The eigenvector method for maximum-likelihood estimation of phase error has better algorithmic performance than phase gradient autofocus (PGA).However

this method requires eigendecomposition of the sample covariance matrix

which is a computationally expensive task and also limits the real-time application.In order to overcome such difficulty

an autofocus algorithm using the projection approximation subspace tracking (PAST) approach is proposed.With this method

the procedures of covariance matrix estimation and eigendecomposition can be avoided and the computational cost can be reduced to the level of that of PGA.Monte Carlo tests and real SAR data validate that the new approach outperforms PGA.