Sparse Signal Bands Selection for Precise Time-based Ranging in Terrestrial Positioning

Abstract

Time-based ranging accuracy is inversely proportional to the signal bandwidth. A larger the signal bandwidth leads to a higher accuracy of time delay estimation, but more complex hardware is needed. Alternatively, we explore the idea of using multiple narrow signal bands (e.g., 10 MHz of each) to create a large virtual signal bandwidth, which maintains the spectral efficiency but largely improves the ranging accuracy. Considering the impact of multipath, the propagation delay of the LoS path is computed from the estimated channel impulse response (CIR). In this paper, we propose an approach to sparsely select signal bands for ranging and positioning based on convex optimization. The Cramér-Rao lower bound (CRLB) for the propagation delay and gain estimators, as a performance criterion, is employed in the constraint of the optimization. The CRLB is derived in a two-path channel, so that the accuracy and the correlation between the LoS path and the reflection are taken into account. Experiments are conducted in a laboratory environment to illustrate the proposed signal design methodology dedicated for ranging with a sub-decimeter accuracy.

A USRP-Based Testbed for Wideband Ranging and Positioning Signal Acquisition

“…The platform has been tested and validated through indoor ToA ranging experiments in a corridor located at the TU Delft campus. More experimental results using this testbed can be found in [37] and [38]. In [37], a ranging system based on sparse selection of narrow signal bands is presented and validated using the testbed.…”

“…More experimental results using this testbed can be found in [37] and [38]. In [37], a ranging system based on sparse selection of narrow signal bands is presented and validated using the testbed. This work aims at increasing the bandwidth occupancy efficiency using a CRLB constrained convex optimization to select the frequency bands.…”

Design of Sparse Multiband Signal for Precise Positioning With Joint Low-Complexity Time Delay and Carrier Phase Estimation

“…Also, to derive the FIM for the propagation delay, the complex gain is assumed to be known a priori. In [33], the FIM for the propagation delay in a two path channel has been derived as follows,…”

“…6(a) shows the corresponding scaling factor sin −1 (ϑ) in the standard deviation of the LoS gain estimator, which is derived from (31). When the measure of dependence |s(τ 2,1 )| = 1, the LoS component a 1 and the reflection component a 2 will be fully dependent, and sin(ϑ) = 0 (see (33)), then the complex gain will be poorly estimated. Using a larger virtual signal bandwidth can reduce the measure of dependence for close-in reflections.…”

Terrestrial Precise Positioning System Using Carrier Phase from Burst Signals and Optically Distributed Time and Frequency Reference

“…OFDM has been adopted in various telecommunication systems which also have been exploited as signal-of-opportunities for positioning, such as in Wi-Fi [9], 4G/5G [10,11,12,13], and DVB-T [14]. As indicated in [15], only a few signal bands, sparsely located in the available signal spectrum, are needed to create a large virtual signal bandwidth to achieve a high ranging precision.…”