We present a parallel distributed solver that enables us to solve incremental dense least squares arising in some parameter estimation problems. This solver is based on ScaLAPACK [8] and PBLAS [9] kernel routines. In the incremental process, the observations are collected periodically and the solver updates the solution with new observations using a QR factorization algorithm. It uses a recently defined distributed packed format [3] that handles symmetric or triangular matrices in ScaLAPACK-based implementations. We provide performance analysis on IBM pSeries 690. We also present an example of application in the area of space geodesy for gravity field computations with some experimental results.