FPGA implementation of a GHKSS filter for real-time noise reduction in nonlinear time series data

The GHKSS nonlinear projective filtering method as a representative of nonlinear time series analysis, has been used as a “posterior filtering” noise reduction technique in a range of applications. Compared to Fourier and model-based techniques it has the advantage of reducing the noise with broadband spectra, without knowledge of the system model. The contamination of time series data with measurement noise may result in an apparent loss of intrinsic dynamical information of the nonlinear systems. A real-time implementation and working principle of the GHKSS algorithm is widely ignored due to its complexity and high computational cost. Here, we present a real-time implementation of this algorithm using a Field Programmable Gate Array (FPGA) and High-level synthesis (HLS) tools. The computational burden is reduced by running the false nearest neighbour (FNN) search and delay estimation part of the GHKSS, on a separate DSP slice using HLS tools. The effect of noise reduction on dynamic preservation using GHKSS was illustrated by estimating the correlation dimension and the maximal Lyapunov exponent of the 3-D Chay model in the chaotic regime. This research is important since the real-time implementation of the GHKSS algorithm will widen its application in nonlinear time series analysis.