Preprocessing of measurements using singular spectrum analysis for parameter estimation of the Lorenz system

The article considers the preprocessing stage of nonlinear parameter estimation. The original data is generated from the Lorenz system, and the measurements are corrupted by an additive noise. Preprocessing of measurements is based on the application of singular spectrum analysis (SSA). The algorithm decomposes time series into additive components. SSA allows to extract components with different dynamics, such as trend, periodic components and noise. In this way, SSA can be used to filtering the measurements. The only parameter of the algorithm is the window length that controls the smoothing level. It is important to choose a proper window length to minimize the error, which defines the difference between the original and the filtered data. Numerical simulations shows that the dependence of the error on the window length has a single minimum, and the optimal values are different for each series of measurements.