We present a new solution to the classical problem of deriving displacements from seismic data that is suitable for real-time monitoring. It relies on an optimal combination of collocated high-rate GPS displacements and very high-rate strong-motion accelerometer data using a Kalman filter that takes advantage of the individual strengths of seismic and geodetic networks while minimizing their weaknesses. The result is a more accurate broadband estimate of velocities and displacements at the higher rate provided by accelerometers. In contrast to displacements inferred through integration of seismic data alone, which are degraded by the presence of unphysical drifts and limited dynamic ranges, broadband displacements do not drift and will not clip. Furthermore, they are more accurate and robust than those obtained solely from GPS receivers. We establish the accuracy and precision of the new solution using earthquake engineering data from the University of California, San Diego’s Large High-Performance Outdoor Shake Table. Then we estimate broadband displacements for the 2010 Mw 7.2 El Mayor–Cucapah earthquake using 1 Hz GPS displacements and 100 Hz accelerometer data from collocated sensors in southern California. We also reconstruct velocity measurements equivalent to those of broadband seismometers, which clipped at stations hundreds of kilometers from the epicenter during the earthquake. The ability to obtain broadband displacement waveforms in three dimensions with millimeter precision is a breakthrough for a number of areas ranging from earthquake source physics to the response of long-period engineered structures. To do so in real time from a dense monitoring network provides distinct advantages for earthquake early warning and rapid earthquake response.