nips nips2003 nips2003-76 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Anton Schwaighofer, Marian Grigoras, Volker Tresp, Clemens Hoffmann
Abstract: In this article, we present a novel approach to solving the localization problem in cellular networks. The goal is to estimate a mobile user’s position, based on measurements of the signal strengths received from network base stations. Our solution works by building Gaussian process models for the distribution of signal strengths, as obtained in a series of calibration measurements. In the localization stage, the user’s position can be estimated by maximizing the likelihood of received signal strengths with respect to the position. We investigate the accuracy of the proposed approach on data obtained within a large indoor cellular network. 1
Reference: text
sentIndex sentText sentNum sentScore
1 at/aschwaig Abstract In this article, we present a novel approach to solving the localization problem in cellular networks. [sent-4, score-0.341]
2 The goal is to estimate a mobile user’s position, based on measurements of the signal strengths received from network base stations. [sent-5, score-0.751]
3 Our solution works by building Gaussian process models for the distribution of signal strengths, as obtained in a series of calibration measurements. [sent-6, score-0.741]
4 In the localization stage, the user’s position can be estimated by maximizing the likelihood of received signal strengths with respect to the position. [sent-7, score-0.7]
5 We investigate the accuracy of the proposed approach on data obtained within a large indoor cellular network. [sent-8, score-0.243]
6 All such services crucially depend on methods to accurately estimate the position of the mobile user within the network (“localization”, “positioning”). [sent-14, score-0.309]
7 We proceed by introducing the localization problem in detail in Sec. [sent-19, score-0.277]
8 3 shows how the required calibration stage of the system can be performed in an optimal manner. [sent-25, score-0.584]
9 We show that the GPPS gives accurate location estimates, in particular when only very few calibration measurements are available. [sent-28, score-0.671]
10 1 Problem Description Our overall goal is to develop a localization system for indoor cellular networks, that is (in order to minimize cost) based solely on existing standard networking hardware. [sent-30, score-0.546]
11 Location estimates can be based on different characteristics of the radio signal received at the mobile station (i. [sent-31, score-0.619]
12 Yet, in most hardware, the only available information about the radio signal is the received signal strength. [sent-34, score-0.453]
13 Information like phase or propagation time from the base station requires additional hardware, and can thus not be used. [sent-35, score-0.463]
14 In general, estimating the user’s position based only on measurements of the signal strength is known to be a very challenging task [7], in particular in indoor networks. [sent-36, score-0.546]
15 Due to reflections, refraction, and scattering of the electromagnetic waves along structures of the building, the received signal is only a distorted version of the transmitted signal. [sent-37, score-0.263]
16 Also, the localization system ought to be robust, since base stations may fail, be switched off, or may be temporarily shielded for unknown reasons. [sent-43, score-0.62]
17 In these cases, a sensible localization system should not draw the conclusion that the user is far from the respective base station. [sent-44, score-0.6]
18 Due to the complex signal propagation behaviour, almost all previous approaches to indoor localization use an initial calibration stage. [sent-45, score-1.059]
19 Calibration here means that signal strengths received from the network base stations are measured at a number of points inside the building. [sent-46, score-0.761]
20 Systems differ in their ways of using this calibration data. [sent-47, score-0.522]
21 In a “forward modelling” approach, a model of signal strength as a function of position is built first. [sent-49, score-0.334]
22 The localization procedure then tries to find the location which best agrees with the measured signal strengths. [sent-50, score-0.452]
23 Alternatively, the mapping from signal strengths to position can be modelled directly (“inverse modelling”). [sent-51, score-0.291]
24 The RADAR system [1], one of the first indoor localization systems, is an inverse modelling approach using a nearest neighbor technique. [sent-52, score-0.515]
25 [7] build simple probabilistic models from the calibration data (forward modelling), in conjunction with maximum likelihood position estimation. [sent-53, score-0.681]
26 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. [sent-59, score-0.933]
27 by searching for the position which best fits the measured signal strengths. [sent-61, score-0.249]
28 Consider a cellular network with a total of B base stations. [sent-62, score-0.349]
29 Assume that, for each of base stations, we have a probabilistic model that describes the distribution of received signal strength. [sent-63, score-0.477]
30 More formally, we denote by p j (s j | t) the likelihood of receiving a signal strength s j from the j-th base station on position t. [sent-64, score-0.778]
31 , B given, localization can be done in a straight-forward way. [sent-68, score-0.246]
32 The user reports a vector s (of length B) of signal strength measurements for all base stations. [sent-69, score-0.637]
33 It may occur that no signal is received from some base stations (indicated by / s j = 0), e. [sent-70, score-0.594]
34 , because the user is too far from this base station, or due to hardware failure. [sent-72, score-0.335]
35 (1) In the above equation, we only use the likelihood contributions of those base stations that are actually received. [sent-74, score-0.358]
36 Alternatively, one could use a very low signal strength as a default value for each base station that is not received [7]. [sent-75, score-0.807]
37 We found that this can give high errors if a base station close to the user fails, since now the low default value indicates that one should expect the user to be far from the base station. [sent-76, score-0.823]
38 Yet, we still need to define and build suitable base station models p j (s j | t), j = 1, . [sent-78, score-0.468]
39 In the GPPS, we use Gaussian process (GP) models for this task, where each base station model is estimated from the calibration data. [sent-82, score-1.003]
40 Secondly, GPs are a nonparametric method that can flexibly adapt to the complex signal propagation behaviour observed in indoor cellular networks. [sent-85, score-0.401]
41 In the following sections, we will describe the GP models in more detail, and also discuss the choice of kernel function, which is of great importance in order to build an accurate localization system. [sent-92, score-0.329]
42 1 Gaussian Process Models for Signal Strengths In the GPPS, a Gaussian process (GP) approach is used for the models p j (s j | t) that describe the signal strength received from a single base station j. [sent-94, score-0.837]
43 1 that the proposed GPPS is based on a set calibration measurements, where the signal strength is measured at a number of points spread over the area to be covered. [sent-98, score-0.818]
44 Consider now the calibration data for a single base station j. [sent-99, score-0.955]
45 We denote this calibration data by D j = {(xi , yi )}N , meaning that a signal strength of yi has been measured i=1 on point xi , with a total of N calibration measurements. [sent-100, score-1.358]
46 , the measured signal strength yi is composed of a “true” signal strength s(xi ) plus independent Gaussian (measurement) noise ei of variance σ2 , with yi = s(xi ) + ei . [sent-103, score-0.602]
47 The Gaussian process assumption for the true signal s implies that the true signal strengths for all calibration 1 Assuming independence of the individual measurements. [sent-104, score-0.9]
48 One could also use a solution inspired from co-kriging, that takes into account the full dependence between signals received from different base stations. [sent-105, score-0.335]
49 Given the calibration data D j , the predictive distribution for the signal strength s j received on some arbitrary point t turns out to be Gaussian. [sent-115, score-0.912]
50 We set them by maximizing the marginal likelihood of the calibration data with respect to the model parameters, which turns out to be [6] ˆ ˆ (σ2 , θ) = arg max − log det Q − y Q−1 y . [sent-128, score-0.564]
51 (4) σ2 ,θ ˆ ˆ The model parameters (σ2 , θ) are set individually for each base station. [sent-129, score-0.214]
52 Firstly, it must be noted that taking calibration measurements is a very time-consuming (thus, expensive) task. [sent-152, score-0.631]
53 The number of calibration data must thus be kept as low as possible, while retaining high localization accuracy. [sent-153, score-0.768]
54 In the actual GPPS, the GP mean is a linear function of the distance to the base station (when signal strength is given on a logarithmic scale). [sent-161, score-0.699]
55 Starting point is the calibration data, with a total of C measurements. [sent-163, score-0.522]
56 ,C}, we / receive a signal strength of ci j from base station j, j ∈ {1, . [sent-167, score-0.693]
57 , B}, or ci j = 0 if base station j has not been received at xi (for example, due to signal obstruction). [sent-170, score-0.738]
58 The calibration data is then split into subsets D j containing those points where base station / j has actually been received, i. [sent-172, score-0.992]
59 For each base station, that is, for each data D j , we proceed as follows: 1. [sent-177, score-0.23]
60 Often, the exact position of base station j is not known. [sent-178, score-0.516]
61 2 In this case, we use a simple estimate for the base station position, that is the average of the 3 calibration points xi with maximum signal strength yi . [sent-179, score-1.263]
62 In particular with sparse calibration measurements, more sophisticated estimates for the base station position are difficult to come up with. [sent-181, score-1.068]
63 Compute the distance of each calibration point to the base station (using either the exact or the estimated position obtained in step 1). [sent-183, score-1.073]
64 As the mean function of the GP model, we fit a linear model3 to the received signal strength as a function of distance to the base station. [sent-184, score-0.601]
65 Subtract the value of the mean function from the 2 When setting up the network, or after modifying the network by moving base stations, the base station positions are often not recorded. [sent-185, score-0.702]
66 In a large assembly hall of 250 × 180 meters, measurements of signal strengths received from DECT base stations were made on 650 points spread over the hall. [sent-193, score-0.806]
67 We observed a very high fluctuation of received signals (up to ±10 dB when repeating measurements, while the total signal range is only −30 to −90 dB), both due to measurement noise, and due to dynamical changes of the environment. [sent-196, score-0.283]
68 We compare the GPPS with a nearest neighbor based localization system (abbreviated by NNLoc in the following), that is quite similar to the RADAR [1] approach. [sent-197, score-0.369]
69 4 This system finds the calibration measurements that best match the signal strength received at test stage. [sent-198, score-1.03]
70 Dense Calibration Points In a first experiment, we investigate the achievable precision of location estimates when using the full set of calibration measurements. [sent-201, score-0.592]
71 The total set of measurements is split up into five equally sized parts, where four of these parts were used as the calibration set. [sent-203, score-0.631]
72 We found that, in this setting, the nearest neighbor based method NNLoc works very fine, and provides an average localization error of 7 meters. [sent-206, score-0.326]
73 With the GPPS, localization is typically based on around 15 base stations, that is, 15 likelihood terms contributing to Eq. [sent-209, score-0.487]
74 Unfortunately, such a high number of calibration measurements is unlikely to be available in practice. [sent-211, score-0.631]
75 Taking calibration measurements is a very costly process, in particular if larger areas need to be covered. [sent-212, score-0.631]
76 Thus, one is very much interested in keeping the number of calibration points as low as possible. [sent-213, score-0.559]
77 Experiments with Sparse Calibration Points In the second experimental setup, we aim at building the positioning system with only a minimal number of calibration points. [sent-214, score-0.739]
78 The localization system is built based on these ˜ C points and evaluated on the fifth part of the data. [sent-217, score-0.342]
79 Out of the given calibration measurements, we select those C points that are closest (in terms of Euclidean distance) to the grid points. [sent-220, score-0.6]
80 1 we plot the localization accuracy, averaged over the 5fold cross validation, ˜ of the GPPS and the nearest neighbor based system built on only C calibration points, 4 We also investigated localization using Eq. [sent-222, score-1.169]
81 (1) with a simplistic propagation model, where the expected signal (on log scale) is a linear function of the distance to the base station. [sent-223, score-0.402]
82 Yet, this approach lead to very poor localization accuracy, and is thus not considered in more detail here. [sent-224, score-0.261]
83 Figure 1: Mean localization error of the GPPS and the NNLoc method, as a function of the number of calibration points used. [sent-225, score-0.805]
84 Vertical bars indicate ±1 standard deviation of the mean localization error. [sent-226, score-0.261]
85 The calibration points are either selected at random, or according to an optimal design criterion ˜ C ∈ {100, 50, 25, 12} calibration measurement. [sent-227, score-1.16]
86 It can be clearly seen that the GPPS system (with optimal design) achieves a high precision for its location estimates, even when using only a minimal number of calibration measurements. [sent-228, score-0.638]
87 With only 12 calibration measurements, GPPS achieves an average error of around 17 meters, while the competing method reaches only 29 meters at best. [sent-229, score-0.553]
88 In this setting, the average distance in between calibration measurements is around 75 meters. [sent-230, score-0.647]
89 Both the NNLoc system and the GPPS system show large improvements of performance when selecting the calibration points according to the optimal design, instead of a purely random fashion. [sent-231, score-0.664]
90 Also, note that the localization error of the GPPS system degrades only slowly when the number of calibration measurements is reduced. [sent-232, score-0.92]
91 In contrast, the curves for the nearest neighbor based method show a sharper increase of positioning error. [sent-233, score-0.211]
92 It is worth noticing that the choice of kernel functions has a strong impact on the localization accuracy of the GPPS. [sent-234, score-0.323]
93 It is also intere esting to consider different methods for selecting the calibration points. [sent-241, score-0.522]
94 2(b) plots the accuracy obtained with GPPS, when calibration points are either placed randomly, on a hexagonal grid (the theoretically optimal procedure) or on a square grid. [sent-243, score-0.748]
95 Somehow counterintuitively, a square grid for calibration gives a performance that is just as good or even worse than a random grid. [sent-244, score-0.584]
96 In contrast, localization with NNLoc performs about the same with either hexagonal or square grid (this is not plotted in the figure). [sent-245, score-0.387]
97 5 Conclusions In this article, we presented a novel approach to solving the localization problem in indoor cellular network networks. [sent-246, score-0.5]
98 Gaussian process (GP) models with the Mat´ rn kernel function e were used as models for individual base stations, so that location estimates could be computed using maximum likelihood. [sent-247, score-0.459]
99 We showed that this new Gaussian process positioning system (GPPS) can provide sufficiently high accuracy when used within a DECT network. [sent-248, score-0.231]
100 Furthermore, we showed how calibration points can be optimally chosen in order to provide high accuracy position estimates. [sent-250, score-0.671]
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