A quaternion represents two things. It has an x, y, and z component, which represents the axis about which a rotation will occur. It also has a w component, which represents the amount of rotation which will occur about this axis. In short, a vector, and a float. With these four numbers, it is possible to build a matrix which will represent all the rotations perfectly, with no chance of gimbal lock. (I actually managed to encounter gimbal lock with quaternions when I was first coding them, but it was because I did something incorrectly. I'll cover that later). So far, quaternions should seem a lot like the axis angle representation. However, there are some large differences, which start....now.
What were the objective improvements ? ie. probability of detection vs false alarm rate ?
For some systems, such as the autonomous vehicle, sensor fusion is the key to the end result. Without it, the reaction is not what you want. Other aplications may provide an improvement in key sensor output and higher probablity of detection fewer false triggers. You do not want to do sensor fusion just for the sake of saying you used it in a product because there is a cost (development time for software and additional hardware) associated with sensor fusion.
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