The attitude estimation of a spacecraft in low Earth orbit is considered with the design of two different adaptation rules in the extended Kalman filter (EKF) algorithm. The adaptations are designed for compensating both the measurement faults and external disturbances by updating the noise covariances of the Kalman filter. First, the measurement noise covariance (R) adaptation is introduced by using the Singular Value Decomposition (SVD) as a preprocessing step in EKF design. The estimation filters might suffer from the large erroneous initialization of the states by diverging from the actual case. The proposed algorithm on the other hand uses SVD measurements as the initial conditions for the filtering stage. This makes the filter resistant to this type of error source. Second, the process noise covariance (Q) adaptation rule is incorporated into the previous filter design. The rules are set simultaneously so that the filter has the capability to be robust against initialization errors, system noise uncertainties, and measurement malfunctions. Numerical simulations based on several scenarios are employed to investigate the robustness of the filter. (C) 2021 COSPAR. Published by Elsevier B.V. All rights reserved.