In my journey to understand the Kalman filter, I understood how a state model representation is derived for a robot and why(to get the robot state for a given input u) it is required.
$$ \boldsymbol{x_t} = A_{t-1} \boldsymbol{x_{t-1}} + B_{t-1} \boldsymbol{u_{t-1}} $$
But I didn't get the essence of the observation model(H), to my understanding, this represents the theoretical sensor behavior of a robot.But I didn't get how the observation model helps me as a layman. Does it give something if I give something to it?
why a sensor model is required? Aren't the sensors(IMU, GPS..etc) have a standard model for each? Observation model is for a sensor/ all sensors in the system(robot)? How to derive H for a mobile robot with sensors imu,GPS,wheel odometry?