Development of methods for analysing telemetry of small spacecraft using machine learning methods

. This article explores the influence of some averaged planetary geomagnetic indices, as well as solar activity indexes (Dst, Kp, Ap and Wolf numbers) on small spacecraft systems. The global experience in the field of research is described, and various directions in which leading specialists work are analysed. Methods of data analysis using Python are also provided. The procedure of correlation between space weather data and telemetry data of small spacecraft at a single moment in time is carried out. At the end of the experiment, a conclusion is drawn on which specific indicators should be focused on. Suggestions for further research on this topic are also provided.


Introduction
Research in the field of space weather observation shows that cooperation between different countries has a history of more than 100 years. The World Meteorological Organization has played an important role in this. It has brought together professional meteorologists from around the world and allowed them to share their experience with each other. And when satellite technology began to develop, this cooperation became even better [1].
Currently, the use of small satellites or CubeSats is a promising area in the satellite industry. This was demonstrated by the successful launch of the first three Russian CubeSats in 2019, developed by the D.V. Skobeltsyn Research Institute of Nuclear Physics, as part of the Roscosmos program called "UniverSat". These CubeSats were launched for the needs of Roshydromet for meteorology purposes. Increasing the orbital group through small satellites is an important step in the development of the space weather monitoring system.
However, due to their small size, CubeSats are vulnerable to space radiation, which poses a threat to the satellite's solar panels and microelectronics. The lack of system duplication and weak protection makes the risk of satellite system failure high. There are also other anomalies associated with space weather, such as geomagnetic anomalies.
This publication opens a series of studies that examine the impact of various space weather factors on small spacecraft. The studies are aimed at developing a methodology for analysing telemetry data from small spacecraft to predict anomalies. This publication answers the question of whether there is a correlation between satellite telemetry data and space weather parameters.
The "Literature review" section describes the experience of respected scientists in this field of research. It shows achievements in the study of space weather and suggestions for improving existing methods.
The "Methods" section describes the experimental data that will be used in the course of the work, methods, and software for analysing this data. Machine learning methods are used to compare telemetry data and space weather data for the same period. The data undergoes correlation procedures to identify dependencies between parameters.
The "Results" section describes the outcome of the correlation procedure.
In the "Discussion" section, the results are interpreted, and conclusions are drawn at this stage of the study. Simplifications during the experiment and limitations that may have influenced the interpretation of the data are also discussed.
The "Conclusion" section formulates the key findings of the study and suggests further research with an expanded dataset.
In several scientific studies exploring the use of small spacecraft for studying space weather, a variety of examples are presented demonstrating how space weather affects satellite equipment.
Researchers studying the effects of space weather factors on small satellites note the occurrence of anomalies in low Earth orbit, mainly in the midnight-morning sector in spring and autumn. Summer and winter occurrences are less frequent [2].
Publications authored by satellite manufacturers highlight the need for more precise anomaly detection tools related to space weather. The use of tools that utilize time-varying input data (measured or modelled) is proposed, allowing anomaly type to be determined by comparing time frames. However, the attribution of anomalies using limited particle flux measurements poses a difficulty [3,7].
In other works, where authors represent the interests of satellite operators and satellite systems, the needs for developing satellite specifications are presented, which are defined in contracts with manufacturers. The presence of specifications already allows reducing damages from anomalies. In addition, there is a need to determine whether the anomaly is related to space weather [7].
Research focused on filling gaps in space weather observations suggests using small satellites. Cube Satellites have a certain advantage over large spacecraft, namely: fast replaceability, low cost (compared to large satellites), and the ability to create groups of satellites for distributed measurements. CubeSats have proven themselves to be a good research platform for studies with high levels of risk [4,8,13].
Researchers are also analysing the capabilities of existing CubeSat satellite health monitoring systems. Among these systems, those based on machine learning methods are noted. Such systems are becoming increasingly important due to the increasing number of CubeSat satellites in orbit [14].
It is noted that the use of small spacecraft will also allow for the exploration and prediction of space weather (including solar activity). Predicting negative factors will help fill gaps and understand the impact of solar activity on equipment in orbit and on Earth [4,6,11].
Works highlighting the role of the Sun in space weather provide a clear understanding of "solar eruptions" -solar flares that have an immediate impact on the geomagnetic field and create disturbances in the ionosphere. There is also a need to predict such flares through machine learning methods [5,9,10].
In the publications of authoritative specialists in this field, international coordination to support activities related to the use of small spacecraft to measure space weather is also discussed. They emphasize the need for closer coordination between global communities and identify several areas where this is necessary:  Ability to timely and cheaply launch small spacecraft.  Training in the use of small spacecraft.  Assistance in predicting space weather using small spacecraft [12].
All the research areas are centered around space weather and the use of small spacecraft to study and forecast it. This speaks to the wide application of small spacecraft and attempts to improve their protection from hazardous factors in orbit. Considerable attention is also devoted to improving their operational efficiency.

Materials and Methods
To conduct the experiment, data on space weather and telemetry data from a small satellite were taken from the period of 2018 to 2020. The telemetry data from the SiriusSat-1 satellite ( Fig.1) was used, and the information was downloaded from the SatNOGS resource [15]. The satellite telemetry is characterized by several indicators:  Usb 1-3 -voltage on the solar panels (mV).  Isb 1-3 -current strength on the solar panels (mA).  Iab -current strength on the battery (mA).  Ich 1-4 -current strength on the battery channels (mA).  T1_pw -T4_pw -temperature of the battery (ºC).  Uab -voltage on the battery (mV).
There was a total of 58,895 records during the specified period. Telemetry data is recorded several times a day (between 100 and 200 times). This space weather data was taken from several ground stations, so it's an average. The information was provided by the Space Weather Analysis Center of the Scientific Research Institute of Nuclear Physics at Moscow State University (a total of 26,304 records) [16]. Space weather parameters are recorded 24 times a day (once an hour). In this experiment, the decision was made to focus on four parameters: Dst, Kp, Ap indices, and the Wolf number (Fig 2). The Dst geomagnetic index was introduced in 1964 as a measure of the magnetic field changes due to ring currents that occur in the magnetosphere during magnetic storms. At the earth's surface, the influence of ring currents results in a decrease in the horizontal component of the magnetic field with maximum reduction at low latitudes. The Dst index is calculated as the average disturbance in the horizontal component of the earth's magnetic field, relative to the quiet level, determined by data from four low-latitude observatories evenly distributed in longitude. The Dst index is calculated at four ground stations (Table  1). Kp is a planetary index that characterizes the global perturbation of the Earth's magnetic field within a three-hour interval. The Kp index is determined as the average value of the disturbance levels of the two horizontal components of the geomagnetic field observed at 13 selected magnetic observatories ( Table 2)   The Ap index is an indicator of the average daily level of geomagnetic activity. The Wolf number characterizes the level of solar activity and is related to the number of sunspots.
MS Visual Studio Code software with installed extensions to support the Python language is used for working with the data. Python software libraries are also used for the work:  Scipy -a library for scientific and engineering calculations.  Pandas -a library for data processing and analysis.
 Matplotlib -a library for creating graphs and diagrams.  Numpy -a library for implementing mathematical functions.
To conduct a correlation between parameters, it is necessary to combine both tables of data by one common parameter. In this case, it is the date/time parameter. This parameter is represented by different types of data in the two tables. Therefore, it is appropriate to convert them to one data type. In this case, the Unix time stamp format is chosen, which represents the current time converted into seconds. The data can be converted to the same format using Python tools.
After that, the data from both tables can be combined based on the date/time column. It should be noted that the number of records per day in the two tables is different. The number of telemetry records per day is higher (from 100 to 200) compared to the records of space weather parameters (24 per day). In this case, the data is combined for one hour. One record in the space weather table corresponds to several records in the telemetry table.
By merging two data tables, a correlation analysis is conducted.

Results
The results of this analysis include the construction of a correlation diagram (Fig. 5) and a correlation matrix (Fig. 6). The results of the correlation analysis indicate that there is a dependency only between the parameters of space weather and telemetry parameters of the satellite separately. There is a correlation between Kp and Ap parameters (0.34), Ap and Wolf number (0.36), Kp and Wolf number (0.18). Additionally, there is a correlation between telemetry parameters T1_pw -T4_pw and space weather parameters Ap and Wolf number (ranging from 0.04 to 0.06). There is also a dependency between Usb3 and Dst parameters (0.05), Isb2 and Dst parameters (0.03), Iab and Dst parameters (0.03), and Ich2 and Dst parameters (0.03).

Discussion
Based on the results, one can draw conclusions that there is a weak correlation (less than 0.5) between the parameters of space weather and the telemetry of the spacecraft. This means that changes in one parameter led to changes in others to a lesser extent. As the results show, within the range of 3% to 36%. The reason for this is that space weather data is taken from several ground stations located in different parts of the world. Then the parameters are averaged. As a result, the experiment results may be distorted. However, it should be noted that the computer calculations were performed with high accuracy.
To overcome this limitation, further research is needed to investigate the dependencies of the data directly from each station separately, considering the satellite travel time over it and the orbit coordinates.
In addition, it is proposed to investigate other parameters of space weather. It is suggested to study the parameters of geomagnetic activity that characterize the perturbation of the magnetic field in the auroral zone (indexes AE, AU, AL, and AO). In addition to planetary geomagnetic indexes, it is possible to investigate the influence of solar activity indicators (besides the Wolf number). Examples of solar activity indexes:  SFI is an index characterizing the intensity of solar radiation (MHz).  SN is an index characterizing the number of spots on the Sun.
 SW is an index characterizing the speed of charged particles passing near the Earth (solar wind) (km/sec).
Research aimed at studying the impact of space weather on satellite systems has revealed several important effects of space weather. Some of these effects include:  Geomagnetically-induced currents: These currents can disrupt the operation of a satellite system on a low Earth orbit due to their proximity to Earth's surface.  Radiation effects due to surface charging and arcing: Radiation from various sources can damage satellite systems, which is why components with radiation protection are necessary in satellite design.  Radiation effects on human health.  Ionospheric effects on satellite communication and navigation: Turbulence in the ionosphere can cause inconsistencies in ionospheric plasma density, which can refract incoming radio signals and cause ionospheric interference.  Thermospheric effects: Expansion of the upper atmosphere during magnetic storms can create atmospheric resistance, which can cause loss of altitude or disruptions to a satellite's orbit [10].
Researchers also identify specific impacts of space weather factors on satellite systems:  Surface Charging. Charged particles accumulate on the spacecraft body, creating high voltage that damages arcs. They also create electromagnetic interference.  Internal Charging. Charge accumulates in internal dielectrics (printed circuit boards or cable insulation) as well as on ungrounded metal. This leads to electrical breakdown and damage to sensitive electronics.  Single Event Effects. Such effects are caused by the passage of a charged particle (ion or proton) through a microelectronic device. This effect causes the device to fail and be damaged. Remedying such malfunctions requires intervention from specialists on Earth.  Total Ionizing Dose and Displacement Damage Dose. The passage of charged particles through satellite microelectronics causes energy loss and reduces its performance [3].
Specialists have also created a computer model for accurate forecasting of resistance of a satellite when it enters orbit. This concerns the effects from space weather. This model is meant for calculating the launch of a small spacecraft into orbit and its return to Earth. In this case, solar activity cycles are being studied. As a result, the influence of the time of launch on the cycles of solar activity has been revealed. As the researchers themselves note, their limitations were also related to the quality of the data, which were too widely distributed over time [7].
The difference of this study from the one already conducted by the specialists lies in its approach. To obtain the result, a comparison is made between the telemetry data of a small satellite and the space weather for a given period to identify dependencies. Quantitative indicators are being researched, considering not only solar activity parameters but also geomagnetic indices. However, studies conducted by experienced specialists provide a more complete picture in specific areas (effects of space weather; factors affecting satellite operations; modeling and forecasting of solar activity).

Conclusion
This work demonstrates that the role of small satellites in space weather research is increasing. This is reflected in the growth of launches of small spacecraft, as well as the ability of such spacecraft to conduct more distributed measurements. Attention is increasing towards improving the protection of small satellites from hazardous factors.
Additionally, the study demonstrates the possibility of applying machine learning methods for analyzing large amounts of data and visualization. Using Python tools, it is convenient to work with arrays of data, as well as to create graphs and diagrams for visual representation.
The experiment results revealed a correlation between satellite telemetry and space weather indices (although it is weak). This motivates further research in this direction, but with an expanded range of data.