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Conference Papers Year : 2023

Constructing annihilators for parameter estimation in nonlinearly parameterized signals

Abstract

This paper studies the theoretical challenge of linearly representing a class of nonlinearly parameterized estimation problems. Conventional linear regression estimation methods can then be used. For illustration purposes, in our work, the DREM method is chosen to estimate the frequencies for a multi-sinusoidal uncertain signal in a fixed time. Identifying annihilators for signals generated by exponential polynomials with unknown parameters is the first step to accomplishing the linear representation. The annihilators are obtained as time-delay operators constructed with an Ore extension. The fundamental idea is to use the action of these operators on exponential polynomials to obtain the linear regression in nonlinear unknown quantities. We precisely characterize the annihilator as a principal ideal using appropriate Ore extensions, substantially simplifying further calculations. Some examples illustrate our annihilator's design.
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Dates and versions

hal-04176149 , version 1 (02-08-2023)

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  • HAL Id : hal-04176149 , version 1

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Rosane Ushirobira, Denis Efimov. Constructing annihilators for parameter estimation in nonlinearly parameterized signals. IFAC 2023 - 22nd IFAC World Congress, Jul 2023, Yokohama, Japan. ⟨hal-04176149⟩
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