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Atomic decomposition (AD) is an adaptive approximation technique that provides a sparse, flexible and physically meaningful representation of signals. Gaussian chirplet is suitable to represent radar signals because linear-frequency modulation is very common for radar signals and chirplet exhibits good time-frequency concentration. Thus, the application of AD, for complex radar emitter detection and estimation, has been extensively investigated. To overcome the resolution problem and the `overfitting` phenomenon caused when previous AD algorithms are used to deal with multiple chirplets that are partially superimposed in the time domain, a novel algorithm using the subspace orthogonal matching pursuit technique is presented in this study. This algorithm can also obtain higher parameter estimation accuracy, compared with other commonly employed AD algorithms, especially at low signal-to-noise ratio. Moreover, the parameter estimates can be further refined by an iterative alternating projection algorithm, which makes the estimation accuracy much closer to the Cramer-Rao bound. The simulation results illustrate the advantages of the two proposed methods.