The problem of estimating mechanical boresight and jitter performance of a laser pointing system in the presence of atmospheric turbulence is considered. A novel estimator based on maximizing an average probability density function (pdf) of the received signal is presented. The proposed estimator uses a Gaussian far-field mean irradiance profile, and the irradiance pdf is assumed to be lognormal. The estimates are obtained using a sequence of return signal values from the intended target. Alternatively, one can think of the estimates being made by a cooperative target using the received signal samples directly. The estimator does not require sample-to-sample atmospheric turbulence parameter information. The approach is evaluated using wave optics simulation for both weak and strong turbulence conditions. Our results show that very good boresight and jitter estimation performance can be obtained under the weak turbulence regime. We also propose a novel technique to include the effect of very low received intensity values that cannot be measured well by the receiving device. The proposed technique provides significant improvement over a conventional approach where such samples are simply ignored. Since our method is derived from the lognormal irradiance pdf, the performance under strong turbulence is degraded. However, the ideas can be extended with appropriate pdf models to obtain more accurate results under strong turbulence conditions.