Decoupled stochastic mapping (DSM) is a computationally efficient approach to large-scale concurrent mapping and localization. DSM reduces the computational burden of conventional stochastic mapping by dividing the environment into multiple overlapping submap regions, each with its own stochastic map. Two new approximation techniques are utilized for transferring vehicle state information from one submap to another, yielding a constant-time algorithm whose memory requirements scale linearly with the size of the operating area. The performance of two different variations of the algorithm is demonstrated through simulations of environments with 110 and 1200 features. Experimental results are presented for an environment with 93 features using sonar data obtained in a 3 by 9 by 1 meter testing tank.

We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models -- hidden Markov models and linear dynamical systems -- and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward-backward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems. We tested the algorithm both on artificial data sets and on a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, Input-Output HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variable-length Markov models and Markov switching state-space models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of biological ...

This paper describes decoupled stochastic mapping (DSM), a new computationally efficient approach to large-scale concurrent mapping and localization (CML). DSM reduces the computational burden of conventional stochastic mapping by dividing the environment into multiple overlapping submap regions, each with its own stochastic map. Two new approximation techniques are utilized for transferring vehicle state information from one submap to another, yielding a constant-time algorithm whose memory requirements scale linearly with the number of submaps. The approach is demonstrated via simulations and experiments. Simulation results are presented for the case of an autonomous underwater vehicle (AUV) navigating in an unknown environments with 110 and 1200 features using simulated observations of point features by a forward look sonar. Empirical tests are used to examine the consistency of the error bounds calculated by the different methods. Experimental results are also presented for an environment with 93 features using sonar data obtained in a 3 by 9 by 1 m testing tank.

Augmented reality deals with the problem of dynamically augmenting or enhancing (images or live video of) the real world with computer generated data (e.g., graphics of virtual objects). This poses two major problems: (a) determining the precise alignment of real and virtual coordinate frames for overlay, and (b) capturing the 3D environment including camera and object motions. The latter is important for interactive augmented reality applications where users can interact with both real and virtual objects. Here we address the problem of accurately tracking the 3D motion of a monocular camera in a known 3D environment and dynamically estimating the 3D camera location. We utilize fully automated landmark-based camera calibration to initialize the motion estimation and employ extended Kalman filter techniques to track landmarks and to estimate the camera location. The implementation of our approach has been proven to be efficient and robust and our system successfully tracks in real-tim...

Electronically steerable arrays of microphones have avariety of uses in speech data ac-quisition systems. Applications include teleconferencing, speech recognition and speaker identification, sound capture in adverse environments, and biomedical devices for the hear-ing impaired. An array of microphones has a number of advantages over a single-microphone system. It may be electronically aimed to provide a high-quality signal from a desired source location while simultaneously attenuating interfering talkers and ambient noise, does not necessitate local placement of transducers or encumber the talker with a hand-held or head-mounted microphone, and does not require physical movement to alter its direction of reception. Additionally, it has capabilities that a single microphone does not; namely automatic detection, localization, and tracking of active talkers in its receptive area. A fundamental requirement of sensor array systems is the ability to locate and track a speech source. An accurate fix on the primary talker, as well as knowledge of any interfering talkers or coherent noise sources, is necessary to effectively steer the array. Source location data may also be used for purposes other than beamforming; e.g. aiming a camera in a video-conferencing system. In addition to high accuracy, the location estimator must be

We introduce a statistical model for times series data with nonlinear dynamics which iteratively segments the data into regimes with approximately linear dynamics and learns the parameters of each of those regimes. This model combines and generalizes two of the most widely used stochastic time series models---the hidden Markov model and the linear dynamical system---and is related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network model (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) alogithm cannot be applied. However, we present a variational approximation which maximizes a lower bound on the log likelihood and makes use of both the forward--backward recursio...

A new algorithm is presented for generating the conditional mean estimates of functions of target positions, orientations and type in recognition, and tracking of an unknown nmnber of targets and target types. Taking a Bayesian approach, a posterior measure is defined on the tracking/target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model, and a prior based on airplane dynanfics. The Newtoninn force equations governing rigid body dynamic s are utilized to form the prior density on airplane motion. The conditional mean estimates are generated using a random sampling algorithm based on jump-diffusion processes [1] i)r empirically generating MMSE estimates of functions of these random target positions, orientations, and type under the posterior measure. Results are presented on target tracking and identification from an implementation of the algorithm on a networked Silicon Graphics workstation and DECmpp/MasPar parallel machine.

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum likelihood estimator in a possibly nonstationary process of this kind for which the hidden state space is compact but not necessarily finite. Consistency and asymptotic normality are shown to follow from uniform exponential forgetting of the initial distribution for the hidden Markov chain conditional on the observations.

This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as non-Gaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR).