Horizon group shift FIR filter: Alternative nonlinear filter using finite recent measurements

• A new horizon group shift (HGS) algorithm to adapt the horizon size of the FIR filter is proposed.
• The HGS algorithm is very effective in nonlinear FIR filtering.
• An alternative nonlinear FIR filter adopting the HGS, called the HGS-FIR filter, is proposed.
• We compare the HGS-FIR filter with existing nonlinear filters.
• The HGS-FIR filter exhibits excellent performance.

In finite impulse response (FIR) filtering using finite recent measurements, horizon size (window length) is an important parameter that influences estimation performance. In this paper, to improve the estimation performance of a nonlinear FIR filter, we propose an alternative nonlinear FIR filter called horizon group shift (HGS) FIR filter and adopt a novel method to manage horizon size. The HGS-FIR filter adjusts horizon size based on the likelihood of observation and achieves a significant performance improvement. We verified that the HGS-FIR filter exhibits excellent performance, exceeding that of existing nonlinear filters, including the extended Kalman filter, unscented Kalman filter, and particle filter.