A new family of stochastic gradient adaptive filter algorithms is prop
osed which is based on mixed error norms. These algorithms combine the
advantages of different error norms, for example the conventional, re
latively well-behaved, least mean square algorithm and the more sensit
ive, but better converging, least mean fourth algorithm. A mixing para
meter is included which controls the proportions of the error norms an
d offers an extra degree of freedom within the adaptation. A system id
entification simulation is used to demonstrate the performance of a le
ast mean mixed-norm (square and fourth) algorithm.