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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this article, a time-of-flight detection technique in the frequency domain is described for an ultrasonic Local Positioning System (LPS) based on encoded beacons. Beacon transmissions have been synchronized and become simultaneous by means of the DS-CDMA (Direct-Sequence Code Division Multiple Access) technique. Every beacon has been associated to a 255-bit Kasami code. The detection of signal arrival instant at the receiver, from which the distance to each beacon can be obtained, is based on the application of the Generalized Cross-Correlation (GCC), by using the cross-spectral density between the received signal and the sequence to be detected. Prior filtering to enhance the frequency components around the carrier frequency (40 kHz) has improved estimations when obtaining the correlation function maximum, which implies an improvement in distance measurement precision. Positioning has been achieved by using hyperbolic trilateration, based on the Time Differences of Arrival (TDOA) between a reference beacon and the others.

The term LPS (Local Positioning System) refers to a system used for location and positioning in indoor (or at least reduced) environments where the use of positioning techniques based on GPS is very limited due to the weakness of the GPS signals. These kinds of systems are the keystone for the implementation of intelligent spaces able to interact with people and robots. Nowadays there are a lot of applications that can be developed in modern buildings with an effective LPS [

LPSs have been developed using different technologies such as infrared [

The determination of TOA (or TDOA) implies the measurement of time delay in the arrival of a signal (or difference of delays in the arrival of two signals) to a receiver. In the case of natural sounds, including speech, intense work has been developed during the last years. The methods used deal with the random nature of these signals and their high relative bandwidth. Different algorithms have been compared in [

This paper presents an ultrasonic LPS, such as that shown in

As has been mentioned, each beacon has assigned a code or sequence for encoding the emission. The arrival instant for each emission is often determined by the correlation between the received signal and the code to be detected. This process is known as

The Inter-Symbol Interference (ISI) caused by the fact that the Auto-Correlation (AC) function of the sequences used, and the Cross-Correlation (CC) between them, is not null near the maximum, implies that it is sometimes difficult to detect the real position of the maxima [

This article is organized as follows: in Section 2 the positioning system model reported here is described, and the classical detection process based on cross-correlation. In Section 3, GCC is explained, as well as its application to detect sequences or codes assigned to each beacon. In Section 4, some results obtained for the detection process by applying GCC are provided, and compared with those obtained from CC. Finally, some conclusions are discussed in Section 5.

In the positioning system model (see _{j}(t)_{j}_{m}(t)_{t}(t)_{j}(t_{j})_{j}^{2}_{j}_{j}

Considering the detection process of a beacon _{j}

Both the auto-correlation function of the sequence transmitted by the beacon _{i}_{j}_{j}

The time difference of arrival (TDOA) between a reference beacon

Another method for computing the arrival instant of a sequence

If it is considered that the received signal _{y}_{x}_{y}_{x}_{xy}_{x}_{y}

Regarding a discrete-time analysis, the generalised cross-correlation in discrete time, between the received signal _{j}_{j}_{j}_{j}_{j}_{Sj,y}_{j}

Note that if Φ_{j}_{j}

Filtering has two objectives. First, it accentuates the signal to be correlated in those frequencies where the signal-to-noise ratio is higher; therefore, _{j}(f)

The filtering function known as PHAse Transform (PHAT filtering), is widely used to estimate signal delay between two receivers located at a given distance from the acoustic source or transmitter. Its expression in this case, considering beacons as transmitters whose signal is _{j}

The advantage over the other filtering functions analysed in [

Since beacons are considered as emitters whose transmitted signal is _{j}

Let consider the received signal from the beacons, defined as _{j}_{j}_{j}_{si,sj}_{i}_{j}_{si,sj}_{j}_{j}_{si,sj}_{i}_{i}_{j}_{N,sj}_{y,sj}_{j}

In this case, it is possible to state

Thus,
_{j}

As the auto-correlation spectrum is a real and positive function:

It becomes:

As can be observed, the searched sequence becomes a unitary delta, whereas the deltas for the other sequences are weighted by

In order to compare the sequence detection method based on cross-correlation (CC) between the received signal and the sequence assigned to each beacon with the method based on generalised cross-correlation (GCC) and on applying phase transform (PHAT) filtering, a LPS with two beacons have been considered. The beacons have been located in a 2D system at positions (_{1}_{1}_{2}_{2}_{x}_{y}

Prior filtering of the signals based on phase transform (PHAT) accentuates the frequencies around the carrier. Then, when the Fourier transform-based correlation is applied, a delta is obtained at the sequence arrival instant.

In the case of a modulation symbol consisting of four carrier cycles (

In order to analyse the GCC behaviour with real signals a practical set-up with a geometric configuration similar to that used for simulations has been arranged and tested. A Prowave (328ST160) transducer [

Two beacons have been used for transmission and the receiver has been positioned on the floor.

When the receiver is in the position 1 (according to the diagram shown in

In the same position 1, the results obtained when using a modulation symbol with four carrier cycles (

In both cases (with

For the position 1, in which both signals arrive with a considerable delay, CC gives a most repetitive result (although looking at

A method based on the GCC for obtaining the TDOA of two signals coming from different beacons to the same receiver has been proposed in this work. It has been applied to an ultrasonic LPS, whose beacons emit encoded signals by means of Kasami sequences. The detection algorithm is based on the cross-spectral density between the received signal and the modulated sequences to be detected (each one related to its corresponding beacon).

The proposed algorithm provides a significant reduction in the lateral lobe effects, when compared with standard correlation, caused by the modulation process, the interference between emissions and the characteristics (attenuation, multipath,

The algorithm has been tested with simulated and real data comparing its performance with that obtained when a basic correlation (CC) is used. GCC gives always a clearer maximum peak than CC with less significant secondary peaks around the main one. When the signals arrive to the receiver with a considerable delay (milliseconds) the performance of both detection algorithms, CC and GCC, is similar, being the CC less sensible to the noise and distortion introduced by the transducer. On the other hand, when the signals arrive to the receiver almost simultaneously (very low DTOA), the GCC allows to compute the DTOA while the CC fails (because the interference between both signals and its influence in the secondary peaks).

This research was supported by the Spanish Ministry for Science and Technology through the LEMUR project (ref. TIN2009-14014-CO4-01).

Block diagram of the ultrasonic LPS.

Block diagram of the receiver.

Block diagram of the proposed positioning system model.

Block diagram of the estimation process of the arrival instant for a sequence

Position of the beacons and the receiver for the analysis of the detection process.

Beacon detection in the absence of noise by applying the cross-correlation (CC) method in the time domain.

Beacon detection in the absence of noise, by applying generalised cross-correlation (GCC) with PHAT filtering.

Beacon detection with a signal-noise ratio of 0 dB, by applying generalised cross-correlation (GCC) with PHAT filtering.

Beacon detection by applying CC, for a modulation symbol formed by four carrier cycles (

Beacon detection by applying generalised cross-correlation (GCC) with PHAT filtering, for a modulation symbol formed by four carrier cycles (

Measured 328ST160 transducer performance:

Experimental setup diagram.

Beacon detection in the position 1 with real signals (

Beacon detection in the position 1 with real signals (

DTOAs measured in positions 1 and 2 when emit beacons 1 and 2 (

Beacon detection in the position 2 with real signals (