A method for adaptive signal processing is provided. In the method, a second vector is obtained by initializing a first vector without regularization of a cost function. The cost function is regularized with the first vector and the second vector as variables. The first vector is updated based on an input signal, according to the regularized cost function. Then, an output signal is provided based on the updated first vector. The second vector is updated based on the update of the first vector. An apparatus for adaptive signal processing is provided accordingly. The method and the apparatus are well compatible with existing adaptive signal processing. The convergence coefficients of the adaptive filter system become more stable. Moreover, impact of an extra penalty added to the cost function on a bias can be minimized, and the increased complexity of the system is very limited.

A method for adaptive signal processing is provided. In the method, a second vector is obtained by initializing a first vector without regularization of a cost function. The cost function is regularized with the first vector and the second vector as variables. The first vector is updated based on an input signal, according to the regularized cost function. Then, an output signal is provided based on the updated first vector. The second vector is updated based on the update of the first vector. An apparatus for adaptive signal processing is provided accordingly. The method and the apparatus are well compatible with existing adaptive signal processing. The convergence coefficients of the adaptive filter system become more stable. Moreover, impact of an extra penalty added to the cost function on a bias can be minimized, and the increased complexity of the system is very limited.

An apparatus for reducing belt slip of a vehicle, in which the vehicle includes an engine as a vibration source and an electric motor connected to the engine through a belt to transmit torque of the engine, includes: a signal generator configured to generate a reference signal with a frequency corresponding to vibration of the engine; an adaptive filter configured to calculate a filter coefficient to remove an error value between a rotational speed of the engine and a rotational speed of the electric motor and apply the filter coefficient to the reference signal to generate a reference torque signal; and a torque compensator configured to generate a belt slip compensation torque signal by changing an amplitude of the reference torque signal, and apply the belt slip compensation torque signal to determine a final torque command of the electric motor.

The present disclosure relates to adaptive filtering optimization methods based on a hyperbolic sine cost function. While the adaptive filtering optimization methods belong to the variable step-size class, however, the present disclosure describes a new approach requiring tuning of only one parameter. The present disclosure is further related to a family of higher order hyperbolic sine cost functions.