Brain-driven interfaces depend on estimation procedures to convert neural signals to inputs for prosthetic devices that can assist individuals with severe motor deficits. Previous estimation procedures were developed on an application-specific basis. Here we report a coherent estimation framework that unifies these procedures and motivates new applications of prosthetic devices driven by action potentials, local field potentials (LFPs), electrocorticography (ECoG), electroencephalography (EEG), electromyography (EMG), or optical methods. The brain-driven interface is described as a probabilistic relationship between neural activity and components of a prosthetic device that may take on discrete or continuous values. A new estimation procedure is developed for action potentials, and a corresponding procedure is described for field potentials and optical measurements. We test our framework against dominant approaches in an arm reaching task using simulated traces of ensemble spiking activity from primary motor cortex (MI) and a wheelchair navigation task using simulated traces of EEG-band power. Adaptive filtering is incorporated to demonstrate performance under neuron death and discovery. Finally, we characterize performance under model misspecification using physiologically realistic history dependence in MI spiking. These simulated results predict that the unified framework outperforms previous approaches under various conditions, in the control of position and velocity, based on trajectory and endpoint mean squared errors.