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In this letter, we consider the problem of estimating gain-phase and position errors for constellation synthetic aperture radar (SAR) systems. In the conventional method, the position error estimation is based on the first-order Taylor series expansion of the position-error exponential function. However, the first-order Taylor series expansion causes an approximation error, resulting in the inaccuracy of the estimation by the conventional method. In this letter, an improved method is developed to overcome this problem, based on the fact that the aforementioned approximation error decreases with the reduction in position errors. In the improved method, we first compensate the position error estimates obtained at the kth iteration in order to reduce the remaining position errors at the (k + 1) th iteration. Then, the position error estimates obtained at all iterations are summed as the estimates of the true position errors. In this way, the improved method removes the aforementioned approximation error, leading to estimates with high accuracy. Simulation results verify that the estimates by the improved method are closer to the true array errors than those by the conventional method. In addition, simulation results show that the improved method is more robust to position errors than the conventional method. Furthermore, the increase in the computational load of the improved method is negligible.