In this paper we present an Android application, called LOCATE-US, that allows accurate indoor positioning of mobile devices by processing the ultrasonic signals coming from a local positioning system (LPS). The LPS operates around 41KHz, and an external hardware based on an ultrasonic microphone digitizes the incoming signals and send them to the mobile device, where they are processed by means of the proposed application. This allows the use of CDMA techniques and overcomes most of the problems to be faced at the 20-22kHz range available in current smartphones, which include audible artifacts and poor resolution. The proposed software allows each mobile device in the environment to compute its own position by means of hyperbolic trilateration and represents the trajectory in the device screen, for future Location Based Services applications. Experimental results show that the proposed application achieves centimeter accuracy and can execute all the data processing for the position estimation in a time less than 0.5s.