Autonomous vehicles with the ability to simultaneously identify obstacles' or targets' position at the same time as estimating their own position have been long sought after. This paper investigates an approach to solving this problem also known as simultaneous localization and mapping or SLAM. Demonstration of the viability of the SLAM problem applied to the unmanned aerial vehicle (UAV) using monocular vision sensors is taken in steps: estimating unknown targets with known vehicle states; estimating vehicle states with known targets; and finally estimating the vehicle's states and the targets' states simultaneously. The targets' states included position, orientation, and area. The vehicle states included position, velocity, orientation, accelerometer biases, and gyroscope biases. Simulations showed that estimating the vehicle states using known targets was possible. Stable solutions to the complete SLAM problem were simulated proving it possible to solve the SLAM problem for a UAV using monocular vision sensors.