Clock and Power-Induced Bias Correction for UWB Time-of-Flight Measurements

Abstract

Ultra-Wide Band (UWB) communication systems can be used to design low cost, power efficient and precise navigation systems for mobile robots, by measuring the Time of Flight (ToF) of messages traveling between on-board UWB transceivers to infer their locations. Theoretically, decimeter level positioning accuracy or better should be achievable, at least in benign propagation environments where Line-of-Sight (LoS) between the transceivers can be maintained. Yet, in practice, even in such favorable conditions, one often observes significant systematic errors (bias) in the ToF measurements, depending for example on the hardware configuration and relative poses between robots. This letter proposes a ToF error model that includes a standard transceiver clock offset term and an additional term that varies with the received signal power (RxP). We show experimentally that, after fine correction of the clock offset term using clock skew measurements available on modern UWB hardware, much of the remaining pose dependent error in LoS measurements can be captured by the (appropriately defined) RxP-dependent term. This leads us to propose a simple bias compensation scheme that only requires on-board measurements (clock skew and RxP) to remove most of the observed bias in LoS ToF measurements and reliably achieve cm-level ranging accuracy. Because the calibrated ToF bias model does not depend on any extrinsic information such as receiver distances or poses, it can be applied before any additional error correction scheme that requires more information about the robots and their environment.

Calibration and Uncertainty Characterization for Ultra-Wideband Two-Way-Ranging Measurements

“…Nonetheless, even after correcting for clock offsets, UWB range measurements typically suffer from a systematic error or bias. A significant contributor to this error is the skew between the clocks of the two ranging tags, as the different tags measure the passage of time in different units [9,10]. This additional bias can be corrected by estimating the clock skew between the tags and embedding a skew-dependent correction factor when computing the range measurement, as proposed in [9].…”

“…A significant contributor to this error is the skew between the clocks of the two ranging tags, as the different tags measure the passage of time in different units [9,10]. This additional bias can be corrected by estimating the clock skew between the tags and embedding a skew-dependent correction factor when computing the range measurement, as proposed in [9]. However, this necessitates estimating the clock skew between all tags involved in ranging.…”

“…Additionally, the learnt models are trained and tested on the same anchor formations and are therefore not necessarily generalizable; calibration must occur for every new anchor formation. In [9], the former issue is addressed by finding a relation between the bias and the received first-path power (FPP) in line-of-sight (LOS) conditions with 2D motion.…”

“…However, the lack of motion introduces a risk of learning the aforementioned relativepose-dependent bias as antenna delays. In [9], experiments involving a pair of tags at a time ranging with each other is used to fit what is referred to as a "pair-dependent constant". Therefore, the calibration procedure involves calibrating the relative delay between one pair at a time, which does not scale well to systems with many UWB tags.…”

“…• A scalable antenna-delay calibration algorithm is presented that is robust to outliers and pose-dependent bias. • The bias-versus-FPP fit presented in [9] is extended to also address the uncertainty of the measurements as a function of FPP, and DS-TWR is utilized to overcome the need to estimate the clock skew. • The proposed antenna-delay and bias-FPP calibration are evaluated on an aerial experiment with no anchors, where all the tags are fitted to moving robots.…”