We propose modeling an angle-of-arrival (AOA) positioning measurement as a 3-dimensional von Mises-Fisher (VMF)-distributed unit vector instead of the conventional normally distributed azimuth and elevation measurements. Describing the 2-dimensional AOA measurement with three numbers removes discontinuities and reduces nonlinearity at the poles of the azimuth-elevation coordinate system. Our computer simulations show that the proposed VMF measurement noise model based approximative Bayesian filters outperform the normal distribution based algorithms in accuracy in a scenario where close-to-pole measurements occur frequently.

In this paper, we present a method for device localization based on the fusion of location data from Global Navigation Satellite System and data from inertial sensors. We use a Kalman filter as well as its non-linear variants for realtime position estimation, and corresponding smoothers for offline position estimation. In all filters we use information about changes of user's heading, which are computed from the acceleration and gyroscope data. Models used with Extended and Unscented Kalman filters also take into account information about step length, whereas Kalman Filter does not, because the measurement is non-linear. In order to overcome this shortcoming, we introduce a modified Kalman Filter which adjusts the state vector according to the step length measurements. Our experiments show that use of step length information does not significantly improve performance when location measurements are constantly available. However, in real situations, when location data is partially unavailable, information about step length and its appropriate integration into the filter design is important, and improve localization accuracy considerably.

In this letter, we propose an iterative Kalman type algorithm based on posterior linearization. The proposed algorithm uses a nested loop structure to optimize the mean of the estimate in the inner loop and update the covariance, which is a computationally more expensive operation, only in the outer loop. The optimization of the mean update is done using a damped algorithm to avoid divergence. Our simulations show that the proposed algorithm is more accurate than existing iterative Kalman filters.

We propose a deterministic recursive algorithm for approximate Bayesian filtering. The proposed filter uses a function referred to as the approximate Gaussian flow transformation that transforms a Gaussian prior random variable into an approximate posterior random variable. Given a Gaussian filter prediction distribution, the succeeding filter prediction is approximated as Gaussian by applying sigma point moment-matching to the composition of the Gaussian flow transformation and the state transition function. This requires linearising the measurement model at each sigma point, solving the linearised models analytically, and introducing the measurement information gradually to improve the linearisation points progressively. Computer simulations show that the proposed method can provide higher accuracy and better posterior covariance matrix approximation than some state-of-the art computationally light approximative filters when the measurement model function is nonlinear but differentiable and the noises are additive and Gaussian. We also present a highly nonlinear scenario where the proposed filter occasionally diverges. In the accuracy-computational complexity axis the proposed algorithm is between Kalman filter extensions and Monte Carlo methods.

Ranked Based Fingerprinting uses only ordering indices instead of actual Wi-Fi RSS values in order to make the algorithm insensitive to devices. A key component of the RBF algorithm is a similarity measure which is used to compare and find the closest ranked fingerprints. Previous papers study a few similarity measures; here we study 49 similarity measures in a test with a benchmark with publicly available indoor positioning database. For different similarity measures the positioning accuracy varies from 15.80 m to 55.22 m. The top 3 similarity measures are Lorentzian, Hamming and Jaccard. Hamming and Jaccard similarity measures have been studied in other papers while Lorenzian had not been studied with that kind of problems.

Knowledge of deployed transmitters’ (Tx) locations in a wireless network improves many aspects of network management. Operators and building administrators are interested in locating unknown Txs for optimizing new Tx placement, detecting and removing unauthorized Txs, selecting the nearest Tx to offload traffic onto it, and constructing radio maps for indoor and outdoor navigation. This survey provides a comprehensive review of existing algorithms that estimate the location of a wireless Tx given a set of observations with the received signal strength indication. Algorithms that require the observations to be location-tagged are suitable for outdoor mapping or small-scale indoor mapping, while algorithms that allow most observations to be unlocated trade off some accuracy to enable large-scale crowdsourcing. This article presents empirical evaluation of the algorithms using numerical simulations and real-world Bluetooth Low Energy data.

Localization accuracy of trilateration methods in long term evolution (LTE) cellular networks, which are based on time-of-arrival, may be highly degraded due to multipath and non-line of sight conditions in urban and indoor environments. Multipath mitigation techniques usually involve a high computational burden and require wideband signals to be effective, which limit their adoption in certain low-cost and low-power mobile applications using narrow-band signals. As an alternative to these conventional techniques, this paper analyzes an expectation maximization (EM) localization algorithm that considers the skewness introduced by multipath in the LTE ranging error distribution. The EM algorithm is extensively studied with realistic emulated LTE signals of 1.4-MHz bandwidth. The EM method is compared with a standard nonlinear least squares (NLS) algorithm under ideal simulated conditions and using realistic outdoor measurements from a laboratory testbed. The EM method outperforms the NLS method when the ranging errors in the training and test stages have similar distributions.

A skew-t variational Bayes filter (STVBF) is applied to indoor positioning with time-of-arrival (TOA) based distance measurements and pedestrian dead reckoning (PDR). The proposed filter accommodates large positive outliers caused by occasional non-line-of-sight (NLOS) conditions by using a skew-t model of measurement errors. Real-data tests using the fusion of inertial sensors based PDR and ultra-wideband based TOA ranging show that the STVBF clearly outperforms the extended Kalman filter (EKF) in positioning accuracy with the computational complexity about three times that of the EKF.

Filtering and smoothing algorithms for linear discrete- time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that have normal prior and skew-$t$-distributed measurement noise. The proposed filter and smoother are compared with conventional low- complexity alternatives in a simulated pseudorange positioning scenario. In the simulations the proposed methods achieve better accuracy than the alternative methods, the computational complexity of the filter being roughly 5 to 10 times that of the Kalman filter.

This article presents a training-free probabilistic pedestrian motion model that uses indoor map information represented as a set of links that are connected by nodes. This kind of structure can be modelled as a graph. In the proposed model, as a position estimate reaches a link end, the choice probabilities of the next link are proportional to the total link lengths (TLL), the total lengths of the subgraphs accessible by choosing the considered link alternative. The TLLs can be computed off-line using only the graph, and they can be updated if training data are available. A particle filter in which all the particles move on the links following the TLL-based motion model is formulated. The TLL-based motion model has advantageous theoretical properties compared to the conventional models. Furthermore, the real-data WLAN positioning tests show that the positioning accuracy of the algorithm is similar or in many cases better than that of the conventional algorithms. The TLL-based model is found to be advantageous especially if position measurements are used infrequently, with 10-second or more time intervals.

Low-complexity Bayesian filtering for nonlinear models is challenging. Approximative methods based on Gaussian mixtures (GM) and particle filters are able to capture multimodality, but suffer from high computational demand. In this paper, we provide an indepth analysis of a generalized GM (GGM), which allows component weights to be negative, and requires significantly fewer components than the traditional GM for ranging models. Based on simulations and tests with real data from a network of UWB nodes, we show how the algorithm's accuracy depends on the uncertainty of the measurements. For nonlinear ranging the GGM filter outperforms the extended Kalman filter (EKF) in both positioning accuracy and consistency in environments with uncertain measurements, and requires only slightly higher computational effort when the number of measurement channels is small. In networks with highly reliable measurements, the GGM filter yields similar accuracy and better consistency than the EKF.

We present a real-time particle filter for 2D and 3D hybrid indoor positioning. It uses wireless local area network (WLAN) based position measurements, step and turn detection from a hand-held inertial sensor unit, floor plan restrictions, altitude change measurements from barometer and possibly other measurements such as occasional GNSS fixes. We also present a particle smoother, which uses future measurements to improve the position estimate for non-real-time applications. A light-weight fallback filter is run in the background for initialization, divergence monitoring and possibly re-initialization. In real-data tests the particle filter is more accurate and consistent than the methods that do not use floor plans. An example is shown on how smoothing helps to improve the filter estimate. Moreover, a floor change case is presented, in which the filter is capable of detecting the floor change and improving the 2D accuracy using the floor change information.

Most of the existing mobile device positioning methods require data connectivity, i.e. they work in the mobile-assisted, or online mode. However, this consumes energy, induces transmission costs and results in unnecessarily long time-to-first-fix. These issues can be alleviated using mobile-based, or offline, mode. In this mode the device carries a subset of the global radio map in memory for fast positioning without data connection. The challenge of this approach is the large size of the offline radio map that needs to be downloaded, stored and updated periodically in the mobile device. This paper presents a method to find the significant APs in the global radio map and proposes using only those in offline positioning in order to compress the size of the required offline radio map. We also propose a method to further compress the size of the offline radio map by hashing the globally unique AP BSSIDs into locally unique shortened BSSIDs. We test the proposed methods with real-world data.

Traditionally, positioning with WLAN Received Signal Strength (RSS) fingerprints involves the laborious task of collecting a radiomap with a reference mobile device. Best accuracy can be guaranteed only in case the user carries the same device, while positioning with different devices requires a calibration step to make the new devices' RSS values compatible with the existing radiomap. We propose a novel device self-calibration method that uses histograms of RSS values. First, we use the existing radiomap to create the RSS histogram of the reference device. Subsequently, when the user enters a building and starts positioning, the observed RSS values are recorded simultaneously in the background to create and update the histogram of the user device. We use these RSS histograms to fit a linear mapping between the user and reference device. Our calibration method is running concurrently with positioning and does not require any user intervention. Experimental results with five smartphones in a real indoor environment indicate that soon after positioning is initiated the device is self-calibrated, thus improving the accuracy to be comparable with the case of using a radiomap created with the same device.

A Bayesian method for dynamical off-line estimation of the position and path loss model parameters of a WLAN access point is presented. Two versions of three different on-line positioning methods are tested using real data. The tests show that the methods that use the estimated path loss parameter distributions with finite precisions outperform the methods that only use point estimates for the path loss parameters. They also outperform the coverage area based positioning method and are comparable in accuracy with the fingerprinting method. Taking the uncertainties into account is computationally demanding, but the Gauss-Newton optimization method is shown to provide a good approximation with computational load that is reasonable for many real-time solutions.

A novel Received Signal Strength (RSS) rank based fingerprinting algorithm for indoor positioning is presented. Because RSS rank is invariant to bias and scaling, the algorithm provides the same accuracy for any receiver device, without the need for RSS calibration. Similarity measures to compare ranked vectors are introduced and their impact on positioning accuracy is investigated in experiments. Experimental results shown that proposed algorithm can achieve better accuracy than commonly used NN and WKNN fingerprinting algorithms.

This paper introduces a novel method for positioning using coverage area estimates of wireless communication nodes. The coverage areas are estimated in a Bayesian inference framework using location fingerprints that are collected in an offline calibration phase, and the estimated coverage areas are stored in a database. In the online positioning phase the coverage areas of the heard communication nodes are used to infer the position of the mobile terminal. Floor plan information is used to enhance the positioning accuracy. In a field study comparing Kalman Filter, Box Filter and Particle Filter using real WLAN measurement data, it is found that Kalman Filter achieves almost the same accuracy as Box Filter and Particle Filter but with smaller computational load.