How can I update statistics adding the data of the last day only?
The first thing to try is experimenting with sampling instead of performing a full scan every time. 

If lower samples are causing poor plans or still taking too long you could consider partitioning and if you are on SQL Server 2014 or higher you could use Incremental Statistics. 

Incremental Statistics allow you to rebuild statistics at the partition level. There is still just one statistics object for the whole table but the statistics for the partition are merged into the histogram.

If you're not running on Enterprise edition or you are on a version prior to 2014 you might consider using partitioned views. This way you can partition your data into completely separate tables with their own statistics objects.

Partitioning and partitioned views bring their own sets of complications but are usually required for very large tables.

You may be suffering from the ascending key problem, see here. If you are then one last option could be to update statistics less often and use the trace flags 2389 and 2390 to improve cardinality estimates in the time between updates.