A Contraction Analysis of the Convergence of Risk-Sensitive Filters

A contraction analysis of risk-sensitive Riccati equations is proposed. When the state-space model is reachable and observable, a block-update implementation of the risk-sensitive filter is used to show that the N-fold composition of the Riccati map is strictly contractive with respect to the Riemannian metric of positive definite matrices, when N is larger than the number of states. The range of values of the risk-sensitivity parameter for which the map remains contractive can be estimated a priori. It is also found that a second condition must be imposed on the risk-sensitivity parameter and on the initial error variance to ensure that the solution of the risk-sensitive Riccati equation remains positive definite at all times. The two conditions obtained can be viewed as extending to the multivariable case an earlier analysis of Whittle for the scalar case.Comment: 22 pages, 6 figure

Cooperative localization for mobile agents: a recursive decentralized algorithm based on Kalman filter decoupling

We consider cooperative localization technique for mobile agents with communication and computation capabilities. We start by provide and overview of different decentralization strategies in the literature, with special focus on how these algorithms maintain an account of intrinsic correlations between state estimate of team members. Then, we present a novel decentralized cooperative localization algorithm that is a decentralized implementation of a centralized Extended Kalman Filter for cooperative localization. In this algorithm, instead of propagating cross-covariance terms, each agent propagates new intermediate local variables that can be used in an update stage to create the required propagated cross-covariance terms. Whenever there is a relative measurement in the network, the algorithm declares the agent making this measurement as the interim master. By acquiring information from the interim landmark, the agent the relative measurement is taken from, the interim master can calculate and broadcast a set of intermediate variables which each robot can then use to update its estimates to match that of a centralized Extended Kalman Filter for cooperative localization. Once an update is done, no further communication is needed until the next relative measurement

Inferring hidden states in Langevin dynamics on large networks: Average case performance

We present average performance results for dynamical inference problems in large networks, where a set of nodes is hidden while the time trajectories of the others are observed. Examples of this scenario can occur in signal transduction and gene regulation networks. We focus on the linear stochastic dynamics of continuous variables interacting via random Gaussian couplings of generic symmetry. We analyze the inference error, given by the variance of the posterior distribution over hidden paths, in the thermodynamic limit and as a function of the system parameters and the ratio {\alpha} between the number of hidden and observed nodes. By applying Kalman filter recursions we find that the posterior dynamics is governed by an "effective" drift that incorporates the effect of the observations. We present two approaches for characterizing the posterior variance that allow us to tackle, respectively, equilibrium and nonequilibrium dynamics. The first appeals to Random Matrix Theory and reveals average spectral properties of the inference error and typical posterior relaxation times, the second is based on dynamical functionals and yields the inference error as the solution of an algebraic equation.Comment: 20 pages, 5 figure

Macroeconomic Factors and the Balanced Value of the Czech Koruna/Euro Exchange Rate (in English)

The authors study the dependence of the Czech koruna’s exchange rate to the euro on risk factors that cannot be reduced to standard macroeconomic fundamentals. For this purpose, they construct an international asset-pricing model in which the exchange rate is codetermined by a risk factor imperfectly correlated with other priced risks in the economy. The model embeds the standard no-arbitrage setup. It also contains an additional equation that links the autarchic currency price with the foreign-exchange order flow. In the state-space form, the unobserved variables that determine the dynamics of the asset markets, the autarchic exchange rate, and the FX order flow span a number of macroeconomic and latent risk factors. The model for the Czech koruna/euro exchange rate uses Kalman filter techniques. The results indicate the existence of a “non-fundamental” source of systematic divergence between the observed and the autarchic (i.e. fundamental) FX returns.exchange rate, latent risk, order flow, pricing kernel, state space

VALIDATION OF KALMAN FILTER METHOD FOR VERTICAL POSITION AND SPEED ESTIMATION IN THE TCV TOKAMAK

openConvalida del metodo del filtro di Kalman su sistema state-space linearizzato da simulatore Forward Grad Shafranov Evolutive (FGE). Design delle matrici di covarianza per la stima della posizione, della velocità del plasma, dalla stima delle correnti di attive e di vessel e delle constraints. Simulazione di diversi shots di TCV.Validation of the Kalman filter method on state-space system linearized by Forward Grad Shafranov Evolutive simulator (FGE). Design of covariance matrices for position and plasma velocity estimation, from estimations of active and vessel currents and constraints. Simulation of several shots of TCV