## 2 Materials  
BIRDS-3 is the third project of the BIRDS program [9]. BIRDS-3 is a constellation of three CubeSats deployed to orbit on 17 June 2019 [10]. Figure 1 shows the BIRDS-3 flight models. The external dimensions and weight of each BIRDS-3 CubeSat are 113.5 mm \(\times\) 100 mm \(\times\) 100 mm and 1.05 kg, respectively. All three satellites re-entered the atmosphere on October 2021.  
The BIRDS-3 CubeSats had four missions, namely the Imaging Mission (CAM), the LoRa Demonstration Mission (LDM), the Attitude Determination and Control System (ADCS), and the Software Configurable Backplane Mission (BPB):BIRDS-3 FM CPLD. The BIRDS-3 CubeSats had two mission boards named Mission Board 1 and Mission Board 2. ADCS and CAM were installed on Mission Board 2. BIRDS-3 satellites have three-axis magnetic torquers for ADCS and were implemented in printed circuit boards in order to save space. The magnetometer was installed in Mission Board 2 in the ADCS section. Figure 2 shows the location of Mission Board 2 (ADCS mission board), and Figure 3 shows the location of the magnetometer. The MMC5883 MA magnetometer was used in BIRDS-3 CubeSats.  
On-orbit magnetometer data were used as part of the BIRDS-3 attitude stabilization system. B-dot control was used to stabilize the CubeSats. The B-dot algorithm [11] is a simple algorithm used to reduce the angular velocity of satellites. It requires the rate of changes in magnetic field flux density, measured by magnetometers. Magnetometer data were the key input of the B-dot algorithm. The attitude stabilization system of BIRDS-3 failed in orbit. It was found that the on-orbit magnetic field data observed by all three magnetometers were different from the expected results when compared to magnetic field models such as the World Magnetic Model (WMM) [12]. Before the flight, a magnetometer calibration test using a Helmholtz coil was conducted on the ground utilizing an engineering model of the magnetometer. This calibration test was performed only for the magnetometer. The whole satellite was not used to calibrate the magnetometer. Moreover, the gain and non-orthogonality angles were not estimated before the flight. Figure 4 shows  
Figure 1: BIRDS-3 Flight models.  
the on-orbit magnetometer data observed by BIRDS-3 CubeSats after their deployment from the International Space Station. The BIRDS-3 CubeSats were deployed into orbit at 7:15 p.m. (JST) on 17 June 2019. The data were collected after 16 s of deployment. The zero in the time axis corresponds to the 16 s after the deployment. Latitude at deployment was approximately 1.433 degrees north, and longitude was \(-\)57.903 degrees.  
Figure 4: The total magnetic field observed by BIRDS-3 (NepaliSat-1, Raavana-1, and Uguisu) and the model magnetic field (WMM: World Magnetic Model).  
Figure 3: Mission Board 2 and the location of the magnetometer.  
Figure 2: Location of Mission Board 2 in the BIRDS-3 CubeSats.  
In Figure 4, the magnetometer data are compared with the WMM. The orange line indicates the magnetometer data of NepaliSat-1, the gray line indicates the magnetometer data of Rauvana-1, the yellow line indicates the magnetometer data of Uguisu, and the blue line indicates the WMM. Figure 4 shows the difference between observed and WMM magnetic fields. There are heavy variations in the observed total magnetic field measured in all three satellites due to the offsets, gains, and non-orthogonal angles in the magnetometers. These errors in the magnetometer data must be corrected.