Indoor localization is of pivotal significance for a wide variety of services in the context of the Internet of Things (IoT). Both ranging-based and fingerprint-based localization techniques are promising for employment in harsh indoor environments. Hence, we propose a unified framework based on factor graphs for ubiquitous high-accuracy indoor localization. Our unified framework efficiently integrates ranging and fingerprinting for striking an appealing accuracy versus deployment cost tradeoff, where the crowdsourcing required for the construction of fingerprinting databases can also be addressed with little human intervention. By intrinsically amalgamating the global grid sampling and the regularized importance-resampling techniques, a nonparametric belief propagation algorithm is proposed for achieving the accurate position estimation at the cost of a moderate computational complexity. For improving the robustness to environmental variations, a likelihood-ratio-based approach is employed to detect ranging outliers. Moreover, a low-complexity serial scheduling scheme defined over factor graphs is designed for real-time localization. We design a hybrid ultrawide bandwidth and Wi-Fi localization system relying on off-the-shelf commercial devices and evaluate the proposed unified framework in a typical office building. Our experimental results show that the proposed algorithm outperforms the existing state-of-the-art methods and it is capable of achieving submeter localization accuracy.

Multi-carrier faster-than-Nyquist (MFTN) signaling constitutes a promising spectrally efficient non-orthogonal physical layer waveform. In this correspondence, we propose a pair of low-complexity generalized approximate message passing (GAMP)-based frequency-domain equalization (FDE) algorithms for MFTN systems operating in multipath channels. To mitigate the ill-condition of the resultant equivalent channel matrix, we construct block circulant interference matrices by inserting a few cyclic postfixes, followed by truncating the duration of the inherent two-dimensional interferences. Based on the decomposition of the block circulant matrices, we develop a novel frequency-domain received signal model using the two-dimensional fast Fourier transform for mitigating the colored noise imposed by the non-orthogonal matched filter. Moreover, we derive a GAMP-based FDE algorithm and its refined version, where the latter relies on approximations for circumventing the emergence of the ill-conditioned matrices. Our simulation results demonstrate that, for a fixed spectral efficiency, MFTN signaling can significantly improve the bit error rate (BER) performance by jointly optimizing the time- and frequency-domain packing factors. Compared to its Nyquist-signaling counterpart, our proposed MFTN systems employing the refined GAMP equalizer can achieve about 39% higher transmission rates at a negligible BER performance degradation.

Fingerprint-based indoor localization holds great potential for the Internet of Things. Despite numerous studies focusing on its algorithmic and practical aspects, a notable gap exists in theoretical performance analysis in this domain. This article aims to bridge this gap by deriving several lower bounds and approximations of mean square error (MSE) for fingerprint-based localization. These analyses offer different complexity and accuracy tradeoffs. We derive the equivalent Fisher information matrix and its decomposed form based on a wireless propagation model, thus obtaining the Cramér–Rao bound (CRB). By approximating the Fisher information provided by constraint knowledge, we develop a constraint-aware CRB. To more accurately characterize nonlinear transformation and constraint information, we introduce the Ziv-Zakai bound (ZZB) and modify it for adapt deterministic parameters. The Gauss–Legendre quadrature method and the trust-region reflective algorithm are employed to make the calculation of ZZB tractable. We introduce a tighter extrapolated ZZB by fitting the quadrature function outside the well-defined domain based on the $Q$ -function. For the constrained maximum likelihood estimator, an approximate MSE (AMSE) expression, which can characterize map constraints, is also developed. The simulation and experimental results validate the effectiveness of the proposed bounds and AMSE.

A low-complexity parametric bilinear generalized approximate message passing (PBiGAMP)-based receiver is conceived for multi-carrier faster-than-Nyquist (MFTN) signaling over frequency-selective fading channels. To mitigate the inherent ill-conditioning problem of MFTN signaling, we construct a segment-based frequency-domain received signal model in the form of a block circulant linear transition matrix, which can be efficiently calculated by applying a two dimensional fast Fourier transform. Based on the eigenvalue decomposition of the block circulant matrices, we can diagonalize the covariance matrix of the complex-valued colored noise process imposed by the associated two dimensional non-orthogonal matched filtering. Building on this model, a PBiGAMP-based parametric joint channel estimation and equalization (JCEE) algorithm is proposed for MFTN systems. In this algorithm, we introduce a pair of additive terms for characterizing the interferences arising from adjacent segments and employ the exact discrete a priori probabilities of the transmitted symbols for improving the bit error rate (BER) performance. To further enhance the system’s robustness in the presence of ill-conditioned matrices, we develop a refined PBiGAMP-based JCEE algorithm by introducing a series of scaled identity matrices. Moreover, the proposed PBiGAMP-based JCEE algorithms may be readily decomposed into GAMP-based equalization algorithms, when the channel state information is perfectly known. The overall complexity of the proposed algorithms only increases logarithmically with the total number of transmitted symbols. Our simulation results demonstrate the benefits of the proposed PBiGAMP-based iterative message passing receiver conceived for MFTN signaling.

Belief propagation (BP) is a popular message passing algorithm for distributed cooperative localization. However, due to the nonlinearity of measurement functions, BP implementation has no closed-form expression and requires message approximations. While nonparametric BP can be used, it suffers from a high computational complexity, thus being impractical in energy-constrained networks. In this paper, a parametric Bayesian method with Gaussian BP implementation is proposed for distributed cooperative localization. With linearization of the Euclidean norm in ranging measurements, the joint posterior distribution of agents’ locations is successively approximated with a sequence of high-dimensional Gaussian distributions. At each iteration of the successive Gaussian approximation, vector-valued Gaussian BP is further adopted to compute the marginal distributions of agents’ locations in a distributed way. It is proved by the principle of majorization-minimization that the proposed successive Gaussian approximation is guaranteed to converge, and the sequence of the estimated agents’ locations converges to a stationary point of the objective function of the maximum a posteriori estimation. Furthermore, although cooperative localization involves loopy network topologies, in which convergence property of Gaussian BP is generally unknown, it is proved in this paper that vector-valued Gaussian BP converges, making the proposed parametric BP-based method being the first one achieving convergence guarantee. Compared to the nonparametric BP counterpart, the proposed method has a much lower computational complexity and communication overhead. Simulation results demonstrate that the proposed method achieves a superior performance in localization accuracy compared to existing cooperative localization methods.

Message passing algorithms on graphical models offer a low-complexity and distributed paradigm for performing marginalization from a high-dimensional distribution. However, the convergence behaviors of message passing algorithms can be heavily affected by the adopted message update schedule. In this paper, we focus on the variational message passing (VMP) applied to Gaussian graphical models and its convergence under different schedules is analyzed. In particular, based on the update equations of VMP under the mean-field assumption, we prove that the mean vectors obtained from VMP are the exact marginal mean vectors under any valid message passing schedule, giving the legitimacy of using VMP in Gaussian graphical models. Furthermore, three categories of valid message passing schedules, namely serial schedule, parallel schedule and randomized schedule are considered for VMP update. In the basic serial schedule, VMP unconditionally converges, but could be slow in large-scale distributed networks. To speed up the serial schedule, a group serial schedule is proposed while guaranteeing the VMP convergence. On the other hand, parallel schedule and its damped variant are applied to accelerate VMP, where the necessary and sufficient convergence conditions are derived. To allow nodes with different local computation resources to compute messages more flexibly and efficiently, a randomized schedule is proposed for VMP update, and the probabilistic necessary and sufficient convergence conditions are presented. Finally, numerical results and applications are presented to illustrate the trade-offs in the ease and speed of convergence.