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Particle localization plays a fundamental role in advanced biological techniques such as single-molecule tracking, superresolution microscopy, and manipulation by optical and magnetic tweezers. Such techniques require fast and accurate particle localization algorithms as well as nanometer-scale stability of the microscope. Here, we present a universal method for three-dimensional localization of single labeled and unlabeled particles based on local gradient calculation of particle images. The method outperforms state-of-the-art localization techniques in high-noise conditions, and it is capable of 3D nanometer accuracy localization of nano- and microparticles with sub-millisecond calculation time. By localizing a fixed particle as fiducial mark and running a feedback loop, we demonstrate its applicability for active drift correction in sensitive nanomechanical measurements such as optical trapping and superresolution imaging. A multiplatform open software package comprising a set of tools for local gradient calculation in brightfield, darkfield, and fluorescence microscopy is shared for ready use by the scientific community.