State Noise Density Identification of LTV System by Kernel Deconvolution

This paper focuses on identification of the state noise density of a linear time-varying system described by the state-space model with the known measurement noise density. For this purpose, a novel method extending the capabilities of the measurement difference method (MDM) is proposed. The proposed method is based on the enhanced MDM residue calculation being a sum of the state and measurement noise, and on the construction of the residue sample kernel density. The state noise density is then estimated by the density deconvolution algorithm utilising the Fourier transform. The developed method is supplemented with automatic selection of the deconvolution user-defined parameters based on the proposed method of the noise moment equality. The state noise density estimation performance is evaluated in numerical examples and supplemented with the MALAB example implementation.