Simultaneous Source Separation, Synchronization, Localization and Mapping for 6G Systems

Multipath-based simultaneous localization and mapping (MP-SLAM) is a promising approach for future 6G networks to jointly estimate the positions of transmitters and receivers together with the propagation environment. In cooperative MP-SLAM, information collected by multiple mobile terminals (MTs) is fused to enhance accuracy and robustness. Existing methods, however, typically assume perfectly synchronized base stations (BSs) and orthogonal transmission sequences, rendering inter-BS interference at the MTs negligible. In this work, we relax these assumptions and address simultaneous source separation, synchronization, and mapping. A relevant example arises in modern 5G systems, where BSs employ muting patterns to mitigate interference, yet localization performance still degrades. We propose a novel BS-dependent data association and synchronization bias model, integrated into a joint Bayesian framework and inferred via the sum-product algorithm on a factor graph. The impact of joint synchronization and source separation is analyzed under various system configurations. Compared with state-of-the-art cooperative MP-SLAM assuming orthogonal and synchronized BSs, our statistical analysis shows no significant performance degradation. The proposed BS-dependent data association model constitutes a principled approach for classifying features by arbitrary properties, such as reflection order or feature type (scatterers versus walls).

Optimizing Sparse Antenna Arrays for Localization and Sensing using Vector Spherical Wave Functions

In increasing number of electronic devices implement wideband radio technologies for localization and sensing purposes, like ultra-wideband (UWB). Such radio technologies benefit from a large number of antennas, but space for antennas is often limited, especially in devices for mobile and IoT applications. A common challenge is therefore to optimize the placement and orientations of a small number of antenna elements inside a device, leading to the best localization performance. We propose a method for systematically approaching the optimization of such sparse arrays by means of Cram\'er-Rao lower bounds (CRLBs) and vector spherical wave functions (VSWFs). The VSWFs form the basis of a wideband signal model considering frequency, direction and polarization-dependent characteristics of the antenna array under test (AUT), together with mutual coupling and distortions from surrounding obstacles. We derive the CRLBs for localization parameters like delay and angle-of-arrival for this model under additive white Gaussian noise channel conditions, and formulate optimization problems for determining optimal antenna positions and orientations via minimization of the CRLBs. The proposed optimization procedure is demonstrated by means of an exemplary arrangement of three Crossed Exponentially Tapered Slot (XETS) antennas.

Multi-Sensor Fusion for Extended Object Tracking Exploiting Active and Passive Radio Signals

Reliable and robust positioning of radio devices remains a challenging task due to multipath propagation, hardware impairments, and interference from other radio transmitters. A frequently overlooked but critical factor is the agent itself, e.g., the user carrying the device, which potentially obstructs line-of-sight (LOS) links to the base stations (anchors). This paper addresses the problem of accurate positioning in scenarios where LOS links are partially blocked by the agent. The agent is modeled as an extended object (EO) that scatters, attenuates, and blocks radio signals. We propose a Bayesian method that fuses ``active'' measurements (between device and anchors) with ``passive'' multistatic radar-type measurements (between anchors, reflected by the EO). To handle measurement origin uncertainty, we introduce an multi-sensor and multiple-measurement probabilistic data association (PDA) algorithm that jointly fuses all EO-related measurements. Furthermore, we develop an EO model tailored to agents such as human users, accounting for multiple reflections scattered off the body surface, and propose a simplified variant for low-complexity implementation. Evaluation on both synthetic and real radio measurements demonstrates that the proposed algorithm outperforms conventional PDA methods based on point target assumptions, particularly during and after obstructed line-of-sight (OLOS) conditions.

Multi-Sensor Fusion of Active and Passive Measurements for Extended Object Tracking

This paper addresses the challenge of achieving robust and reliable positioning of a radio device carried by an agent, in scenarios where direct line-of-sight (LOS) radio links are obstructed by the agent. We propose a Bayesian estimation algorithm that integrates active measurements between the radio device and anchors with passive measurements in-between anchors reflecting off the agent. A geometry-based scattering measurement model is introduced for multi-sensor structures, and multiple object-related measurements are incorporated to formulate an extended object probabilistic data association (PDA) algorithm, where the agent that blocks, scatters and attenuates radio signals is modeled as an extended object (EO). The proposed approach significantly improves the accuracy during and after obstructed LOS conditions, outperforming the conventional PDA (which is based on the point-target-assumption) and methods relying solely on active measurements.

A Sigma Point-based Low Complexity Algorithm for Multipath-based SLAM in MIMO Systems

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 (BSs). Particlebased methods offer high flexibility and can approximate posterior probability density functions (PDFs) with complex shapes. However, they often require a large number of particles to counteract degeneracy in high-dimensional parameter spaces, leading to high runtimes. Conversely using too few particles leads to reduced estimation accuracy. In this paper, we propose a low-complexity algorithm for MP-SLAM in MIMO systems that employs sigma point (SP) approximations via the sum-product algorithm (SPA). Specifically, we use Gaussian approximations through SP-transformations, drastically reducing computational overhead without sacrificing accuracy. Nonlinearities are handled by SP updates, and moment matching approximates the Gaussian mixtures arising from probabilistic data association (PDA). Numerical results show that our method achieves considerably shorter runtimes than particle-based schemes, with comparable or even superior performance.

Variational Message Passing-based Multiobject Tracking for MIMO-Radars using Raw Sensor Signals

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 close-by 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 neighbour data association and a Kalman filter.

A Block-Sparse Bayesian Learning Algorithm with Dictionary Parameter Estimation for Multi-Sensor Data Fusion

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

Direct Multipath-Based SLAM

In future wireless networks, the availability of information on the position of mobile agents and the propagation environment can enable new services and increase the throughput and robustness of communications. Multipath-based simultaneous localization and mapping (SLAM) aims at estimating the position of agents and reflecting features in the environment by exploiting the relationship between the local geometry and multipath components (MPCs) in received radio signals. Existing multipath-based SLAM methods preprocess received radio signals using a channel estimator. The channel estimator lowers the data rate by extracting a set of dispersion parameters for each MPC. These parameters are then used as measurements for SLAM. Bayesian estimation for multipath-based SLAM is facilitated by the lower data rate. However, due to finite resolution capabilities limited by signal bandwidth, channel estimation is prone to errors and MPC parameters may be extracted incorrectly and lead to a reduced SLAM performance. We propose a multipath-based SLAM approach that directly uses received radio signals as inputs. A new statistical model that can effectively be represented by a factor graph is introduced. The factor graph is the starting point for the development of an efficient belief propagation (BP) method for multipath-based SLAM that avoids data preprocessing by a channel estimator. Numerical results based on synthetic and real data in challenging single-input, single-output (SISO) scenarios demonstrate that the proposed method outperforms conventional methods in terms of localization and mapping accuracy.

Variational Signal Separation for Automotive Radar Interference Mitigation

Algorithms for joint mutual interference mitigation and object parameter estimation are a key enabler for automotive applications of frequency-modulated continuous wave (FMCW) radar. The underlying signal model poses a challenge for signal separation, since both the coherent radar echo and the non-coherent interference influenced by individual multipath propagation channels must be considered. In particular, under certain assumptions, the model is described as a superposition of multipath channels weighted by parametric chirp envelopes in the case of interference. In this paper, we introduce a method inspired by sparse Bayesian learning (SBL) to detect and estimate radar object parameters while also estimating and successively canceling the interference signal. An augmented probabilistic model is employed that uses hierarchical Gamma-Gaussian prior model for each multipath channel separately. Based on this model an iterative inference algorithm is derived using the variational expectation-maximization (EM) methodology. The algorithm is statistically evaluated in terms of object parameter estimation accuracy and robustness, indicating that it is fundamentally capable of achieving the Cramer-Rao lower bound (CRLB) with respect to the accuracy of object estimates and it closely follows the radar performance achieved when no interference is present.

Multipath-based SLAM with Cooperation and Map Fusion

Multipath-based simultaneous localization and mapping (MP-SLAM) is a promising approach in wireless networks for obtaining position information of transmitters and receivers as well as information on the propagation environment. MP-SLAM models specular reflections of radio frequency (RF) signals at flat surfaces as virtual anchors (VAs), the mirror images of base stations (BSs). Conventional methods for MP-SLAM consider a single mobile terminal (MT) which has to be localized. The availability of additional MTs paves the way for utilizing additional information in the scenario. Specifically enabling MTs to exchange information allows for data fusion over different observations of VAs made by different MTs. Furthermore, cooperative localization becomes possible in addition to multipath-based localization. Utilizing this additional information enables more robust mapping and higher localization accuracy.