An adaptive Huber-based Kalman filter (AHF) is presented to deal with model error and unknown measurement noise in this article. The adaptive method for model error is obtained using an upper bound for the predicted state error covariance matrix. The measurement noise uncertainty is tackled at each time step by minimizing a criterion function that is original from the Huber technique. A recursive algorithm is also provided to solve the criterion function. The proposed AHF algorithm has been tested in an attitude estimation problem using a gyroscope and star tracker sensors for a single spacecraft in flight simulations in the presence of both model error and non-Gaussian random measurement errors. Simulation results demonstrate the superior performance of the proposed filter compared with the previous filter algorithms. The main contribution of this work can be considered the new application of an existing method.