stream (ON or OFF) and vice versa. It also

manages the issue of commands, i.e., when and where to send the data.

Human Operator Operation / Interfaction with System

Remote System Software Deliberator

Environment Interaction through Sensors and Actuators

system can be considered to have the ability to make its own decisions.

without affecting other running tasks such as hardware controls.

Executor, and Driver functions.

Fig. 16. The three-layer architecture for remote system software consisting of Deliberator,

A human operator at a remote station communicates with a remote system by telecomands (CMD) and telemetry (TLM). The operator reads TLM data to determine the event that has occurred at the remote system and then sends CMDs so that the system can operate as planned to achieve its mission goals, resulting in a human-in-the-loop control system. To make the remote system autonomous, the deliberator layer should behave in the same way as the human operator. If this can be achieved, the lower layers will act in the same way under both a human operator and autonomous control. If this situation can be realized, the

Here is an example to show how to implement such architecture in Fig. 17. The driver and executor layers is implemented as real-time tasks running on a real-time OS and the deliberator is implemented as a script engine running on the same OS so that it is easy to communicate between the three layers by an intertask communication mechanism provided by the OS kernel. The reason why a script engine is used on the deliberator layer is that it is expected that algorithms for system monitoring such as SVM should change its target according to operation purposes and circumstances of the system: many algorithms should be loaded to detect many potential failures throughout its mission. FOG bias drift detection was explained in this chapter, but it is not only possible trouble on onboard hardware. Using usual tasks programmed in C/C++, it is hard to change onboard algorithm for system monitoring after starting up the system. However, script engines seem to be an only option to change algorithm frequently. By changing the script, the algorithms can be changed

Executor

CMD / TLM / Planing

Sequence of commands

Close-loop Control

HW Access Interface

Driver

Hardware Hardware

CMD / TLM

Fig. 15. Classification results by the SVM generated using OK and NG data sets. The result using one month statistics case successfully detects all the changes in FOG bias drifts, while the 10 days statistics case have one false positive detection (miss detection of change in FOG bias).
