# Round-Trip Time Ranging to Wi-Fi Access Points Beats GNSS Localization
## 1 Introduction  
Indoor localization using fine-time measurement (FTM) round-trip time (RTT) with respect to Wi-Fi access points (APs) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] has been shown to work well, achieving 1-2 m accuracy [9, 19, 20] in houses and office spaces. All this without the impractical detailed surveying that some competing localization methods require. FTM RTT depends on Wi-Fi APs implementing the IEEE 802.11 mc protocol (\"two-sided\" RTT) incorporated in IEEE 802.11-2016 [32]. More recently, it has also become possible to range to \"uncooperative\" APs using \"one-sided\" RTT [27]. This allows one to make use of more types of APs, albeit with somewhat reduced accuracy, typically 3-4 m. There are applications available that implement localization methods using RTT ranging, including Google's WiFiRttLocator [33], which uses least-squares (LSQ) multilateration, and FTMRTT [34] which uses a Bayesian grid update (BGU) method (in 2D and 3D). The BGU method is described in papers on indoor localization [19, 20], and in the chapter \"Updating Occupancy Grids Using Bayesian Estimation\" in [PERSON]'s \"An Introduction to AI Robotics\" [35].  
The accuracy of RTT measurements is roughly inversely proportional to the bandwidth. However, in practice, the results are not nearly as good as suggested by the Cramer-Rao bound [27; 36] for a given bandwidth. There are several reasons for this. One is the so-called \"position-dependent\" error [19], which can induce meter-size changes in a reported distance when the user equipment is moved just a few millimeters. This is prevalent indoors where reflections off various surfaces lead to interference patterns with texture elements about one-half wavelength in size [37]. A related problem is multi-path where the algorithm for detecting the first arrival may be misled by contributions from later arrivals (note that there is no path diversity in IEEE 802.11 mc since it does not exploit the multi-input multi-output (MIMO) method, introduced in IEEE 802.11 ac Wave 2).  
Another contribution to measurement error is the retardation of radio frequency signals by material of high refractive index along the path. The refractive index \(n\) equals \(\sqrt{\varepsilon_{\mathrm{r}}\mu_{\mathrm{r}}}\), where \(\varepsilon_{\mathrm{r}}\) is the relative permittivity and \(\mu_{\mathrm{r}}\) is the relative permeability. Many materials have high relative permittivity at Wi-Fi frequencies [38; 39; 40; 41], so the refractive index can be quite large (e.g., \(\varepsilon_{\mathrm{r}}\approx 79\) and \(n\approx 8.9\) for water at 2.4 GHz). The resulting \"refractive retardation\" adds \((n-1)\)\(\delta\) to the measured distance, where \(\delta\) is the thickness of the material. This is less of a problem for outdoor applications of RTT ranging since the radiation typically has to go through just one or two walls near the AP but does not have to traverse additional obstacles.  
To date, there has been little effort to apply RTT methods outdoors. RTT potentially can work even better outdoors than indoors because, typically, most of the path between the AP and the UE is free of obstacles. It is also desirable to provide a smooth transition from navigating indoors to navigating outdoors. Methods based on RTT ranging will work both indoors and outdoors. Naturally, there are limitations on the distance one can stray from areas that have Wi-Fi APs.