Source localization and denoising: a perspective from the TDOA space

In this manuscript, we formulate the problem of denoising Time Differences of Arrival (TDOAs) in the TDOA space, i.e. the Euclidean space spanned by TDOA measurements. The method consists of pre-processing the TDOAs with the purpose of reducing the measurement noise. The complete set of TDOAs (i.e., TDOAs computed at all microphone pairs) is known to form a redundant set, which lies on a linear subspace in the TDOA space. Noise, however, prevents TDOAs from lying exactly on this subspace. We therefore show that TDOA denoising can be seen as a projection operation that suppresses the component of the noise that is orthogonal to that linear subspace. We then generalize the projection operator also to the cases where the set of TDOAs is incomplete. We analytically show that this operator improves the localization accuracy, and we further confirm that via simulation.Comment: 25 pages, 9 figure

Asymptotically efficient estimators for geometric shape fitting and source localization

Solving the nonlinear estimation problem is known to be a challenging task because of the implicit relationship between the measurement data and the unknown parameters to be estimated. Iterative methods such as the Taylor-series expansion based ML estimator are presented in this thesis to solve the nonlinear estimation problem. However, they might suffer from the initialization and convergence problems. Other than the iterative methods, this thesis aims to provide a computational effective, asymptotically efficient and closed-form solution to the nonlinear estimation problem. Two kinds of classic nonlinear estimation problems are considered: the geometric shape fitting problem and the source localization problem. For the geometric shape fitting, the research in this thesis focuses on the circle and the ellipse fittings. Three iterative methods for the fitting of a single circle: the ML method, the FLS method and the SDP method, are provided and their performances are analyzed. To overcome the limitations of the iterative methods, asymptotically efficient and closed-form solutions for both the circle and ellipse fittings are derived. The good performances of the proposed solutions are supported by simulations using synthetic data as well as experiments on real images. The localization of a source via a group of sensors is another important nonlinear estimation problem studied in this thesis. Based on the TOA measurements, the CRLB and MSE results of a source location when sensor position errors are present are derived and compared to show the estimation performance loss due to the sensor position errors. A closed-formed estimator that takes into account the sensor position errors is then proposed. To further improve the sensor position and the source location estimates, an algebraic solution that jointly estimates the source and sensor positions is provided, which provides better performance in sensor position estimates at higher noise level comparing to the sequential estimation-refinement technique. The TOA based CRLB and MSE studies are further extended to the TDOA and AOA cases. Through the analysis one interesting result has been found: there are situations exist where taking into account the sensor position errors when estimating the source location will not improve the estimation accuracy. In such cases a calibration emitter with known position is needed to limit the estimation damage caused by the sensor position uncertainties. Investigation has been implemented to find out where would be the optimum position to place the calibration emitter. When the optimum calibration source position may be of theoretical interest only, a practical suboptimum criterion is developed which yields a better calibration emitter position than the closest to the unknown source criterion

5G multi-BS positioning with a single-antenna receiver

Cellular localization generally relies on timedifference-of-arrival (TDOA) measurements. In this paper, we investigate a novel scenario where the mobile user estimates its own position by jointly exploiting TDOA and angle of departure (AOD) measurements, which are estimated from downlink transmissions in a millimeter-wave (mmWave) multiple-input singleoutput (MISO) setup. We first perform a Fisher information analysis to derive the lower bounds on the estimation accuracy, and then propose a novel localization algorithm, which is able to provide improved performance also with few transmit antennas and limited bandwidth

Consistent and Asymptotically Efficient Localization from Range-Difference Measurements

We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the consistency and asymptotic normality of the maximum likelihood (ML) estimator. Then, we devise an estimator that owns the same asymptotic property as the ML one. Specifically, we prove that the negative log-likelihood function converges to a function, which has a unique minimum and positive definite Hessian at the true source's position. Hence, it is promising to execute local iterations, e.g., the Gauss-Newton (GN) algorithm, following a consistent estimate. The main issue involved is obtaining a preliminary consistent estimate. To this aim, we construct a linear least-squares problem via algebraic operation and constraint relaxation and obtain a closed-form solution. We then focus on deriving and eliminating the bias of the linear least-squares estimator, which yields an asymptotically unbiased (thus consistent) estimate. Noting that the bias is a function of the noise variance, we further devise a consistent noise variance estimator that involves $3$-order polynomial rooting. Based on the preliminary consistent location estimate, a one-step GN iteration suffices to achieve the same asymptotic property as the ML estimator. Simulation results demonstrate the superiority of our proposed algorithm in the large sample case

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

EXPERIMENTAL EVALUATION OF MODIFIED PHASE TRANSFORM FOR SOUND SOURCE DETECTION

The detection of sound sources with microphone arrays can be enhanced through processing individual microphone signals prior to the delay and sum operation. One method in particular, the Phase Transform (PHAT) has demonstrated improvement in sound source location images, especially in reverberant and noisy environments. Recent work proposed a modification to the PHAT transform that allows varying degrees of spectral whitening through a single parameter, andamp;acirc;, which has shown positive improvement in target detection in simulation results. This work focuses on experimental evaluation of the modified SRP-PHAT algorithm. Performance results are computed from actual experimental setup of an 8-element perimeter array with a receiver operating characteristic (ROC) analysis for detecting sound sources. The results verified simulation results of PHAT- andamp;acirc; in improving target detection probabilities. The ROC analysis demonstrated the relationships between various target types (narrowband and broadband), room reverberation levels (high and low) and noise levels (different SNR) with respect to optimal andamp;acirc;. Results from experiment strongly agree with those of simulations on the effect of PHAT in significantly improving detection performance for narrowband and broadband signals especially at low SNR and in the presence of high levels of reverberation

Mathematical modelling ano optimization strategies for acoustic source localization in reverberant environments

La presente Tesis se centra en el uso de técnicas modernas de optimización y de procesamiento de audio para la localización precisa y robusta de personas dentro de un entorno reverberante dotado con agrupaciones (arrays) de micrófonos. En esta tesis se han estudiado diversos aspectos de la localización sonora, incluyendo el modelado, la algoritmia, así como el calibrado previo que permite usar los algoritmos de localización incluso cuando la geometría de los sensores (micrófonos) es desconocida a priori. Las técnicas existentes hasta ahora requerían de un número elevado de micrófonos para obtener una alta precisión en la localización. Sin embargo, durante esta tesis se ha desarrollado un nuevo método que permite una mejora de más del 30\% en la precisión de la localización con un número reducido de micrófonos. La reducción en el número de micrófonos es importante ya que se traduce directamente en una disminución drástica del coste y en un aumento de la versatilidad del sistema final. Adicionalmente, se ha realizado un estudio exhaustivo de los fenómenos que afectan al sistema de adquisición y procesado de la señal, con el objetivo de mejorar el modelo propuesto anteriormente. Dicho estudio profundiza en el conocimiento y modelado del filtrado PHAT (ampliamente utilizado en localización acústica) y de los aspectos que lo hacen especialmente adecuado para localización. Fruto del anterior estudio, y en colaboración con investigadores del instituto IDIAP (Suiza), se ha desarrollado un sistema de auto-calibración de las posiciones de los micrófonos a partir del ruido difuso presente en una sala en silencio. Esta aportación relacionada con los métodos previos basados en la coherencia. Sin embargo es capaz de reducir el ruido atendiendo a parámetros físicos previamente conocidos (distancia máxima entre los micrófonos). Gracias a ello se consigue una mejor precisión utilizando un menor tiempo de cómputo. El conocimiento de los efectos del filtro PHAT ha permitido crear un nuevo modelo que permite la representación 'sparse' del típico escenario de localización. Este tipo de representación se ha demostrado ser muy conveniente para localización, permitiendo un enfoque sencillo del caso en el que existen múltiples fuentes simultáneas. La última aportación de esta tesis, es el de la caracterización de las Matrices TDOA (Time difference of arrival -Diferencia de tiempos de llegada, en castellano-). Este tipo de matrices son especialmente útiles en audio pero no están limitadas a él. Además, este estudio transciende a la localización con sonido ya que propone métodos de reducción de ruido de las medias TDOA basados en una representación matricial 'low-rank', siendo útil, además de en localización, en técnicas tales como el beamforming o el autocalibrado

Indoor Positioning Using Acoustic Pseudo-Noise Based Time Difference of Arrival

The Global Positioning System (GPS) provides good precision on a global scale, but is not suitable for indoor applications. Indoor positioning systems (IPS) aim to provide high precision position information in an indoor environment. IPS has huge market opportunity with a growing number of commercial and consumer applications especially as Internet of Things (IoT) develops. This paper studies an IPS approach using audible sound and pseudo-noise (PN) based time difference of arrival (TDoA). The system’s infrastructure consists of synchronized speakers. The object to be located, or receiver, extracts TDoA information and uses multilateration to calculate its position. The proposed IPS utilizes sound waves since they travel much slower compared to electromagnetic waves, allowing for easier measurements. Additionally, the audible spectrum has a large availability of low directivity speakers and microphones allowing for a large coverage area compared to highly directive ultrasonic transceivers. This paper experimentally evaluates the feasibility of the proposed IPS