Unsupervised State-Space Modeling Using Reproducing Kernels

This is the accepted manuscript. The final version is available at http://dx.doi.org/10.1109/TSP.2015.2448527.A novel framework for the design of state-space models (SSMs) is proposed whereby the state-transition function of the model is parametrised using reproducing kernels. The nature of SSMs requires learning a latent function that resides in the state space and for which input-output sample pairs are not available, thus prohibiting the use of gradient-based supervised kernel learning. To this end, we then propose to learn the mixing weights of the kernel estimate by sampling from their posterior density using Monte Carlo methods. We first introduce an offline version of the proposed algorithm, followed by an online version which performs inference on both the parameters and the hidden state through particle filtering. The accuracy of the estimation of the state-transition function is first validated on synthetic data. Next, we show that the proposed algorithm outperforms kernel adaptive filters in the prediction of real-world time series, while also providing probabilistic estimates, a key advantage over standard methods.Felipe Tobar acknowledges financial support from EPSRC grant number EP/L000776/1

Clustering for filtering: multi-object detection and estimation using multiple/massive sensors

Advanced multi-sensor systems are expected to combat the challenges that arise in object recognition and state estimation in harsh environments with poor or even no prior information, while bringing new challenges mainly related to data fusion and computational burden. Unlike the prevailing Markov-Bayes framework that is the basis of a large variety of stochastic filters and the approximate, we propose a clustering-based methodology for multi-sensor multi-object detection and estimation (MODE), named clustering for filtering (C4F), which abandons unrealistic assumptions with respect to the objects, background and sensors. Rather, based on cluster analysis of the input multi-sensor data, the C4F approach needs no prior knowledge about the latent objects (whether quantity or dynamics), can handle time-varying uncertainties regarding the background and sensors such as noises, clutter and misdetection, and does so computationally fast. This offers an inherently robust and computationally efficient alternative to conventional Markov–Bayes filters for dealing with the scenario with little prior knowledge but rich observation data. Simulations based on representative scenarios of both complete and little prior information have demonstrated the superiority of our C4F approach