In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

Two localization algorithms for multilateration systems are derived and analyzed. Instead of the classical time difference of\ud arrival (TDOA), a direct use of the time of arrival (TOA) is made. The algorithms work for arbitrary spatial dimensions and\ud overdetermined systems. These derivations are tested in a real-case implementation with simulated data (in particular, the\ud multilateration (MLAT) system installed on the Malpensa Airport in Milan was considered for the MLAT simulation and its\ud possible extension to wide area multilateration (WAM) system was considered forWAMtrials). The results are also compared\ud with the present-day algorithms performance, mostly based on TDOA

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