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We consider the problem of processing data for a sensor system detecting radiation from several sources. For application to problems on satellite measurements (localization), we propose new approaches to initialization of the iteration process used to estimate the coordinates of sources using signal-subspace methods.The problem of processing the measurement data produced by array sensors for localization or approximation of trajectories when several sources of radiation simultaneously act on the sensor has recently been the subject of much interest [1, 2]. Simple processing methods used for locating a single source (see, for example, [3, 4]) cannot be applied to multiple independent sources. This raises a series of new problems that can be considered in applications to two situations, which we present below in order of increasing complexity.1. Signals from different sources are separated by finite time intervals, and the times at which they arrive at the sensor (the "nulls" of the corresponding functions) are easily recorded. The properties of multiple radiators appear only in possible confusion of sources when the nulls registered by a sensor for a mixed signal are juxtaposed. We call this situation the problem of identification of nulls in the problem of locating multiple radiators.2. Signals from different sources overlap in time. This makes it impossible to determine nulls with the usual methods of localizing single sources. A problem that arises is that of separating superimposed signals and extracting, from the recorded data (measurement results) information on each of the signals separately, and information about the times they arrive at the array sensors. We call this problem the problem of separating superimposed signals during localization of multiple sources.Problem of Identification of Nulls. The problem of identification of nulls registered by a system is comparatively simple. It is solved by comparing versions of the localization problem for a single source for "virtual radiators" combined with different combinations of nulls.We assume that an array detector contains N sensors that are located at different points in three dimensions. The system is subject to the simultaneous action of M radiation sources. Each sensor registers M nulls ti k (i is the sensor number, k is the null number registered by the i-th sensor) for the number of sources acting on it. The problem is to find the proper partition k .

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The task of having to locate sources of radiation by means of several spatially dispersed detection units (DUs) is often part of the solution of problems concerning long-distance probing within different wavelength ranges (see [1, 2], for example). The passive location of optical radiation sources --for which the algorithms to be discussed here were primarily developed --was examined in [3]. The initial data for source location consists of differences in distance from an object with the coordinates (x, y, z) to the i-th and j-th DUs, with the coordinates (xi, Yi, zi) and (xj, y], zj), respectively. Let us introduce notation to represent the distance difference dij, having taken d,~ =~-rj:r, =~/(x-x,f +(/-y,? +(z-z,f ; i.j,k=l,N. (1)The location of the source can be determined by using measurements of dip The number of such measurements m can be three or more. When m > 3, the problem is one of statistical averaging and from a computational standpoint reduces to the class of least-squares (LS) problems [4] (also see [5]).The parameters being estimated, x, y, and z, are related to the data from the measurements of dij by nonlinear relations (I). The initial relations are linearized locally in most methods by expansion of the functions r i = ri(x i, Yi, z) into Taylors series in the neighborhood of a "nominal" point chosen on the basis of apriori information. This leads to iterative estimation algorithms that are usually accurate (see [2, 5], for example) but require a large number of operations. The low efficiency of iterative algorithms becomes particularly apparent when the problem involves locating several independent radiation sources which might be "confused" with one another. The volume of operations that must be performed increases sharply in this case: for M sources and N detectors, it increases by the factor 0 (MN).Whenever information (measurment data) has to be analyzed in real time, it is best to use the more efficient (from a computational standpoint) and more reliable (from the viewpoint of convergence) results obtained from direct non-iterative estimation algorithms. Their accuracy is sufficient for most of the applications encountered in practice. If more accurate results are needed, such algorithms can be used to supply the initial data for subsequent iterations. We will develop a procedure for using such algorithms on the basis of the reduction of (1) to linear form throughout the possible ranges of x, y, and z. The initial data consists of equations that are equivalent to system (I) but differ from (I) in structure

Results are presented from a model (numerical) experiment performed to check the efficiency of three groups of direct data-analysis algorithms to be used in satellite location of ground or ocean sources of radiation. The methodology belu'nd the experiment is also explained.