LEE- Uçak ve Uzay Mühendisliği-Doktora
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ÖgeDevelopment of single-frame methods aided kalman-type filtering algorithms for attitude estimation of nano-satellites(Graduate School, 2021-08-20) Çilden Güler, Demet ; Hacızade, Cengiz ; Kaymaz, Zerefşan ; 511162104 ; Aeronautics and Astronautics Engineering ; Uçak ve Uzay MühendisliğiThere is a growing demand for the development of highly accurate attitude estimation algorithms even for small satellite e.g. nanosatellites with attitude sensors that are typically cheap, simple, and light because, in order to control the orientation of a satellite or its instrument, it is important to estimate the attitude accurately. Here, the estimation is especially important in nanosatellites, whose sensors are usually low-cost and have higher noise levels than high-end sensors. The algorithms should also be able to run on systems with very restricted computer power. One of the aims of the thesis is to develop attitude estimation filters that improve the estimation accuracy while not increasing the computational burden too much. For this purpose, Kalman filter extensions are examined for attitude estimation with a 3-axis magnetometer and sun sensor measurements. In the first part of this research, the performance of the developed extensions for the state of art attitude estimation filters is evaluated by taking into consideration both accuracy and computational complexity. Here, single-frame method-aided attitude estimation algorithms are introduced. As the single-frame method, singular value decomposition (SVD) is used that aided extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nanosatellite's attitude estimation. The development of the system model of the filter, and the measurement models of the sun sensors and the magnetometers, which are used to generate vector observations is presented. Vector observations are used in SVD for satellite attitude determination purposes. In the presented method, filtering stage inputs are coming from SVD as the linear measurements of attitude and their error covariance relations. In this step, UD is also introduced for EKF that factorizes the attitude angles error covariance with forming the measurements in order to obtain the appropriate inputs for the filtering stage. The necessity of the sub-step, called UD factorization on the measurement covariance is discussed. The accuracy of the estimation results of the SVD-aided EKF with and without UD factorization is compared for the estimation performance. Then, a case including an eclipse period is considered and possible switching rules are discussed especially for the eclipse period, when the sun sensor measurements are not available. There are also other attitude estimation algorithms that have strengths in coping well with nonlinear problems or working well with heavy-tailed noise. Therefore, different types of filters are also tested to see what kind of filter provides the largest improvements in the estimation accuracy. Kalman-type filter extensions correspond to different ways of approximating the models. In that sense, a filter takes the non-Gaussianity into account and updates the measurement noise covariance whereas another one minimizes the nonlinearity. Various other algorithms can be used for adapting the Kalman filter by scaling or updating the covariance of the filter. The filtering extensions are developed so that each of them is designed to mitigate different types of error sources for the Kalman filter that is used as the baseline. The distribution of the magnetometer noises for a better model is also investigated using sensor flight data. The filters are tested for the measurement noise with the best fitting distribution. The responses of the filters are performed under different operation modes such as nominal mode, recovery from incorrect initial state, short and long-term sensor faults. Another aspect of the thesis is to investigate two major environmental disturbances on the spacecraft close enough to a planet: the external magnetic field and the planet's albedo. As magnetometers and sun sensors are widely used attitude sensors, external magnetic field and albedo models have an important role in the accuracy of the attitude estimation. The magnetometers implemented on a spacecraft measure the internal geomagnetic field sources caused by the planet's dynamo and crust as well as the external sources such as solar wind and interplanetary magnetic field. However, the models that include only the internal field are frequently used, which might remain incapable when geomagnetic activities occur causing an error in the magnetic field model in comparison with the sensor measurements. Here, the external field variations caused by the solar wind, magnetic storms, and magnetospheric substorms are generally treated as bias on the measurements and removed from the measurements by estimating them in the augmented states. The measurement, in this case, diverges from the real case after the elimination. Another approach can be proposed to consider the external field in the model and not treat it as an error source. In this way, the model can represent the magnetic field closer to reality. If a magnetic field model used for the spacecraft attitude control does not consider the external fields, it can misevaluate that there is more noise on the sensor, while the variations are caused by a physical phenomenon (e.g. a magnetospheric substorm event), and not the sensor itself. Different geomagnetic field models are compared to study the errors resulting from the representation of magnetic fields that affect the satellite attitude determination system. For this purpose, we used magnetometer data from low Earth-orbiting spacecraft and the geomagnetic models, IGRF and T89 to study the differences between the magnetic field components, strength, and the angle between the predicted and observed vector magnetic fields. The comparisons are made during geomagnetically active and quiet days to see the effects of the geomagnetic storms and sub-storms on the predicted and observed magnetic fields and angles. The angles, in turn, are used to estimate the spacecraft attitude, and hence, the differences between model and observations as well as between two models become important to determine and reduce the errors associated with the models under different space environment conditions. It is shown that the models differ from the observations even during the geomagnetically quiet times but the associated errors during the geomagnetically active times increase more. It is found that the T89 model gives closer predictions to the observations, especially during active times and the errors are smaller compared to the IGRF model. The magnitude of the error in the angle under both environmental conditions is found to be less than 1 degree. The effects of magnetic disturbances resulting from geospace storms on the satellite attitudes estimated by EKF are also examined. The increasing levels of geomagnetic activity affect geomagnetic field vectors predicted by IGRF and T89 models. Various sensor combinations including magnetometer, gyroscope, and sun sensor are evaluated for magnetically quiet and active times. Errors are calculated for estimated attitude angles and differences are discussed. This portion of the study emphasizes the importance of environmental factors on the satellite attitude determination systems. Since the sun sensors are frequently used in both planet-orbiting satellites and interplanetary spacecraft missions in the solar system, a spacecraft close enough to the sun and a planet is also considered. The spacecraft receives electromagnetic radiation of direct solar flux, reflected radiation namely albedo, and emitted radiation of that planet. The albedo is the fraction of sunlight incident and reflected light from the planet. Spacecraft can be exposed to albedo when it sees the sunlit part of the planet. The albedo values vary depending on the seasonal, geographical, diurnal changes as well as the cloud coverage. The sun sensor not only measures the light from the sun but also the albedo of the planet. So, a planet's albedo interference can cause anomalous sun sensor readings. This can be eliminated by filtering the sun sensors to be insensitive to albedo. However, in most of the nanosatellites, coarse sun sensors are used and they are sensitive to albedo. Besides, some critical components and spacecraft systems e.g. optical sensors, thermal and power subsystems have to take the light reflectance into account. This makes the albedo estimations a significant factor in their analysis as well. Therefore, in this research, the purpose is to estimate the planet's albedo using a simple model with less parameter dependency than any albedo models and to estimate the attitude by comprising the corrected sun sensor measurements. A three-axis attitude estimation scheme is presented using a set of Earth's albedo interfered coarse sun sensors (CSSs), which are inexpensive, small in size, and light in power consumption. For modeling the interference, a two-stage albedo estimation algorithm based on an autoregressive (AR) model is proposed. The algorithm does not require any data such as albedo coefficients, spacecraft position, sky condition, or ground coverage, other than albedo measurements. The results are compared with different albedo models based on the reference conditions. The models are obtained using either a data-driven or estimated approach. The proposed estimated albedo is fed to the CSS measurements for correction. The corrected CSS measurements are processed under various estimation techniques with different sensor configurations. The relative performance of the attitude estimation schemes when using different albedo models is examined. In summary, the effects of two main space environment disturbances on the satellite's attitude estimation are studied with a comprehensive analysis with different types of spacecraft trajectories under various environmental conditions. The performance analyses are expected to be of interest to the aerospace community as they can be reproducible for the applications of spacecraft systems or aerial vehicles.