Section: New Results

Algebraic Technique For Estimation, Differentiation And Its Applications

Elementary techniques from operational calculus, differential algebra, and non-commutative algebra lead to a new algebraic approach for estimation and detection. It is investigated in various areas of applied sciences and engineering. The following lists only some applications:

• The article [19] presents an algebraic on-line parameters estimation method for Linear Time Invariant (LTI) systems subject to polynomial perturbations. Particular attention is given to practical implementation.

• In the paper [43] , we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.

• The paper [17] presents a new sensorless parameter identification method for permanent magnet stepper motors. The method exploits derived linear parameterizations and least-squares algorithms.

• In [36] a continuous-time least-squares parameter estimation method through evolution equations is proposed. A deterministic framework for the estimation under noisy measurements is proposed using a Sobolev space with negative index to model of the noise.

• Causation between time series is a most important topic in econometrics, financial engineering, biological and psychological sciences, and many other fields. A new setting is introduced in [42] for examining this rather abstract concept. The corresponding calculations, which are much easier than those required by the celebrated Granger-causality, do not necessitate any deterministic or probabilistic modeling.

• The paper [59] proposes a solution to the problem of velocity and position estimation for a class of oscillating systems whose position, velocity and acceleration are zero mean signals. The proposed scheme considers that the dynamic model of the system is unknown and only noisy acceleration measurements are available.

• The communications [63] , [78] are devoted to solar irradiance and irradiation short-term forecasts, which are useful for electricity production. Several different time series approaches are employed.

• In [68] we present a simple algorithm to compute the factors of a Unimodular-Upper polynomial matrix decomposition. Such decomposition is useful for spatial multiplexing in multi-input multi-output(MIMO) channel transmission system since it enables to reduce the MIMO channel matrix into independent channels by a pre- and post-filtering.

• A fault-tolerant control method based on algebraic derivative estimation is introduced in [32] . It is applied on an electromagnetically supported plate as an example of a nonlinear and an open-loop unstable system.