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.

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%.

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.

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.

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.

This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpolation, a sparse network with 8 stations and a dense network with 19 stations from continuously operating reference stations (CORS) of the Netherlands are selected as the reference. In addition, other 15 CORS stations are selected as users, which are divided into three blocks: 5 stations located approximately in the center of the networks, 5 stations on the edge of the networks and 5 stations outside the networks. The zenith tropospheric wet delays are estimated at the network and user stations through the ionosphere-free positioning model; meanwhile, the predicted wet delays at the user stations are generated by the Kriging interpolation in the use of the tropospheric estimations at the network. The root mean square errors (RMSE) are calculated by comparing the predicted wet delays and estimated wet delays at the same user station. The results show that RMSEs of the stations inside the network are at a sub-centimeter level with an average value of 0.74 cm in the sparse network and 0.69 cm in the dense network. The stations on edge and outside the network can also achieve 1-cm level accuracy, which overcomes the limitation that accurate interpolations can only be attained inside the network. This contribution also presents an insignificant improvement of the prediction accuracy from the sparse network to the dense network over 1-year’s data processing and a seasonal effect on the tropospheric wet delay predictions.