Compressive sensing (CS) exploits the sparsity or compressibility of signals to recover themselves from a small set of nonadaptive, linear measurements. The number of measurements is much smaller than Nyquist-rate, thus signal recovery is achieved at relatively expense. Thus, many signal processing problems which do not require exact signal recovery have attracted considerable attention recently. In this paper, we establish a framework for parameter estimation of a signal corrupted by additive colored Gaussian noise (ACGN) based on compressive measurements. We also derive the Cramer-Rao lower bound (CRB) for the frequency estimation problems in compressive domain and prove some useful properties of the CRB under different compressive measurements. Finally, we show that the theoretical conclusions are along with experimental results.