Multipath propagation represents a dominant error source limiting the accuracy of radio-based ranging and positioning in urban environments. Conventional ranging estimators typically estimate only the range of the first arriving path while neglecting the multipath components. This introduces a bias and causes the estimator's variance to diverge from the Cramér-Rao Bound (CRB). While extensive research has established performance bounds for estimators that jointly estimate all paths, the specific impact on the variance of ignoring these components remains largely unexplored. This paper derives bounds on the bias, variance, and mean square error (MSE) for ranging in multipath channels for the purpose of positioning. We consider Orthogonal Frequency Division Multiplexing (OFDM) signals in multipath channels with deterministic path delays and gains. The paper focuses on time-delay estimation (TDE) in the mid-to-high signal-to-noise ratio (SNR) regime under two scenarios: (i) when the receiver jointly estimates all propagation paths, and (ii) when the receiver underestimates the number of paths. Specifically, for the latter case, we derive a semi closed-form expression for the variance of the time-delay estimator that considers a single-path when in reality there are L paths. This derivation is based on the misspecified Cramér-Rao bound (MCRB). Although unmodelled multipath has been traditionally viewed as detrimental to time-delay estimation, we reveal that in some cases the estimation variance improves. For a two-path channel we show that the variance depends on the relative gain, carrier phase, and separation of the paths. Additionally, the estimation bias is upper-bounded by constructive and destructive path interference. Finally, we empirically process a six-path simulated channel frequency response with fixed path delays and gains, to demonstrate that the derived MSE bound is tight for mid-to-high SNRs. This work characterizes the impact of multipath propagation on the variance of time-delay estimation, which is essential for designing accurate ranging signals and estimators in urban scenarios.

Navigation with radio-signals using GNSS or a terrestrial positioning system in urban environments is susceptible to multipath propagation, which can severely degrade positioning accuracy. In a Line-of-Sight (LOS) multipath channel, the received signal is composed of a direct path component and a sum of time-shifted and attenuated replicas of the transmitted signal. When these multipath components are not accounted for in the time-delay estimation (TDE) model, they may introduce substantial estimation bias. For positioning, only the first arriving path is of interest. Therefore, it is crucial to focus on estimating the reflections that most significantly affect the TDE of this primary path, while ignoring others with negligible impact. To reduce the impact of close-in multipath in TDE, we propose Maximum Likelihood estimators that account for the strongest reflections, with models considering either one or two multi-path components. The Maximum Likelihood Estimation (MLE) problem is optimized using the Space Alternating Generalized Expectation-Maximization (SAGE) method. To reduce computational load, the delay search space for each path is constrained based on the maximum bias observed in the multipath error envelope (MPEE). To assess the ranging accuracy for the various MLE estimators that account for multiple paths, we utilize a synthetically generated channel based on the Saleh-Valenzuela model. Additionally, we benchmark the positioning performance of these estimators using channel impulse responses recorded with a terrestrial positioning prototype system tested at The Green Village on the TU Delft campus.

This paper presents a terrestrial networked positioning system that obtains a reliable time reference from a national time scale realization and distributes it in a prototype to six roadside base stations through a fiber-optic Gigabit Ethernet network. Wireless wideband signals are transmitted by the base stations, thereby enabling positioning by a mobile receiver with an accuracy of one decimeter in a multipath urban environment. The scalability and compatibility of this system with existing telecommunication-network technologies paves the way for wide-area global navigation satellite system-independent back-up systems for timing and positioning with improved coverage and performance. The results presented in this paper are based on research carried out within the scope of a project funded by the Dutch Research Council (NWO, project 13970).

Global navigation satellite systems (GNSS) are widely used for navigation and time distribution^1–3, features that are indispensable for critical infrastructure such as mobile communication networks, as well as emerging technologies such as automated driving and sustainable energy grids^3,4. Although GNSS can provide centimetre-level precision, GNSS receivers are prone to many-metre errors owing to multipath propagation and an obstructed view of the sky, which occur particularly in urban areas where accurate positioning is most needed^1,5,6. Moreover, the vulnerabilities of GNSS, combined with the lack of a back-up system, pose a severe risk to GNSS-dependent technologies⁷. Here we demonstrate a terrestrial positioning system that is independent of GNSS and offers superior performance through a constellation of radio transmitters, connected and time-synchronized at the subnanosecond level through a fibre-optic Ethernet network⁸. Using optical and wireless transmission schemes similar to those encountered in mobile communication networks, and exploiting spectrally efficient virtual wideband signals, the detrimental effects of multipath propagation are mitigated⁹, thus enabling robust decimetre-level positioning and subnanosecond timing in a multipath-prone outdoor environment. This work provides a glimpse of a future in which telecommunication networks provide not only connectivity but also GNSS-independent timing and positioning services with unprecedented accuracy and reliability.

In wireless networks, an essential step for precise range-based localization is the high-resolution estimation of multipath channel delays. The resolution of traditional delay estimation algorithms is inversely proportional to the bandwidth of the training signals used for channel probing. Considering that typical training signals have limited bandwidth, delay estimation using these algorithms often leads to poor localization performance. To mitigate these constraints, we exploit the multiband and carrier frequency switching capabilities of wireless transceivers and propose to acquire channel state information (CSI) in multiple bands spread over a large frequency aperture. The data model of the acquired measurements has a multiple shift-invariance structure, and we use this property to develop a high-resolution delay estimation algorithm. We derive the Cramér-Rao Bound (CRB) for the data model and perform numerical simulations of the algorithm using system parameters of the emerging IEEE 802.11be standard. Simulations show that the algorithm is asymptotically efficient and converges to the CRB. To validate modeling assumptions, we test the algorithm using channel measurements acquired in real indoor scenarios. From these results, it is seen that delays (ranges) estimated from multiband CSI with a total bandwidth of 320 MHz show an average RMSE of less than 0.3 ns (10 cm) in 90% of the cases.

For validation and demonstration of high accuracy ranging and positioning algorithms and systems, a wideband radio signal generation and acquisition testbed, tightly synchronized in time and frequency, is needed. The development of such a testbed requires solutions to several challenges. Tight time and frequency synchronization, derived from a centrally distributed time-frequency reference signal, needs to be maintained in the hardware of the transmitter and receiver nodes, and wideband signal acquisition requires sustainable data throughput between the receiver and host PC as well as data storage at GB level. This article presents a testbed for wideband radio signal acquisition, for validation and demonstration of high accuracy ranging and positioning. It consists of multiple Ettus X310 universal software radio peripherals (USRPs) and supports high accuracy (<100 ps) time-deterministic, sustainable signal transmission and acquisition, with a bandwidth up to 320 MHz (in dual channel mode) and frequencies up to 6 GHz. Generation and processing of wideband arbitrary signal waveforms is done offline. To realize these features, radio frequency on chip (RFNoC) compatible HDL units were developed for integration in the X310 SDR platform. Wideband transmission and signal acquisition at a lower duty cycle is applied to reduce the data offloading throughput to the host's personal computer (PC). Benchmarking of the platform was performed to demonstrate sustainable long duration dual channel acquisition. Indoor range measurements with the synchronous operation of the testbed show a decimeter-level accuracy.

Terrestrial positioning systems are being investigated as the complement to the global navigation satellite systems (GNSS), to provide precise and reliable positioning services in a GNSS-challenged environment. In this paper, we present the positioning performance of a ground-based positioning system, in which a multiband OFDM burst is used as a ranging signal to estimate carrier phase, and all transmitters are tightly synchronized by optically distributed time and frequency reference signals. The receiver, like in GNSS, runs on its own clock. An experiment has been carried out in an outdoor living lab environment to demonstrate the flexibility of precise positioning using carrier phase with the proposed ground-based system. During the experiment, the receiver was moved over a trajectory of 17 m forth and back, and acquired the ranging signal for 71 seconds. Without calibrating the different initial phase offsets among the transmitters, we keep the carrier phase cycle ambiguities as float numbers and compute the so called float position solutions. The root mean-squared error (RMSE) of the position solution in East and North direction are 4.22 cm and 4.63 cm, respectively, demonstrating the high-accuracy potential of the proposed burst oriented hybrid optical-wireless terrestrial positioning system.

This paper presents a methodology to design a sparse multiband ranging signal with a large virtual bandwidth, from which time delay and carrier phase are estimated by a low complexity multivariate maximum likelihood (ML) method. In the estimation model for a multipath channel, not all reflected paths are considered, and time delay and carrier phase are estimated in a step-wise manner to further reduce the computational load. By introducing a measure of dependence and a measure of bias for a multipath reflection, we analyse the bias, precision and accuracy of time delay and carrier phase estimation. Since these two indicators are determined by the signal spectrum pattern, they are used to formulate an optimization for signal design. By solving the optimization problem, only a few bands from the available signal spectrum are selected for ranging. Consequently, the designed signal only occupies a small amount of signal spectrum but has a large virtual bandwidth and can thereby still offer a high ranging precision with only a small bias, based on the low-complexity simplified ML method. Numerical and laboratory experiments are carried out to evaluate the ranging performance of the proposed estimation method based on sparsely selected signal bands. Relative positioning, in which we only measure a change in position, based on either the time delay estimates or the carrier phase estimates, is presented as a proof-of-concept for precise positioning. The results show that positioning based on only 7 out of 16 signal bands, sparsely placed in the available spectrum, achieves a decimeter level accuracy when using time delay estimates, and a millimeter level accuracy when using carrier phase estimates. Compared with the case of using all available bands, and without largely decreasing the positioning performance, the computational complexity when using the sparse multiband signal can be reduced by about 80%.

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.

In developing a high accuracy terrestrial radio navigation system, as a complement to a global navigation satellite system (GNSS), it is recognized that the performance of time delay estimation is proportional to, and thereby limited by, the signal bandwidth. Given a possibly narrow signal bandwidth, the central carrier phase can, alternatively, provide a better distance accuracy, though the central carrier phase cycle ambiguity should be resolved. In practice, the carrier phase may be perturbed by multipath. In this paper, considering an orthogonal frequency division multiplexing (OFDM) signal, we propose a two-step carrier phase estimation method to reduce the error introduced by multipath. First, the propagation delay of the LoS path is coarsely determined, then the carrier phase is estimated using the earlier determined coarse time delays. Furthermore, a positioning model only based on carrier phase estimates is presented in this paper. The proposed technique is evaluated by statistical analyses and a simulated OFDM-based terrestrial positioning system in different roadway multipath environments. The results show that the impact of multipath on carrier phase estimation can be largely mitigated, so that the carrier phase can be used for precise positioning. In addition, fixing the integer carrier phase cycle ambiguities can significantly reduce the time for the position solution to converge to high precision.

Achieving high resolution time-of-arrival (TOA) estimation in multipath propagation scenarios from bandlimited observations of communication signals is challenging because the multipath channel impulse response (CIR) is not bandlimited. Modeling the CIR as a sparse sequence of Diracs, TOA estimation becomes a problem of parametric spectral inference from observed bandlimited signals. To increase resolution without arriving at unrealistic sampling rates, we consider multiband sampling approach, and propose a practical multibranch receiver for the acquisition. The resulting data model exhibits multiple shift invariance structures, and we propose a corresponding multiresolution TOA estimation algorithm based on the ESPRIT algorithm. The performance of the algorithm is compared against the derived Cramér Rao Lower Bound, using simulations with standardized ultra-wideband (UWB) channel models. We show that the proposed approach provides high resolution estimates while reducing spectral occupancy and sampling costs compared to traditional UWB approaches.

Synchronization and ranging in internet of things (IoT) networks are challenging due to the narrowband nature of signals used for communication between IoT nodes. Recently, several estimators for range estimation using phase difference of arrival (PDoA) measurements of narrowband signals have been proposed. However, these estimators are based on data models which do not consider the impact of clock-skew on the range estimation. In this paper, clock-skew and range estimation are studied under a unified framework. We derive a novel and precise data model for PDoA measurements which incorporates the unknown clock-skew effects. We then formulate joint estimation of the clock-skew and range as a two-dimensional (2-D) frequency estimation problem of a single complex sinusoid. Furthermore, we propose: (i) a two-way communication protocol for collecting PDoA measurements and (ii) a weighted least squares (WLS) algorithm for joint estimation of clock-skew and range leveraging the shift invariance property of the measurement data. Finally, through numerical experiments, the performance of the proposed protocol and estimator is compared against the Cramér Rao lower bound demonstrating that the proposed estimator is asymptotically efficient.