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...ochastic interpretation as the covariance of the error xk1 x̂k1jk1. The same conclusion is obtained for the deterministic setting for continuous time Kalman filter for usual state-space systems (=-=Willems 2004-=-). œ Remark 4.8: Note also that the proof presented in Darouach et al. (1993) is not completely deterministic, since Pkjk was calculated as a covariance matrix (and therefore, stochastic arguments wer...

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...torisation N , E. However, it is known in the l2 setting that this deterministic least squares estimator NE can be realised by a process of determining the residuals in a Kalman filter bank, see [4], =-=[13]-=-. For p ∈ P , k ∈ N let estimator A with h =∞ in equation (2.9) be given by: EA(w2)(k)(p) = argmin x∈Wp(k,k) ‖x‖ where Wp(k, k) is the set of all truncated disturbance signals consistent with the obse...

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...and a specific form of pruning/projection, based on clustering, which serves to facilitate the numerical efficiency of these methods. I. INTRODUCTION Deterministic filtering approaches [1], [2], [3], =-=[4]-=- have been studied as an alternative to stochastic methods of filtering. These deterministic methods are especially appealing in cases where the disturbance statistics are not known apriori. In fact, ...

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...rediction errors or likelihood computation in the stochastic setting. In both cases Kalman filtering or smoothing algorithms are used. A deterministic equivalent of the Kalman filter is considered in =-=[23]-=-, [24], [25] VI. SIMULATION EXAMPLES A. Errors-in-variables setup In this section, we show examples of identification problems with missing data. The data wd is generated in the errors-in-variables se...

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... filter obtained via both these approaches for the linear system case with white noise processes (and a quadratic energy function with L2 noise processes) turns out to be the Kalman filter [6], [15], =-=[16]-=-. The articles [2], [3] address the sensor scheduling problem in the case of linear systems with Gaussian input noise. An alternative approach for optimal sensor scheduling in nonlinear systems, formu...

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...sulting filter obtained via both these approaches for the linear system case with white noise processes (and a quadratic energy function with L2 noise processes) turns out to be the Kalman filter [3]–=-=[5]-=-. In the case of nonlinear systems (or non-normal noise) the congruence in these two approaches no longer holds. There are various extensions of the Kalman filter to nonlinear systems (e.g. unscented ...

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...re needed to drive the dynamics (7) of agent i. Minimum-energy filtering [10], [15] is a deterministic filtering approach that for linear systems results in the same Kalman filter [14] equations, cf. =-=[7]-=-. Several arguments have been suggested in favor of minimum-energy filtering [7]. In this work, since we face a non-standard distributed filtering problem, we utilize minimum-energy filtering due its ...