Abstract: Event cameras are bioinspired sensors with reaction times in the order of microseconds. This property makes them appealing for use in highly-dynamic computer vision applications. In this work, we explore the limits of this sensing technology and present an ultra-fast tracking algorithm able to estimate six-degree-of-freedom motion with dynamics over 25.8g, at a throughput of 10kHz, processing over a million events per second. Our method is capable of tracking either camera motion or the motion of an object in front of it, using an error-state Kalman filter formulated in a Lie-theoretic sense. The method includes a robust mechanism for the matching of events with projected line segments with very fast outlier rejection. Meticulous treatment of sparse matrices is applied to achieve real-time performance. Different motion models of varying complexity are considered for the sake of comparison and performance analysis.