On the retrieval of lightning radio sources from time-of-arrival data (original) (raw)

1996, Journal of Geophysical Research

We examine the problem of retrieving three-dimensional lightning locations from radio frequency time-of-arrival (TOA) measurements. Arbitrary antenna locations are considered. By judiciously differencing measurements that are related to the location of the antennas and their excitation times, the problem is converted from the initial spherical nonlinear form to a system of linear equations. In the linear formalism, the source location and time-of-occurrence is viewed geometrically as an intersection of hyperplanes in the four-dimensional Minkowski space (x,y, z, t). The linear equations are solved to obtain explicit analytic expressions for the location and time variables. Retrieval errors are not interpreted with conventional Geometrical Dilution of Precision (GDOP) arguments as discussed by Holmes and Reedy [ 1951], but with more recent inversion analyses considered by Twomey [ 1977]. Measurement errors are propagated analytically so that the specific effect of these errors on the solution is clarified. The sensitivity of the solution on the number of antennas used, antenna network geometry, source position, and measurement differencing schemes are discussed in terms of the eigenvalues of the linear system. 1. Introduction A variety of data analysis techniques and hardware have been used in the retrieval of lightning locations from ground-based radio frequency time-of-arrival (TEA) measurements [Holmes and Reedy, 1951; Lewis et al., 1960; Oetzel and Pierce, 1969; Proctor, 1971; Cianos et al. , 1972; Murty and MacClement , 1973; MacClement and Murty, 1978; Taylor, 1978; Rustan et al., 1980; Bent et al., 1983; Thomson et al., 1994; and Hager and . Primary differences between these studies include the number and type of antennas used, the antenna baseline, whether a two-dimensional or three-dimensional fix of the source is desired, the mathematical means for retrieving source location, and the procedure for estimating retrieval error.