I'm using a range sensor (Infrared Sensor) to measure the distance between the robot and an obstacle. However I did some measurements and their variances change over distance.
I took 1000 samples of a few distances (10cm, 20cm, 30cm, 40cm, 50cm ...) and their mean value matches the distance, however the variance increases about 2x at every 10cm increments. What is the best way to deal with it? I can create my covariance matrix R dinamically based on its values or what should be the best approach in this case?
You should calculate the variance including all the measurements and use that for your measurement covariance, $R$. I am not familiar with any method that does what you describe. Using an adaptive Kalman filter, the process covariance, $Q$, and the measurement covariance $R$, are dynamically modified, but those methods do not do what you describe (e.g. specify a different variance for each different magnitude of the measurement).