Drones are becoming more and more popular nowadays. They are small in size, low in cost, and reliable in operation. They contain a variety of sensors and can perform a variety of flight tasks, reaching places that are difficult or inaccessible for humans. Earthquakes damage a lot of infrastructure, making it impossible for rescuers to reach some areas. But drones can help. Many amateur and professional photographers like to use drones for aerial photography. Drones play a non-negligible role in agriculture and transportation too. Drones can be used to spray pesticides, and they can also transport supplies. A quadcopter is a four-rotor drone and has been studied in this paper. In this paper, random noise is added to the quadcopter system and its effects on the drone system are studied. An extended Kalman filter has been used to estimate the state based on noisy observations from the sensor. Based on a SDE system, a linear quadratic Gaussian controller has been implemented. The expectation maximization algorithm has been applied for parameter estimation of the quadcopter. The results of offline parameter estimation and online parameter estimation are presented. The results show that the online parameter estimation has a slightly larger range of convergence values than the offline parameter estimation.