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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?

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An observation model is what relates your measurement to your states. For example, you might have a state that is vehicle speed, but the only thing you can measure is tire RPM. Tire RPM is not vehicle speed, but you could use information like wheel radius to calculate speed from tire RPM.

Similarly, you might not be able to directly measure the steering angle for the front wheels, but you could calculate it based on steering wheel angle, steering gearbox ratio, and steering knuckle geometry.

In practice, usually you're able to just measure the states directly, and your $H$ matrix winds up being a lot of ones.

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