We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and observation models. Instead, we formulate a generic recurrent neural network framework and seek to learn directly a recursive mapping from observational inputs to the desired estimator statistics. The main focus of this article is the approximation capabilities of this framework. We provide approximation error bounds for filtering in general non-compact domains. We also consider strong time-uniform approximation error bounds that guarantee good long-time performance. We discuss and illustrate a number of practical concerns and implications of these results.

As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the mainstream method due to their principled characterization and competitive performances. Here, we propose a novel PGM without imposing any distributional assumptions on attributes, which is superior to the existing PGMs that require attributes to be categorical or Gaussian distributed. Based on the block model of graph structure, our model incorporates the attribute by describing its effect on node popularity. To characterize the effect quantitatively, we analyze the community detectability for our model and then establish the requirements of the node popularity term. This leads to a new scheme for the crucial model selection problem in choosing and solving attributed community detection models. With the model determined, an efficient algorithm is developed to estimate the parameters and to infer the communities. The proposed method is validated from two aspects. First, the effectiveness of our algorithm is theoretically guaranteed by the detectability condition. Second, extensive experiments indicate that our method not only outperforms the competing approaches on the employed datasets, but also shows better applicability to networks with various node attributes.

The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental process, a Cox process under which the square root of the intensity is a Gaussian process. In particular we exploit connections with reproducing kernel Hilbert spaces, to derive efficient approximate Bayesian inference algorithms based on the Laplace approximation to the predictive distribution and marginal likelihood. We obtain a simple algorithm which we apply to toy and real-world problems, obtaining orders of magnitude speed improvements over previous work.

A set-valued descriptor state estimation algorithm is given for determining all those descriptor state values consistent with a given uncertain descriptor system model, sensor model and a general class of uncertainty model. An approach for detecting faults or attacks signals that are corrupting the uncertain descriptor system and/or the set of sensor readings is also provided.

In this paper we address the problem of simultaneous object class and pose estimation using nothing more than object class label measurements from a generic object classifier. We detail a method for designing a likelihood function over the robot configuration space. This function provides a likelihood measure of an object being of a certain class given that the robot (from some position) sees and recognizes an object as being of some (possibly different) class. Using this likelihood function in a recursive Bayesian framework allows us to achieve a kind of spatial averaging and determine the object pose (up to certain ambiguities to be made precise). We show how inter-class confusion from certain robot viewpoints can actually increase the ability to determine the object pose. Our approach is motivated by the idea of minimalistic sensing since we use only class label measurements albeit we attempt to estimate the object pose in addition to the class.

This paper introduces and surveys a number of determinant constraints on the measurement errors in a variety of positioning scenarios. An algorithm for exploiting the constraints for accurate positioning is introduced and the relationship between the proposed algorithm and a so-called traditional maximum likelihood algorithm is examined.

Tracking a target from a video stream (or a sequence of image frames) involves nonlinear measurements in Cartesian coordinates. However, the target dynamics, modeled in Cartesian coordinates, result in a linear system. We present a robust linear filter based on an analytical nonlinear to linear measurement conversion algorithm. Using ideas from robust control theory, a rigorous theoretical analysis is given which guarantees that the state estimation error for the filter is bounded, i.e., a measure against filter divergence is obtained. In fact, an ellipsoidal set-valued estimate is obtained which is guaranteed to contain the true target location with an arbitrarily high probability. The algorithm is particularly suited to visual surveillance and tracking applications involving targets moving on a plane.

This paper provides a novel solution for robocentric mapping using an autonomous mobile robot. The robot dynamic model is the standard unicycle model and the robot is assumed to measure both the range and relative bearing to the landmarks. The algorithm introduced in this paper relies on a coordinate transformation and an extended Kalman filter like algorithm. The coordinate transformation considered in this paper has not been previously considered for robocentric mapping applications. Moreover, we provide a rigorous stochastic stability analysis of the filter employed and we examine the conditions under which the mean-square estimation error converges to a steady-state value.

This paper investigates the problem of estimating the location and velocity of a mobile agent using the received signal strength (RSS) measurements. Typical power measurements are inherently nonlinear and in this approach we derive a linear measurement scheme using an analytical measurement conversion technique which can readily be used with RSS measuring sensors. Power measurements are hence used in our robust version of a linear Kalman filter to estimate the dynamic parameters of the moving transmitter.

In this letter, we provide a robust version of a linear Kalman filter for target tracking based on a measurement conversion technique on the nonlinear radar measurements. We prove that the state estimation error is bounded in a probabilistic sense. We compare our approach with the current state of the art in converted radar measurement-based linear filtering.

In this paper we develop a robust method of target/mobile agent tracking involving two independent estimators with separate measurement systems. The outputs of the two estimators are combined using simple trigonometry (post-estimation data fusion) and provide a robust and reliable tracking path. We demonstrate that through the use of recent advances in robust set-value state estimation, our robust parallel filter approach performs well even when the individual filters do not. Brief comparisons with common data fusion methods are conducted in order to demonstrate the advantages of our parallel (post-estimation fusion) approach

In this paper we discuss the ghost node problem found when triangulation of 2 or more nodes is required. We present and discuss a simple algorithm, termed ABLE (Angle Based Location Estimation), that will position randomly placed emitters in a wireless sensor network using a mobile antenna array. The individual nodes in the network are relieved of the localization task by the mobile antenna system and require no modifications to account for location determination. Furthermore, no beacon nodes (i.e. nodes that know their own position) are required. We provide analysis that indicates a reasonably small number of measurements are required to guarantee the successful localization of the emitting nodes and demonstrate our results through simulation.