Space travelers in science fiction can drop out of hyperspace and make a pinpoint landing on any strange new world without stopping to get their bearings, but real-life space navigation is an art characterized by limited information and complex mathematics that yield no easy answers. This study investigates, for the first time ever, what position and velocity estimation errors can be expected by a starship arriving at a distant star - specifically, a miniature probe like those proposed by the Breakthrough Starshot initiative arriving at Proxima Centauri. Such a probe consists of nothing but a small optical camera and a small microprocessor, and must therefore rely on relatively simple methods to determine its position and velocity, such as observing the angles between its destination and certain guide stars and processing them in an algorithm known as an extended Kalman filter. However, this algorithm is designed for scenarios in which the position and velocity are already known to high accuracy. This study shows that the extended Kalman filter can reliably estimate the position and velocity of the Starshot probe at speeds characteristic of current space probes, but does not attempt to model the filter’s performance at speeds characteristic of Starshot-style proposals. The gravity of the target star is also estimated using the same methods.