In Analysis Services 2008-R2, there are several impersonation options:
•Use a specific Windows username and password
•Use the service account
•Use the credentials of the current user
•Inherit (or default)
Try Out below things
1-Error implies impersonation info on connection string, security context failes.
Check for the service account on test server, and under impersonation info put service account.
2- Processing manually from SSMS and see if you get the same error or not.
3- You can go through these steps:
-Ensure that there is nothing deployed to your SSAS instance
-Open the project in BIDS Application
-Check project to make sure you are deploying to the right server
-Data Source - is it pointing to the correct location and does Test Connection succeed?
-Check the Impersonation Information tab and make sure that the option there will work for SSAS to connect to the database server - as in there is a login for the option
-Click on process and see if the solution gets deployed properly
Learning Office 2010 + SharePoint 2010 + SQL Server 2008 R2