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Spatial Interpolation of Wi-Fi RSS Fingerprints using model-based universal Kriging
Abstract
Wi-Fi RSS Fingerprint based navigation has enjoyed increasing popularity as a solution for indoor navigation in the last decade. Recently, methods for interpolation of Wi-Fi databases have become the focus of research. This paper shows how common models for Wi-Fi signal propagation can be included into the interpolation method by using universal Kriging, a method that relies on mixed model containing both spatially stochastic and deterministic components. It is shown that, theoretically, it can achieve a very precise reproduction of the spatial distribution of Wi-Fi RSS. The major remaining challenge of this method, however, is to find a suitable representation of the spatial depedency in the variogram, which cannot be estimated properly from recorded Wi-Fi signals. Both the high potential and this vulnerability are highlighted using simulation and measurement results.
... More specifically, Kriging methods have been proposed for this problem in [4][5] [6], yielding the best linear unbiased predictor (BLUP) of the RSS propagation based on a set of known observations. In [7] a solution for database enhancement using universal Kriging was presented showing good interpolation results as long as the spatial covariance of the database can be calculated and the beacon positions are known. RSS-based methods typically achieve a positioning accuracy in the meter range, while many other radio-based localization systems, albeit with higher installation costs, achieve accuracies in the centimeter range [8]. ...
... In the following, a compact explanation of universal Kriging in the context of fingerprint-based positioning is presented. A more complete derivation of universal Kriging for radio propagation is included in [7]. A set of N O available observations (fingerprints) at each location p 1 to p N O are described as outcomes of a spatial function Z(p). ...
... In practice, γ yy (d) is calculated from observed data using the so called empirical variogram and curve-fitting methods. Details about this procedure can be found e.g. in [13] [14], or, on the application for RSS propagation in [7]. The problem of variogram estimation from data with a drift is a complex subject, as it is only representative of the stochastic process Y (p), but not of the drift functions, neither of which are known. ...
... • Extrapolation methods applied variants based on log-distance path loss model [21]- [23]; on the ray tracing model [24], [25] or the radiosity model [26]- [28]. • Regression methods largely includes the application of Gaussian Process Regression (GPR) [29]- [33], although others have also applied Kriging [14], [34]- [36], Geography Weighted Regression (GWR) [37] and Support Vector Regression (SVR) [38]. It is common that radio map enrichment works provide the proportions between points used for fitting and those used for estimations. ...
... Moghtadaiee et al. [21] fitted a log-distance model independently for each architectural zone and created an interpolation that considered only sample at similar distances to the target AP. Some authors [14], [34]- [36] used Kriging, but only considered the Euclidean distance for describing the spatial dependency, which does not hold true for indoor environments. [39] fitted a log distance path loss model for each target position, giving to the samples used for fitting distinct weights (using a kernel density estimation) based on their distances to the target position. ...
Data enrichment through interpolation or regression is a common approach to deal with sample collection for Indoor Localization with WiFi fingerprinting. This paper provides guidelines on where to collect WiFi samples, and proposes a new model for received signal strength regression. The new model creates vectors that describe the presence of obstacles between an access point and the collected samples. The vectors, the distance between the access point and the positions of the samples, and the collected, are used to train a Support Vector Regression. The experiments included some relevant analyses and showed that the proposed model improves received signal strength regression in terms of regression residuals and positioning accuracy.
... Other alternatives eliminate the need to build and maintain the RM through interpolation (estimation of signal strength values) based on Radial Basis Functions (RBF) [10], universal Kriging [25], Voronoi tesselation [11], Inverse Distance Weighted (IDW) [12], or Log-Distance Path Loss (LDPL) [13]. The main drawback of these solutions is that they provide approximations of signal strength levels (that do not account for signal effects like reflection, refraction and multipath). ...
The deployment of an Indoor Position System (IPS) in the real-world raised many challenges, such as installation of infrastructure, the calibration process or modelling of the building’s floor plan. For Wi-Fi-based IPSs, deployments often require a laborious and time-consuming site survey to build a Radio Map (RM), which tends to become outdated over time due to several factors. In this paper, we evaluate different deployment methods of a Wi-Fi-based IPS in an industrial environment. The proposed solution works in scenarios with different space restrictions and automatically builds a RM using industrial vehicles in operation. Localization and tracking of industrial vehicles, equipped with low-cost sensors, is achieved with a particle filter, which combines Wi-Fi measurements with heading and displacement data. This allows to automatically annotate and add new samples to a RM, named vehicle Radio Map (vRM), without human intervention. In industrial environments, vRMs can be used with Wi-Fi fingerprinting to locate human operators, industrial vehicles, or other assets, allowing to improve logistics, monitoring of operations, and safety of operators. Experiments in an industrial building show that the proposed solution is capable of automatically building a high-quality vRM in different scenarios, i.e., considering a complete floor plan, a partial floor plan or without a floor plan. Obtained results revealed that vRMs can be used in Wi-Fi fingerprinting with better accuracy than a traditional RM. Sub-meter accuracies were obtained for an industrial vehicle prototype after deployment in a real building.
... Reference Signal Receiving Power (RSRP), Received Signal Strength (RSS), Sounding Reference Signal (SRS) and other signals are used for positioning [13][14][15]. RSS-based positioning system includes a radio propagation distance loss model and fingerprinting method [16,17]. The radio propagation distance loss model requires multiple BSs to perform trilateral positioning and applies in simple environments, while it is not easy to observe multiple NR BSs in a room in the early deployment phase. ...
Fingerprinting technique for indoor positioning based on 5G system has attracted attention. Kalman filter (KF) is used as preprocessing of raw data to reduce the disturbance of Received Signal Strength (RSS) values. After preprocessing, Universal Kriging (UK) algorithm is adopted to reduce the efforts of establishing a fingerprinting database by Spatial Interpolation. A machine learning algorithm named K-Nearest Neighbour (KNN) is used to calculate user equipment’s position. Real experiments are setup with 5G signals over the air. Two indoor scenarios are considered depending whether the base station is located in the same room with user equipment or not. In test room A, the proposed KF and UK algorithms achieve 53% positioning accuracy improvement. In test room B, 43% performance improvement is obtained by the proposed algorithm. 1.44-meter positioning error is observed as the best case for 80% test samples.
... This approach ordinarily, removes the need for knowledge regarding the specifics of the propagation parameters and also, minimizes large scale path loss data as required by the empirical models, even though, it requires some sample data be collected before interpolation can be made as contrast to a well-developed empirical model. There are quite some works that have applied KIM for different predictions, these include: quantification of beam vibration (Krishnan & Ganguli, 2021); Raster data projection (Meng, 2021); prediction of rock joint shear strength (Hasanipanah, Meng, Keshtegar, Trung, & Thai, 2021) and Wi-Fi RSS fingerprints (Kram, Nickel, Seitz, Patino-Studencka & Thielecke, 2017). Recently, Hybrid Kriging and multilayer perceptron neural network technique was used to predict coverage prediction in cellular networks (Mezhoud, Oussalah, Zaatri, & Hammoudi, 2020). ...
For decades now, a lot of radio wave path loss propagation models have been developed for predictions across different environmental terrains. Amongst these models, empirical models are practically the most popular due to their ease of application. However, their prediction accuracies are not as high as required. Therefore, extensive path loss measurement data are needed to develop novel measurement-oriented path loss models with suitable correction factors for varied frequency, capturing both local terrain and clutter information, this have been found to be relatively expensive. In this paper, a large-scale radio propagation path loss measurement campaign was conducted across the VHF and UHF frequencies. A multi-transmitter propagation set-up was employed to measure the strengths of radio signals from seven broadcasting transmitters (operating at 89.30, 103.5, 203.25, 479.25, 615.25, 559.25 and 695.25 MHz respectively) at various locations covering a distance of 145.5 km within Nigerian urban environments. The measurement procedure deployed ensured that the data obtained strictly reflect the shadowing effects on radio signal propagation by filtering out the small-scale fading components. The paper also, examines the feasibilities of applying Kriging method to predict distanced-based path losses in the VHF and UHF bands. This method was introduced to minimize the cost of measurements, analysis and predictions of path losses in built-up propagation environments.
... The kriging interpolation method is a geostatistical method for optimal spatial prediction at unobserved locations, and it has certain advantages over some other spatial interpolation methods [31]. Kram [32] added a mixed model to a kriging interpolation method for Wi-Fi signal propagation. Zuo [33] adopted a kriging-based interpolation method to efficiently generate a missing iBeacon fingerprint database where some regions were inaccessible. ...
Indoor positioning is of great importance in the era of mobile computing. Currently, considerable focus has been on RSS-based locations because they can provide position information without additional equipment. However, this method suffers from two challenges: (1) fingerprint ambiguity and (2) labour-intensive fingerprint collection. To overcome these drawbacks, we provide a near relation-based indoor positioning method under a sparse Wi-Fi fingerprint. To effectively obtain the fingerprint database, certain interpolation methods are used to enrich sparse Wi-Fi fingerprints. A near relation boundary is provided, and Wi-Fi fingerprints are constrained to this region to reduce fingerprint ambiguity, which can also improve the efficiency of fingerprint matching. Extensive experiments show that the kriging interpolation method performs well, and a positioning accuracy of 2.86 m can be achieved with a near relation under a 1 m interpolation density.
... Many technologies have been proposed for indoor RF-based positioning like Ultra-wideband (UWB) [1], WiFi [2] and RFID [3]. UWB systems, which make use of the time-of-flight (ToF) estimate the time-of-arrival (TOA) or time-difference of arrival (TDOA), achieve accuracies in the decimeter range, given mild propagation conditions. ...
Indoor environments often pose challenges to RF-based positioning systems. Typically, objects within the environment influence the signal propagation due to absorption, reflection, and scattering effects. This results in errors in the estimation of the time or arrival (TOA) and hence leads to errors in the position estimation. Recently, different approaches based on classical, feature-based machine learning (ML) have successfully detected such obstructions based on CIRs of ultra wideband (UWB) positioning systems. This paper applies different convolutional neural network architectures (ResNet, Encoder, FCN) to detect non line-of-sight (NLOS) channel conditions directly from the CIR raw data. A realistic measurement campaign is used to train and evaluate the algorithms. The proposed methods highly outperform the feature-based ML baselines while still using low network complexities. We also show that the models generalize well to unknown receivers and environments and that positioning filters benefit significantly from the identification of NLOS measurements.
... The proposed time-frequency representation could be improved by a thorough investigation of the various related parameters (e.g., window type/size, overlap size, and FFT length). Spatial distributions of the CIRs were used for visualization, but a representation based on Gaussian process regression [39][40][41] may directly yield a statistical model usable for positioning [42]. In the future, a comparison or combination of the proposed features with a deep learning approach will also be investigated, such as a comparison with the latent layers in a variational autoencoder [36]. ...
Radio signal-based positioning in environments with complex propagation paths is a challenging task for classical positioning methods. For example, in a typical industrial environment, objects such as machines and workpieces cause reflections, diffractions, and absorptions, which are not taken into account by classical lateration methods and may lead to erroneous positions. Only a few data-driven methods developed in recent years can deal with these irregularities in the propagation paths or use them as additional information for positioning. These methods exploit the channel impulse responses (CIR) that are detected by ultra-wideband radio systems for positioning. These CIRs embed the signal properties of the underlying propagation paths that represent the environment. This article describes a feature-based localization approach that exploits machine-learning to derive characteristic information of the CIR signal for positioning. The approach is complete without highly time-synchronized receiver or arrival times. Various features were investigated based on signal propagation models for complex environments. These features were then assessed qualitatively based on their spatial relationship to objects and their contribution to a more accurate position estimation. Three datasets collected in environments of varying degrees of complexity were analyzed. The evaluation of the experiments showed that a clear relationship between the features and the environment indicates that features in complex propagation environments improve positional accuracy. A quantitative assessment of the features was made based on a hierarchical classification of stratified regions within the environment. Classification accuracies of over 90% could be achieved for region sizes of about 0.1 m 2 . An application-driven evaluation was made to distinguish between different screwing processes on a car door based on CIR measures. While in a static environment, even with a single infrastructure tag, nearly error-free classification could be achieved, the accuracy of changes in the environment decreases rapidly. To adapt to changes in the environment, the models were retrained with a small amount of CIR data. This increased performance considerably. The proposed approach results in highly accurate classification, even with a reduced infrastructure of one or two tags, and is easily adaptable to new environments. In addition, the approach does not require calibration or synchronization of the positioning system or the installation of a reference system.
... Ai et al. [182] and [183] applied GPR over samples from in route-based (walking) collection for BLE and WiFi samples, respectively. Li et al. [184], Liu et al. [185], Jan et al. [186], Kram et al. [187] applied Kriging, which can be seen as a variant of GPR. Other works using regressions are Du et al. [188], which used Geography Weighted Regression (GWR) for WiFi samples, and Hernández et al. [157], which used Support Vector Regression (SVR). ...
An accurate and reliable Indoor Positioning System (IPS) applicable to most indoor scenarios has been sought for many years. The number of technologies, techniques, and approaches in general used in IPS proposals is remarkable. Such diversity, coupled with the lack of strict and verifiable evaluations, leads to difficulties for appreciating the true value of most proposals. This paper provides a meta-review that performed a comprehensive compilation of 62 survey papers in the area of indoor positioning. The paper provides the reader with an introduction to IPS and the different technologies, techniques, and some methods commonly employed. The introduction is supported by consensus found in the selected surveys and referenced using them. Thus, the meta-review allows the reader to inspect the IPS current state at a glance and serve as a guide for the reader to easily find further details on each technology used in IPS. The analyses of the meta-review contributed with insights on the abundance and academic significance of published IPS proposals using the criterion of the number of citations. Moreover, 75 works are identified as relevant works in the research topic from a selection of about 4000 works cited in the analyzed surveys.
... The GP method. (b) PLM [16]. The method was implemented by learning the PLM model by using the training data and predicting RSS at the evaluation points with the learned PLM model. ...
This paper proposes a crowdsourcing-based local-ization and mapping framework. In contrast to the existing works that directly use machine learning (ML) methods such as Gaussian process (GP) to model raw localization features (LFs), the proposed method separates LFs to the deterministic and stochastic components. The deterministic LF database can be described by parametric models that are trained through crowdsoucing. Meanwhile, the stochastic LF database is learned by ML. Furthermore, to alleviate the issue of database outage in crowdsourcing, GP is used to predict LFs at unvisited locations. The latest Bluetooth long range (BT5) signals have been used to verify the effectiveness of the proposed method in enhancing LF prediction (mapping) and indoor localization.
... Seamless coverage with GNSS is not feasible due to weak coverage of GNSS signal indoors. Hence, a wide variety of systems are developed ranging from wireless local area network (WLAN) fingerprinting [5][6][7], proximity detection using bluetooth beacons [8] and ultra wide band (UWB) positioning systems [9,10]. One of the major problem surrounding the signals in the Gigahertz band is multipath propagation, which limits the precision. ...
Recent localization frameworks exploit spatial information of complex channel measurements (CMs) to estimate accurate positions even in multipath propagation scenarios. State-of-the art CM fingerprinting(FP)-based methods employ convolutional neural networks (CNN) to extract the spatial information. However, they need spatially dense data sets (associated with high acquisition and maintenance efforts) to work well -- which is rarely the case in practical applications. If such data is not available (or its quality is low), we cannot compensate the performance degradation of CNN-based FP as they do not provide statistical position estimates, which prevents a fusion with other sources of information on the observation level. We propose a novel localization framework that adapts well to sparse datasets that only contain CMs of specific areas within the environment with strong multipath propagation. Our framework compresses CMs into informative features to unravel spatial information. It then regresses Gaussian processes (GPs) for each of them, which imply statistical observation models based on distance-dependent covariance kernels. Our framework combines the trained GPs with line-of-sight ranges and a dynamics model in a particle filter. Our measurements show that our approach outperforms state-of-the-art CNN fingerprinting (0.52 m vs. 1.3 m MAE) on spatially sparse data collected in a realistic industrial indoor environment.
A framework that incorporates channel modeling, position estimation, and error analysis methods is developed for network-based indoor positioning with radio signal strength (RSS) measurements of WiFi access points (APs). To construct an accurate channel model with RSS measurements severely influenced by propagation attenuations, multipath reflections, and shadowing effects, a novel sparse Bayesian learning algorithm is developed to model the radio power map (RPM) in indoor space. Based on the proposed RPM model, a 2-stage positioning method is further developed. In the first stage for coarse positioning, the location is determined up to a room-scale indoor space. Then, in the second stage for fine positioning, the RPMs of the given indoor space are used for location estimation in the space with a Bayesian estimator. The mean squared positioning errors are verified with the Bayesian Cramer-Rao lower bound. Extensive experiments show that the average positioning error of the proposed RPM-based approach is 1.98 meters which achieve 22% improvements over the state-of-the-art RSS-based indoor positioning methods. More importantly, the proposed modeling and positioning method can effectively exploit the spatial relationship in the RSS samples to improve positioning accuracy.
This paper presents a low-cost localization system for the high-resolution tracking of bats. The system bases on a ground network consisting of multiple low-cost receiver stations, and ultra-lightweight transmitters mounted on the bats. A main challenge of the received signal strength based localization is the limited dynamic range of the employed low-cost receivers. This challenge is solved using an efficient 2-stage differential correlation concept. It significantly improves the dynamic wrt. conventional power detection methods. In addition, this concept requires low processing power and is robust wrt. frequency offsets. Finally, this paper presents a performance evaluation employing reference measurements recorded in the rain forest of Panama.
The main approach for a Wi-Fi indoor positioning system is based on the received signal strength (RSS) measurements, and the fingerprinting method is utilized to determine the user position by matching the RSS values with the pre-surveyed RSS database. To build a RSS fingerprint database is essential for an RSS based indoor positioning system, and building such a RSS fingerprint database requires lots of time and effort. As the range of the indoor environment becomes larger, labor is increased. To provide better indoor positioning services and to reduce the labor required for the establishment of the positioning system at the same time, an indoor positioning system with an appropriate spatial interpolation method is needed. In addition, the advantage of the RSS approach is that the signal strength decays as the transmission distance increases, and this signal propagation characteristic is applied to an interpolated database with the Kriging algorithm in this paper. Using the distribution of reference points (RPs) at measured points, the signal propagation model of the Wi-Fi access point (AP) in the building can be built and expressed as a function. The function, as the spatial structure of the environment, can create the RSS database quickly in different indoor environments. Thus, in this paper, a Wi-Fi indoor positioning system based on the Kriging fingerprinting method is developed. As shown in the experiment results, with a 72.2% probability, the error of the extended RSS database with Kriging is less than 3 dBm compared to the surveyed RSS database. Importantly, the positioning error of the developed Wi-Fi indoor positioning system with Kriging is reduced by 17.9% in average than that without Kriging.
A tracking algorithm for position and azimuth estimation based on Wi-Fi fingerprinting with directional antennas is analyzed and evaluated. A particle filter is used for fusing received signal strength of Wi-Fi with sensor readings of an inertial measurement unit, which is combined with pedestrian dead reckoning. Two setups for different application scenarios were developed and evaluated in an industry-like environment. The proposed approach reduces position error by up to 58% in sub-optimal scenarios, such as fewer available access points or a single directional antenna. In addition, the estimation of azimuth of the subject improves up to 64%.
Describing the relevant detection and estimation theory, this detailed guide provides the background knowledge needed to tackle the design of practical WLAN positioning systems. It sets out key system-level challenges and design considerations in increasing positioning accuracy and reducing computational complexity, and it also examines design trade- offs and experimental results. Radio characteristics in real environments are discussed, as are the theoretical aspects of non-parametric statistical tools appropriate for modeling radio signals, statistical estimation techniques and the model- based stochastic estimators often used for positioning. A historical account of positioning systems in also included, giving graduate students, researchers and practitioners alike the perspective needed to understand the benefits and potential applications of WLAN positioning.
Tracking algorithms for estimating and tracking the azimuth angle regarding north and a two-dimensional position of a mobile unit carried by a pedestrian are presented. Outdoors, the azimuth angle of a device can be easily detected using an electronic compass. The position can be calculated using a global navigation satellite system. Indoors, magnetic disturbances lead to unreliable compass outputs. Also, indoors there exists no standard positioning system. Using Wi-Fi signal strength measurements the position of a receiver can be tracked using so called fingerprinting methods. If the signal strengths measurements are collected with directional antennas additionally the azimuth can be tracked. For the presented tracking filters we extended Wi-Fi based Markov localization algorithms for evaluating directional antennas to calculate azimuth besides position. Furthermore, these techniques have been adapted to use a particle filter for the estimation. Well known Wi-Fi fingerprinting approaches are included in the measurement models and pedestrian dead reckoning in the prediction models. Measurements have been collected inside and outside of an office building to evaluate the performance of the different tracking algorithms. Especially in indoor environments these approaches facilitate the use of electronic guides that offer additional information by means of augmented reality, e.g. on museum exhibits in visual range.
Multiple-input multiple-output (MIMO) technology constitutes a breakthrough in the design of wireless communication systems, and is already at the core of several wireless standards. Exploiting multi-path scattering, MIMO techniques deliver significant performance enhancements in terms of data transmission rate and interference reduction. This book is a detailed introduction to the analysis and design of MIMO wireless systems. Beginning with an overview of MIMO technology, the authors then examine the fundamental capacity limits of MIMO systems. Transmitter design, including precoding and space-time coding, is then treated in depth, and the book closes with two chapters devoted to receiver design. Written by a team of leading experts, the book blends theoretical analysis with physical insights, and highlights a range of key design challenges. It can be used as a textbook for advanced courses on wireless communications, and will also appeal to researchers and practitioners working on MIMO wireless systems.