A position estimation apparatus comprising: a first trajectory generator configured to generate one or more first trajectories, each first trajectory being a motion trajectory of a respective moving object in a first coordinate system, each moving object being detected from a video; a second trajectory generator configured to generate one or more second trajectories from time-series data of positional information output from one or more respective position sensors, each second trajectory being a motion trajectory of a respective moving object having a position sensor in a second coordinate system; a trajectory matcher configured to associate a first trajectory among the one or more first trajectories with a second trajectory among the one or more second trajectories, the first trajectory and the second trajectory being estimated to be a motion trajectory of the same moving object based on a similarity in shape determined using higher-order local autocorrelation, HLAC, features between the first trajectory and the second trajectory; a deriver configured to derive a transformation matrix that transforms the second coordinate system into the first coordinate system based on one or more pairs of a first trajectory and a second trajectory associated with each other by the trajectory matcher; and an estimator configured to estimate, subsequent to the deriving of the transformation matrix, a position of a moving object in the first coordinate system by mapping a second trajectory among the one or more second trajectories in the first coordinate system by using the transformation matrix, wherein the estimator is configured, subsequent to the deriving of the transformation matrix and for each moving object, to integrate a first trajectory for the moving object among the one or more first trajectories with a second trajectory mapped in the first coordinate system for the moving object and to estimate a position of the moving object in the first coordinate system at each instant of time based on an integrated motion trajectory of the moving object, and each position sensor is associated with unique information for identifying a moving object having the position sensor. a first trajectory generator configured to generate one or more first trajectories, each first trajectory being a motion trajectory of a respective moving object in a first coordinate system, each moving object being detected from a video; a second trajectory generator configured to generate one or more second trajectories from time-series data of positional information output from one or more respective position sensors, each second trajectory being a motion trajectory of a respective moving object having a position sensor in a second coordinate system; a trajectory matcher configured to associate a first trajectory among the one or more first trajectories with a second trajectory among the one or more second trajectories, the first trajectory and the second trajectory being estimated to be a motion trajectory of the same moving object based on a similarity in shape determined using higher-order local autocorrelation, HLAC, features between the first trajectory and the second trajectory; a deriver configured to derive a transformation matrix that transforms the second coordinate system into the first coordinate system based on one or more pairs of a first trajectory and a second trajectory associated with each other by the trajectory matcher; and an estimator configured to estimate, subsequent to the deriving of the transformation matrix, a position of a moving object in the first coordinate system by mapping a second trajectory among the one or more second trajectories in the first coordinate system by using the transformation matrix, wherein the estimator is configured, subsequent to the deriving of the transformation matrix and for each moving object, to integrate a first trajectory for the moving object among the one or more first trajectories with a second trajectory mapped in the first coordinate system for the moving object and to estimate a position of the moving object in the first coordinate system at each instant of time based on an integrated motion trajectory of the moving object, and each position sensor is associated with unique information for identifying a moving object having the position sensor.