This paper presents a multi-layer reproducing kernel Hilbert space (RKHS) approach for probability distribution to real and probability distribution to function regressions. The approach maps the distributions into RKHS by distribution embeddings and, then, constructs a multi-layer RKHS within which the multi-kernel distribution regression can be implemented using an existing kernel regression algorithm, such as kernel recursive least squares (KRLS). The numerical simulations on synthetic data obtained via Gaussian mixtures show that the proposed approach outperforms existing probability distribution (DR) regression algorithms by achieving smaller mean squared errors (MSEs) and requiring less training samples.

This paper presents a camera control approach for learning unknown nonlinear target dynamics by approximating information value functions using particles that represent targets' position distributions. The target dynamics are described by a non-parametric mixture model that can learn a potentially infinite number of motion patterns. Assuming that each motion pattern can be represented as a velocity field, the target behaviors can be described by a non-parametric Dirichlet process-Gaussian process (DP-GP) mixture model. The DP-GP model has been successfully applied for clustering time-invariant spatial phenomena due to its flexibility to adapt to data complexity without overfitting. A new DP-GP information value function is presented that can be used by the sensor to explore and improve the DP-GP mixture model. The optimal camera control is computed to maximize this information value function online via a computationally efficient particle-based search method. The proposed approach is demonstrated through numerical simulations and hardware experiments in the RAVEN testbed at MIT.

This paper presents a visibility-based method for planning the motion of a mobile robotic sensor with bounded field-of-view to optimally track a moving target while localizing itself. The target and robot states are estimated from online sensor measurements and a set of a priori known landmarks, using an extended Kalman filter (EKF), and thus the proposed method is applicable to robots without a global positioning system. It is shown that the problem of optimizing the target tracking and robot localization performance is equivalent to optimizing the visibility or probability of detection in the EKF framework under mild assumptions. The control law that maximizes the probability of detection for a robotic sensor with a sector-shaped field-of-view (FoV) is derived as a function of the robot heading and aperture. Simulations have been conducted on synthetic experiments and the results show that the optimized-visibility approach is effective at avoiding target loss, and outperforms a state-of-the-art potential method based on robot trailer models [1].

There is considerable precedence in the sensor tracking and estimation literature for modeling maneuvering targets by Markov motion models in order to estimate the target state from multiple, distributed sensor measurements. Although the transition probability density functions of these Markov models are routinely outputted by tracking and estimation algorithms, little work has been done to use them in sensor coordination and control algorithms. This paper presents a geometric transversals approach for representing the probability of track detection by multiple, distributed sensors, as a function of the Markov model transition probabilities. By this approach, the Markov parameters of maneuvering targets that may be detected by the sensors are represented by three-dimensional cones that are finitely generated by the sensors fields-of-view in a spatiotemporal Euclidian space. Then, the problem of deploying a sensor network for the purpose of maximizing the expected number of target detections can be formulated as a nonlinear program that can be solved numerically for the optimal sensor placement. Numerical results show that the optimal sensor placements obtained by this geometric transversals approach significantly outperform greedy, grid, or randomized sensor deployments.