## 3 Related Work  
This section introduces positioning methods that are applicable for today's commercial off-the-shelf (COTS) smartphone hardware. Hardware components found in all modern smartphones, positioning methods that rely on this hardware as well as limitations of the underlying technology, are discussed and compared. Among positioning methods used for locating smartphones, methods that involve the use of radio frequency (RF) signals are the most prevalent. Four RF hardware sensors normally found on modern smartphones are GPS, GSM, Wi-Fi, and Bluetooth. Position can be calculated using one of the following properties of an RF signal: Time-of-Arrival (ToA), Received Signal Strength (RSS), Bit Error Rate (BER), and Angle of Arrival (AoA). RF Time-of-Arrival is associated with the use of very precise clocks and very accurate synchronization because RF signals travel at the speed of light. Hardware designed primarily for data transmission is not optimal for this positioning method. GPS is the only sensor normally found in a smartphone designed to accurately detect ToA of an RF signal. Because signals sent from GPS satellites are too weak after travelling through ceilings and walls, indoor GPS positioning uses pseudolites. Presently, the use of pseudolites is associated with a number of problems: pseudolites are fairly expensive and hard to acquire, they tend to interfere with commercial GPS receivers, and they are incompatible with GPS sensors found in smartphones [1]. Despite these hardware limitations, it was shown by [PERSON] _et al._ that ToA can be used with Wi-Fi [2]. This technique has not been tested yet on smartphones and reports an accuracy comparable to conventional Wi-Fi based methods (e.g., \(\pm 4\) m). Theoretically there exists an inverse relationship between the received signal strength and the distance it travelled [3]. RSS is the most widely used parameter in positioning systems based on GSM or Wi-Fi, and there are several ways in which it can be used to calculate position. RSS readings for multiple control points can be collected for each unique indoor location in a process called fingerprinting. If the number of access points is sufficient and the fingerprint grid is not too dense, each fingerprint reading will be unique, in which case the reading can simply be attributed to a point in the grid. Because such positioning is only as accurate as its grid is dense, collecting all the required fingerprints entails a great deal of manual effort. There is also a need to take multiple readings per point to filter out noise. The number of required fingerprints can be greatly reduced by creating a model to predict what RSS readings are expected to be in a location that was not fingerprinted. There are two distinct ways to generate such a prediction model. A wave propagation model can be created that takes into account how much the wave will attenuate when passing through obstacles and empty space. In a study done by [PERSON] _et al._ it was shown that fingerprinting can be avoided altogether with this approach [4]. Alternatively, RSS readings can be predicted with the help of a mathematical model. [PERSON] _et al._ have shown that this can be accurately done with Gaussian Processes (GP) [5]. A significant finding was that GP are able to accurately extrapolate the model into rooms that were not covered during the training phase. Indoor positioning methods in the literature that rely on Bit Error Rate (BER) do not appear as a viable option. Changes in BER are a byproduct of changes in RSS, and have even worse correlation with distance due to their random nature. It may be practical to use BER where the initial signal strength cannot be obtained, otherwise RSS is a more reliable parameter. Angle-of-Arrival methods use the direction from which the signal arrived to determine position through triangulation. It is not possible to determine direction from which the signal arrived on a COTS smartphone because it does not have directional antennas.