This paper presents a binocular vision-IMU (Inertial Measurement Unit) tightly-coupled structure based on a Minimum sigma set Square-Root Unscented Kalman Filter (M-SRUKF) for real time navigation applications. Though the M-SRUKF has only half the sigma points of the SRUKF, it has the same accuracy as the SRUKF when applied to the binocular vision-IMU tightly-coupled system. As the Kalman filter flow is a kind of square-root system, the stability of the system can be guaranteed. The measurement model and the outlier rejection model of this tightly-coupled system not only utilises the epipolar constraint and the trifocal tensor geometry constraint between the consecutive two image pairs, but also uses the quadrifocal tensor geometry among four views. The structure of the binocular vision-IMU tightly-coupled system is in the form of an error state, and the time updates of the state and the state covariance are directly estimated without using Unscented Transformation (UT). Experiments are carried out based on an outdoor land vehicle open source dataset and an indoor Micro Aerial Vehicle (MAV) open source dataset. Results clearly show the effectiveness of the proposed new mechanisation.