Design of multi innovation fractional LMS algorithm for parameter estimation of input nonlinear control autoregressive systems

•This study presents a novel fractional order adaptive algorithm, called MIFLMS.•The MIFLMS extends the scalar innovation into a vector innovation.•It reveals a faster convergence speed than the FLMS with no noticeable increase in the computational burden.•The proposed algorithm effectively estimates the parameters of nonlinear systems.•The MIFLMS is more robust than the FLMS and provide consistent accurate and convergent performance. The development of procedures based on fractional calculus is an emerging research area. This paper presents a new perspective regarding the fractional least mean square (FLMS) adaptive algorithm, called multi innovation FLMS (MIFLMS). We verify that the iterative parameter adaptation mechanism of the FLMS uses merely the current error value (scalar innovation). The MIFLMS expands the scalar innovation into a vector innovation (error vector) by considering data over a fixed window at each iteration. Therefore, the MIFLMS yields better convergence speed than the standard FLMS by increasing the length of innovation vector. The superior performance of the MIFLMS is verified through parameter identification problem of input nonlinear systems. The statistical performance indices based on multiple independent trials confirm the consistent accuracy and reliability of the proposed scheme.