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Received signal strength based localization
Received signal strength based localization
18
Signal-strength based positioning Unless I know where I am, I cannot possibly know if I have reached where I ought to be. Dr. Kshitij Tiwari
Contents 18.1 Localization based on signal strength 218 18.2 Challenges to received signal-strength based localization 18.2.1 Lack of labeled training data 219 18.2.2 Sparsity of training data 220 18.2.3 Propagating location uncertainty while training
219
221
18.3 Summary 221 References 221
Highlights • • •
Received Signal-Strength (RSS) based Localization Challenges to RSS based localization Scope of further research
When designing Gaussian Process (GP) regression models to fit the natural phenomenon for monitoring the spatial variations and temporal evolutions of the environment, two key factors need to be considered: (i) the measurements and (ii) the locations where these measurements are gathered from. Together, they are referred to as inputs to the GPs. While the on-board sensor being used for data acquisition provides the measurement of interest, what is often lacking is the location where the measurement is gathered from. This is owing to the fact that the robot operates in unknown environments and needs to “localize” itself with respect to the environment which then also informs the model of the geo-tagged observations that need to be used for training the model. This chapter describes one of the possible solutions to localization. The approach is called received signal-strength based localization (RSS), which, as the name suggests, aims at inferring the location based on the signal strength being observed by the sensors. In what follows, the state-of-the-art for such models is disMulti-Robot Exploration for Environmental Monitoring. https://doi.org/10.1016/B978-0-12-817607-8.00035-6 Copyright © 2020 Elsevier Inc. All rights reserved.
218
Multi-Robot Exploration for Environmental Monitoring
cussed that endow coupling GPs with RSS seamlessly. This allows for one model to solve multiple problems simultaneously.
18.1 Localization based on signal strength
Figure 18.1 Illustration showing robot operating in an indoor environment trying to localize based on received WiFi signal strength. The closer the robot to the WiFi router, the higher the signal strength (shown in green). The farther the robot is from WiFi, the lower the signal strength, i.e., in the red zone. Used with permission from Ekahau HeatMapper www.ekahau.com.
The notion of RSS encompasses deciphering of self-location based on the strength of the measurements being acquired. Consider the illustration shown in Fig. 18.1. Given a WiFi signal-strength map in an operational environment (here indoors), the robot uses the WiFi signal strength to decode its own location. The closer the robot to the source, the higher the signal strength, and vice-versa. Mathematically, this would be represented as Dist ∝
1 , RSS
(18.1)
where Dist refers to the distance from the signal source and RSS is the strength of the received signal. In [1], Schwaighofer et al. describe a positioning system aimed at providing customized location based services to mobile users. The key idea of the Gaussian process positioning system (GPPS) is to use Gaussian process models for the signal strength received from each base station, and to obtain position estimates via maximum likelihood, i.e., by searching for the position which best fits the measured signal strengths. This work was further extended in [2], wherein the authors introduced a Bayesian filter in the architecture that can be used to represent free spaces for constraining the
Received signal strength based localization
219
robot motion. While hallways, stair cases, and elevators are represented by edges in a graph, areas such as rooms are represented by bounded polygons. Using this representation, one can model both constrained motion such as moving down a hallway, or going upstairs, and less constrained motion through rooms and open spaces. The likelihood of signal strength measurements is extracted from a GP that is learned from calibration data. In contrast to existing approaches, this technique explicitly models the probability of not detecting an access point, which can greatly increase the quality of the global localization process (previously described in Chap. 4). In [3], the authors discuss signal-strength based localization in the GPS-denied indoor environments where other signals like WiFi, which are very likely to be found in most of the indoor settings, can be used to estimate the position. In [4], the authors propose a method for RSS-based localization of robots operating in outdoor environments by proposing hardware modifications to reduce electrical interference. Additionally, a particle filter was used to fuse the odometric, RSS, and ultrasonic sensor information to bring down the localization error to sub-meter levels.
18.2
Challenges to received signal-strength based localization
There are several challenges when relying on received signal-strength based localization mechanisms. Some of them are described in further detail below along with the state-of-the-art works that serve to address these problems.
18.2.1 Lack of labeled training data The key problem in RSS-based localization strategies is the need for labeled signal strength training data against the locations on a ground-truth map. In terms of Eq. (18.1), this refers to the fact that just by knowing the distance Dist from the source, one cannot directly transform that into a 2D (or 3D) location in space unless an explicit model is provided to do so with labeled training data samples. To illustrate this, consider an example of the recent buzzword: the rabbit–duck “illusion” [5] which is shown in Fig. 18.2. Some researchers have argued against this being an illusion altogether. For instance, John F. Kihlstrom from the University of California, Berkeley, describes it as an ambiguous (bistable)1 figure. Such optical “illusions” have confused humans for over 100 years, and now this also confuses computer vision techniques, too.2 Thus, if both these training samples were to be fed to a machine learning model, the confidence of the model in labeling the images will constantly fluctuate between 1 Further details can be found in the article here: https://www.ocf.berkeley.edu/~jfkihlstrom/JastrowDuck.
htm. 2 For an illustration, the readers are encouraged to visit https://tinyurl.com/y4cqph9k.
220
Multi-Robot Exploration for Environmental Monitoring
the image being a rabbit or a duck based on the orientation. The key takeaway point from this optical illusion and many others like this is that apt training data are a key requirement for supervised learning methods. The same is also valid for RSS-based localization settings as well. However, this can often be prohibitive to collect or maintain as the size of the map and the domain grows. For instance, imagine labeling all the potential optical illusions explicitly in the whole wide world. This would require quite some effort. To remedy this, [6] suggest utilizing the GP-latent variable model (GP-LVM) [7] to determine the latent-space locations of unlabeled signal strength data. This model, when coupled with an appropriate motion model, can be used to reconstruct a topological connectivity graph from a signal strength sequence which, in combination with the learned Gaussian Process signal-strength model, can be used to perform efficient localization. In [8], GP-localization framework was presented that harnesses the spatial correlations in measurements to train a GP model online as opposed to relying on a priori acquired training data. Given that the model incurs constant time and memory overheads per filtering step, it was claimed to be optimal for persistent robot localization.
Figure 18.2 The famous rabbit–duck “illusion” example. (A) Original image looks like a rabbit. (B) Rotated image looks like a duck. Images taken from [9].
18.2.2 Sparsity of training data The observations that are acquired by robots or mobile sensor nodes, in general, are not only noisy but also sparse. In [10], the authors address the challenge of localization in both indoor and outdoor settings whilst acquiring sparse set of noisy observations. The basic approach is to fit an interpolant to the training data, representing the expected observation, and to assume additive sensor noise. This paper takes a Bayesian view of the problem, maintaining a posterior over interpolants rather than simply the maximum-likelihood interpolant, giving a measure of uncertainty in the map at any point.
Received signal strength based localization
221
18.2.3 Propagating location uncertainty while training All the aforementioned works have shown meter to sub-meter accuracy in estimating the location of the robot/sensor being used to monitor the received signal strength. This induces uncertainty in localization and must be accounted for when utilizing the location information for preparing training data for GPs. There are few works that illustrate how to handle this aspect. In [11], Jadaliha et al. discuss the GP inference problem under localization uncertainty. This is an important aspect to account for as the localization mechanisms are noisy and can only provide estimates within accuracy of the order of meters.
18.3 Summary Previous chapters in the book have described how to “map” an environmental phenomenon, and this chapter describes how to localize the robot/sensor with respect to the received signal strength of the signal being observed. Both these aspects utilize the strengths of GPs, and hence lay the groundwork for combining them to work towards simultaneous localization and mapping (SLAM). In the following chapter, concluding remarks along with an executive summary of the overall contents are presented.
References [1] A. Schwaighofer, M. Grigoras, V. Tresp, C. Hoffmann, GPPS: a Gaussian process positioning system for cellular networks, in: Advances in Neural Information Processing Systems, 2004, pp. 579–586. [2] B.F.D. Hähnel, D. Fox, Gaussian processes for signal strength-based location estimation, in: Proceeding of Robotics: Science and Systems, Citeseer, 2006. [3] Y. Sun, M. Liu, M.Q.H. Meng, WiFi signal strength-based robot indoor localization, in: Information and Automation (ICIA), 2014 IEEE International Conference on, IEEE, 2014, pp. 250–256. [4] J. Graefenstein, M.E. Bouzouraa, Robust method for outdoor localization of a mobile robot using received signal strength in low power wireless networks, in: Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, IEEE, 2008, pp. 33–38. [5] R. Malach, I. Levy, U. Hasson, The topography of high-order human object areas, Trends in Cognitive Sciences 6 (4) (2002) 176–184. [6] B. Ferris, D. Fox, N. Lawrence, WiFi-SLAM using Gaussian process latent variable models, in: Proceedings of the 20th International Joint Conference on Artificial Intelligence, IJCAI’07, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2007, pp. 2480–2485, URL http://dl.acm.org/citation.cfm?id=1625275.1625675. [7] N.D. Lawrence, Gaussian process latent variable models for visualisation of high dimensional data, in: Advances in Neural Information Processing Systems, 2004, pp. 329–336. [8] K.H. Low, N. Xu, J. Chen, K.K. Lim, E.B. Özgül, Generalized online sparse Gaussian processes with application to persistent mobile robot localization, in: Joint European Con-
222
Multi-Robot Exploration for Environmental Monitoring
ference on Machine Learning and Knowledge Discovery in Databases, Springer, 2014, pp. 499–503. [9] https://tinyurl.com/c35jty. [10] A. Brooks, A. Makarenko, B. Upcroft, Gaussian process models for indoor and outdoor sensor-centric robot localization, IEEE Transactions on Robotics 24 (6) (2008) 1341–1351. [11] M. Jadaliha, Y. Xu, J. Choi, N.S. Johnson, W. Li, Gaussian process regression for sensor networks under localization uncertainty, IEEE Transactions on Signal Processing 61 (2) (2013) 223–237.
18
Signal-strength based positioning Unless I know where I am, I cannot possibly know if I have reached where I ought to be. Dr. Kshitij Tiwari
Contents 18.1 Localization based on signal strength 218 18.2 Challenges to received signal-strength based localization 18.2.1 Lack of labeled training data 219 18.2.2 Sparsity of training data 220 18.2.3 Propagating location uncertainty while training
219
221
18.3 Summary 221 References 221
Highlights • • •
Received Signal-Strength (RSS) based Localization Challenges to RSS based localization Scope of further research
When designing Gaussian Process (GP) regression models to fit the natural phenomenon for monitoring the spatial variations and temporal evolutions of the environment, two key factors need to be considered: (i) the measurements and (ii) the locations where these measurements are gathered from. Together, they are referred to as inputs to the GPs. While the on-board sensor being used for data acquisition provides the measurement of interest, what is often lacking is the location where the measurement is gathered from. This is owing to the fact that the robot operates in unknown environments and needs to “localize” itself with respect to the environment which then also informs the model of the geo-tagged observations that need to be used for training the model. This chapter describes one of the possible solutions to localization. The approach is called received signal-strength based localization (RSS), which, as the name suggests, aims at inferring the location based on the signal strength being observed by the sensors. In what follows, the state-of-the-art for such models is disMulti-Robot Exploration for Environmental Monitoring. https://doi.org/10.1016/B978-0-12-817607-8.00035-6 Copyright © 2020 Elsevier Inc. All rights reserved.
218
Multi-Robot Exploration for Environmental Monitoring
cussed that endow coupling GPs with RSS seamlessly. This allows for one model to solve multiple problems simultaneously.
18.1 Localization based on signal strength
Figure 18.1 Illustration showing robot operating in an indoor environment trying to localize based on received WiFi signal strength. The closer the robot to the WiFi router, the higher the signal strength (shown in green). The farther the robot is from WiFi, the lower the signal strength, i.e., in the red zone. Used with permission from Ekahau HeatMapper www.ekahau.com.
The notion of RSS encompasses deciphering of self-location based on the strength of the measurements being acquired. Consider the illustration shown in Fig. 18.1. Given a WiFi signal-strength map in an operational environment (here indoors), the robot uses the WiFi signal strength to decode its own location. The closer the robot to the source, the higher the signal strength, and vice-versa. Mathematically, this would be represented as Dist ∝
1 , RSS
(18.1)
where Dist refers to the distance from the signal source and RSS is the strength of the received signal. In [1], Schwaighofer et al. describe a positioning system aimed at providing customized location based services to mobile users. The key idea of the Gaussian process positioning system (GPPS) is to use Gaussian process models for the signal strength received from each base station, and to obtain position estimates via maximum likelihood, i.e., by searching for the position which best fits the measured signal strengths. This work was further extended in [2], wherein the authors introduced a Bayesian filter in the architecture that can be used to represent free spaces for constraining the
Received signal strength based localization
219
robot motion. While hallways, stair cases, and elevators are represented by edges in a graph, areas such as rooms are represented by bounded polygons. Using this representation, one can model both constrained motion such as moving down a hallway, or going upstairs, and less constrained motion through rooms and open spaces. The likelihood of signal strength measurements is extracted from a GP that is learned from calibration data. In contrast to existing approaches, this technique explicitly models the probability of not detecting an access point, which can greatly increase the quality of the global localization process (previously described in Chap. 4). In [3], the authors discuss signal-strength based localization in the GPS-denied indoor environments where other signals like WiFi, which are very likely to be found in most of the indoor settings, can be used to estimate the position. In [4], the authors propose a method for RSS-based localization of robots operating in outdoor environments by proposing hardware modifications to reduce electrical interference. Additionally, a particle filter was used to fuse the odometric, RSS, and ultrasonic sensor information to bring down the localization error to sub-meter levels.
18.2
Challenges to received signal-strength based localization
There are several challenges when relying on received signal-strength based localization mechanisms. Some of them are described in further detail below along with the state-of-the-art works that serve to address these problems.
18.2.1 Lack of labeled training data The key problem in RSS-based localization strategies is the need for labeled signal strength training data against the locations on a ground-truth map. In terms of Eq. (18.1), this refers to the fact that just by knowing the distance Dist from the source, one cannot directly transform that into a 2D (or 3D) location in space unless an explicit model is provided to do so with labeled training data samples. To illustrate this, consider an example of the recent buzzword: the rabbit–duck “illusion” [5] which is shown in Fig. 18.2. Some researchers have argued against this being an illusion altogether. For instance, John F. Kihlstrom from the University of California, Berkeley, describes it as an ambiguous (bistable)1 figure. Such optical “illusions” have confused humans for over 100 years, and now this also confuses computer vision techniques, too.2 Thus, if both these training samples were to be fed to a machine learning model, the confidence of the model in labeling the images will constantly fluctuate between 1 Further details can be found in the article here: https://www.ocf.berkeley.edu/~jfkihlstrom/JastrowDuck.
htm. 2 For an illustration, the readers are encouraged to visit https://tinyurl.com/y4cqph9k.
220
Multi-Robot Exploration for Environmental Monitoring
the image being a rabbit or a duck based on the orientation. The key takeaway point from this optical illusion and many others like this is that apt training data are a key requirement for supervised learning methods. The same is also valid for RSS-based localization settings as well. However, this can often be prohibitive to collect or maintain as the size of the map and the domain grows. For instance, imagine labeling all the potential optical illusions explicitly in the whole wide world. This would require quite some effort. To remedy this, [6] suggest utilizing the GP-latent variable model (GP-LVM) [7] to determine the latent-space locations of unlabeled signal strength data. This model, when coupled with an appropriate motion model, can be used to reconstruct a topological connectivity graph from a signal strength sequence which, in combination with the learned Gaussian Process signal-strength model, can be used to perform efficient localization. In [8], GP-localization framework was presented that harnesses the spatial correlations in measurements to train a GP model online as opposed to relying on a priori acquired training data. Given that the model incurs constant time and memory overheads per filtering step, it was claimed to be optimal for persistent robot localization.
Figure 18.2 The famous rabbit–duck “illusion” example. (A) Original image looks like a rabbit. (B) Rotated image looks like a duck. Images taken from [9].
18.2.2 Sparsity of training data The observations that are acquired by robots or mobile sensor nodes, in general, are not only noisy but also sparse. In [10], the authors address the challenge of localization in both indoor and outdoor settings whilst acquiring sparse set of noisy observations. The basic approach is to fit an interpolant to the training data, representing the expected observation, and to assume additive sensor noise. This paper takes a Bayesian view of the problem, maintaining a posterior over interpolants rather than simply the maximum-likelihood interpolant, giving a measure of uncertainty in the map at any point.
Received signal strength based localization
221
18.2.3 Propagating location uncertainty while training All the aforementioned works have shown meter to sub-meter accuracy in estimating the location of the robot/sensor being used to monitor the received signal strength. This induces uncertainty in localization and must be accounted for when utilizing the location information for preparing training data for GPs. There are few works that illustrate how to handle this aspect. In [11], Jadaliha et al. discuss the GP inference problem under localization uncertainty. This is an important aspect to account for as the localization mechanisms are noisy and can only provide estimates within accuracy of the order of meters.
18.3 Summary Previous chapters in the book have described how to “map” an environmental phenomenon, and this chapter describes how to localize the robot/sensor with respect to the received signal strength of the signal being observed. Both these aspects utilize the strengths of GPs, and hence lay the groundwork for combining them to work towards simultaneous localization and mapping (SLAM). In the following chapter, concluding remarks along with an executive summary of the overall contents are presented.
References [1] A. Schwaighofer, M. Grigoras, V. Tresp, C. Hoffmann, GPPS: a Gaussian process positioning system for cellular networks, in: Advances in Neural Information Processing Systems, 2004, pp. 579–586. [2] B.F.D. Hähnel, D. Fox, Gaussian processes for signal strength-based location estimation, in: Proceeding of Robotics: Science and Systems, Citeseer, 2006. [3] Y. Sun, M. Liu, M.Q.H. Meng, WiFi signal strength-based robot indoor localization, in: Information and Automation (ICIA), 2014 IEEE International Conference on, IEEE, 2014, pp. 250–256. [4] J. Graefenstein, M.E. Bouzouraa, Robust method for outdoor localization of a mobile robot using received signal strength in low power wireless networks, in: Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, IEEE, 2008, pp. 33–38. [5] R. Malach, I. Levy, U. Hasson, The topography of high-order human object areas, Trends in Cognitive Sciences 6 (4) (2002) 176–184. [6] B. Ferris, D. Fox, N. Lawrence, WiFi-SLAM using Gaussian process latent variable models, in: Proceedings of the 20th International Joint Conference on Artificial Intelligence, IJCAI’07, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2007, pp. 2480–2485, URL http://dl.acm.org/citation.cfm?id=1625275.1625675. [7] N.D. Lawrence, Gaussian process latent variable models for visualisation of high dimensional data, in: Advances in Neural Information Processing Systems, 2004, pp. 329–336. [8] K.H. Low, N. Xu, J. Chen, K.K. Lim, E.B. Özgül, Generalized online sparse Gaussian processes with application to persistent mobile robot localization, in: Joint European Con-
222
Multi-Robot Exploration for Environmental Monitoring
ference on Machine Learning and Knowledge Discovery in Databases, Springer, 2014, pp. 499–503. [9] https://tinyurl.com/c35jty. [10] A. Brooks, A. Makarenko, B. Upcroft, Gaussian process models for indoor and outdoor sensor-centric robot localization, IEEE Transactions on Robotics 24 (6) (2008) 1341–1351. [11] M. Jadaliha, Y. Xu, J. Choi, N.S. Johnson, W. Li, Gaussian process regression for sensor networks under localization uncertainty, IEEE Transactions on Signal Processing 61 (2) (2013) 223–237.