A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals

Journal ArticleAbstract This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this work, the static nonlinearity is modeled using a polynomial system and the linear filter that follows the nonlinerity is an infinite impulse response system. The adaptation of the nonlinear components is enhanced in the algorithm by orthogonalizing the inputs to the coefficients of the polynomial system. The linear system is implemented as a recursive higher-order filter. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input, bounded-output stability of the overall system. Experimental results included in the paper show that the algorithm performs well and always converges to the global minimum of the input signal is white

Identification of nonlinear, memoryless systems using chebyshev nodes

Journal ArticleABSTRACT This paper describes an approach for identification of static nonlinearities from input-output measurements. The approach is based on minimax approximation of memoryless nonlinear systems using Chebyshev polynomials. For memoryless nonlinear systems that are finite and continuous with finite derivatives, it is known that the error caused by the K th order Chebyshev approximation in a specified interval is bounded by a quantity that is proportional to the maximum value of the (K + 1) th derivative of the inputoutput relationship and decays exponentially with K. The method of the paper identifies the system by first estimating the system output at the Chebyshev nodes using localized linear model around the nodes, and then solving for the coefficients associated with the Chebyshev polynomials of the first kind

Stochastic mean-square performance analysis of an adaptive Hammerstein filter

Journal ArticleAbstract-This paper presents an almost sure mean-square performance analysis of an adaptive Hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence. The system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter. A bound for the long-term time average of the squared a posteriori estimation error of the adaptive filter is derived using a basic set of assumptions on the operating environment. This bound consists of two terms, one of which is proportional to a parameter that depends on the step size sequences of the algorithm and the other that is inversely proportional to the maximum value of the increment process associated with the coefficients of the underlying system. One consequence of this result is that the long-term time average of the squared a posteriori estimation error can be made arbitrarily close to its minimum possible value when the underlying system is time-invariant

A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals

Journal ArticleAbstract-This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this paper, the static nonlinearity is modeled using a polynomial system, and the linear filter that follows the nonlinearity is an infinite-impulse response (IIR) system. The adaptation of the nonlinear components is improved by orthogonalizing the inputs to the coefficients of the polynomial system. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input bounded-output (BIBO) stability of the overall system. This paper also presents experimental results that show that the algorithm performs well in a variety of operating environments, exhibiting stability and global convergence of the algorithm