Measurement‐based indoor NLoS ToA/RSS range error modelling

Abstract

The time of arrival (ToA) and received signal strength (RSS) estimation errors are modelled based on channel measurements in a non-line-of-sight indoor environment. It is found interesting that their errors are largely independent. Suboptimal hybrid ToA/RSS ranging estimators are derived in closed form based on the obtained error models, and shown to achieve near-optimal performance. The performance of all the estimators improves as the bandwidth increases.Introduction: State-of-the-art ranging systems exploit the time of arrival (ToA) or the received signal strength (RSS) of wireless signals [1]. Owing to the weak direct path and rich scattering, it is a challenging task to design and evaluate the performance of indoor ranging systems under non-line-of-sight (NLoS) scenarios. To the best of our knowledge, ToA and RSS error models have been studied separately [2, 3], but never jointly, through real-world measurement under NLoS scenarios.In this Letter, we study the ToA-and/or RSS-based ranging performance in a typical NLoS indoor environment, under the OFDM system assumption. Our main contributions are: (i) a channel measurement campaign, taking both the ToA-and the RSS-based ranging into account, was carried out in the indoor environment; (ii) the ToA and the RSS estimation errors are modelled into functions of the bandwidth based on the measurement; (iii) suboptimal hybrid ToA/RSS ranging estimators are derived in closed form and shown to achieve near-optimal performance, especially when the bandwidth is large.

Hybrid TOA/RSS Range-Based Localization with Self-Calibration in Asynchronous Wireless Networks

“…Therefore, such an information can be actually provided to the blind node by the i-th transmitting anchor. Although the TOA Model (3) neglects the presence of multipath and the drift of the clocks, it is widely-adopted in different WSN applications and several experiments have shown that it is a reasonable approximation in many cases [40][41][42]52,53].…”

“…It is worth noting that Equation 7represents the actual likelihood under the assumption that both RSS and TOA information are measured from independent sources. Indeed, the experimental campaigns conducted in [52,53] clearly show that measurements extracted from the same signal are weakly correlated; hence, assuming independence in Equation 7is not detrimental to generality. The hybrid TOA/RSS ML estimation problem can be written as:…”

“…The proposed hybrid estimator is computed using A = −1 and B = 37 as in [44], and it is compared against the most natural competitor algorithms based on Newton-Raphson iterations, given in [53] and in the following labeled as NR1 and NR2. The basic difference among the NR1 and NR2 methods consists in the number of Newton-Raphson iterations performed to compute the distance estimate.…”

“…As concerns the poor performance of the NR-based methods, it can be attributed to the fact that the hybrid TOA/RSS ranging problem is solved via a suboptimal approach based on Newton-Raphson iterations. More precisely, from the closed-form expressions of the estimators provided in [53], it can be noticed that the Newton-Raphson procedure is initialized with a coarse range estimate obtained using the sole TOA measurement; hence, it is reasonable to expect that the performance of both NR1 and NR2 approaches heavily depend on the accuracy of such data. Such theoretical considerations are in agreement with the performance of the NR1 method, whose performance curves are superimposed to the ones provided by the TOA-only estimator, hence are not visible in the figures, meaning that in the considered scenario one iteration of the Newton-Raphson method is indeed not sufficient to find a good approximate solution to the joint TOA/RSS ML problem.…”

Target Localization in NLOS Environments Using RSS and TOA Measurements

“…Hybrid algorithms based on received signal strength (RSS) and angle of arrival were studied in [1] and [2], but only localization in line-of-sight (LOS) conditions was considered. In [3]- [5] and [7], hybrid algorithms based on RSS and time of arrival (TOA) were presented. Zhang et al [3] and Coluccia and Fascista [4] studied the range estimation problem based on these two quantities, whereas the attention in [5] and [7] was on target localization problem.…”