TY - CONF AB - In this contribution we derive the Maximum A-Posteriori (MAP) estimates of the parameters of a Gaussian Mixture Model (GMM) in the presence of noisy observations. We assume the distortion to be white Gaussian noise of known mean and variance. An approximate conjugate prior of the GMM parameters is derived allowing for a computationally efficient implementation in a sequential estimation framework. Simulations on artificially generated data demonstrate the superiority of the proposed method compared to the Maximum Likelihood technique and to the ordinary MAP approach, whose estimates are corrected by the known statistics of the distortion in a straightforward manner. AU - Chinaev, Aleksej AU - Haeb-Umbach, Reinhold ID - 11740 KW - Gaussian noise KW - maximum likelihood estimation KW - parameter estimation KW - GMM parameter KW - Gaussian mixture model KW - MAP estimation KW - Map-based estimation KW - maximum a-posteriori estimation KW - maximum likelihood technique KW - noisy observation KW - sequential estimation framework KW - white Gaussian noise KW - Additive noise KW - Gaussian mixture model KW - Maximum likelihood estimation KW - Noise measurement KW - Gaussian mixture model KW - Maximum a posteriori estimation KW - Maximum likelihood estimation SN - 1520-6149 T2 - 38th International Conference on Acoustics, Speech and Signal Processing (ICASSP 2013) TI - MAP-based Estimation of the Parameters of a Gaussian Mixture Model in the Presence of Noisy Observations ER - TY - CONF AB - In this paper, we consider the Maximum Likelihood (ML) estimation of the parameters of a GAUSSIAN in the presence of censored, i.e., clipped data. We show that the resulting Expectation Maximization (EM) algorithm delivers virtually biasfree and efficient estimates, and we discuss its convergence properties. We also discuss optimal classification in the presence of censored data. Censored data are frequently encountered in wireless LAN positioning systems based on the fingerprinting method employing signal strength measurements, due to the limited sensitivity of the portable devices. Experiments both on simulated and real-world data demonstrate the effectiveness of the proposed algorithms. AU - Hoang, Manh Kha AU - Haeb-Umbach, Reinhold ID - 11816 KW - Gaussian processes KW - Global Positioning System KW - convergence KW - expectation-maximisation algorithm KW - fingerprint identification KW - indoor radio KW - signal classification KW - wireless LAN KW - EM algorithm KW - ML estimation KW - WiFi indoor positioning KW - censored Gaussian data classification KW - clipped data KW - convergence properties KW - expectation maximization algorithm KW - fingerprinting method KW - maximum likelihood estimation KW - optimal classification KW - parameters estimation KW - portable devices sensitivity KW - signal strength measurements KW - wireless LAN positioning systems KW - Convergence KW - IEEE 802.11 Standards KW - Maximum likelihood estimation KW - Parameter estimation KW - Position measurement KW - Training KW - Indoor positioning KW - censored data KW - expectation maximization KW - signal strength KW - wireless LAN SN - 1520-6149 T2 - 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013) TI - Parameter estimation and classification of censored Gaussian data with application to WiFi indoor positioning ER - TY - CONF AB - In this paper we present a novel noise power spectral density tracking algorithm and its use in single-channel speech enhancement. It has the unique feature that it is able to track the noise statistics even if speech is dominant in a given time-frequency bin. As a consequence it can follow non-stationary noise superposed by speech, even in the critical case of rising noise power. The algorithm requires an initial estimate of the power spectrum of speech and is thus meant to be used as a postprocessor to a first speech enhancement stage. An experimental comparison with a state-of-the-art noise tracking algorithm demonstrates lower estimation errors under low SNR conditions and smaller fluctuations of the estimated values, resulting in improved speech quality as measured by PESQ scores. AU - Chinaev, Aleksej AU - Krueger, Alexander AU - Tran Vu, Dang Hai AU - Haeb-Umbach, Reinhold ID - 11745 KW - MAP parameter estimation KW - noise power estimation KW - speech enhancement T2 - 37th International Conference on Acoustics, Speech and Signal Processing (ICASSP 2012) TI - Improved Noise Power Spectral Density Tracking by a MAP-based Postprocessor ER - TY - CONF AB - In this paper we present a novel vehicle tracking algorithm, which is based on multi-level sensor fusion of GPS (global positioning system) with Inertial Measurement Unit sensor data. It is shown that the robustness of the system to temporary dropouts of the GPS signal, which may occur due to limited visibility of satellites in narrow street canyons or tunnels, is greatly improved by sensor fusion. We further demonstrate how the observation and state noise covariances of the employed Kalman filters can be estimated alongside the filtering by an application of the Expectation-Maximization algorithm. The proposed time-variant multi-level Kalman filter is shown to outperform an Interacting Multiple Model approach while at the same time being computationally less demanding. AU - Bevermeier, Maik AU - Peschke, Sven AU - Haeb-Umbach, Reinhold ID - 11723 KW - covariance matrices KW - expectation-maximisation algorithm KW - expectation-maximization algorithm KW - global positioning system KW - Global Positioning System KW - GPS KW - inertial measurement unit KW - interacting multiple model approach KW - Kalman filters KW - multilevel sensor fusion KW - narrow street canyons KW - narrow tunnels KW - online parameter estimation KW - parameter estimation KW - road vehicles KW - robust vehicle localization KW - sensor fusion KW - state noise covariances KW - time-variant multilevel Kalman filter KW - vehicle tracking algorithm T2 - 6th Workshop on Positioning Navigation and Communication (WPNC 2009) TI - Robust vehicle localization based on multi-level sensor fusion and online parameter estimation ER - TY - CONF AB - In this paper we present a novel vehicle tracking method which is based on multi-stage Kalman filtering of GPS and IMU sensor data. After individual Kalman filtering of GPS and IMU measurements the estimates of the orientation of the vehicle are combined in an optimal manner to improve the robustness towards drift errors. The tracking algorithm incorporates the estimation of time-variant covariance parameters by using an iterative block Expectation-Maximization algorithm to account for time-variant driving conditions and measurement quality. The proposed system is compared to an interacting multiple model approach (IMM) and achieves improved localization accuracy at lower computational complexity. Furthermore we show how the joint parameter estimation and localizaiton can be conducted with streaming input data to be able to track vehicles in a real driving environment. AU - Bevermeier, Maik AU - Peschke, Sven AU - Haeb-Umbach, Reinhold ID - 11724 KW - computational complexity KW - expectation-maximisation algorithm KW - Global Positioning System KW - inertial measurement unit KW - inertial navigation KW - interacting multiple model KW - iterative block expectation-maximization algorithm KW - Kalman filters KW - multi-stage Kalman filter KW - parameter estimation KW - road vehicles KW - vehicle positioning KW - vehicle tracking T2 - IEEE 69th Vehicular Technology Conference (VTC 2009 Spring) TI - Joint Parameter Estimation and Tracking in a Multi-Stage Kalman Filter for Vehicle Positioning ER - TY - JOUR AB - In this paper, parameter estimation of a state-space model of noise or noisy speech cepstra is investigated. A blockwise EM algorithm is derived for the estimation of the state and observation noise covariance from noise-only input data. It is supposed to be used during the offline training mode of a speech recognizer. Further a sequential online EM algorithm is developed to adapt the observation noise covariance on noisy speech cepstra at its input. The estimated parameters are then used in model-based speech feature enhancement for noise-robust automatic speech recognition. Experiments on the AURORA4 database lead to improved recognition results with a linear state model compared to the assumption of stationary noise. AU - Windmann, Stefan AU - Haeb-Umbach, Reinhold ID - 11938 IS - 8 JF - IEEE Transactions on Audio, Speech, and Language Processing KW - AURORA4 database KW - blockwise EM algorithm KW - covariance analysis KW - linear state model KW - noise covariance KW - noise-robust automatic speech recognition KW - noisy speech cepstra KW - offline training mode KW - parameter estimation KW - speech recognition KW - speech recognition equipment KW - speech recognizer KW - state-space methods KW - state-space model TI - Parameter Estimation of a State-Space Model of Noise for Robust Speech Recognition VL - 17 ER -