This paper presents a computationally simple near-optimal filter for spacecraft motion estimation. This is particularly important in applications where the computational resources are very limited, such as in cube-satellite and nano-satellite missions. The proposed filter consists of two scalar gains, and has analytically guaranteed performance under given bounds on the process and measurement noise covariances. Unlike the Kalman filter or its variants, there is no associated covariance propagation. Favorable performance of the presented filter, compared with a conventional extended Kalman filter, is demonstrated via a hardware-in-the-loop simulation of a dual spacecraft formation navigation problem. (C) 2015 Elsevier Ltd. All rights reserved.