Stochastic Sensor Scheduling via Distributed Convex Optimization

In this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.Comment: Proof errors and typos are fixed. One section is removed from last versio

Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter

This paper proposes a unified state-space formulation for parameter estimation of exponential-affine term structure models. This class of models, charaterized by Duffie and Kan (1993), contains models such as Vasicek (1977), Cox, Ingersoll and Ross (1985) and Chen and Scott (1992), among others. The proposed method uses an approximate linear Kalman filter which only requires specifying the conditional mean and variance of the system in an approximate sense. The method allows for measurement errors in the observed yields to maturitiy, and can simultaneously deal with many yields on bonds with different maturities. A Monte Carlo study indicates thet the proposed method is a reliable procedure for moderate sample sizes. An empirical analysis of three existing exponential-affine term structure models is carried out using monthly U.S. Treasury yield data with four different maturities. Our test results indicate a strong rejection of all three models. Cette recherche propose une approche unificatrice pour l'estimation des paramètres de modèles de structure de taux d'intérêt de la classe exponentielle-affine. Cette famille de modèles, caractérisée par Duffie et Kan (1993), contient entre autres les modèles de Vasicek (1977), Cox, Ingersoll et Ross (1985) et Chen et Scott (1992). La méthode proposée utilise un filtre de Kalman approximatif qui requiert la spécification de l'espérance et de la variance conditionnelle du système. La méthode utilise simultanément plusieurs séries de rendements et permet l'ajout d'erreurs de mesure pour chaque serie. Une étude de simulation indique que la méthode proposée est fiable pour des échantillons de taille modérée. Une étude empirique utilisant trois modèles différents de la classe exponentielle-affine est présentée.Term Structure, Kalman Filter, Exponential Affine, State Space Model, Quasi Maximum Likelihood, Lagrange Multiplier Test, Structure à Terme, Filtre de Kalman, Exponentielle-affine, Modèle State-Space, Quasi-maximum de vraisemblance, Test du Multiplicateur de Lagrange

Proprioceptive Robot Collision Detection through Gaussian Process Regression

This paper proposes a proprioceptive collision detection algorithm based on Gaussian Regression. Compared to sensor-based collision detection and other proprioceptive algorithms, the proposed approach has minimal sensing requirements, since only the currents and the joint configurations are needed. The algorithm extends the standard Gaussian Process models adopted in learning the robot inverse dynamics, using a more rich set of input locations and an ad-hoc kernel structure to model the complex and non-linear behaviors due to frictions in quasi-static configurations. Tests performed on a Universal Robots UR10 show the effectiveness of the proposed algorithm to detect when a collision has occurred.Comment: Published at ACC 201

Equilibrium Sampling From Nonequilibrium Dynamics

We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual non-equilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths

Decentralized Estimation over Orthogonal Multiple-access Fading Channels in Wireless Sensor Networks - Optimal and Suboptimal Estimators

Optimal and suboptimal decentralized estimators in wireless sensor networks (WSNs) over orthogonal multiple-access fading channels are studied in this paper. Considering multiple-bit quantization before digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate the channel coefficients and exploits the estimated CSI in an optimal way. To reduce the computational complexity, we propose suboptimal estimators. These estimators exploit both signal and data level redundant information to improve the estimation performance. The proposed MLEs reduce to traditional fusion based or diversity based estimators when communications or observations are perfect. By introducing a general message function, the proposed estimators can be applied when various analog or digital transmission schemes are used. The simulations show that the estimators using digital communications with multiple-bit quantization outperform the estimator using analog-and-forwarding transmission in fading channels. When considering the total bandwidth and energy constraints, the MLE using multiple-bit quantization is superior to that using binary quantization at medium and high observation signal-to-noise ratio levels

APPLICATION OF THE KALMAN FILTER FOR ESTIMATING CONTINUOUS TIME TERM STRUCTURE MODELS: THE CASE OF UK AND GERMANY

The purpose of this paper is to see how the term structure of interest rates has evolved in the sterling and euro treasury bond markets over the period 1999-2003. German bonds have been used as a proxy for euro-denominated bonds. A state-space representation for the single-factor Cox, Ingersoll and Ross (1985) model is employed to analyse the intertemporal dynamics of the term structure. Quasi-maximum likelihood estimates of the model parameters are obtained by using the Kalman filter to calculate the likelihood function. Results of the empirical analysis show that while the unobserved instantaneous interest rate exhibits mean reverting behaviour in both the UK and Germany, the mean reversion of the interest rate process has been relatively slower in the UK. The volatility component, which shocks the process at each step in time is also higher in the UK as compared to Germany.