On an algebraic method for derivatives estimation and parameter estimation for partial derivatives systems

International audience— In this communication, we discuss two estimation problems dealing with partial derivatives systems. Namely, estimating partial derivatives of a multivariate noisy signal and identifying parameters of partial differential equations. The multivariate noisy signal is expressed as a truncated Taylor expression in a small time interval. An algebraic method can be then used to estimate its partial derivatives in the opera-tional domain. The same approach applies for the parameter identification problem. The main objects in the aforementioned algebraic method are particular differential operators called annihilators. Stafford's theorem can be applied to formalize the left ideal in the Weyl algebra formed by the annihilators. In the spatial domain, iterated integrals present in the estimates yield noise filtering