Recently I began to build a car-like robot and I stumbled upon dead reckoning. I use one motor for steering and one for traction. I want to be able to get the position of the robot. From what I have read 2 encoders should be used. But I am curious if you can use only one encoder on the motor shaft to get distance and a gyro + accelerometer to get the orientation of the robot.
Dead reckoning is not a measurement, it's a form of estimation. It is by definition inaccurate, and accumulates error over time. We use it when more precise forms of position measurement aren't available (because it's better than nothing) and only to the extent that the accumulated error stays below a desired bound. In other words: after your error reaches a certain threshold, you're better off not using the estimate than relying on something that you know is wrong.
To keep the accumulated error as low as possible, you'll want to use as much sensor data as you can. This is the opposite of what you're attempting to do (eliminating one of the encoders). So the answer to your question is "yes", you can use only one encoder... but your estimates will suffer for it.