A Computationally Efficient algorithm to estimate the Parameters of a Two-Dimensional Chirp Model with the product term

Chirp signal models and their generalizations have been used to model many natural and man-made phenomena in signal processing and time series literature. In recent times, several methods have been proposed for parameter estimation of these models. These methods however are either statistically sub-optimal or computationally burdensome, specially for two dimensional (2D) chirp models. In this paper, we consider the problem of parameter estimation of 2D chirp models and propose a computationally efficient estimator and establish asymptotic theoretical properties of the proposed estimators. And the proposed estimators are observed to have the same rates of convergence as the least squares estimators (LSEs). Furthermore, the proposed estimators of chirp rate parameters are shown to be asymptotically optimal. Extensive and detailed numerical simulations are conducted, which support theoretical results of the proposed estimators

On estimating parameters of a multi-component Chirp Model with equal chirp rates

Multi-component chirp signal models with equal chirp rates appear in various radar applications, e.g., synthetic aperture radar, echo signal of a rapid mobile target, etc. Many sub-optimal estimators have been developed for such models, however, these suffer from the problem of either identifiability or error propagation effect. In this paper, we have developed theoretical properties of the least squares estimators (LSEs) of the parameters of multi-component chirp model with equal chirp rates, where the model is contaminated with linear stationary errors. We also propose two computationally efficient estimators as alternative to LSEs, namely sequential combined estimators and sequential plugin estimators. Strong consistency and asymptotic normality of these estimators have been derived. Interestingly, it is observed that sequential combined estimator of the chirp rate parameter is asymptotically efficient. Extensive numerical simulations have been performed, which validate satisfactory computational and theoretical performance of all three estimators. {We have also analysed a simulated radar data with the help of our proposed estimators of multi-component chirp model with equal chirp rates, which performs efficiently in recovery of inverse synthetic aperture radar (ISAR) image of a target from a noisy data

The estimation of geoacoustic properties from broadband acoustic data, focusing on instantaneous frequency techniques

The compressional wave velocity and attenuation of marine sediments are fundamental to marine science. In order to obtain reliable estimates of these parameters it is necessary to examine in situ acoustic data, which is generally broadband. A variety of techniques for estimating the compressional wave velocity and attenuation from broadband acoustic data are reviewed. The application of Instantaneous Frequency (IF) techniques to data collected from a normal-incidence chirp profiler is examined. For the datasets examined the best estimates of IF are obtained by dividing the chirp profile into a series of sections, estimating the IF of each trace in the section using the first moments of the Wigner Ville distribution, and stacking the resulting IF to obtain a composite IF for the section. As the datasets examined cover both gassy and saturated sediments, this is likely to be the optimum technique for chirp datasets collected from all sediment environments

Adaptive Waveforms for Flow Velocity Estimation Using Acoustic Signals

International audienceIn this paper, we introduce a general framework for waveform design and signal processing, dedicated to the study of turbulent flow phenomena. In a bi-static configuration, by transmitting a specific waveform with a predefined instantaneous frequency law (IFL), within the bounds of the Kolmogorov spectrum, the turbulent media will modify the IFL at the receiving side. We propose a new methodology to estimate this change and to exploit it for velocity estimation using acoustic signals. In this way, the amplitude based velocity estimation techniques can be substituted by non stationary time - frequency signal processing. This technique proves to be more robust in terms of interferences and can provide a more detailed representation of any turbulent environment

Binary compact object coalescence rates: The role of elliptical galaxies

We estimate binary compact object merger detection rates for LIGO, including the binaries formed in ellipticals long ago. Specifically, we convolve hundreds of model realizations of elliptical- and spiral-galaxy population syntheses with a model for elliptical- and spiral-galaxy star formation history as a function of redshift. Our results favor local merger rate densities of 4\times 10^{-3} {Mpc}^{-3}{Myr}^{-1} for binary black holes (BH), 3\times 10^{-2} {Mpc}^{-3}{Myr}^{-1} for binary neutron stars (NS), and 10^{-2} {Mpc}^{-3}{Myr}^{-1} for BH-NS binaries. Mergers in elliptical galaxies are a significant fraction of our total estimate for BH-BH and BH-NS detection rates; NS-NS detection rates are dominated by the contribution from spiral galaxies. Using only models that reproduce current observations of Galactic NS-NS binaries, we find slightly higher rates for NS-NS and largely similar ranges for BH-NS and BH-BH binaries. Assuming a detection signal-to-noise ratio threshold of 8 for a single detector (as part of a network), corresponding to radii \Cv of the effective volume inside of which a single LIGO detector could observe the inspiral of two 1.4 M_\sun neutron stars of 14 Mpc and 197 Mpc, for initial and advanced LIGO, we find event rates of any merger type of 2.9* 10^{-2} -- 0.46 and 25-400 per year (at 90% confidence level), respectively. We also find that the probability P_{detect} of detecting one or more mergers with this single detector can be approximated by (i) P_{detect}\simeq 0.4+0.5\log (T/0.01{yr}), assuming \Cv=197 {Mpc} and it operates for T years, for T between 2 days and 0.1 {yr}); or by (ii) P_{detect}\simeq 0.5 + 1.5 \log \Cv/32{Mpc}, for one year of operation and for \Cv between 20 and 70 Mpc. [ABRIDGED]Comment: 22 pages, 11 figures. Accepted by ApJ. v2 adds several figures, an electronic-only table of all intermediate binary evolution simulations (tab1.txt here), and new subsections outlining broader significance (e.g., 5.4; 4.6; 6.1