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The Kitanidis filter is a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs or disturbances. Though the optimality of the Kitanidis filter was founded for general time varying systems more than 30 years ago, its boundedness and stability analysis is still limited to time-invariant systems, up to the authors’ knowledge. In the framework of general time varying systems, this article establishes upper and lower bounds of the error covariance of the Kitanidis filter, as well as upper bounds of all the auxiliary variables involved in the filter. By preventing data overflow, upper bounds are crucial for all recursive algorithms in real-time applications. The upper and lower bounds of the error covariance will also serve as the basis of the Kitanidis filter stability analysis, such as in the case of the time-varying system Kalman filter.

AbstractSuppose that a mobile sensor describes a Markovian trajectory in the ambient space and at each time the sensor measures an attribute of interest, e.g. the temperature. Using only the location history of the sensor and the associated measurements, we estimate the average value of the attribute over the space. In contrast to classical probabilistic integration methods, e.g. Monte Carlo, the proposed approach does not require any knowledge of the distribution of the sensor trajectory. We establish probabilistic bounds on the convergence rates of the estimator. These rates are better than the traditional `root n'-rate, where nis the sample size, attached to other probabilistic integration methods. For finite sample sizes, we demonstrate the favorable behavior of the procedure through simulations and consider an application to the evaluation of the average temperature of oceans.

Let Ω be an open convex domain of . We study constants K such that Ω is K-spectral or complete K-spectral for each continuous linear Hilbert space operator with numerical range included in Ω. Several approaches are discussed.

We provide frequency domain tests for early detection of slight changes in input/output transfer functions. The experimental setup consists in recording successive pairs of i/o spectra. We propose a frequency domain test based on LeCam's local approach, by extending the techniques of Basseville & Benveniste to nonparametric frequency domain. The target application which motivated our study is quality control in mechanics.

Adaptive control is considered for a two-dimensional linear discrete-time plant with randomly drifting parameters. The “certainty equivalent minimum variance” control law along with the projection-like identification algorithm are used. The stability of the parameter estimates and exponential stability of the closed-loop system are proved in the absence of any “persistent excitation” assumption.

A recursive stochastic optimization procedure under dependent disturbances is studied. It is based on the Polyak-Ruppert algorithm with trajectory averaging. Almost sure convergence of the algorithm is proved as well as asymptotic normality of the delivered estimates. It is shown that the presented algorithm attains the highest possible asymptotic convergence rate for stochastic approximation algorithms

The sampling theorem tells us how a band-limited signal can be reconstructed from its samples when the sampling period satisfies the Nyquist rate. If the sampling period is smaller, the information in the samples is redundant and there are many ways to reconstruct the signal. Among these we single out the one that has minimal ℓ1norm. The advantage of this specific reconstruction formula is that it leads to a localizedformula : to reconstruct the signal at a given point it somehow draws as much information as possible from the two closest samples.

We consider fast algorithms of wavelet decomposition of a functionfwhen discrete observations off(suppf⊆[0, 1]d) are available. The properties of the algorithms are studied for three types of observation design which ford=1 can be described as follows: the regular design, when the observationsf(xi) are taken on the regular gridxi=i/N,i=1, …, N; the case of a jittered regular grid, when it is only known that for all 1⩽i⩽N,i/N⩽xi