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Comparison of links selection criteria for mobile terminal positioning in cooperative heterogeneous networks
Abstract
In this paper we consider using different links selection criteria to assist mobile terminals positioning in heterogeneous wireless networks. These indicators enable parsimonious cooperation under power, latency and complexity constraints. In particular, we verify that the Geometric Dilution of Precision (GDOP) and the approximated Cramer Rao Lower Bound (CRLB) indicators can reliably characterize instantaneous Weighted Least Squares (WLS) location errors along mobile trajectories, while experiencing varying and limited connectivity. These indicators are thus helpful to identify and predict relevant combinations of range measurements based on Received Signal Strength Indicators (RSSI). Links selection is performed with respect to fixed Access Points (APs) (e.g. WiFi) and/or mobile terminals over short-range peer-to-peer links (e.g. Zigbee). Simulations are herein carried out in a realistic dynamic heterogeneous context to assess the reliability of such indicators, as well as the benefits of the proposed selection strategy, in comparison with exhaustive cooperation or random/nearest neighbors selection schemes.
... Unfortunately, mobility has not been considered either in this study. In [9], cooperative localization has also been investigated in a heterogeneous WiFi/Zigbee wireless indoor context, where located MTs broadcast their estimated positions to help unlocated MTs during the steady-state positioning stage. Different links selection criteria based on static performance indicators have thus been compared, although final localization performance has been assessed in dynamic scenarios. ...
... Note that in the most standard case, the first decision about links selection can be made right at time t i4 = t i3 once sufficient information has been received from the neighbors and the selection remains unchanged between t i3 and t i5 , enabling optimized Rx and sleep modes. The decentralized selection criterion can for instance rely on the CRLB characterizing the minimal instantaneous error that would affect MT i's unbiased location estimates under given combinations of measurements (of a certain assumed quality) with respect to available neighboring MTs seen as virtual anchors, like in [9]. ...
... including anchors and MTs) [1]. However, in real systems and in first approximation, the latter coordinates can be practically substituted by the corresponding latest estimates available [2], [9]. III. ...
In this paper we consider adapting links selection criteria to assist the localization of Mobile Terminals in heterogeneous and cooperative wireless networks. Integrating asynchronously the velocity and location estimates of neighboring terminals in a performance indicator based on a Cramer Rao Lower Bound, one can reliably anticipate on the instantaneous location estimation errors that would be committed along mobile trajectories, while experiencing limited connectivity. This new dynamic indicator is thus helpful to predict in a reasonably short-term the most relevant combination of range measurements, for instance based on Received Signal Strength Indicators, with respect to other neighboring mobile terminals over peer-to-peer links. The idea is to limit in turn power consumption, computational complexity and latency, for instance by postponing as much as possible a complete refreshment of the serving neighbors. Coupling further this selection scheme with a decentralized and cooperative Extended Kalman Filter, simulation results are provided in a realistic dynamic heterogeneous indoor context, including fixed WiFi Access Points and multi-standard WiFi/Zigbee mobile terminals under pedestrian mobility.
... The CRBs for both received signal strength indicator (RSSI) and time of arrival (TOA) distance measurements are derived in [9], [10]. Some later works [11]- [13] apply this criterion to propose diverse selection algorithms. But these criteria do not take the uncertainty of agents into account. ...
... dB. Three conventional algorithms, including the MT [15], selection scheme based on utility function and gridiron spatial correlation (UF-GSC) [17] [21] and links selection strategy inspired by monoobjective genetic algorithm (MGA) [13], are simulated as benchmarks. The program runs 100 times on MATLAB for every set of configuration. ...
When implementing cooperative positioning (CP), there are a number of challenges and issues including the high computation complexity, the high probability of encountering unreliable reference nodes and coordinate uncertainty, which may offset the benefit of CP. To address these challenges, we study the impact of node reliability and propose a cooperative positioning scheme that identifies unreliable reference nodes in the system and adaptively adjusts the scoring threshold based on the geographic locations of reference nodes. When compared with other three conventional cooperative positioning schemes, our simulation results indicate that the proposed scheme can achieve the best accuracy of about 2 meters within five iterations, and it is about 32% better than the conventional schemes in terms of accuracy.
... In [6], unreliable links are consecutively discarded based on CRLB analysis. A comparison of different selection criteria, namely CRLB and GDOP, and analysis of their correlation with localization error in both cooperative and noncooperative scenarios have been given in [12]. Here, the mobile scenario has been studied, so the selection criteria are used for predicting the best set of anchor nodes. ...
... If F(x) contains any unknown parameters, they are replaced by their estimated values, and the resultant bound is called estimated CRLB, which is denoted as CRLB . For example, the CRLB of RSS-based ranging in a two-dimensional space derived in [12,14] is a function of the true distances d n , which are in practice unknown. Hence, it is only feasible to calculate the estimated CRLB usingd n . ...
Range-based positioning is capable of achieving better accuracy in heterogeneous networks, where mobile nodes enabled with multiple radio access technologies are allowed to deploy not only the faraway access points but also high spatial density peer nodes as anchor nodes. However, due to peer node energy supply constraint and network capacity constraint, an efficient cooperation strategy is required. In this paper, we propose a cooperation method to track the position of a moving target with high accuracy and reduce the energy consumption and signaling overhead via node selection. It is demonstrated by simulation that in a specific practical scenario, the proposed method is capable of reducing the signaling overhead by about 34% to within 0.5-m degradation of accuracy compared to exhaustive cooperation. We also evaluate the achievable performance averaged over randomly located node configurations and compare the proposed scheme with the mostly used nearest-node selection algorithm in terms of accuracy and cost.
... [2], [3], [4]) on the one hand, and cooperative links selection (e.g. [5], [6]) on the other hand, but the localization performance has been most often assessed through simulations so far. The latter evaluations cannot account for complex phenomena inherent to cooperative and heterogeneous contexts, such as space-time correlations between the different involved radio access technologies (RATs), the conjunction of harmful sparse connectivity and poor geometric dilution of precision (GDoP) conditions, or erratic radio obstructions experienced along the MT trajectory (e.g. ...
... This example illustrates the benefits of identifying and incorporating solely the most reliable cooperative nodes. This problem is one of the ongoing topics in WHERE2 (e.g. based on link quality, GDoP, theoretical bounds, or combined criteria [5], [6]). Including RTD measurements (see bottom curves of Fig. 7), we observe only a small benefit for position errors larger than 3.8 m in the VMP algorithm, whereas quite significant gains are observed with TP-NBP while performing selective hybrid data fusion, that is, after incorporating only LoS measurements under the standard Gaussian error assumption or both NLoS and LoS measurements under a global bi-modal error assumption. ...
In this paper we present the results of real-life localization experiments performed in an unprecedented cooperative and heterogeneous wireless context. These measurements are based on ZigBee and orthogonal frequency division multiplexing (OFDM) devices, respectively endowed with received signal strength indicator (RSSI) and round trip delay (RTD) estimation capabilities. More particularly we emulate a multi-standard terminal, moving in a typical indoor environment, while communicating with fixed OFDM-based femto-base stations (Femto-BSs) and with other mobiles or fixed anchor nodes (through peer-to-peer links) forming a wireless sensor network (WSN). We introduce the measurement functionalities and metrics, the scenario and set-up, providing realistic connectivity and obstruction conditions. Out of the experimental data, preliminary positioning results based on cooperative and geometric algorithms are finally discussed, showing benefits through mobile-to-mobile cooperation, selective hybrid data fusion and detection of unreliable nodes.
... Recently, research work has been focusing on two main approaches in hybrid data fusion: centralized and distributed. Iterative positioning [77][78][79] and cooperative link selection [80,81] are used with the distributed approach. In iterative multilateration, once the position is estimated for unknown nodes, this node is used as the anchor node for other unknown sensor nodes. ...
Localization is an important aspect in the field of wireless sensor networks (WSNs) that has developed significant research interest among academia and research community. Wireless sensor network is formed by a large number of tiny, low energy, limited processing capability and low-cost sensors that communicate with each other in ad-hoc fashion. The task of determining physical coordinates of sensor nodes in WSNs is known as localization or positioning and is a key factor in today’s communication systems to estimate the place of origin of events. As the requirement of the positioning accuracy for different applications varies, different localization methods are used in different applications and there are several challenges in some special scenarios such as forest fire detection. In this paper, we survey different measurement techniques and strategies for range based and range free localization with an emphasis on the latter. Further, we discuss different localization-based applications, where the estimation of the location information is crucial. Finally, a comprehensive discussion of the challenges such as accuracy, cost, complexity, and scalability are given.
... 1) Conventional HDF Techniques: Recently, research work has been focusing on two main approaches in HDF, the centralized and non-centralized approaches. Iterative positioning (e.g., [60]- [62]) and cooperative links selection (e.g., [63] and [64]) are used with the non-centralized approach. Moreover, such heterogeneous and cooperative environments include complex phenomena such as the conjunction of harmful sparse connectivity, space-time correlations among various radio access technologies and poor Geometric Dilution Of Precision (GDOP) conditions. ...
The availability of location information has become a key factor in today’s communications systems allowing location based services. In outdoor scenarios, the mobile terminal position is obtained with high accuracy thanks to the Global Positioning System (GPS) or to the standalone cellular systems. However, the main problem of GPS and cellular systems resides in the indoor environment and in scenarios with deep shadowing effects where the satellite or cellular signals are broken. In this paper, we survey different technologies and methodologies for indoor and outdoor localization with an emphasis on indoor methodologies and concepts. Additionally, we discuss in this review different localization-based applications, where the location information is critical to estimate. Finally, a comprehensive discussion of the challenges in terms of accuracy, cost, complexity, security, scalability, etc. is given. The aim of this survey is to provide a comprehensive overview of existing efforts as well as auspicious and anticipated dimensions for future work in indoor localization techniques and applications.
Cooperative positioning is a popular approach for indoor localization, which significantly outperforms conventional positioning techniques. This paper presents a method for iterative node localization, with a relatively small number of initial anchor nodes. In order to reduce error propagation in iterative schemes, it is necessary to use only reliable information among nodes. We introduce a reference node selection strategy based on utility functions. The method is completely distributed and involves only information from local neighborhood. Compared to the nearest neighbor and random node selection scheme, simulation results show that selecting subsets of nodes with highest utility values leads to more accurate position estimates.
The recent demonstration of precise ranging measurements through low power low data rate (LDR) impulse radio-ultra wideband (IR-UWB) communications has disclosed new perspectives for cooperative location-enabled wireless networks. With this respect, joint ranging and distributed positioning mechanisms supported by specific protocol transactions have already been proposed within user-centric infrastructureless applications. However, in spite of advanced medium access techniques, those approaches still suffer from resource inefficiency. In this paper, we describe and compare new scheduling strategies regarding the joint update of ranging measurements and positional information. One goal is to accelerate the convergence of positioning errors and hence to reduce network latency and overhead accordingly. As an example, one scheduling option considers discarding so-called useless pair-wise links based on the prior analysis of the conditional Cramer Rao lower bound (CRLB) of positioning errors at each mobile node.
Cooperative positioning is an emerging topic in wireless sensor networks and navigation. It can improve the positioning accuracy and coverage in GPS-challenged conditions such as inside tunnels, in urban canyons, and indoors. Different algorithms have been proposed relying on iteratively exchanging and updating positional information. For the purpose of computational complexity, network traffic, and latency, it is desirable to minimize the amount of information shared between devices, while still maintaining acceptable performance. We show that information that is not reliable should not be shared, and information that is not informative should not be used. This naturally leads to censoring schemes. We consider different censoring schemes based on the Cramér Rao bound (CRB). We find that by blocking the broadcasts of the nodes that do not have reliable estimates (transmit censoring) and selecting the most usable links after receiving signals from neighbors (receive censoring), complexity and traffic can be reduced significantly without degrading positioning performance.
Self-configuration in wireless sensor networks is a general class of estimation problems that we study via the Cramer-Rao bound (CRB). Specifically, we consider sensor location estimation when sensors measure received signal strength (RSS) or time-of-arrival (TOA) between themselves and neighboring sensors. A small fraction of sensors in the network have a known location, whereas the remaining locations must be estimated. We derive CRBs and maximum-likelihood estimators (MLEs) under Gaussian and log-normal models for the TOA and RSS measurements, respectively. An extensive TOA and RSS measurement campaign in an indoor office area illustrates MLE performance. Finally, relative location estimation algorithms are implemented in a wireless sensor network testbed and deployed in indoor and outdoor environments. The measurements and testbed experiments demonstrate 1-m RMS location errors using TOA, and 1- to 2-m RMS location errors using RSS.
This paper addresses the problem of localization in mobile networks. Our goal is to make localization possible even for off-the-shelf communication devices like smartphones or sensor nodes, not equipped with GPS or operating in areas where the GPS does not work well. In our approach, a user estimates its position by exploiting opportunistic exchanges with other devices (peer devices). The localization information provided by peers include their own position estimation and can be used even though it may be highly inaccurate. In a heterogeneous setup, peers can provide different ranging technologies (e.g. RSSI and UWB). We investigate the performance of two existing localization algorithms based on Weighted Centroid (WC) and Linear Matrix Inequalities (LMI) under different conditions of accuracy and heterogeneity. The study is performed by means of simulations that, however, make use of realistic ranging models, derived from an extensive set of RSSI and UWB measurements. The simulation results show that in most cases LMI provides a better user position estimation than WC, with an error of 1 to 4 meters for 10 opportunistic interactions, and that heterogeneity of peer positioning accuracy has a limited but positive impact on the localization performance.
This paper proposes a cooperative game-theoretic approach for efficient measurement allocation in unattended ground sensor networks when they are engaged in localizing a target. The game-theoretic approach evolves around the idea that localization is achieved as a result of collaboration among the nodes. Hence this process can be modeled as a cooperative game and the solution concept of the Shapley value can be exploited to determine the value of each node for localization. Furthermore, it is proved that by iteratively allocating measurements according to the Shapley value, stochastic observability-a measure of the predicted level of accuracy in localization-desirably improves.
This paper consider cooperative localization in cellular networks. In this scenario, several located mobile terminals (MTs) are employed as reference nodes to find the location of an un-located MT. The located MTs sent training sequences in the uplink, then the un-located MT perform distance estimation using received signal strength techniques. The localization accuracy of the un-located MT is characterized in terms of squared position error bound (SPEB). By taking into account the imperfect a priori location knowledge of the located MTs, the SPEB is derived in a closed-form. The closed-form indicate that the effect of the imperfect location knowledge on SPEB is equivalent to the increase of the variance of distance estimation. Moreover, based on the obtained closed-form, a MT selection scheme is proposed to decrease the number of located MTs sending training sequences, thus reduce the training overhead for localization. The simulation results show that the proposed scheme can reduce the training overhead with the paid of accuracy. And with the same training overhead, the accuracy of the proposed scheme is better than that of random selection.
This paper addresses the problem of resource allocation in formations of mobile robots localizing as a group. Each robot receives measurements from various sensors that provide relative (robot-to-robot) and absolute positioning information. Constraints on the sensors' bandwidth, as well as communication and processing requirements, limit the number of measurements that are available or can be processed at each time step. The localization uncertainty of the group, determined by the covariance matrix of the equivalent continuous-time system at steady state, is expressed as a function of the sensor measurements' frequencies. The trace of the weighted covariance matrix is selected as the optimization criterion, under linear constraints on the measuring frequency of each sensor and the cumulative rate of the extended Kalman filter updates. This formulation leads to a convex optimization problem (semidefinite program) whose solution provides the sensing frequencies, for each sensor on every robot, required in order to maximize the positioning accuracy of the group. Simulation and experimental results are presented that demonstrate the applicability of this method and provide insight into the properties of the resource-constrained cooperative localization problem
The author addresses the problem of selecting an optimum
n-satellite subset from m visible satellites (m>n). The optimality
criteria is minimum geometric dilution of precision (GDOP) subject to
the integrity constraint. To solve this problem an efficient algorithm
is developed using a revolving door method and matrix inversion lemma.
The revolving door method generates each n-subset from its immediate
predecessor by deleting some single element and adjoining some other
single element. Then using the matrix inversion lemma, the GDOP for each
new n-subset is recursively calculated from the incoming and outgoing
elements. The matrix inversion lemma is also used to check the
satisfaction of the integrity constraint