This paper focuses on the identification of the process noise density of a linear time-varying system described by the state-space model with the known measurement noise density. A novel method is proposed that enhances the measurement difference method (MDM). The proposed method relies on a refined calculation of the MDM residue, which accounts for both process and measurement noises, as well as constructing the kernel density of the residue sample. The process noise density is then estimated by the density deconvolution algorithm utilising the Fourier transform. The method is supplemented with automatic selection of the deconvolution parameters based on the method of moments. The performance of process noise density estimation is evaluated in numerical examples and the paper is supplemented with a MATLAB implementation.