Time delay estimation algoritms for echo cancellation

The following case study describes how to eliminate echo in a VoIP network using delay estimation algorithms. It is known that echo with long transmission delays becomes more noticeable to users. Thus, time delay estimation, as a part of echo cancellation, is an important topic during transmission of voice signals over packetswitching telecommunication systems. An echo delay problem associated with IP-based transport networks is discussed in the following text. The paper introduces the comparative study of time delay estimation algorithm, used for estimation of the true time delay between two speech signals. Experimental results of MATLab simulations that describe the performance of several methods based on cross-correlation, normalized crosscorrelation and generalized cross-correlation are also presented in the paper

Frequency-Sliding Generalized Cross-Correlation: A Sub-band Time Delay Estimation Approach

The generalized cross correlation (GCC) is regarded as the most popular approach for estimating the time difference of arrival (TDOA) between the signals received at two sensors. Time delay estimates are obtained by maximizing the GCC output, where the direct-path delay is usually observed as a prominent peak. Moreover, GCCs play also an important role in steered response power (SRP) localization algorithms, where the SRP functional can be written as an accumulation of the GCCs computed from multiple sensor pairs. Unfortunately, the accuracy of TDOA estimates is affected by multiple factors, including noise, reverberation and signal bandwidth. In this paper, a sub-band approach for time delay estimation aimed at improving the performance of the conventional GCC is presented. The proposed method is based on the extraction of multiple GCCs corresponding to different frequency bands of the cross-power spectrum phase in a sliding-window fashion. The major contributions of this paper include: 1) a sub-band GCC representation of the cross-power spectrum phase that, despite having a reduced temporal resolution, provides a more suitable representation for estimating the true TDOA; 2) such matrix representation is shown to be rank one in the ideal noiseless case, a property that is exploited in more adverse scenarios to obtain a more robust and accurate GCC; 3) we propose a set of low-rank approximation alternatives for processing the sub-band GCC matrix, leading to better TDOA estimates and source localization performance. An extensive set of experiments is presented to demonstrate the validity of the proposed approach.Comment: Article accepted in IEEE/ACM Transactions on Audio, Speech, and Language Processin

The enigma of GCIRS 3 - Constraining the properties of the mid-infrared reference star of the central parsec of the Milky Way with optical long baseline interferometry

GCIRS3 is the most prominent MIR source in the central pc of the Galaxy. NIR spectroscopy failed to solve the enigma of its nature. The properties of extreme individual objects of the central stellar cluster contribute to our knowledge of star and dust formation close to a supermassive black hole. We initiated an interferometric experiment to understand IRS3 and investigate its properties as spectroscopic and interferometric reference star at 10um. VISIR imaging separates a compact source from diffuse, surrounding emission. The VLTI/MIDI instrument was used to measure visibilities at 10mas resolution of that compact 10um source, still unresolved by a single VLT. Photometry data were added to enable simple SED- and full radiative transfer-models of the data. The luminosity and size estimates show that IRS3 is probably a cool carbon star enshrouded by a complex dust distribution. Dust temperatures were derived. The coinciding interpretation of multiple datasets confirm dust emission at several spatial scales. The IF data resolve the innermost area of dust formation. Despite observed deep silicate absorption towards IRS3 we favor a carbon rich chemistry of the circumstellar dust shell. The silicate absorption most probably takes place in the outer diffuse dust, which is mostly ignored by MIDI measurements. This indicates physically and chemically distinct conditions of the local dust, changing with the distance to IRS3. We have demonstrated that optical long baseline interferometry at infrared wavelengths is an indispensable tool to investigate sources at the Galactic Center. Our findings suggest further studies of the composition of interstellar dust and the shape of the 10um silicate feature at this outstanding region.Comment: accepted by A&A, now in press; 19 pages, 22 figures, 5 table

Optimizing Techniques and Cramer-Rao Bound for Passive Source Location Estimation

This work is motivated by the problem of locating potential unstable areas in underground potash mines with better accuracy more consistently while introducing minimum extra computational load. It is important for both efficient mine design and safe mining activities, since these unstable areas may experience local, low-intensity earthquakes in the vicinity of an underground mine. The object of this thesis is to present localization algorithms that can deliver the most consistent and accurate estimation results for the application of interest. As the first step towards the goal, three most representative source localization algorithms given in the literature are studied and compared. A one-step energy based grid search (EGS) algorithm is selected to address the needs of the application of interest. The next step is the development of closed-form Cram´er-Rao bound (CRB) expressions. The mathematical derivation presented in this work deals with continuous signals using the Karhunen-Lo`eve (K-L) expansion, which makes the derivation applicable to non-stationary Gaussian noise problems. Explicit closed-form CRB expressions are presented only for stationary Gaussian noise cases using the spectrum representation of the signal and noise though. Using the CRB comparisons, two approaches are proposed to further improve the EGS algorithm. The first approach utilizes the corresponding analytic expression of the error estimation variance (EEV) given in [1] to derive an amplitude weight expression, optimal in terms of minimizing this EEV, for the case of additive Gaussian noise with a common spectrum interpretation across all the sensors. An alternate noniterative amplitude weighting scheme is proposed based on the optimal amplitude weight expression. It achieves the same performance with less calculation compared with the traditional iterative approach. The second approach tries to optimize the EGS algorithm in the frequency domain. An analytic frequency weighted EEV expression is derived using spectrum representation and the stochastic process theory. Based on this EEV expression, an integral equation is established and solved using the calculus of variations technique. The solution corresponds to a filter transfer function that is optimal in the sense that it minimizes this analytic frequency domain EEV. When various parts of the frequency domain EEV expression are ignored during the minimization procedure using Cauchy-Schwarz inequality, several different filter transfer functions result. All of them turn out to be well known classical filters that have been developed in the literature and used to deal with source localization problems. This demonstrates that in terms of minimizing the analytic EEV, they are all suboptimal, not optimal. Monte Carlo simulation is performed and shows that both amplitude and frequency weighting bring obvious improvement over the unweighted EGS estimator

Near Infrared Polarimetry: A Tool for Testing Properties of Sagittarius A*

In this thesis I focus on the results of the data modelings and simulations of near-infrared (NIR) observations of the Sagittarius A* (Sgr A*) counterpart associated with the super-massive black hole at the Galactic Center (GC). My goal is to investigate and understand the physical processes behind the variability associated with the NIR flaring emission from Sgr A*. The NIR observations have been carried out using the NACO adaptive optics (AO) instrument at the European Southern Observatory's (ESO's) Very Large Telescope (VLT) and the CIAO NIR camera on the Subaru telescope (13 June 2004, 30 July 2005, 1 June 2006, 15 May 2007, 17 May 2007 and 28 May 2008). I used a model of synchrotron emission from relativistic electrons in the inner parts of an accretion disk. The relativistic simulations have been carried out using the Karas-Yaqoob (KY) ray-tracing code. I also probed the existence of a correlation between the modulations of the observed flux density light curves and changes in polarimetric data. Furthermore, I confirmed that the same correlation is also predicted by the so-called hot spot model. Correlations between intensity and polarimetric parameters of the observed light curves, as well as a comparison of predicted and observed light curve features through a pattern recognition algorithm result in the detection of a signature of orbiting matter under the influence of strong gravity. This pattern is proved to be statistically significant against randomly polarized red noise. The observed correlations between flux modulations and changes in linear polarization degree and angle can be a sign that the NIR flares have properties that are not expected from purely random red-noise. I found that the geometric shape of the emitting region plays a major role in the predictions of the model. From fully relativistic simulations of a spiral shaped emitting region, I concluded that the observed swings in polarization angle during NIR flares support the idea of compact orbiting spots instead of extended patterns. The effects of gravitational shearing, fast synchrotron cooling of the components, and confusion from a variable accretion disk have been taken into account. Furthermore, I discussed the expected results from future observations of VLT interferometry (VLTI) like the GRAVITY experiment. Simulated centroids of NIR images led me to the conclusion that a clear observation of position wander of the center of NIR images with future infrared interferometers will prove the existence of orbiting hot spots in the vicinity of our Galactic super-massive black hole. Finally, I described a novel approach to constrain the physical parameters of the Galactic black hole by using time resolved NIR polarimetric observations. Even though basically the method is developed for Sgr A*, it can be used to test intrinsic properties of several types of compact objects with QPO behavior

Performance of astrometric detection of a hotspot orbiting on the innermost stable circular orbit of the galactic centre black hole

The galactic central black hole Sgr A* exhibits outbursts of radiation in the near infrared (so-called IR flares). One model of these events consists in a hotspot orbiting on the innermost stable circular orbit (ISCO) of the hole. These outbursts can be used as a probe of the central gravitational potential. One main scientific goal of the second generation VLTI instrument GRAVITY is to observe these flares astrometrically. Here, the astrometric precision of GRAVITY is investigated in imaging mode, which consists in analysing the image computed from the interferometric data. The capability of the instrument to put in light the motion of a hotspot orbiting on the ISCO of our central black hole is then discussed. We find that GRAVITY's astrometric precision for a single star in imaging mode is smaller than the Schwarzschild radius of Sgr A*. The instrument can also demonstrate that a body orbiting on the last stable orbit of the black hole is indeed moving. It yields a typical size of the orbit, if the source is as bright as m_K=14. These results show that GRAVITY allows one to study the close environment of Sgr A*. Having access to the ISCO of the central massive black hole probably allows constraining general relativity in its strong regime. Moreover, if the hotspot model is appropriate, the black hole spin can be constrained.Comment: 13 pages, 11 figures ; accepted by MNRA