Localizing users and mapping the environment using radio signals is a key task in emerging applications such as reliable low-latency communications, location-aware security, and safety-critical navigation. Recently introduced multipath-based simultaneous localization and mapping (SLAM) methods can jointly localize a mobile agent and map reflective surfaces in radio frequency (RF) environments. Most existing approaches assume that map features and their corresponding RF propagation paths are statistically independent, conditioned on the state of the mobile agent. This assumption neglects inherent dependencies that arise when a single reflective surface contributes to multiple propagation paths or when an agent communicates with multiple base stations. Existing approaches that aim to fuse information across propagation paths are further limited by their inability to perform ray tracing in RF environments with nonconvex geometries. In this paper, we propose a Bayesian multipath-based SLAM method for distributed multiple-input-multiple-output (MIMO) systems that addresses these limitations. In particular, we exploit amplitude statistics to establish adaptive, time-varying detection probabilities. Based on the resulting “soft” ray-tracing strategy, the proposed method can fuse information across propagation paths in RF environments with nonconvex geometries. A Bayesian estimation framework for the joint estimation of map features and agent state is developed by applying the message passing rules of the sum-product algorithm (SPA) to a factor graph representation of the proposed statistical model. We further introduce a new initialization procedure for reflective surfaces that enables the introduction of new surface states even when measurements arise solely from double-bounce paths. The proposed method is validated using both synthetic and real RF measurements obtained in challenging scenarios with nonconvex geometries and obstructed line-of-sight conditions. The results demonstrate that it provides accurate localization and mapping performance and approaches the posterior Cramér–Rao lower bound.

Multipath-based simultaneous localization and mapping (MP-SLAM) is a promising approach in wireless networks to jointly obtain position information of transmitters/receivers and information of the propagation environment. MP-SLAM models specular reflections at flat surfaces as virtual anchors (VAs), which are mirror images of base stations. Particle-based methods offer high flexibility and can approximate posterior probability density functions of the mobile agent state and the map feature states, (i.e., VA states) with complex shapes. However, they often require a large number of particles to counteract degeneracy in high-dimensional parameter spaces, leading to high computational complexity. Conversely using an insufficient number of particles leads to reduced estimation accuracy. In this paper, we introduce a low-complexity MP-SLAM algorithm using a sigma point (SP)-based implementation of the sum-product algorithm (SPA). We model the messages of continuous states of the agent and the VAs as Gaussian distributions and approximate nonlinearities via SP-transformations. This approach substantially reduces the computational complexity without decreasing accuracy. Since probabilistic data association yields Gaussian mixtures for the agent and VA states, we use moment matching to combine each mixture into a single Gaussian. Numerical results using synthetic and real data demonstrate that our method achieves significantly reduced computational runtimes compared to particle-based schemes, while exhibiting comparable (or even superior) localization and mapping performance.

We propose an sparse Bayesian learning (SBL)based method that leverages group sparsity and multiple parameterized dictionaries to detect the relevant dictionary entries and estimate their continuous parameters by combining data from multiple independent sensors. In a MIMO multi-radar setup, we demonstrate its effectiveness in jointly detecting and localizing multiple objects, while also emphasizing its broader applicability to various signal processing tasks. A key benefit of the proposed SBL-based method is its ability to resolve correlated dictionary entries-such as closely spaced objects-resulting in uncorrelated estimates that improve subsequent estimation stages. Through numerical simulations, we show that our method outperforms the newtonized orthogonal matching pursuit (NOMP) algorithm when two objects cross paths using a single radar. Furthermore, we illustrate how fusing measurements from multiple independent radars leads to enhanced detection and localization performance.

In this paper, we propose a direct multiobject tracking (MOT) approach for MIMO-radar signals that operates on raw sensor data via variational message passing (VMP). Unlike classical track-before-detect (TBD) methods, which often rely on simplified likelihood models and exclude nuisance parameters (e.g., object amplitudes, noise variance), our method adopts a superimposed signal model and employs a mean-field approximation to jointly estimate both object existence and object states. By considering correlations within in the radar signal due to closely spaced objects and jointly estimating nuisance parameters, the proposed method achieves robust performance for closeby objects and in low-signal-to-noise ratio (SNR) regimes. Our numerical evaluation based on MIMO-radar signals demonstrate that our VMP-based direct-MOT method outperforms a detect-then-track (DTT) pipeline comprising a super-resolution sparse Bayesian learning (SBL)-based estimation stage followed by classical MOT using global nearest neighbor data association and a Kalman filter.

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are relaxed. We derive sufficient conditions that lead, on the one hand, to f inite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and reduce to the pruning condition of fast SBL (F-SBL). Thereby, our results offer a novel insight into the fundamental internal features that lead to the pruning mechanism of F-SBL.

Multipath-based simultaneous localization and mapping (MP-SLAM) is a well established approach to obtain position information of transmitters and receivers as well as information regarding the propagation environments in future multiple input multiple output (MIMO) communication systems. Conventional methods for MP-SLAM consider specular reflections of the radio signals occurring at smooth, flat surfaces, which are modeled by virtual anchors (VAs) that are mirror images of the physical anchors (PAs), with each VA generating a single multipath component (MPC). However, non-ideal reflective surfaces (such as walls covered by shelves or cupboards) cause dispersion effects that violate the VA model and lead to multiple MPCs that are associated to a single VA. In this paper, we introduce a Bayesian particle-based sum-product algorithm (SPA) for MP-SLAM in MIMO communications systems. Our method considers non-ideal reflective surfaces by jointly estimating the parameters of individual dispersion models for each detected surface in delay and angle domain leveraging multiple-measurement-to-feature data association. We demonstrate that the proposed SLAM method can robustly and jointly estimate the positions and dispersion extents of ideal and non-ideal reflective surfaces using numerical simulation.

In this paper, we present an iterative algorithm that detects and estimates the specular components (SCs) and estimates the dense component (DC) of single-input—multiple-output (SIMO) ultra-wide-band (UWB) multipath channels. Specifically, the algorithm super-resolves the SCs in the delay–angle-of-arrival domain and estimates the parameters of a parametric model of the delay-angle power spectrum characterizing the DC. Channel noise is also estimated. In essence, the algorithm solves the problem of estimating spectral lines (the SCs) in colored noise (generated by the DC and channel noise). Its design is inspired by the sparse Bayesian learning (SBL) framework. As a result the iteration process contains a threshold condition that determines whether a candidate SC shall be retained or pruned. By relying to results from extreme-value analysis the threshold of this condition is suitably adapted to ensure a prescribed probability of detecting spurious SCs. Studies using synthetic and real channel measurement data demonstrate the virtues of the algorithm: it is able to still detect and accurately estimate SCs, even when their separation in delay and angle is down to half the Rayleigh resolution limit (RRL) of the equipment; it is robust in the sense that it tends to return no more SCs than the actual ones. Finally, the algorithm is demonstrated to outperform a state-of-the-art super-resolution channel estimator in terms of robustness in the estimation of the amplitudes of specular components closely spaced in the dispersion domain.

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 that the proposed algorithm significantly outperforms state-of-the-art multipath-aided tracking algorithms and show that the performance of our algorithm constantly attains the posterior Cramér-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.

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 multipath components (MPCs) for the estimation of the agent position without using any prior information such as floorplan information or training data. Using simulated and real measurements in different channel conditions, we demonstrate that the algorithm can provide high-accuracy position estimates even in fully obstructed line-of-sight (OLOS) situations and show that the performance of our algorithm constantly attains the posterior Cramér-Rao lower bound (P-CRLB), facilitating the additional information contained in the presented FA model. The algorithm is shown to provide robust estimates in both, dense multipath channels as well as channels showing specular, resolved MPCs, significantly outperforming state-of-the-art radio-based localization methods.

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.

Multiple-Input Multiple-Output (MIMO) systems are essential for wireless communications. Since classical algorithms for symbol detection in MIMO setups require large computational resources or provide poor results, data-driven algorithms are becoming more popular. Most of the proposed algorithms, however, introduce approximations leading to degraded performance for realistic MIMO systems. In this paper, we introduce a neural-enhanced hybrid model, augmenting the analytic backbone algorithm with state-of-the-art neural network components. In particular, we introduce a self-attention model for the enhancement of the iterative Orthogonal Approximate Message Passing (OAMP)-based decoding algorithm. In our experiments, we show that the proposed model can outperform existing data-driven approaches for OAMP while having improved generalization to other SNR values at limited computational overhead.

We present a variational message passing (VMP)-based approach to detect the presence of a person based on their respiratory chest motion using multistatic ultra-wideband (UWB) radar. In the process, the respiratory motion is estimated for contact-free vital sign monitoring. The received signal is modeled as a backscatter channel and the respiratory motion and propagation channels are estimated using VMP. We use the evidence lower bound (ELBO) to approximate the model evidence for the detection. Numerical analyses and measurements demonstrate that the proposed method leads to a significant improvement in the detection performance compared to a fast Fourier transform (FFT)-based detector or an estimator-correlator in low-signal-to-noise ratio (SNR) conditions, since the multipath components (MPCs) are better incorporated into the detection procedure. Specifically, the proposed method has a detection probability of 0.95 at −20dB SNR, while the estimator-correlator and FFT-based detector have 0.32 and 0.05, respectively.

Cooperative localization is an enabling technology for the IoT that will introduce innovative services for modern convenience and public safety. Particle-based belief propagation (BP) is a state-of-the-art method for cooperative localization. However, in large and dense cooperative localization networks, particle-based BP suffers from particle degeneracy. In this paper, we propose a new method that combines particle-based BP and particle flow (PF) and can avoid this detrimental effect. To perform operations on the graph effectively, particles are moved towards regions of high likelihood based on the solution of a partial differential equation. We show that the proposed PF-BP algorithm can significantly outperform conventional particle-based BP in accuracy and runtime.

This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath component (MPC) parameters based on radio signals. Under dynamic channel conditions with moving transmitter/receiver, the number of MPCs, the MPC dispersion parameters, 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 step, a snapshot-based parametric 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, and estimation of the time-varying MPC parameters and the mean number of false alarm measurements, by means of the sum-product algorithm rules. The algorithm also exploits amplitude information enabling the reliable detection of “weak” MPCs with very low component signal-to-noise ratios (SNRs). The performance of the proposed algorithm compares well to state-of-the-art algorithms for high SNR MPCs, but it significantly outperforms them for medium or low SNR MPCs. Results using real radio measurements demonstrate the excellent performance of the proposed algorithm in realistic and challenging scenarios.

This paper proposes a channel model for ultra-wideband (UWB) off-body radio signals considering the human body in close proximity to a radio transceiver as an extended object (EO). The EO representing the human body adds scattered signal paths to the multipath components commonly encountered in indoor environments and accounts for attenuation of specular components by the human body. The purpose of this work is to describe the impact of such multipath effects, in order to develop robust algorithms for ranging and positioning in these environments. For a qualitative validation, we compare synthetically generated channel realizations based on our proposed off-body channel model with off-body measurements acquired in an indoor environment. To evaluate the human body effects on UWB range estimation, we compare the results obtained with a maximum likelihood (ML) multipath parameter estimator applied to channel measurements with synthetically generated channel realization, showing good correspondence.

We propose an improvement over a modulus zero-forcing (MZF) detector proposed earlier in [1] for multi-input multi-output (MIMO) detection, namely, the joint MZF (JMZF) detector. The MZF detector provides better detection-performance than a traditional ZF detector through preserving controllable interferences, which are mitigated later by nonlinear modulus arithmetic operation. However, the MZF detector has a constraint that the effective MIMO channel after modulus operation is diagonal, which yields separate detections on different transmit layers and is suboptimal. In this paper, we propose the JMZF detector by considering a general effective channel which can further boost the detection-performance.

We present a simultaneous localization and mapping (SLAM) algorithm that is based on radio signals and the association of specular multipath components (MPCs) with geometric features. Especially in indoor scenarios, robust localization from radio signals is challenging due to diffuse multipath propagation, unknown MPC-feature association, and limited visibility of features. In our approach, specular reflections at flat surfaces are described in terms of virtual anchors (VAs) that are mirror images of the physical anchors (PAs). The positions of these VAs and possibly also of the PAs are unknown. We develop a Bayesian model of the SLAM problem and represent it by a factor graph, which enables the use of belief propagation (BP) for efficient marginalization of the joint posterior distribution. The resulting BP-based SLAM algorithm detects the VAs associated with the PAs and estimates jointly the time-varying position of the mobile agent and the positions of the VAs and possibly also of the PAs, thereby leveraging the MPCs in the radio signal for improved accuracy and robustness of agent localization. The algorithm has a low computational complexity and scales well in all relevant system parameters. Experimental results using both synthetic measurements and real ultra-wideband radio signals demonstrate the excellent performance of the algorithm in challenging indoor environments.

In this paper, we present a robust multipath-based localization and mapping framework that exploits the phases of specular multipath components (MPCs) using a massive multiple-input multiple-output (MIMO) array at the base station. Utilizing the phase information related to the propagation distances of the MPCs enables the possibility of localization with extraordinary accuracy even with limited bandwidth. The specular MPC parameters along with the parameters of the noise and the dense multipath component (DMC) are tracked using an extended Kalman filter (EKF), which enables to preserve the distance-related phase changes of the MPC complex amplitudes. The DMC comprises all non-resolvable MPCs, which occur due to finite measurement aperture. The estimation of the DMC parameters enhances the estimation quality of the specular MPCs and, therefore, also the quality of localization and mapping. The estimated MPC propagation distances are subsequently used as input to a distance-based localization and mapping algorithm. This algorithm does not need prior knowledge about the surrounding environment and base station position. The performance is demonstrated with real radio-channel measurements using an antenna array with 128 ports at the base station side and a standard cellular signal bandwidth of 40MHz. The results show that the high accuracy localization is possible even with such a low bandwidth.

Highly accurate location information is a key facilitator to stimulate future services for the commercial and public sectors. Positioning and tracking of absolute positions of wireless nodes usually requires information provided from technical infrastructure, e.g., satellites or fixed anchor nodes, whose maintenance is costly and whose limited operating coverage narrows the positioning service. In this paper, we present an algorithm aimed at the tracking of absolute positions without using information from fixed anchors, odometers, or inertial measurement units. We perform radio channel measurements, in order to exploit position-related information contained in multipath components (MPCs). Tracking of the absolute node positions is enabled by the estimation of MPC parameters followed by the association of these parameters to a floorplan. To account for uncertainties in the floorplan and for propagation effects like diffraction and penetration, we recursively update the provided floorplan using the measured MPC parameters. We demonstrate the ability to localize two agent nodes without the employment of further infrastructure, using data from ultra-wideband channel measurements. Furthermore, we show the potential performance gain if also one fixed anchor is available, and we validate the algorithm for a range of different signal bandwidths and a number of nodes.

This paper provides an initial investigation on the application of convolutional neural networks (CNNs) for fingerprint-based positioning using measured massive MIMO channels. When represented in appropriate domains, massive MIMO channels have a sparse structure which can be efficiently learned by CNNs for positioning purposes. We evaluate the positioning accuracy of state-of-the-art CNNs with channel fingerprints generated from a channel model with a rich clustered structure: the COST 2100 channel model. We find that moderately deep CNNs can achieve fractional-wavelength positioning accuracies, provided that an enough representative data set is available for training.

Location awareness is a key factor for a wealth of wireless indoor applications. Its provision requires the careful fusion of diverse information sources. For agents that use radio signals for localization, this information may either come from signal transmissions with respect to fixed anchors, from cooperative transmissions between agents, or from radar-like monostatic transmissions. Using a priori knowledge of a floor plan of the environment, specular multipath components can be exploited, based on a geometric-stochastic channel model. In this paper, a unified framework is presented for the quantification of this type of position-related information, using the concept of equivalent Fisher information. We derive analytical results for the Cramér-Rao lower bound of multipath-assisted positioning, considering bistatic transmissions between agents and fixed anchors, monostatic transmissions from agents, cooperative measurements between agents, and combinations thereof, including the effect of clock offsets. Awareness of this information enables highly accurate and robust indoor positioning. Computational results show the applicability of the framework for the characterization of the localization capabilities of a given environment, quantifying the influence of different system setups, signal parameters, and the impact of path overlap.

Sub-band divided ray tracing (RT) has been widely used to reproduce as reliably as possible the ultra-wideband (UWB) radio wave propagation channel in realistic indoor environments. However, its accuracy is strictly limited by the available description of the environment. Moreover, its computational complexity scales with the number of selected subbands and the number of propagation paths. In the present work, our RT tool considers not only deterministic propagation paths but also diffuse scattering components. Based on a low-complexity sub-band divided RT implementation, we propose a calibration method for indoor UWB sub-band divided RT. The method estimates the optimal material parameters, including the dielectric parameters and the scattering parameters, using channel measurements and multiobjective simulated annealing (MOSA). This calibration can improve the accuracy of sub-band divided RT in terms of the power delay profile (PDP) and the root mean square (RMS) delay spread for all test locations including those not considered by the calibration. A measurement campaign is used to verify the calibration technique.

Ray tracing has been extensively used to simulate indoor channel characteristics. For an ultra-wideband system, the channel characteristics vary significantly over the entire bandwidth. To cope with this, sub-band divided RT has been proposed by dividing the frequency of interest into multiple subbands and superposing the RT results at the individual center frequency of each subband. Thus, the computational complexity is directly proportional to the number of subbands. In this paper, we propose a mathematical method to significantly reduce the computational complexity of the sub-band divided RT, making it almost independent of the number of subbands. It is important to note that, based on our approach, not only the determination of the rays reaching a give location is made only once, but also the electromagnetic calculation of the received signal is not needed to perform repeatedly. The accuracy of low-complexity subband divided RT algorithm is verified through a measurement campaign.