Source Localization by Conjugated Delays Method Main Description of a New Process of Passive Localization

The method of the combined delays is a passive tracking process. It is a triangulation method employed to locate the signal hearth, which can be, according to the application area, of acoustic or electromagnetic origin. This method is based on the process of the delays combination, (delays which result from the differences in distances between the source and the sensors of the reception station), which makes it possible to determine emission direction. By knowledge of angles measurements of the signal arrivals on the reception sensors of station, one completely determines the triangles, which establish the source position.


Introduction
The purpose of goniometry is to estimate wave incidence angles. These waves may be electromagnetic or acoustic. Gon io meters are made up of an antenna or network of antennas comprising several sensors configured in a given geometry, and a calcu lation algorith m. A radiogonio meter is a system capable of measuring the arrival d irection of an electro magnetic wave with respect to a reference direction. The radiogoniometer samp les an interpretation of the wave front of the electro magnetic wave over a network of several sensors to determine the arrival direction. The acoustic goniometer is a system that measures the arrival direct ion of sounds and thus estimates the direction of the emission source. Like the radiogoniometer, it is made up of an antenna configured in a geo metry corresponding to the acoustic domain and a calculat ion algorith m. The localisation of sound sources by acoustic goniometry is based on a space-time process implemented in two steps. The temporal step extracts the arrival time of the signal or the differences in propagation times at the sensors of an antenna. The second step determines the direct ion of arrival according to the spatial configuration of the antenna.
For both the electro magnetic and acoustic domains, these passive instruments use sensors that cover a very wide spectrum. They have the advantage of being discreet, unlike radar or sonar which emit pulses

Localisation by Conjugated Delays
Localisation by conjugated delays is a goniomet ric method based on the conjugation of propagation delays. This method is independent of the application field. When, at an instant t unknown , an event is triggered by a source (electro magnetic o r acoustic), the wavefront propagates up to the station receivers, which record the signals corresponding to the emitted signal, delayed by the propagation times. A specialised circuit measures the arrival instants of the signal for each antenna sensor with respect to its internal clock. These measurements are processed by the microprocessor that conjugates the delays and determines the direction and range of the signal source. Regardless of whether the field of application is electro magnetic or acoustic, this method requires an antenna of specific geometry

Antenna Configuration
The antenna is an assembly of base elements, or in short "base". Each base comprises three omnid irectional receiver transducers that are aligned and equally spaced. In other words, a base comprises omnid irectional receivers equipping the ends and centre of a straight-line segment. See figure 1 below.
The antenna is built with bases of length, configuration and number suited for the intended use. Locating a source in a three-dimensional propagation space requires that the antenna be made up of at least three bases that are not aligned and which are not all positioned in the same p lane, or of two non-aligned bases and an additional receiver, external to the plane defined by the two bases. The addition of this receiver allows the identification of the part of the space the signal originates fro m. Th is elementary antenna is static and none of its co mponents requires mechanical or electronic orientation.

Organisation of Data
The data used by this method can be classed into the following four main groups.
Construction data: They determine antenna geometry by defining the spacing between the receivers of each base and the configuration of the bases with respect to each other. (Antenna bases may be of different lengths and any configuration).
Assigned data: For each antenna base, three different symbols or letters are assigned to its three receivers and with which an index is associated to distinguish the base. As an illustration, the indexed letters A n and B n can be assigned to the sensors at the ends of the base, the indexed letter R n assigned to a receiver positioned in the centre of base n . The distance between receivers A n and R n is equal to the distance between the receivers R n and B n , with this length between two base receivers called l n .
Physical data: This description of principle does not take account of the physical variables required for a practical application, keeping only signal propagation speed. Here, the propagation speed is considered constant. Signal speed is represented by v.
Acquisition data: once the signal of the source to be located has arrived at each antenna receiver, the station's acquisition system produces a report for the arrival times on the receivers A n , R n and B n for each base. These arrival times are called: DA n on A n , DR n on R n , DB n on B n .
The table below shows acollection of TOA sampled fro m acoustic or electro magnetic source The principle o f the conjugated delays method is simple, the first step consisting of measuring, independently the instant of emission, the signal arrival t ime on each antenna sensor with respect to the system's temporal reference. The other informat ion (antenna geometry and propagation speed) is already known. The second step is the calculation procedure, operated identically for each of the bases making up the antenna. To generalise, in the fo llo wing section we consider only one base equipped with the receivers A, R, B. The length l, is the distance between A and R or R and B, it therefo re corresponds to the half-length of the base. This base receives the signal emitted, at an instant t unknown , by the remote source to be located. The difference in separations between the signal source and the base receivers A, R and B, result in differences in the arrival t imes DA, DR and DB for the wave acquired on these receivers. The signal propagates at the speed v, and the distance covered by the wave between the mo ment DR and the mo ment DA can be deduced. This distance is a = v*(DA -DR). In the same way, the distance covered by the wave between the mo ment DR and the mo ment DB can also be deducted. This distance is b = v*(DB -DR). Depending on the emission source, the signal may reach base extremity receivers before reaching the central receiver, and g iven that the arrival t ime at receiver R is the reference time, then measurement of the distance covered is a negative value. We may note that, logically, regardless of the position of the source, the absolute values of a andb remain lower than or equal to the value ofl.

Method
By conjugating the delay d istance a, delay d istance b and length l via the expression below (1), we obtain the cosine of the angle α between the emission direction and the axis of this base at the point occupied by the receiver R, in the plane formed by this base and the signal source. This process is applied to each base and the knowledge of antenna geometry and the cosine of each arrival angle leadsto the determination of the position of the source using well-known triangulation methods.
In practice, the performance of this method is mainly dependent on the precision of timing of the arrival t imes of the wave at the antenna receivers and various environmental phenomena such as index variation, reflections, etc.

Conclusions
The passive detection and localization has gained much importance for both military and civilian applicat ions. It has several advantages over active methods, which make it a very viable alternative and sometimes indispensable. The techniques currently in use imp lements following principles.The radiogoniometry of amp litude using directly the diagram of radiat ion of the antenna.The radiogoniometry Watson-Watt or with antennas Adcock.The radiogoniometry Doppler, obtained by rotation of an omnid irectional antenna around a center with a rotation speed Ω.The radiogoniometry by interfero met ry. The radiogoniometry o f amp litude and phase based on the high-resolution vectorial correlation or not. While, the passive acoustic localizat ion systems can be subcategorized into two groups. Those using the indirect method determine position by a step of estimat ing time delays between pairs of sensors (TDOA, t ime differences of arrival) and then step that determines the position based on these delays. Those using the direct method determine the position of the source in one step, by various techniques of beamforming. The main difference with existing techniques is that LCD method, can universally, be imp lemented in the field of electro magnetic or acoustic applications. This new principle responds to the needs of applications that are based on the capacity of systems to deliver location informat ion instantly and precisely. Regard less of the domain and environ ment of use, the simp licity of the antenna and the processing resources allo w the construction of robust systems that provide determining advantages both in terms of technology and cost.