In fluorescence microscopy, high-speed imaging is often necessary for the proper visualization and analysis of fast subcellular dynamics. Here, we examine how the speed of image acquisition affects the accuracy with which parameters such as the starting position and speed of a microscopic non-stationary fluorescent object can be estimated from the resulting image sequence. Specifically, we use a Fisher information-based performance bound to investigate the detector-dependent effect of frame rate on the accuracy of parameter estimation. We demonstrate that when a charge-coupled device detector is used, the estimation accuracy deteriorates as the frame rate increases beyond a point where the detector's readout noise begins to overwhelm the low number of photons detected in each frame. In contrast, we show that when an electron-multiplying charge-coupled device (EMCCD) detector is used, the estimation accuracy improves with increasing frame rate. In fact, at high frame rates where the low number of photons detected in each frame renders the fluorescent object difficult to detect visually, imaging with an EMCCD detector represents a natural implementation of the Ultrahigh Accuracy Imaging Modality, and enables estimation with an accuracy approaching that which is attainable only when a hypothetical noiseless detector is used.