## 3 Related Work
While ultrasound trilateration of mobile phones does not appear in the literature, there are many examples of indoor positioning systems that utilize custom hardware to send and receive ultrasonic signals [17, 18, 19, 20, 21, 22]. These systems report centimeter or even millimeter-level accuracy. Sensors and receivers used in such ultrasonic systems normally operate at around 40 KHz, much higher frequenciesthan what standard mobile phone speakers can produce. Compared to audible frequencies, sound at these frequencies is known to be highly directional, have a high attenuation rate and poor obstacle penetration. The 20-22 KHz range available on smartphones is expected to share some properties with higher frequencies, although to what extent had to be determined through experiment. Directionality and attenuation rate experimental results are described in Section 5. Positioning methods that do not rely on signal propagation are also possible on smartphones. One such method is computer vision. All modern smartphones have a camera on the back of the phone and sometimes a second camera on the front. Computer vision, while potentially very accurate, is characterized by high computational load, poor performance under low light conditions, complicated procedures of recovery from tracking failures, and susceptibility to camera shake and motion blur. These problems are addressed in studies done by [PERSON] _et al._[23] and [PERSON] _et al._[24]. Another difficulty associated with computer vision is that the user is supposed to be looking through the display screen when using the device. Currently Simultaneous Localization and Mapping (SLAM) appears to be the most promising computer vision technique, considered by many as an operational technology still in its infancy [25]. Magnetometers (digital compass), accelerometers, and gyroscopes that are now common sensors found in smartphones could be used for Dead Reckoning (DR). Dead Reckoning is a method of estimating position by continuously projecting current direction and speed from the known initial position (fix) [26]. Apart from the fix, which for example could be obtained from a passive RFID tag located on a doorway, a DR system only needs a constant flow of information about current direction and speed. There are several ways to estimate current velocity using accelerometers, the most straightforward approach is to monitor acceleration or deceleration of the unit. Unfortunately, accelerometers are very sensitive to vibrations, which is a major problem for mobile devices. Another problem is that, similar to gyroscopes, accelerometers register the rate of change in movement speed, which leads to a buildup of positioning error over time [25], especially if the user \"swings\" the device by their side while walking or often takes it in/out of their pocket _etc._  
A much more reliable use of accelerometers for estimating pedestrian movement is step detection. The spikes of acceleration are used to detect if and how frequently the user takes a step. In a study done by [PERSON] _et al._[27] it was shown that provided the user received some sort of training, pedestrian Dead Reckoning can offer better accuracy than GPS over short distances. However if an untrained user was equipped with such a system, the results are worse [28]. Another problem with indoor DR is that magnetometers can be very unreliable indoors, which makes direction estimation a major source of error [27]. A comparison of contemporary indoor positioning systems is given in Table 1. It shows that solutions available on mobile phones predominantly use RF technologies but are yet unable to pass the one-meter accuracy threshold. At the same time, ultrasound based systems have centimeter and millimeter accuracy levels, but are not compatible with COTS smartphones. Our solution (Lok8) combines the best of both, bringing together smartphone multimodal flexibility with the positioning accuracy and robustness of least squares based ultrasound trilateration.