— This paper presents a theoretical investigation in the framework of visual-inertial sensor fusion and the results here provided are the extension of our previous contribution in [10], [11]. The general goal of this research is to establish minimalistic visual-inertial sensors settings, which still provide full information even in the most challenging situations, i.e., in the case of unknown camera extrinsic calibration, unknown magnitude of the gravity, unknown inertial sensor bias and when only a single point feature is available. The investigation here provided allows us to conclude that, even in the case of a single point feature, the information provided by a sensor suit composed by a monocular camera and two inertial sensors (along two independent axes and where at least one is an accelerometer) is the same as in the case of a complete inertial measurement unit (i.e., when the inertial sensors consist of three orthogonal accelerometers and three orthogonal gyroscopes). To derive this result, an observability analysis of systems with only one and two inertial sensors is performed. This analysis requires to approach an open problem in control theory, called the Unknown Input Observability (UIO). In this paper we adopt the same method introduced in [10], [11] to solve this UIO problem. The method has been here improved in order to deal with systems more complex than the ones analyzed in [10], [11]. The paper also provides a general discussion on UIO and in particular on the proposed solution.