Linear system identification with derivative shift operator representations

A new operator which combines the two commonly used operators, the shift(q) and the delta(δ) operators is used in system identification. It is shown that by using this operator the condition number of the information matrix in the identification is significantly lower than that using the q or δ-operator. It is also shown that more accurate and faster converging parameter identification can be achieved by using the new operator especially for high order systems with wide bandwidth and when sampling rates are high. The numerical superiority of the new operator over the q- and δ-operator is demonstrated by simulation results