Some Signal Processing Techniques for Wireless Cooperative Localization and Tracking Hadi Noureddine CominLabs UEB/Supélec Rennes SCEE Supélec seminar February 20, 2014
Acknowledgments This work was performed in the context of PhD thesis at Mitsubishi Electric R&D Center Europe and Telecom Bretagne WHERE2 FP7 European project #2
Introduction Unique solvability & identifiability Cooperative localization RSS tracking Conclusions Outline 1. Introduction 2. Unique solvability and identifiability in cooperative networks 3. Cooperative localization algorithms 4. Position tracking based on RSS 5. Conclusions #3
Outline 1. Introduction Needs for localization Wireless localization solutions Design and optimization of localization systems Work context 2. Unique solvability and identifiability in cooperative networks 3. Cooperative localization algorithms 4. Position tracking based on RSS 5. Conclusions #4
Needs for localization A wide variety of location aware applications and services Navigation (route planning, real-time traffic information, eco-driving) Tracking (fleet management, security) Emergency calls (e-911, e-112) Telematics (active road-safety) Sensor networks (environment monitoring, animal tracking) Location based-services (point-of-interest, advertising, social apps) Real-time Traffic Indoor navigation #5
Wireless localization solutions Wireless localization: Estimating the location of a device based on location dependent parameters of the transmitted signals in a wireless system A fundamental localization solution: Global Navigation Satellite Systems (GNSS) (e.g., GPS, Galileo, GLONASS, COMPASS) GNSS Augmentation (by satellites or by terrestrial systems) Improved coverage and accuracy Improved start-up and reduced time-to-first-fix GNSS solutions are not available in all environments (e.g., urban canyons and indoor) Ubiquitous localization solutions: Measurements in terrestrial wireless systems #6
Wireless localization solutions Cellular and broadcast networks Cell identification Time difference of arrival (TDoA) Angle of arrival (AoA) Wireless LAN and PAN (WiFi, Bluetooth, Zigbee, UWB) Fingerprints database Time of arrival (ToA) Received signal strength (RSS) #7
Dense Indoor Design and optimization of localization systems Technology selection Measurements acquisition & modeling Data fusion algorithms urban Urban Rural UWB GNSS (GPS, Galileo, GLONASS, COMPASS) WiFi, Bluetooth, Zigbee, FemtoCell Cellular Cellular Dealing with ambiguities Time-of-arrival (ToA) Received Signal Strength (RSS), Proximity 10 Accuracy (meters) 10 2 10 3 Time-difference-of arrival Fingerprinting Cell-ID #8
Introduction Unique solvability & identifiability Cooperative localization RSS tracking Conclusions Design and optimization of localization systems Technology selection Measurements acquisition & modeling Data fusion algorithms Measurements acquisition: Estimation of location dependent parameters from the received signals The accuracy of a measurement is impacted by several factors: - The waveform of the transmitted signal - The propagation environment - The estimator Measurements modeling: - Mathematical formulation using parametric models - Purposes: Design estimators, study of theoretical limits, simulations Dealing with ambiguities Multipath propagation environment #9
Introduction Unique solvability & identifiability Cooperative localization RSS tracking Conclusions Design and optimization of localization systems Technology selection Classification of localization algorithms according to the kind of information exploited Cooperative localization - Nodes of unknown positions cooperate with each other to compute their positions Measurements acquisition & modeling Anchor node Target node Pair-wise measurement Target not connected to any anchor Data fusion algorithms Dynamic localization - Tracking over time a moving target node based on a motion model Dealing with ambiguities #10
Introduction Unique solvability & identifiability Cooperative localization RSS tracking Conclusions Design and optimization of localization systems Partially connected static cooperative network Technology selection Ranging measurement Measurements acquisition & modeling Data fusion algorithms Dealing with ambiguities In large networks of distant nodes, the ambiguities result in high location estimation errors Needs for detecting the ambiguities - Deployment purposes (e.g., number and positions of anchors, connectivity ranges) - Mitigation purposes (e.g., making additional measurements) #11
Introduction Unique solvability & identifiability Cooperative localization RSS tracking Conclusions Work context Technology selection Measurements acquisition & modeling 1. Cooperative static localization based on ranging measurements (i.e., RSS, ToA) Conditions of absence of ambiguity: - Noise-free measurements: Unique solvability - Noisy measurements: Identifiability Cooperative localization algorithms Data fusion algorithms Dealing with ambiguities 2. Dynamic localization algorithms based on RSS measurements Improving the position tracking accuracy in the presence of random shadowing #12
Outline 1. Introduction 2. Unique solvability and identifiability in cooperative networks Unique solvability via graph rigidity Correspondence between rigidity and identifiability Unique solvability via semidefinite programming 3. Cooperative localization algorithms 4. Position tracking based on RSS 5. Conclusions #13
Unique solvability Consider a network of N communicating nodes deployed in a d-dimensional space Network connectivity graph G=(V,E): V = set of vertices/nodes E = set of edges Two nodes are connected if their separating distance is known Node i is located at vector x i d Distance between nodes i and j: d i,j = x i x j #14
Unique solvability Assumption: Noise free ranging measurements Network localization problem (constraint satisfaction problem) Find Positions of target nodes Subject to Positions of anchors nodes Distance constraints Unique feasible solution: All the nodes positions are uniquely solvable Constraint-satisfaction problem with linear constraints Y = AX Unique solvability A is full column rank The constraints of the network localization problem are non-linear Tools for checking unique solvability Graph rigidity Semidefinite programming (SDP) #15
Graph rigidity Graph rigidity theory: Determining whether a graph has a unique realization in a given space dimension verifying a set of inter-vertex distance values Graph rigidity defines three kinds of frameworks: For a network having d+1 anchor nodes in general positions: All the nodes are uniquely solvable The network framework is globally rigid A node belongs to a globally rigid sub-framework the node has a unique solution This condition is not necessary No sufficient and necessary condition for unique solvability is yet known Generic frameworks Flexible Rigid Globally rigid Rigidity and global rigidity depend only on network graph connectivity #16
Identifiability in cooperative localization Ranging measurement between two nodes u and v is random due to noise: Unknown vector of targets positions: Observation vector: y : vector of all ranging measurements {y u,v } Likelihood function: Identifiability theory: Possibility of drawing inference from parametric models Two parameters are observationally equivalent if A parameter is globally identifiable if there is no other observationally equivalent to it. #17
Identifiability and rigidity Derivation of several correspondences between rigidity and identifiability: verifies some properties Theorem For a d-dimensional network having at least d+1 anchor nodes in general positions Global rigidity Global identifiability For generic networks, identifiability is a graph connectivity property independent of measurements and positions values Asymptotic estimation properties: Consistency Asymptotic normality as the number of measurements trials Derivation of sufficient conditions for consistency and asymptotic normality Global identifiability is among these sufficient conditions #18
Consistent estimation Example of a consistent estimator: Maximum-Likelihood ToA measurements: y i,j = d i,j + e i,j ; e i,j (0,1) #19
Unique solvability via semidefinite programming Another tool for checking unique solvability: Semidefinite programming (SDP) SDP does not detect all the uniquely solvable nodes We developed an iterative SDP based algorithm (ISDP) that improves the detection of these nodes compared to the state of the art algorithm (SSDP) SDP vs. Global rigidity Generic/Non-generic SDP Not restricted to generic Global rigidity Restricted to generic Information needed True distance values Connectivity Complexity O(N 3 + E N 2 + E 3 ) O(N 3 ) Centralized/Distributed Centralized Centralized #20
Global rigidity vs. SDP Performance comparison Network size: N = 10 nodes Number of anchor nodes: m=3 anchors Random deployment inside a square area and random connectivity based on received power Probability distribution of the number uniquely solvable nodes #21
Outline 1. Introduction 2. Unique solvability and identifiability in cooperative networks 3. Cooperative localization algorithms Distributed algorithms Cooperative localization via message passing Flip ambiguity 4. Position tracking based on RSS 5. Conclusions #22
Distributed algorithms: Incremental algorithms Incremental algorithms perform iteratively: Additional nodes are localized at each iteration, and then promoted to anchors Advantages: Simple to implement (complexity linear in the number of nodes) Not restricted to isotropic topologies Drawbacks: Do not apply to all networks Error accumulation (hard decision) Errors due to flips can propagate in an avalanche way #23
Distributed algorithms: Successive refinement Successive refinement algorithms: Iterative algorithms At iteration (k) Node i obtains the estimates of its neighbors Neigh(i) at iteration (k-1) Then it updates its estimate locally (e.g., by minimizing a local cost function) Drawbacks: - Very sensitive to initialization - High number of iterations #24
Distributed algorithms: Message passing Probabilistic estimation: Exploiting the probabilistic models for the measurements and the a priori information Joint posterior distribution: Message passing algorithms: Distributed computation of the marginal distribution functions by exchanging messages between the nodes, iteratively Positions can be estimated locally Representation of uncertainties A suitable message passing algorithm for the localization problem: Belief propagation (BP) Numerical implementation using nonparametric belief propagation (NBP) A new variant of NBP: Two-phased NBP (TP-NBP) Extension of the classical NBP with a phase of inference in discrete state space Reduction of the size of exchanged messages Improved positioning accuracy Small increase of the number of iterations #25
Message passing using belief propagation Messages to node 5 at iteration#1 Messages to node 5 at iteration#2 Belief of node 5 at iteration#1 Belief of node 5 at iteration#2 #26
Message passing using belief propagation Handling outliers N = 25 nodes, 4 anchors Positions randomly generated in an area of size 100mx100m Connectivity range : 100m Measurements affected by additive error with outliers #27
Introduction Unique solvability & identifiability Cooperative localization RSS tracking Conclusions Flip ambiguity Flips correspond to erroneous geometrical realizations (identifability, topology, noise) Belief of node 5 MAP estimate for node 5 MMSE estimate for node 5 Flips mitigation: Exploiting the connectivity information Non-direct neighbors are more likely to be far from each other k-step neighbors: separated by k hops Implementation via message passing: Exchange messages up to k-step neighbors Node of interest 2-step neighbor TP-NBP reduces the amount of exchanged data Direct neighbor #28
Outline 1. Introduction 2. Unique solvability and identifiability in cooperative localization 3. Cooperative localization algorithms 4. Position tracking based on RSS Joint position and shadowing estimation On-line shadowing maps estimation 5. Conclusions #29
Position tracking based on RSS Tracking consists in estimating the position over time of a moving terminal: Accuracy improvement over static localization: The history of observations is exploited Motion subject to constraints (kinematic laws and space layout) Possibility of integrating inertial navigation sensors (INS) (e.g. accelerometers) We consider the use of RSS Measurements available by default Problem: Presence of random shadowing due to propagation environment A classical solution for mitigating the shadowing: Fingerprinting Drawback: Substantial time and effort are required to construct the database and to maintain it up-to-date Two Bayesian tracking solutions were developed 1. Joint position and shadowing tracking by exploiting the shadowing spatial correlation 2. Shadowing maps estimation during the on-line tracking phase #30
Shadowing process modeling RSS measurement (in db) with one base station (or anchor node) Deterministic function White noise (time varying shadowing, ) Positions dependent shadowing Absence of information about the shadowing: Modeling as a realization of a spatially correlated Gaussian random field For one moving terminal, we define : position of the terminal at time kt White shadowing Correlated shadowing shadowing components of the N BS base stations at time kt For a moving terminal, the spatial correlation of the shadowing is transformed into a temporal one Given the positions, can be modeled by a k-order Gaussian process #31
Joint position and shadowing tracking Hidden state at time kt: Kinematic component s 0 s 1 s k-1 s k RSS observation vector at time kt: Bayesian tracking: y 1 y k-1 y k Computation of the joint posterior distribution Application of a Bayesian estimator Example MMSE No closed form solution for approximation using particle filters #32
Joint position and shadowing tracking Classical particle filter: Representation of all the components of the state vector with particles : For a given trajectory of kinematic components Linear auto-regressive model: Linear observation w.r.t. the shadowing: Rao-Blackwellized particle filter: The shadowing is tracked analytically At time (k-1)t: At time kt, for each sampled trajectory #33
Application to vehicle tracking in a Macro-cellular system Motion model: Kinematic vector: : acceleration delivered by an INS, error std: 0.5m/s 2 Tracking with map constraints Macro cell deployment: 4 base stations with 3 sectors Shadowing: Standard deviation Exponential correlation with at 50m #34
Application to vehicle tracking in a Macro-cellular system Traj#1: Average speed = 57km/h Sampling step T=0.4 seconds #35
Application to vehicle tracking in a Macro-cellular system Traj#2: Average speed = 34 km/h Sampling step T=1 seconds #36
On-line shadowing maps estimation Shadowing map and shadowing atlas N BS base stations are deployed For the i th BS, representation of the shadowing using basis expansion Deterministic function Shadowing map: Shadowing atlas: Collection of the N BS maps: Solutions for estimating the atlas Solution#1: Fingerprinting RSS measurements at known positions Solution#2: Use of unlabeled traces Unlabeled trace: Collection of observations made with a mobile terminal at unknown positions RSS observations: Other positioning observations: Gaussian coefficient Application of Monte Carlo methods to compute the atlas distribution: #37
Application to indoor tracking Motion model: N BS = 4 base stations Shadowing: Standard deviation Exponential correlation with at 2m Other positioning observations: : ToA with #38
Application to indoor tracking Tracking based on RSS and using estimated atlas #39
Outline 1. Introduction 2. Unique solvability and identifiability in cooperative localization 3. Cooperative localization algorithms 4. Position tracking based on RSS 5. Conclusions #40
Conclusions Cooperative static localization Unique solvability and Identifiability Development of a solution that improves the detection of uniquely solvable nodes Derivation of correspondences between the rigidity and the identifiability Cooperative static localization Development of solution based on NBP that improves the positioning accuracy and exploits the connectivity information Tracking based on RSS Development of solutions for improving the accuracy in the presence of random shadowing Wireless localization has been an active research topic during the last decade Some research topics Propagation and mobility models NLoS identification and mitigation Hybrid positioning and data fusion algorithms Seamless indoor/outdoor localization Communication-oriented means supporting localization #41
References Thesis dissertation: Some Signal Processing Techniques for Wireless Cooperative Localization and Tracking, Hadi Noureddine, Nov. 2012 WHERE2 project deliverables : www.kn-s.dlr.de/where2/ #42
WHERE 2 project Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2 European FP7 porject Duration: 36 Months (June 2010-June 2013) 15 partners (universities, R&D centers, SMEs, industrials) Objectives of WHERE2: Enhancing Positioning features by communication networks and non- radio sensors Improving Communications by geo-location information Developing integrated hardware platform to confirm performance and feasibility of cooperative positioning and communications algorithms Four research workpackages Deliverables available online: www.kn-s.dlr.de/where2/ #43
WHERE 2 project WP1 Scenarios, relevant models and market feedback Task 1.1 Scenarios and Parameters Task 1.2 Wireless channel characterization Task 1.3 Report on market and standardization WP2 Heterogeneous Context-aware Cooperative Positioning Task 2.1 Synergetic Cooperative Location and Communications for Dynamic Heterogeneous Networks - Dynamic and cooperative localization -Links selection and communication-oriented means supporting the localization Task 2.2 location information extraction - Inertial sensors - Geometry of the environment and map constrains - Fingerprinting database generation using Ray Tracing Task 2.3 Self-learning positioning using inferred context information - Retrieving the shape and the physical properties of indoor environments - Anchor-less localization - Mobility learning for enhancing the tracking functionality #44
WHERE 2 project WP3 Geo-location aided cooperation for future wireless networks Task 3.1: Coordination and Cooperation between Network Nodes - Coordination and cooperation between of cell sites - Reducing signaling overhead Task 3.2 Realization and usage of geo-location based clustering and mobile relaying - Cluster head selection for mobile nodes, - Secure and trustworthy management and location discovery protocols - Handover optimization, two-hop relay selection Task 3.3 Location-aided PHY/MAC Layer Design for Advanced Cognitive Radios - Spectrum sensing, multi-antenna cognitive radios - Spectrum sharing and cognitive medium access techniques WP4 Heterogeneous test bed for location and communications - Measurement campaigns with several technologies: Wifi, UWB, ZigBee, LTE and OFDM - Database of the measurements is available - Application of different localization algorithms to the real data - Vertical Handover demonstrator #45
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