Clock Error Analysis of Common Time of Flight based Positioning Methods

Abstract

Today, many applications such as production or rescue settings rely on highly accurate entity positioning. Advanced Time of Flight (ToF) based positioning methods provide highaccuracy localization of entities. A key challenge for ToF based positioning is to synchronize the clocks between the participating entities. This paper summarizes and analyzes ToA and TDoA methods with respect to clock error robustness. The focus is on synchronization-less methods, i.e. methods which reduce the infrastructure requirement significantly. We introduce a unified notation to survey and compare the relevant work from literature. Then we apply a clock error model and compute worst case location-accuracy errors. Our analysis reveals a superior error robustness against clock errors for so called Double-Pulse methods when applied to radio based ToF positioning.

Spoofing Evident and Spoofing Deterrent Localization Using Ultrawideband (UWB) Active–Passive Ranging

“…In practical scenarios, (∆ RT + ∆ DT ) and (−ρ AT + ρ BT − ρ AB ) are related to time-of-flight and thus should be on the scale of nano-seconds, i.e. 10 −9 s, and 2(R B1 +R B2 ) contains radio response delays, which should be on the scale of milliseconds [49], i.e. 10 −3 s. Therefore, the difference between the spoofing distances ∆ρ BT − ∆ρ AT should be on the scale of 10 −15 s, which is equivalent to 10 −7 meters in distance.…”

A Generalized TDoA/ToA Model for ToF Positioning

“…The detailed and unified analysis and comparision of the errors of [4, 2, 1, 3, 5] can be found in our other publication [6].…”

“…Where μ X and μ Z designate the error with the calculation method ( 5) or (6). While μZ XY represents the erroneous µ value resulting with application of the combining transformation from (7).…”

“…We have conducted a detailed analysis of those methods in a different publication [6]. While this paper is independent and self contained we recommend the lecture of that other work as an overview of the state-of-the-art of ToF methods.…”