USE OF NEURAL NETWORKS IN INDOOR GEOLOCATION APPLICATIONS

P O ZN AN UN IV ER S IT Y O F T EC HN O LO G Y AC AD EM IC J OUR NA LS

No Electrical Engineering 2007

Tomasz KACPRZAK*

Maciej RUTECKI*

USE OF NEURAL NETWORKS IN INDOOR GEOLOCATION

APPLICATIONS

The aim of this paper is to present new method of placing radio stations used for geolocation in indoor applications. It takes advantages of use neural networks, resilience phenomenon, Brownian motion and Monte Carlo method. This allow to significantly reduce time needed to compute optimal position of antennas, number of it, while keeping good precision of calculation.

Keywords: indoor geolocation, neural network, resilience phenomenon, Brownian motion

1. INTRODUCTION

Main reason to conduct research under geolocation in indoor applications is to create system, that assists the blind or handicapped people to find objects (e.g. keys, documents, medicaments, etc.), which are equipped with small radio personal assistant of the form of transponders (eg. RFID). Person who has personal assistant choose from lists of register things this one, that has been lost. Radio station of known positions measurement distance between lost object and them and pass information about computing location to blind people. Information may have form like: “keys are on desk”. Such system should be reliable, user-friendly and sufficiently accurate, which results in measured localization error of no more then 50 centimeters. Also we require small size and weight, it should uses free of charge waveband and be easy to practicable. The accuracy of radio-signal localization is a difficult problem, especially when the room layout and interior obstacles (e.g. walls, furniture) are random, resulting in noise and signal reflections.

In ideal case (see Fig. 1), when we have three radio stations BS-1, BS-2 and BS-3 situated at known positions (xi, yi), i=1,2,3 as reference points, the positioning

system finds coordinates of the object O by calculating distances d_1, d_2 and d_3 using one of the method described in [3] (received-signal-strength, time-of-arrival, etc.). When no noise is assumed and direct (line-of-sigth) radio path is detected, the

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* Technical University of Lodz, Wólczańska st. 211/215, 90-924 Łódź, Poland.

2007

Poznańskie Warsztaty Telekomunikacyjne Poznań 6 - 7 grudnia 2007 POZNAN UNIVERSITY OF TECHNOLOGY ACADEMIC JOURNALS

coordinates of the unknown positioned object is calculated by finding minimum of the function: f  x ,y =

_∑







radio stations (N=3, as in example). In case when at least one undirect path is detected the estimation of the object position is erroneous.

Fig. 1. Three radio stations (BS-1, BS-2 and BS-3) of known positions, performing measurements of distance (adequately - d_1, d_2 and d_3) from the object O

There are two sources for ranging error [5]. First, caused by bandwidth limitations, when time of detection first signal peak of received signal (depending of radio channel profile) was shifted from expected time of arrival, consequently decreases error of distance measurement. Second source of ranging error is undetected direct path. Because of interference, in time-of-arrival (TOA) based methods range errors in multipath channels can by many times greater than those caused by bandwidth limitations. In some places signal from direct path will be attenuated by other multipath components. Also many multipath signals arrive very soon after the line-of-straight signal. Measurements shows [1] that if distance between transmitter and receiver increases participation of direct path in whole signal decreases. The phenomenon is more noticeable in indoor environment.

There are many solutions of these problems: replicate the signal in multiple frequency channels to provide frequency diversity, use a variety coding techniques, multiple antennas, modulations (e.g. orthogonal frequency-division multiplexing modulation – OFDM, space time coding techniques [9]), but because of complexity of problem, models developed for indoor propagations characteristics for telecommunication applications are not useful for indoor geolocation. Main problem is how to place radio stations, and how many required it for decrease measurement error. Therefore in this paper we propose new method of location a

given number of radio station within the given room layout in order to satisfy requirements, that in any search position the object is directly illuminated by at least three base stations.

2. THE PROPOSAL OF SOLUTION

Given room layout (two-dimensional case) and the number of radio stations initially randomly located find the final position of each one to ensure that at least three stations are visible from each point. Solution of this problem enables to determine coordinates of any unknown positioned object by finding minimum of the function (1). Also is necessary to take into consideration other constraints, like: any two or more radio stations should not be placed in the same position, range (depends on power, profile of antenna). We propose an algorithm which is adaptation of resilience phenomenon of the mass points and their Brownian motion. From physics [2], resilience is defined as the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading to have this energy recovered. In presented method this model is used to compute change position of each base station. Brownian motion [2] is either the random movement of particles suspended in a fluid or the mathematical model used to describe such random movements, often called a Wiener process. Based on this approach we propose the following model of the algorithm. Every radio station is treated as point, that repeal other stations (also points). The force between any two points is proportional to potential energy between them, calculated from resilience phenomenon: if distance between two points is increased, energy decreases and increment distance decreases. For N radio stations the total number of combination of two points is equal to N(N–1). The ensemble of points that represents radio stations try to get minimum energy by change of their positions. When the distance increases, the change of position in next step is smaller. For each two base stations (A and B in figure 2) at distance ri and each coordinate i is calculated, Δri:

{

y=r_yab (2)

where: a and b are constants.

Based on resilience phenomenon we estimate local minima, therefore to search global minimum we adopted Brownian motion model. This approach provides easy way to escape local minima especially for discontinuous and nonconvex objective functions. The infinitesimal generator [2] (characteristic operator) of a Brownian motion on Rn _{space is easily calculated to be ½Δ, where Δ denotes the Laplace}

operator. This observation is useful in defining Brownian motion on a m-dimensional Riemannian manifold (M, g). Brownian motion on M is defined to be a diffusion on M whose characteristic operator Ă in local coordinates xi, 1 ≤ i ≤ m,

is given by ½ΔLB, where ΔLB is the Laplace-Beltrami operator given in local

coordinates by: _LB= 1



∑





∑



Such stochastic optimization method offers remarkable advantages over other solutions particularly for complex problems with numerous local minima, when it is required to reach the global minimum. They are robust, reliable and suitable for nonconvex and discountinous functions also with discrete type variables. The only drawback is the huge computational effort and slow convergence. To compute area of any shape we used Monte Carlo method. For example, to compute area limited to circle located in square of known area P, it is needed to generate m random points, and to check how many from it (k) is within the circle. Area Pc occupied by

circle can be easy computed from:

P_c=P⋅k

m (4)

3. ALGORITHM AND MODEL OF NEURON

The flow diagram of the algorithm of the proposed solution described in Section II is presented in figure 3 while figure 4 presents neuron-like model. At the beginning all data and variables were checked if they are in a correct range. In next steep the algorithm is divided into 2 threads separately: first connected with resilience phenomenon, second connected with Brownian motion. Divide this steps reduce time needed to calculate new positions on multi-threaded operating systems and on symmetric multiprocessing (SMP) architecture. SMP systems allow any processor to work on any task no matter where the data for that task are located in memory; with proper operating system support, SMP systems can easily move tasks between processors to balance the workload efficiently. When proposal of shift position was computed new coordinates is added taking weight of neurons into consideration. After vectorial summation of the change of base stations positions we check out if invisible area is smaller or not. If yes the coordinates are

updated, otherwise not, and weight of all neurons are also updated if needed. The algorithm stops until maximum of steps is reached.

This algorithm for each base station is modeled by the linear neuron (Fig. 4). It consists of vector adder A, an amplifier with gain k, and decision block D. Input data are current coordinates of radio station (xn, yn), suggested shift (Δxn, Δyn),

which are amplify or reduce depending on value of k. At the output we receive sum of coordinates (x*, y*). Decision block D compares proposed coordinates with current position, and calculate area that is out of direct visible from at least three radio station. If area is smaller coordinates is updated and neuron is a winner, in another case coordinates is not changed, and neuron is a loser. Decision block also change gain k, which increases when neuron wins, and decreases when not. To prevent situation, when one of selected neuron permanently wins or loses was added adequately the phenomenon of tiredness or stimulates neurons, when count of wins or lost exceed fixed threshold.

4.

SIMULATION RESULTS

As environment was used GNU Octave – a high-level language, primarily intended for numerical computations. It is Matlab-like, but is freely redistributable under the terms of the GNU General Public License (GPL) as published by the Free Software Foundation and provides tools essential to perform simulations.

A room layout of double “L” shape (figure 5) with one obstacle S was simulated. Six radio stations were initially placed down the corridor. The proposed algorithm is supposed to change positions of antennas, to decrease area out of direct reach of at least three radio stations. Figure 6 shows results obtained. As we can see suggested new coordinates are better located than the initial ones. Positions was change in wide range. Arrow shows change of position of one selected the radio station. Displacement one of them does not occur. According to expectations radio stations prefer places at edge of room.

Figure 7 presents changes of area out of reach for each iteration. Neural networks reduce it from 22% to 1,25% only in seven steps. The fastest bottom out was observed in first three steps. Non-zero value at the end of simulation means that more radio stations is required. Figure 8 demonstrate changes of weight (k) of selected neuron. Initially two times neuron does not change its gain, three times won and lost. From seventh step its state has not changed. Result agreed with time needed to reduce area out of reach (Fig. 6).

7. CONCLUSIONS

To conclude, using proposed method and the neural network model we can significantly reduce the effort of calculations (through divide algorithm into two threads). Also it helps to reduce the number of radio stations. It is relatively simple

and easy to implement into hardware. In future we plan to include priorities in radio stations and expand simulation to three dimensional areas.

Fig. 3. Algorithm of positioning radio stations

Fig. 4. Neuron-like model of the algorithm. It consists of vector adder A, amplifier with gain k, and decision block D. Input data are current coordinates of radio station (xn, yn) and

Fig. 5. Initial posistion of radio station in the room. The shaded area is an example area out of reach by at least three base stations.

Fig. 6. Posistion of radio station after optimisation. Arrow shows change of posision of one of the radio stations.

Fig. 7. Changes of area out of reach for each iteration

Fig. 8. Changes of weight of selected neuron

REFERENCES

[1] P. Kirshnamurthy, K. Pahlavan, J. Beneat Radio Propagation Modelling for Indoor Gelolocation Applications Personal, Indoor and Mobile Radio Communications, The Ninth IEEE International Symposium, Vol. 1, pp. 446 – 450, 8-11 Sept. 1998. [2] Wikipedia http://www.en.wikipedia.org.

[3] N. Patwari, J.N. Ash, S. Kyperountas, A. O. Hero III, R. L. Moses, N. S. Correal Location the Nodes IEEE Signal Processing Magazine, July 2005.

[4] L. Girod, V. Bychkovskiy, J. Elson, D. Estrin Locating tiny sensors in time and space: a case study Computer Design: VLSI in Computers and Processors, 2002. Proceedings. 2002 IEEE International Conference, pp. 214 – 219, 16-18 Sept. 2002. [5] K. Pahlavan, F. O. Akgul, M. Heidari, A. Hatami Indoor Geolocation Absence of

Direct Path IEEE Wireless Communications, December 2006.

[6] K. Pahlavan, P. Kirshnamurthy, J. Beneat Wide-band Radio Channel Modelling for Indoor Geolocation Applications IEEE Commun. Mag., vol. 36, no. 36, Apr. 1998, pp. 60–65.