A New Continually Growing Recursive Lean Instant Slope Constant Estimator for Online Measurement of Derivative and Actual Value of Oversampled Signals

This paper introduces a novel, recursive finite impulse response filter with continually growing regression window length. The algorithm implements an adaptive linear Least Squares (LS) regression and optimally computes the slope and actual value in real time at the sampled data rate within a finite set of samples. This can be effectively used in various domains of power electronics such as online parameter identification and predictive control methods. The growing window length allows for highest noise attenuation and highly dynamic runtime characteristics at the same time which is especially useful for measuring switching-state-dependent quantities. Due to the recursive structure, even very large sample windows can be implemented with insignificantly increased hardware demand while maintaining very low latency. Efficient hardware realization on a Field Programmable Gate Array (FPGA) with fixed-point arithmetics is presented and actual measurement data proves the outstanding performance. Finally, computational effort is benchmarked against non-recursive and fixed-window implementations.