This paper presents a new method for determining the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials. The simplicity of this method lies in the online generation of a set of independent linear time-invariant algebraic equations in the unknown parameters.The development of this method is based on the novel approach of treating the excitation and response signals as distributions, and expanding them in exponentially weighted series of the generalised time derivatives of the impulse distribution. These expansion coefficients are used to form the algebraic equations in the unknown parameters. A practical means of obtaining the expansion coefficients online consists of Poisson filtering the process signals and sampling the filter outputs simultaneously.