We consider a class of control systems where the plant model is unknown and the feedback contains only partial quantized measurements of the state. We use a nonlinear optimization that is taking place over both the model parameters and the state of the plant in order to estimate these quantities. We propose a computationally efficient algorithm for solving the optimization problem, and prove its convergence using tools from convex and non-smooth analysis. We demonstrate the importance of this class of control systems, and our method of solution, using the following application: having a fixed wing airplane follow a desired glide slope on approach to landing. The only feedback is from a camera mounted at the front of the airplane and looking at a runway of unknown dimensions. The quantization is due to the finite resolution of the camera. Using this application we also compare our method to the basic method prevalent in the literature, where the optimization is only taking place over the plant model parameters.