Estimating Shape of Target Object Moving on Unknown Trajectory by Using Location-Unknown Distance Sensors: Theoretical Framework

By using directional distance sensors that have unknown locations, this paper proposes a method of estimating the shape of a location-unknown target object $T$ moving with unknown speed on an unknown straight line trajectory. Regardless of many unknown factors, the proposed method can estimate the shape by using each sensor's continuous report of the measured distance to $T$ without using side information or additional mechanisms such as locations of anchor sensors and angle-of-arrival measurements. By using the sensor reports, the proposed method estimates (i) the moving speed of $T$, (ii) the length and direction of an edge of $T$, and (iii) the order of consecutive edges. As a result, we can obtain the shape of $T$.