Barometer recalibration

Would it be possible to recalibrate barometer in pixhawk or any other barometer to have reference level at ground level (which area one intends to use it) instead of sea level?
And how accurate does these barometric sensor get?

When using the Mission Planner and PixHawk you have two data about Altitude:

]Absolute Altitude pertains to altitude above sea level/:m]
]Relative Altitude pertains to altitude above home/launch position/:m]
Is that what you are looking for ?

The sensor is used in conjunction with the GPS to give precise altitude hold.

I am trying to fly drone at certain height, And I will be using ultrasonic and barometer to make sure I maintain height. I do not want to use GPS for it. So, I was wondering if I could use barometer and ultrasonic to maintain certain height even if there is something in theground that will be detected by ultrasonic sensor and give me wrong height. I guess I am asking if I can rely on barometer when ultrasonic sensor detects object and gives me height from the object instead of height from the ground level?

Compare the two values and filter so you use the correct height from the Barometer ?
The pressure sensor is affected by air turbulence and is not accurate enough to give a very precise flight height alone.