This paper describes possible factors of spatial error distribution in a given indoor space based upon a local positioning system which utilizes spread spectrum ultrasonic waves generated by narrow directional ultrasonic transmitters. The positioning error has been interestingly discussed from the viewpoints of the dilution of precision (DOP) and the ranging error mainly due to the transmitter directional characteristics. The indoor 3-D position is calculated by means of an algorithm using distances from the transmitters located at the four corners of the ceiling to a mobile receiver. As the result of this experiment, it has been usefully found that the positioning error could be more largely influenced in the vertical direction DOP than the horizontal ones, and that the obtainable positioning error could be averaged to 3.43 [cm] rms for all 3-D measured points. These findings obtained in this work imply that the 3-D indoor positioning can be realized with an acceptable centimeter-order of precision. More importantly, the 3-D indoor positioning has to be prepared with the viewpoints of not only the ranging error, which could be yielded by the distance measurement, but also DOP, which is inevitably given by a geometrical arrangement of transmitter/receiver relation.