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This paper presents a neural-enhanced probabilistic model and corresponding factor graph-based sum-product algorithm for robust localization and tracking in multipath-prone environments. The introduced hybrid probabilistic model consists of physics-based and data-driven measurement models capturing the information contained in both, the line-of-sight (LOS) component as well as in multipath components (NLOS components). The physics-based and data-driven models are embedded in a joint Bayesian framework allowing to derive from first principles a factor graph-based algorithm that fuses the information of these models. The proposed algorithm uses radio signal measurements from multiple base stations to robustly estimate the mobile agent's position together with all model parameters. It provides high localization accuracy by exploiting the position-related information of the LOS component via the physics-based model and robustness by exploiting the geometric imprint of multipath components independent of the propagation channel via the data-driven model. In a challenging numerical experiment involving obstructed LOS situations to all anchors, we show that the proposed sequential algorithm significantly outperforms state-of-the-art methods and attains the posterior Cramér-Rao lower bound even with training data limited to local regions.

The accuracy of radio-based positioning is heavily influenced by a dense multipath (DM) channel, leading to poor position accuracy. The DM affects both time of flight (ToF) measurements extracted from wideband (WB) signals—specifically, if the bandwidth is below 100 MHz—as well as received signal strength (RSS) measurements, due to the interference of multipath signal components onto the information-bearing line-of-sight (LoS) component. This work proposes an approach for combining these two different measurement technologies, leading to a robust position estimation in the presence of DM. We assume that a large ensemble of densely-spaced devices is to be positioned. We use RSS measurements to determine “clusters” of devices in the vicinity of each other. Joint processing of the WB measurements from all devices in a cluster efficiently suppresses the influence of the DM. We formulate an algorithmic approach for the information fusion of the two technologies and derive the corresponding Cramér-Rao lower bound (CRLB) to gain insight into the performance trade-offs at hand. We evaluate our results by simulations and validate the approach with real-world measurement data. The results show that the clustering approach can halve the root-mean-square error (RMSE) from about 2 m to below 1 m, using WB signal transmissions in the 2.4 GHz ISM band at a bandwidth of about 80 MHz.

In this paper, we propose a factor-graph-based cooperative positioning algorithm that uses RSS radio measurements and accounts for the directivity of the antennas. This is achieved by modeling the directivity with a parametric antenna pattern and jointly estimating position and orientation of the agents. We propose two different approaches whereas the first one uses a continuous representation of the orientation state and the second one a discrete representation. We validate our proposed methods with simulations and measurements in a static sensor network with more than 900 agents in an indoor environment and show that the positioning accuracy can be improved significantly by considering the influence of orientations.

High-accuracy indoor radio positioning can be achieved by using (ultra) wideband (UWB) radio signals. Multiple fixed anchor nodes are needed to compute the position or alternatively, specular multipath components (SMCs) extracted from radio signals can be exploited. In this work, we study a multipath-based, single-anchor positioning system that acquires directional measurements non-coherently. These non-coherent measurements can be obtained, e.g., from a single-chain mm-wave transceiver with analog beam steering or from a low-complexity ultra-wideband transceiver with switched directional antennas. The directional antennas support the separation of SMCs and the suppression of the undesired diffuse multipath component (DMC) with the benefit that the required signal bandwidth can be drastically reduced. The paper analyzes the Cramér-Rao lower bound (CRLB) on the position estimation error to gain insight in the influence of the system design parameters as well as the impact of the DMC on the position error. The CRLB is compared between the non-coherent antenna setup, a conventional array with coherent processing, and a single-antenna setup. A maximum-likelihood position estimation algorithm is formulated. Its performance is evaluated with synthetically generated data as well as with UWB measurements. We show that the accuracy and robustness are significantly improved due to the processing of angular information. Analyzing the measured data for a line-of-sight link, the median error decreases from 22 down to 7 cm, the measurements better than 20 cm increase from 46 to 95 %, and outliers above 50 cm reduce from 12 to 0%.

Ultra-Wide Bandwidth (UWB) and mm-wave radio systems can resolve specular multipath components (SMCs) from estimated channel impulse response measurements. A geometric model can describe the delays, angles-of-arrival, and angles-of-departure of these SMCs, allowing for a prediction of these channel features. For the modeling of the amplitudes of the SMCs, a data-driven approach has been proposed recently, using Gaussian Process Regression (GPR) to map and predict the SMC amplitudes. In this paper, the applicability of the proposed multipath-resolved, GPR-based channel model is analyzed by studying features of the propagation channel from a set of channel measurements. The features analyzed include the energy capture of the modeled SMCs, the number of resolvable SMCs, and the ranging information that could be extracted from the SMCs. The second contribution of the paper concerns the potential applicability of the channel model for a multipath-resolved, single-anchor positioning system. The predicted channel knowledge is used to evaluate the measurement likelihood function at candidate positions throughout the environment. It is shown that the environmental awareness created by the multipath-resolved, GPR-based channel model yields higher robustness against position estimation outliers.

The consideration of ultra-wideband (UWB) and mm-wave signals allows for a channel description decomposed into specular multipath components (SMCs) and dense/diffuse multipath. In this paper, the amplitude and phase of SMCs are studied. Gaussian Process regression (GPR) is used as a tool to analyze and predict the SMC amplitudes and phases based on a measured training data set. In this regard, the dependency of the amplitude (and phase) on the angle-of-arrival/angle-of-departure of a multipath component is analyzed, which accounts for the incident angle and incident position of the signal at a reflecting surface—and thus for the reflection characteristics of the building material—and for the antenna gain patterns. The GPR model describes the similarities between different data points. Based on its model parameters and the training data, the amplitudes of SMCs are predicted at receiver positions that have not been measured in the experiment. The method can be used to predict a UWB channel impulse response at an arbitrary position in the environment.

The accuracy of radio-based positioning systems will be limited by multipath interference in realistic application scenarios. This paper derives closed-form expressions for the Cramér⁻Rao lower bound (CRLB) on the achievable time-of-arrival (ToA) and angle-of-arrival (AoA) estimation-error variances, considering the presence of multipath radio channels, and extends these results to position estimation. The derivations are based on channel models comprising deterministic, specular multipath components as well as stochastic, diffuse/dense multipath. The derived CRLBs thus allow an evaluation of the influence of channel parameters, the geometric configuration of the environment, and system parameters such as signal bandwidth and array geometry. Our results quantify how the ToA and AoA accuracies decrease when the signal bandwidth is reduced, because more multipath will then interfere with the useful LoS component. Antenna arrays can (partly) compensate this performance loss, exploiting diversity among the multipath interference. For example, the AoA accuracy with a 16-element linear array at 1 MHz bandwidth is similar to a two-element array at 1 GHz , in the magnitude order of one degree. The ToA accuracy, on the other hand, still scales by a factor of 100 from the cm-regime to the m-regime because of the dominating influence of the signal bandwidth. The position error bound shows the relationship between the range and angle information under realistic indoor channel conditions and their different scaling behaviors as a function of the anchor⁻agent placement. Specular multipath components have a maximum detrimental influence near the walls. It is shown for an L-shaped room that a fairly even distribution of the position error bound can be achieved throughout the environment, using two anchors equipped with 2 × 2 -array antennas. The accuracy limit due to multipath increases from the 1⁻10-cm-range at 1 GHz bandwidth to the 0.5⁻1-m-range at 100 MHz .

The IEEE 802.15.4a standard for wireless sensor networks is designed for high-accuracy ranging using ultra-wideband (UWB) signals. It supports coherent and noncoherent (energy detector) receivers, thus the performance-complexity-tradeoff can be decided by the implementer. In this paper, the maximum operating range and the maximum allowed pathloss are analyzed for ranging and both receiver types, under FCC/CEPT regulations. The analysis is based on the receiver working points and a link budget calculation assuming a frees-pace pathloss model. It takes into consideration the parameters of the preamble, which influence the transmit power allowed by the regulators. The best performance is achieved with the code sequences having the longest pulse spacing. Coherent receivers can achieve a maximum operating range up to several thousand meters and energy detectors up to several hundred meters.