Mesoscale eddies are one of the dominant sources of variability in the world's oceans. With eddy-resolving global ocean models, it becomes important to assimilate observations of mesoscale eddies to correctly represent the state of the mesoscale. Here, we investigate strategies for assimilating a reduced number of sea-surface height observations by focusing on the coherent mesoscale eddies. The study is carried out in an idealized perfect-model framework using two-layer forced quasigeostrophic dynamics, which captures the dominant dynamics of ocean mesoscale eddies. We study errors in state-estimation as well as error growth in forecasts and find that as fewer observations are assimilated, assimilating at vortex locations results in reduced state estimation and forecast errors.