Not sure how you would use ultrasonic sensors to determine an exact position, but if the target is the closest thing to you then you could get an approximate position by sweeping a sensor past it and finding the range of bearings at which the object could be detected. The mid point of that range of angles would give you the approximate heading. The ping response time would give you range.
That would give you enough information to know the position of the target relative to the ping sensors, and you could represent that it polar or cartesian coordinates. If you also knew the position and orientation of the ping sensors, then you could convert that to an absolute position.