Ivan Marković

Speaker localization and tracking with a microphone array on a mobile robot using von Mises distribution and particle filtering

This paper deals with the problem of localizing and tracking a moving speaker over the full range around the mobile robot. The problem is solved by taking advantage of the phase shift between signals received at spatially separated microphones. The proposed algorithm is based on estimating the time difference of arrival by maximizing the weighted cross-correlation function in order to determine the azimuth angle of the detected speaker. The cross-correlation is enhanced with an adaptive signal-to-noise estimation algorithm to make the azimuth estimation more robust in noisy surroundings. A post-processing technique is proposed in which each of these microphone-pair determined azimuths are further combined into a mixture of von Mises distributions, thus producing a practical probabilistic representation of the microphone array measurement. It is shown that this distribution is inherently multimodal and that the system at hand is non-linear. Therefore, particle filtering is applied for discrete representation of the distribution function. Furthermore, the two most common microphone array geometries are analysed and exhaustive experiments were conducted in order to qualitatively and quantitatively test the algorithm and compare the two geometries. Also, a voice activity detection algorithm based on the before-mentioned signal-to-noise estimator was implemented and incorporated into the existing speaker localization system. The results show that the algorithm can reliably and accurately localize and track a moving speaker.

Moving object detection, tracking and following using an omnidirectional camera on a mobile robot

Equipping mobile robots with an omnidirectional camera is very advantageous in numerous applications as all information about the surrounding scene is stored in a single image frame. In the given context, the present paper is concerned with detection, tracking and following of a moving object with an omnidirectional camera. The camera calibration and image formation is based on the spherical unified projection model thus yielding a representation of the omnidirectional image on the unit sphere. Detection of moving objects is performed by calculating a sparse optical flow in the image and then lifting the flow vectors on the unit sphere where they are discriminated as dynamic or static by analytically calculating the distance of the terminal vector point to a great circle arc. The flow vectors are then clustered and the center of gravity is calculated to form the sensor measurement. Furthermore, the tracking is posed as a Bayesian estimation problem on the unit sphere and the solution based on the von Mises-Fisher distribution is utilized. Visual servoing is performed for the object following task where the control law calculation is based on the projection of a point on the unit sphere. Experimental results obtained by a camera with a fish-eye lens mounted on a differential drive mobile robot are presented and discussed.

Bearing-only tracking with a mixture of von Mises distributions

This paper presents a novel method for Bayesian bearing-only tracking. Unlike the classical approaches, which involve using Gaussian distribution, the tracking procedure is completely covered with the von Mises distribution, including state representation, transitional probability, and measurement model, since it captures and models well the peculiarities of directional data. The state is represented with a mixture of von Mises distributions, thus offering advantages of being able to model multimodal distributions, handle nonlinear state transition and measurement models, and to completely cover the whole state space, all with a modest number of parameters. The tracking procedure is solved by convolution with a von Mises distribution (prediction step) and multiplication with a mixture representing the measurement model (update step). Since in the update step the number of mixture components grows exponentially, a method is presented for component reduction of a von Mises mixture. Furthermore, a closed-form solution is derived for quadratic Rényi entropy of the von Mises mixture. The algorithm is tested and compared to a particle filter representation in a speaker tracking scenario on a synthetic data set and real-world recordings. The results supported the proposed approach and showed similar performance to the particle filter.

Radar and stereo vision fusion for multitarget tracking on the special Euclidean group

Reliable scene analysis, under varying conditions, is an essential task in nearly any assistance or autonomous system application, and advanced driver assistance systems (ADAS) are no exception. ADAS commonly involve adaptive cruise control, collision avoidance, lane change assistance, traffic sign recognition, and parking assistance-with the ultimate goal of producing a fully autonomous vehicle. The present paper addresses detection and tracking of moving objects within the context of ADAS. We use a multisensor setup consisting of a radar and a stereo camera mounted on top of a vehicle. We propose to model the sensors uncertainty in polar coordinates on Lie Groups and perform the objects state filtering on Lie groups, specifically, on the product of two special Euclidean groups, i.e., SE ( 2 ) 2 . To this end, we derive the designed filter within the framework of the extended Kalman filter on Lie groups. We assert that the proposed approach results with more accurate uncertainty modeling, since used sensors exhibit contrasting measurement uncertainty characteristics and the predicted target motions result with banana-shaped uncertainty contours. We believe that accurate uncertainty modeling is an important ADAS topic, especially when safety applications are concerned. To solve the multitarget tracking problem, we use the joint integrated probabilistic data association filter and present necessary modifications in order to use it on Lie groups. The proposed approach is tested on a real-world dataset collected with the described multisensor setup in urban traffic scenarios. Radar and stereo camera integration for tracking in ADAS.Detection and tracking of moving objects by filtering on matrix Lie groups.State space formed as a product of two special Euclidean groups.Employed banana-shaped uncertainties typical for range-bearing sensors and vehicles in motion.JIPDA filter for multitarget tracking on matrix Lie groups.

Active speaker localization with circular likelihoods and bootstrap filtering

This paper deals with speaker localization in two dimensions from a mobile binaural head. A bootstrap particle filtering scheme is used to perform active localization, i.e. to infer source location by fusing the binaural perception with the sensor motor commands. It relies on an original pseudo-likelihood of the source azimuth which captures both the interaural level and phase differences. Since the pseudo-likelihood is discrete, it is fitted with a mixture of circular distributions in order to enhance its resolution. For the fitting task two mixtures are compared and evaluated, namely the mixture of von Mises and wrapped Cauchy distributions. Furthermore, a solution is presented for calculating the von Mises curvefitting with low uncertainty, since the direct implementation can quickly surpass double precision floating number representation. The performance of the filter is compared using both the raw and fitted pseudo-likelihoods on experiments recorded in an acoustically prepared room with ground-truth obtained from a motion capture system. The results show that the proposed algorithm successfully localizes the speaker with an advantage in the direction of the fitted von Mises mixture likelihood.

Composite distance based approach to von Mises mixture reduction

Abstract This paper presents a systematic approach for component number reduction in mixtures of exponential families, putting a special emphasis on the von Mises mixtures. We propose to formulate the problem as an optimization problem utilizing a new class of computationally tractable composite distance measures as cost functions, namely the composite Renyi α -divergences, which include the composite Kullback–Leibler distance as a special case. Furthermore, we prove that the composite divergence bounds from above the corresponding intractable Renyi α -divergence between a pair of mixtures. As a solution to the optimization problem we synthesize that two existing suboptimal solution strategies, the generalized k-means and a pairwise merging approach, are actually minimization methods for the composite distance measures. Moreover, in the present paper the existing joining algorithm is also extended for comparison purposes. The algorithms are implemented and their reduction results are compared and discussed on two examples of von Mises mixtures: a synthetic mixture and a real-world mixture used in people trajectory shape analysis.

Von Mises Mixture PHD Filter

This letter deals with the problem of tracking multiple targets on the unit circle, a problem that arises whenever the state and the sensor measurements are circular, i.e. angular-only, random variables. To tackle this problem, we propose a novel mixture approximation of the probability hypothesis density filter based on the von Mises distribution, thus constructing a method that globally captures the non-Euclidean nature of the state and the measurement space. We derive a closed-form recursion of the filter and apply principled approximations where necessary. We compared the performance of the proposed filter with the Gaussian mixture probability hypothesis density filter on a synthetic dataset of 100 randomly generated multitarget trajectory examples corrupted with noise and clutter, and on the PETS2009 dataset. We achieved respectively a decrease of 10.5% and 2.8% in the optimal subpattern assignment metric (notably 16.9% and 10.8% in the localization component).

Partial Mutual Information Based Input Variable Selection for Supervised Learning Approaches to Voice Activity Detection

The paper presents a novel approach for voice activity detection. The main idea behind the presented approach is to use, next to the likelihood ratio of a statistical model-based voice activity detector, a set of informative distinct features in order to, via a supervised learning approach, enhance the detection performance. The statistical model-based voice activity detector, which is chosen based on the comparison to other similar detectors in an earlier work, models the spectral envelope of the signal and we derive the likelihood ratio thereof. Furthermore, the likelihood ratio together with 70 other various features was meticulously analyzed with an input variable selection algorithm based on partial mutual information. The resulting analysis produced a 13 element reduced input vector which when compared to the full input vector did not undermine the detector performance. The evaluation is performed on a speech corpus consisting of recordings made by six different speakers, which were corrupted with three different types of noises and noise levels. In the end, we tested three different supervised learning algorithms for the task, namely, support vector machine, Boost, and artificial neural networks. The experimental analysis was performed by 10-fold cross-validation due to which threshold averaged receiver operating characteristics curves were constructed. Also, the area under the curve score and Matthews correlation coefficient were calculated for both the three supervised learning classifiers and the statistical model-based voice activity detector. The results showed that the classifier with the reduced input vector significantly outperformed the standalone detector based on the likelihood ratio, and that among the three classifiers, Boost showed the most consistent performance.

Extended information filter on matrix Lie groups

In this paper we propose a new state estimation algorithm called the extended information filter on Lie groups. The proposed filter is inspired by the extended Kalman filter on Lie groups and exhibits the advantages of the information filter with regard to multisensor update and decentralization, while keeping the accuracy of stochastic inference on Lie groups. We present the theoretical development and demonstrate its performance on multisensor rigid body attitude tracking by forming the state space on the SO(3)×R3 group, where the first and second component represent the orientation and angular rates, respectively. The performance of the filter is compared with respect to the accuracy of attitude tracking with parametrization based on Euler angles and with respect to execution time of the extended Kalman filter formulation on Lie groups. The results show that the filter achieves higher performance consistency and smaller error by tracking the state directly on the Lie group and that it keeps smaller computational complexity of the information form with respect to high number of measurements.

Short-Term Map Based Detection and Tracking of Moving Objects with 3D Laser on a Vehicle

Detection and tracking of moving objects is an essential problem in situational awareness context and hence crucial for many robotic applications. Here we propose a method for the detection of moving objects with a 3D laser range sensor and a variation of the method for tracking multiple detected objects. The detection procedure starts with the ground extraction using random sample consensus approach for model parameter estimation. The resulting point cloud is then downsampled using voxel grid approach and filtered using a radius outlier rejection method. Within the approach, we have utilized a procedure for building short-term maps of the environment by using the octree data structure. This data structure enables an efficient comparison of the current scan and the short-term local map, thus detecting dynamic parts of scene. The ego-motion of the mobile platform is compensated using the available odometry information, which is rather imperfect, and hence is refined using the iterative closest point registration technique. Furthermore, due to sensor characteristics, the iterative closest point is carried out in 2D between the short-term map and the current, where the non-ground filtered scans are projected onto 2D. The tracking task is based on the joint probabilistic data association filter and Kalman filtering with variable process and measurement noise which take into account velocity and position of the tracked objects. Since this data association approach assumes a constant and known number of objects, we have utilized a specific entropy based track management. The experiments performed using Velodyne HDL-32E laser sensor mounted on top of a mobile platform demonstrate the suitability and efficiency of the proposed method.