Fusion of Active and Passive Measurements for Robust and Scalable Positioning

This paper addresses the challenge of achieving reliable and robust positioning of a mobile agent, such as a radio device carried by a person, in scenarios where direct line-of-sight (LOS) links are obstructed or unavailable. The human body is considered as an extended object that scatters, attenuates and blocks the radio signals. We propose a novel particle-based sum-product algorithm (SPA) that fuses active measurements between the agent and anchors with passive measurements from pairs of anchors reflected off the body. We first formulate radio signal models for both active and passive measurements. Then, a joint tracking algorithm that utilizes both active and passive measurements is developed for the extended object. The algorithm exploits the probabilistic data association (PDA) for multiple object-related measurements. The results demonstrate superior accuracy during and after the obstructed line-of-sight (OLOS) situation, outperforming conventional methods that solely rely on active measurements. The proposed joint estimation approach significantly enhances the localization robustness via radio sensing.

Graph-based Simultaneous Localization and Bias Tracking

We present a factor graph formulation and particle-based sum-product algorithm for robust localization and tracking in multipath-prone environments. The proposed sequential algorithm jointly estimates the mobile agent's position together with a time-varying number of multipath components (MPCs). The MPCs are represented by "delay biases" corresponding to the offset between line-of-sight (LOS) component delay and the respective delays of all detectable MPCs. The delay biases of the MPCs capture the geometric features of the propagation environment with respect to the mobile agent. Therefore, they can provide position-related information contained in the MPCs without explicitly building a map of the environment. We demonstrate that the position-related information enables the algorithm to provide high-accuracy position estimates even in fully obstructed line-of-sight (OLOS) situations. Using simulated and real measurements in different scenarios we demonstrate the proposed algorithm to significantly outperform state-of-the-art multipath-aided tracking algorithms and show that the performance of our algorithm constantly attains the posterior Cramer-Rao lower bound (P-CRLB). Furthermore, we demonstrate the implicit capability of the proposed method to identify unreliable measurements and, thus, to mitigate lost tracks.

A Neural-enhanced Factor Graph-based Algorithm for Robust Positioning in Obstructed LOS Situations

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 Cramer-Rao lower bound even with training data limited to local regions.

Multipath-based SLAM for Non-Ideal Reflective Surfaces Exploiting Multiple-Measurement Data Association

Multipath-based simultaneous localization and mapping (SLAM) is a promising approach to obtain position information of transmitters and receivers as well as information regarding the propagation environments in future mobile communication systems. Usually, specular reflections of the radio signals occurring at flat surfaces are modeled by virtual anchors (VAs) that are mirror images of the physical anchors (PAs). In existing methods for multipath-based SLAM, each VA is assumed to generate only a single measurement. However, due to imperfections of the measurement equipment such as non-calibrated antennas or model mismatch due to roughness of the reflective surfaces, there are potentially multiple multipath components (MPCs) that are associated to one single VA. In this paper, we introduce a Bayesian particle-based sum-product algorithm (SPA) for multipath-based SLAM that can cope with multiple-measurements being associated to a single VA. Furthermore, we introduce a novel statistical measurement model that is strongly related to the radio signal. It introduces additional dispersion parameters into the likelihood function to capture additional MPCs-related measurements. We demonstrate that the proposed SLAM method can robustly fuse multiple measurements per VA based on numerical simulations.

Data Fusion for Multipath-Based SLAM: Combing Information from Multiple Propagation Paths

Multipath-based simultaneous localization and mapping (SLAM) is an emerging paradigm for accurate indoor localization with limited resources. The goal of multipath-based SLAM is to detect and localize radio reflective surfaces to support the estimation of time-varying positions of mobile agents. Radio reflective surfaces are typically represented by so-called virtual anchors (VAs), which are mirror images of base stations at the surfaces. In existing multipath-based SLAM methods, a VA is introduced for each propagation path, even if the goal is to map the reflective surfaces. The fact that not every reflective surface but every propagation path is modeled by a VA, complicates a consistent combination "fusion" of statistical information across multiple paths and base stations and thus limits the accuracy and mapping speed of existing multipath-based SLAM methods. In this paper, we introduce an improved statistical model and estimation method that enables data fusion for multipath-based SLAM by representing each surface by a single master virtual anchor (MVA). We further develop a particle-based sum-product algorithm (SPA) that performs probabilistic data association to compute marginal posterior distributions of MVA and agent positions efficiently. A key aspect of the proposed estimation method based on MVAs is to check the availability of single-bounce and double-bounce propagation paths at a specific agent position by means of ray-launching. The availability check is directly integrated into the statistical model by providing detection probabilities for probabilistic data association. Our numerical simulation results demonstrate significant improvements in estimation accuracy and mapping speed compared to state-of-the-art multipath-based SLAM methods.

Data Fusion for Multipath-Based SLAM

Multipath-based simultaneous localization and mapping (SLAM) is an emerging paradigm for accurate indoor localization with limited resources. The goal of multipath-based SLAM is to detect and localize radio reflective surfaces to support the estimation of time-varying positions of mobile agents. Radio reflective surfaces are typically represented by so-called virtual anchors (VAs), which are mirror images of base stations at the surfaces. In existing multipath-based SLAM methods, a VA is introduced for each propagation path, even if the goal is to map the reflective surfaces. The fact that not every reflective surface but every propagation path is modeled by a VA, complicates a consistent combination "fusion" of statistical information across multiple paths and base stations and thus limits the accuracy and mapping speed of existing multipath-based SLAM methods. In this paper, we introduce an improved statistical model and estimation method that enables data fusion for multipath-based SLAM by representing each surface by a single master virtual anchor (MVA). We further develop a particle-based sum-product algorithm (SPA) that performs probabilistic data association to compute marginal posterior distributions of MVA and agent positions efficiently. A key aspect of the proposed estimation method based on MVAs is to check the availability of single-bounce and double-bounce propagation paths at a specific agent position by means of ray-launching. The availability check is directly integrated into the statistical model by providing detection probabilities for probabilistic data association. Our numerical simulation results demonstrate significant improvements in estimation accuracy and mapping speed compared to state-of-the-art multipath-based SLAM methods.

A Graph-based Algorithm for Robust Sequential Localization Exploiting Multipath for Obstructed-LOS-Bias Mitigation

This paper presents a factor graph formulation and particle-based sum-product algorithm (SPA) for robust sequential localization in multipath-prone environments. The proposed algorithm jointly performs data association, sequential estimation of a mobile agent position, and adapts all relevant model parameters. We derive a novel non-uniform false alarm (FA) model that captures the delay and amplitude statistics of the multipath radio channel. This model enables the algorithm to indirectly exploit position-related information contained in the MPCs for the estimation of the agent position. Using simulated and real measurements, we demonstrate that the algorithm can provide high-accuracy position estimates even in fully obstructed line-of-sight (OLOS) situations, significantly outperforming the conventional amplitude-information probabilistic data association (AIPDA) filter. We show that the performance of our algorithm constantly attains the posterior Cramer-Rao lower bound (PCRLB), or even succeeds it, due to the additional information contained in the presented FA model.

Graph-based Robust Sequential Localization in Obstructed LOS Situations

This paper presents a factor graph formulation and particle-based sum-product algorithm (SPA) for robust sequential localization in multipath-prone environments. The proposed algorithm jointly performs data association, sequential estimation of a mobile agent position, and adapts all relevant model parameters. We derive a novel non-uniform false alarm (FA) model that captures the delay and amplitude statistics of the multipath radio channel. This model enables the algorithm to indirectly exploit position-related information contained in the MPCs for the estimation of the agent position. Using simulated and real measurements, we demonstrate that the algorithm can provide high-accuracy position estimates even in fully obstructed line-of-sight (OLOS) situations, significantly outperforming the conventional amplitude-information probabilistic data association (AIPDA) filter. We show that the performance of our algorithm constantly attains the posterior Cramer-Rao lower bound (PCRLB), or even succeeds it, due to the additional information contained in the presented FA model.

Sequential Detection and Estimation of Multipath Channel Parameters Using Belief Propagation

This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath components (MPCs) parameters based on radio signals. Under dynamic channel conditions with moving transmitter and/or receiver, the number of MPCs reflected from visible geometric features, the MPC dispersion parameters (delay, angle, Doppler frequency, etc), and the number of false alarm contributions are unknown and time-varying. We develop a Bayesian model for sequential detection and estimation of MPC dispersion parameters, and represent it by a factor graph enabling the use of BP for efficient computation of the marginal posterior distributions. At each time instance, a snapshot-based channel estimator provides parameter estimates of a set of MPCs which are used as noisy measurements by the proposed BP-based algorithm. It performs joint probabilistic data association, estimation of the time-varying MPC parameters, and the mean number of false alarm measurements by means of the sum-product algorithm rules. The results using synthetic measurements show that the proposed algorithm is able to cope with a high number of false alarm measurements originating from the snapshot-based channel estimator and to sequentially detect and estimate MPCs parameters with very low signal-to-noise ratio (SNR). The performance of the proposed algorithm compares well to existing algorithms for high SNR MPCs, but significantly it outperforms them for medium or low SNR MPCs. In particular, we show that our algorithm outperforms the Kalman enhanced super resolution tracking (KEST) algorithm, a state-of-the-art sequential channel parameters estimation method. Furthermore, results with real radio measurements demonstrate the excellent performance of the algorithm in realistic and challenging scenarios.