International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 453157, 11 pages

http://dx.doi.org/10.1155/2015/453157

## Source Geolocation in Urban Environments Using Multipath Fingerprinting

^{1}Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802, USA^{2}The Applied Research Laboratory, State College, PA 16803, USA

Received 16 December 2014; Revised 18 March 2015; Accepted 18 March 2015

Academic Editor: Ana Alejos

Copyright © 2015 Ram M. Narayanan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A method for determining the location of Global Systems for Mobile Communications (GSM) mobile transmitters is proposed. Our approach estimates the location of a source without the use of multilateration or Line-of-Sight (LOS) techniques. A Multipath Characteristic Database (MCD) containing the multipath feature vectors, for each possible transmitter location within an area of interest, is populated via ray-tracing software simulations. The multipath characteristics of interest are angle-of-arrival (AOA) (azimuth) and time-of-arrival (TOA). By minimizing the “distance” between estimated and simulated multipath feature vectors, an estimate for the actual source location can be obtained. The development of the estimation method is presented, followed by a detailed analysis of its estimation accuracy. Since the proposed method utilizes a simulated multipath signature database based upon the knowledge of the environment and the terrain, the need for *a priori* soundings from the area of interest is eliminated, thus making this location estimation system suitable for application in denied territories. Location accuracies compare favorably with the requirements for the location of wireless 9-1-1 callers as recommended by the Federal Communications Commission (FCC).

#### 1. Introduction

Spatial localization of cellular emitters in dense urban environments can provide a valuable tool for a variety of users such as emergency services, law enforcement, and military personnel. Navigation, social media, and location-dependent searching would also benefit from advances in localization techniques. The ability to use Non-Line-of-Sight (NLOS) and nonmultilateration techniques would allow the end user to perform the localization from an arbitrary position anywhere within a given range of the target.

The concept of using the multipath fingerprint composed of time- and angle-of-arrival data for wireless location finding in urban environments was developed using electromagnetic ray-tracing techniques and validated using computer-aided design (CAD) models of a real city [1]. The fundamental premise of this approach is to extract the features of the multipath signals to create a unique fingerprint, such as angle-of-arrival, time delay, and signal strength, which is then compared to a database of known fingerprints, each corresponding to a known location. A matching fingerprint found in the database provides an estimate for the correct location of the transmitter. A fingerprinting technique using the channel’s impulse response information combined with an artificial neural network was developed for geolocation in mines or other confined environments with rough sidewall surfaces with a location accuracy of 2 m [2]. A fingerprinting technique exploiting the spatial-temporal characteristics of the multipath signals received by the base station antenna array was proposed in [3]. The spatial-temporal fingerprint was based on a lower dimensional subspace of the spatial-temporal covariance matrix capturing the AOAs and the differential delays of the dominant multipath reflections. Localization accuracies of about 1 m were achieved in typical indoor environments. Similar fingerprinting techniques were also proposed and developed for emergency location services [4], Global Navigation Satellite System (GNSS) indoor positioning [5], indoor geolocation for ultrawideband (UWB) systems [6], and channel estimation in multipath-rich mobile communication scenarios [7].

The method discussed here compares simulated and measured signal characteristics based only upon multipath propagation to provide an estimate for the location of a GSM emitter. Our approach is different from the one adopted in [1] in that while their base station is located solely within their area of interest, ours may be located both inside and outside of the area of interest, the latter generally occurring in denied environments. Having the base station in the center yields higher variability in the AOA. For base stations located within the area of interest, AOAs are distributed over a 360-degree spread. However, for base stations located outside the area of interest, AOAs are mostly restricted to be within a 180-degree spread.

The Federal Communications Commission (FCC) recently issued its Third Further Notice of Proposed Rulemaking and proposed the following specific measures in their E911 location accuracy rules to ensure accurate indoor location information [8]. According to their guidelines, location accuracies must be within 100 meters for 67 percent of calls and 300 meters for 90 percent of calls for network-based technologies and within 50 meters for 67 percent of calls and 150 meters for 90 percent of calls for handset-based technologies. Network-based technologies have less stringent requirements compared to handset-based technologies. Our approach addresses the network-based case and, therefore, aims to satisfy the first set of requirements stated above. In addition, our approach avoids the use of received signal strength (RSS) as these are dependent on various unknown factors, such as transmit power, reflectivity of walls, and propagation characteristics, which do not largely impact TOA and AOA.

Through the use of ray-tracing software, a MCD is populated via simulations, which contains a feature vector for possible transmitter locations within an area of interest. The MCD is then used to find possible transmit locations that have similar multipath characteristics to that of the estimated parameters. The multipath characteristic estimators used here are joint angle delay estimation-multiple signal classification (JADE-MUSIC) and JADE Estimation of Signal Parameters via Rotational Invariance Techniques (JADE-ESPRIT). A -Weighted Nearest Neighbor (KWNN) distance metric between the estimated and simulated feature vectors is used to determine the final geolocation estimate. An analysis on the geolocation algorithm’s performance is presented which shows the effect of SNR, receiver location, oversampling rate, and number of antenna elements. The computational complexity of the JADE-MUSIC and JADE-ESPRIT is also analyzed.

Although GSM telephony was used in the analysis presented in subsequent sections, our proposed estimation techniques can be applied to all narrowband Time Division Multiple Access (TDMA) systems (which operate in multipath-rich environments). This paper discusses the results of an investigation of our proposed localization technique and extends the work previously reported by us in [9]. New results reported here include geolocation estimates derived from the JADE-ESPRIT algorithm, as well a comparison between estimates using a receiver located inside and outside the area of interest. A summary of the implemented algorithms is included, as well as result comparisons for various SNRs, oversampling rates, and number of antenna elements used.

This paper is organized as follows. Section 2 provides the linear approximation of GSM signals used in the estimation portion of the localization technique. Section 3 provides an introduction to the JADE estimation techniques. Section 4 discusses the creation of the MCD via ray-tracing software. Section 5 discusses the geolocation fingerprint matching technique. An analysis of the performance of the geolocation estimator is given in Section 6. Finally, Section 7 contains a summary and future work for the development of the proposed method.

#### 2. Linear Approximation of Gaussian Minimum-Shift Keying (GMSK)

GSM systems utilize a GMSK modulation scheme [10]. A method for representing digital phase modulations via superposition of amplitude modulated pulses was introduced by Laurent in [11]; this method was further investigated for signals with modulation index 1/2 in [12] and for GMSK in [13]. Wiesler et al. show that a GMSK signal with the GSM parameters can be decomposed into linear and nonlinear parts [13]:where is defined asand is the NRZ data stream. Since and (for ) are only found in the , we have omitted their definitions here. General expressions for and are given in equations 11 and 13 of [11], respectively. Wiesler et al. show that approximating solely by its linear term results in a BER performance as good as or (for good SNR) even better than the exact GMSK representation. We further simplify our representation of the GMSK modulated signal by setting the exponential term in of (1) equal to . Therefore, our linear approximation yieldswhere can be considered to represent the pulse shaping modulation function of a linear modulation scheme. This result is used in JADE techniques presented in subsequent sections.

#### 3. Joint Angle Delay Estimation (JADE)

The coherence time of the (Rayleigh) fading in the mobile channel is roughly given by [14]. This yields a coherence time of 160 ms for a mobile moving at a walking speed and 5.6 ms for a mobile moving at a highway speed. The fading can, therefore, be modeled as time-invariant for a single GSM frame at highway speeds and for up to 30 frames for walking speeds. Subsequently, for a transmitter moving at highway speeds or lower, the wireless channel has path fadings that are constant over multiple GSM time slots. An adaptation to the JADE techniques discussed here is presented in [15], which considers channels with path fadings varying within the duration of a time slot. The angles and delays of the received multipaths vary much slower than the mobile channel fading; therefore, we model these as time-invariant over many GSM frames [14].

Vanderveen et al. have developed JADE techniques based on the above assumptions. The -multipath channel model for a -element antenna array takes the following form (see [14, 16] for a complete analysis):where is the steering vector of the th multipath and is the steering matrix. The diagonal matrix of values denotes the complex attenuations associated with each multipath, denotes the th delayed pulse shaping modulation function, as shown in (2), and is a matrix containing the time-delayed pulse shaping functions. defines the length of the channel impulse response in symbol periods, and is the oversampling factor.

Unlike GSM’s modulation scheme which can be decomposed into both linear and nonlinear parts, the pulse-shaping modulation function is associated with an entirely linear modulation scheme. The aforementioned linear approximation of the GSM signal was used to accommodate this requirement.

##### 3.1. JADE-MUSIC Algorithm

Vanderveen et al. eventually arrive at a vectorized noisy channel estimate of the following form [16]:where denotes a column-wise Kronecker product, denotes the estimate noise, and the superscript denotes the th channel estimate. Here is time-invariant over channel estimates, where is determined based on the stationarity of the AOAs and TOAs for a given multipath scenario. The channel estimation rate is determined by the temporal coherence of the channel path fadings. The channel should be estimated once over the coherence time of the channel path fadings (i.e., the channel can be estimated on the order of a frame for a mobile moving at highway speeds and once every 30 frames for a mobile moving at a walking speed). After estimating channels, (6) can be represented in matrix form aswhere and and have similar form. A 2-dimensional MUSIC algorithm can now be applied to find and . The MUSIC algorithm will result in a joint delay and angle estimation under the following restrictions.(1)The number of multipaths, , must be less than .(2)The number of channel estimates used must be greater than the number of multipaths.(3)The collection time must be longer than the coherence time (for fadings) of the mobile channel.

A significant consequence of these restrictions is that the number of antenna elements needed can be reduced to less than the number of multipaths, if an adequate number of samples are obtained.

##### 3.2. JADE-ESPRIT Algorithm

The JADE-ESPRIT algorithm manipulates the form of the channel estimate matrix so that a 2D ESPRIT-like algorithm can be applied. First, the discrete Fourier transform is applied to the in (5). The pulse shaping function is then deconvolved from the Fourier-transformed channel estimate (see [16] for details), whereby the channel now satisfies the following model:where , and , and . Applying a similar vectorization and stacking operation as in the JADE-MUSIC algorithm, the vectorized noisy channel estimate becomeswhere . Next, a basis of the column span of is estimated via the left singular vectors which correspond to the largest values of covariance matrix, . A 2D ESPRIT algorithm is now applied and estimates for and can be obtained.

The restrictions of the JADE-ESPRIT algorithm are slightly stricter than those of the JADE-MUSIC algorithm, in addition to the aforementioned JADE-MUSIC restrictions. The number of multipaths must be less than , where is a factor used in the DFT (taken as 1 here).

#### 4. Multipath Characteristic Database Analysis

Remcom’s Wireless InSite ray-tracing software was used to populate the MCD, which contains location-based multipath feature vectors to be used as a basis for a fingerprint matching algorithm. A grid of transmitters was placed over the area of interest and then various multipath characteristics of the received signal are collected for each transmitter location. For the analysis here, only the AOA (azimuth) and TOA were considered for utmost simplicity and for minimizing processing and time requirements; however, the multipath feature vector could be expanded to contain (a) number of received multipaths; (b) AOA (azimuth and elevation) of each multipath; (c) TOA of each multipath; (d) received signal strength (RSS) of each multipath; (e) delay spread amongst rays; and (f) mean and standard deviation of all aforementioned multipath characteristics. Although adding additional features may doubtlessly increase the location accuracy, this would entail higher latency owing to excessive processing requirements.

A model of downtown State College, Pennsylvania, was used in the ray-tracing simulation. The model consisted of concrete buildings placed on top of the appropriate elevation (i.e., landscape). Transmitters were spaced in 3.5-meter increments along the - and -axes at a height of 2 meters (with respect to the ground). The grid covered a 1 km^{2} area and consisted of 81,796 transmitters. The receiver was placed at two different locations represented by Scenario A located outside the area of interest and Scenario B located within the area of interest. For Scenario A, the receiver was placed on top of the Applied Research Laboratory building of The Pennsylvania State University, at a height of 10 meters (approximately 2 meters above the building height). For Scenario B, the receiver was placed on top of the HUB-Robeson Center of The Pennsylvania State University, at a height of 12 meters (approximately 2 meters above the building height). Figure 1 shows the 2D representation of the Wireless InSite model overlaid on a satellite image of State College, PA. The transmit antennas were dipoles aligned perpendicular to the ground, and isotropic antennas were used in the receiver antenna array.