Magnetic fields have attracted considerable attention in indoor localization due to their ubiquitous and infrastructure-free characteristics. This survey provides a comprehensive review of magnetic-field-based indoor localization methods. We first introduce characteristics of the magnetic field, its advantages, and its challenges. We then describe the magnetometer model and the effect of ferromagnetic interference. We also present coordinate systems commonly used for magnetic field localization and describe their transformation relationships. We then compare the existing publicly available magnetic field benchmark datasets, present magnetometer calibration algorithms, and show how efficiently magnetic field maps can be built. We also summarize state-of-the-art magnetic field localization methods (e.g., magnetic landmarks, dynamic time warping, magnetic fingerprinting, filters, simultaneous localization and mapping, and neural network). The smartphone-based pedestrian dead reckoning approach is also reviewed.

Tensor decomposition has been demonstrated to be successful in a wide range of applications, from neuroscience and wireless communications to social networks. In an online setting, factorizing tensors derived from multidimensional data streams is however nontrivial due to several inherent problems of real-time stream processing. In recent years, many research efforts have been dedicated to developing online techniques for decomposing such tensors, resulting in significant advances in streaming tensor decomposition or tensor tracking. This topic is emerging and enriches the literature on tensor decomposition, particularly from the data stream analystics perspective. Thus, it is imperative to carry out an overview of tensor tracking to help researchers and practitioners understand its developments and achievements, summarise the current trends and advances, and identify challenging problems. In this article, we provide a contemporary and comprehensive survey on different types of tensor tracking techniques. We particularly categorize the state-of-the-art methods into three main groups: streaming CP decompositions, streaming Tucker decompositions, and streaming decompositions under other tensor formats (i.e., tensor-train, t-SVD, and BTD). In each group, we further divide the existing algorithms into sub-categories based on their main optimization framework and model architectures. Finally, we present several applications, research challenges, open problems, and potential directions of tensor tracking in the future.

Infrastructure-free magnetic fields are ubiquitous and have attracted tremendous interest in magnetic field-based indoor positioning. However, magnetic field-based indoor positioning applications face challenges such as low discernibility, heterogeneous devices, and interference from ferromagnetic materials. This paper first analyzes the statistical characteristics of magnetic field (MF) measurements from heterogeneous smartphones. It demonstrates that, in the absence of disturbances, the MF measurements in indoor environments follow a Gaussian distribution with temporal stability and spatial discernibility. It shows the fluctuations in magnetic field intensity caused by the rotation of a smartphone around the Z-axis. Secondly, it suggests that the RLOWESS method can be used to eliminate magnetic field anomalies, using magnetometer calibration to ensure consistent MF measurements in heterogeneous smartphones. Thirdly, it tests the magnetic field positioning performance of homogeneous and heterogeneous devices using different machine learning methods. Finally, it summarizes the feasibility/limitations of using only MF measurement for indoor positioning.

Canonical Polyadic (CP) decomposition is a powerful multilinear algebra tool for analyzing multiway (a.k.a. tensor) data and has been used for various signal processing and machine learning applications. When the underlying tensor is derived from data streams, adaptive CP decomposition is required. In this paper, we propose a novel method called robust adaptive CP decomposition (RACP) for dealing with high-order incomplete streaming tensors that are corrupted by outliers. At each time instant, RACP first performs online outlier rejection to accurately detect and remove sparse outliers, and then performs tensor factor tracking to efficiently update the tensor basis. A unified convergence analysis of RACP is also established in that the sequence of generated solutions converges asymptotically to a stationary point of the objective function. Extensive experiments were conducted on both synthetic and real data to demonstrate the effectiveness of RACP in comparison with state-of-the-art adaptive CP algorithms.

Traditional magnetic-field positioning methods collect magnetic-field information from each spatial point to construct a magnetic-field fingerprint database. During the positioning phase, real-time magnetic-field measurements are matched to a magnetic-field map to predict the user’s location. However, this approach requires a significant amount of time to traverse the entire magnetic-field fingerprint database and does not effectively leverage the magnetic-field sequence’s unique patterns to improve the accuracy and robustness of the positioning system. In recent years, the application of deep learning for the indoor positioning of magnetic fields has grown rapidly, especially by using the magnetic-field sequence as a time series and a trained long short-term memory (LSTM) model to predict the position, directly avoiding the time-consuming matching process. However, the training of LSTM is time-consuming, and the degradation problem occurs as the stack of layers increases. This article proposes a temporal convolutional network (TCN)-based magnetic-field positioning system that extracts magnetic-field sequence features by preprocessing them with coordinate transformation, smoothing filtering, and first-order differencing. The proposed method is seamlessly applicable to heterogeneous smartphones. The trained TCN models are compared with the LSTM and gated recurrent unit (GRU) models, showing the high accuracy and robustness of the proposed algorithm.

In estimation, the misspecified Cramer–Rao bound (MCRB), which is an extension of the well-known Cramer–Rao bound (CRB) when the underlying system model is misspecified, has recently attracted much attention. In this paper, we introduce a new interpretation of the MCRB, called the generalized MCRB (GMCRB), via the Moore–Penrose inverse operator. This bound is useful for singular problems and particularly blind channel estimation problems in which the Hessian matrix is noninvertible. Two closed-form expressions of the GMCRB are derived for unbiased blind estimators when the channel order is misspecified. The first bound deals with deterministic models where both the channel and unknown symbols are deterministic. The second one is devoted to stochastic models where we assume that transmitted symbols are unknown random variables i.i.d. drawn from a Gaussian distribution. Two case studies of channel order misspecification are investigated to demonstrate the effectiveness of the proposed GMCRBs over the classical CRBs. When the channel order is known or accurately estimated, both generalized bounds reduce to the classical bounds. Besides, the stochastic GMCRB is lower than the deterministic one, especially at high SNR.