Indoor positioning using time of flight with respect to WiFi access points

The animation above shows floor plans of three levels of a building with six “responders” (WiFi access points advertizing IEEE 802.11mc FTM RTT) shown in green, and the estimates of positions computed by an Android smartphone shown in red, as it is carried upstairs and around floors. The position is recovered in 3-D and then quantized to floor level for plotting. Here the floor plan is only for visualization and not used in the computation of the position of the phone. As a result, the red dot may at times appear to pass through a wall or even appear outside the building.

The final position accuracy is about a meter or two (aside from the occasional outlier), while the raw distance measurements have a 10% to 90% CDF (cumulative distribution function) range of between say 0.2 and 0.8 meter, depending on circumstances (see Measurement Error). The “dilution of precision” (noise gain), depends on the positions of the responders, and varies throughout the volume. Optimal placement of responders is an open problem (see FTM RTT Placement), as is the best way to deal with the measurement errors.

  • Sample videos of FTM RTT indoor localization:
  • (*) Refractive retardation: Construction materials, and merchandise on shelves, have large relative permittivity \(\varepsilon_{\mathrm {r} }\) — in the range 2–40 — (with relative permeability \(\mu_{\mathrm {r} }\) around 1). The equivalent refractive index \(n\) is proportional to the square root of the product of permittivity and permeability, i.e. \( n={\sqrt {\varepsilon _{\mathrm {r} }\mu _{\mathrm {r} }}} \). The speed of propagation of electromagnetic radiation is inversely proportional to the refractive index. As a result, FTM RTT “distances” are larger than the actual distances, often much larger.

  • Publications on indoor localization using FTM RTT:
    1. “Doubling the Accuracy of Indoor Positioning: Frequency Diversity,”
      Sensors, special issue on:
      Sensors and Sensing Technologies for Indoor Positioning and Indoor Navigation,
      Vol. 20, No. 5, March 2020.

    2. “Observation Models for Indoor Positioning,
      Sensors special issue on:
      Positioning and Navigation,
      Vol. 20, No. 14, July 2020.

    3. “Analysis of the Position-Dependent Error in FTM RTT Indoor Navigation,”
      David E. Houle, Jr.,
      MIT thesis, May 2021.

    4. “Indoor Localization using Uncooperative Wi-Fi Access Points,”
      Sensors special issue on:
      Indoor Wi-Fi Positioning: Techniques and Systems,
      Vol. 22, pp. 3091, April 2022.

    5. “Simultaneous Localization and Calibration in a Wireless Network of Uncooperative Nodes”
      Kai Yee Wan,
      MIT thesis, May 2023.

  • Why not just use Signal Strength (RSSI)?
  • WiFi Fine Time Measurement (FTM) Round Trip Time (RTT)
  • Recovering position from distance measurements
  • Recovering position using Bayesian grid update
  • Where to place the responders?
  • Measurement Error
  • Peculiarities of FTM RTT — the “Position-Dependent Error”
  • Some Issues, Problems and Current Limitations
  • Which Wi-Fi access points support the FTM RTT protocol?
  • Some Related Material and Web Links

  • Sample FTM RTT measurements:
    In the above screenshot, each line shows BSSID (MAC address), average dBm, distance measurement in meter (d), standard deviation (s) and SSID. The averages and standard deviations are over 16 runs (each of which consists of 7 round trip measurements). (Note: the SSID of the first five APs include some icons from above the UNICODE basic language plane (BPL), set up in Compulab WILD APs using UTF-8 encoding). The negative distance measurement in the first row is because of a 5.5 m offset discussed in Some Issues, Problems, and Current Limitations (that offset affects all of the first five lines above).

    You can download the WifiRttScan App from Google (the app will only install on phones that support FTM RTT and run Android Pie or later). They say the following: “The WifiRttScan app is a research, demonstration, and testing tool for developers, vendors, universities, and more. With this app it is possible to obtain a 1-2 meter range accuracy to nearby WiFi RTT (IEEE 802.11mc) capable access points. This is especially useful indoors where GPS is not available. Developers, OEMs and researchers can use this tool to validate range measurements enabling the development of positioning, navigation and context-aware applications based on the WiFi-RTT API.”

    See also WifiRttScanX, an app originally based on the same open source code, but with slightly different features and production of log files.

    Click on the following image

    for a short video of an Android phone being carried around in a seminar room. The green spots are the positions of three AP responders. For scale, the distance from the left edge to the right edge of the displayed area is 18 meter. The update rate here is two samples per second (Android takes 30 to 60 msec per AP to do the actual ranging). In this case, the floor plan is used only for visualization and not used in the computation of the position of the phone, and no use is made of remembered state or prior probability distributions (i.e. previously computed positions are not used).
    Berthold K.P. Horn,