Optimum nonlinear correntropy filter

1. A signal processing method, comprising

receiving a signal input;

filtering the signal input using a nonlinear correntropy filter to produce a filtered signal; and

generating an output signal based upon the filtered signal,

wherein the nonlinear correntropy filter comprises an algorithm that computes an autocorrentropy matrix of the input signal multiplied by a cross correntropy vector between the signal input and a target signal, wherein the target signal comprises a user specified function.

2. The method of claim 1 , wherein the target signal is a current sample of the input signal, and a filter input to the nonlinear correntropy filter is delayed by one sample such that the nonlinear correntropy filter predicts the future values of the input signal.

3. The method of claim 2 , wherein the target signal is a sample of a previously received portion of the input signal, such that the correntropy filter smoothes a noisy component associated with the input signal.

4. The method of claim 1 , wherein generating an output signal comprises generating an identification of a nonlinear system.

5. The method of claim 1 , wherein generating an output signal comprises generating an inverse model representing a best fit to a noisy plant.

6. A nonlinear filter, comprising:

a signal input configured to receive a signal input;

a processing unit configured to generated a filtered signal input using a linear correntropy filter; and

the processing unit further configured to generate an output signal based upon the filtered signal input;

wherein the linear correntropy filter comprises an algorithm that computes a linear finite impulse response filter, wherein the coefficients of the linear finite impulse response filter are adapted with a correntropy cost function.

7. The nonlinear filter of claim 6 , wherein the signal input comprises a plurality of lagged discrete signals mapped by the correntropy cost function, and wherein the processing unit is configured to filter the projected signal input by applying a plurality of filter weights in the projected space to the lagged discrete signals.

8. The nonlinear filter of claim 7 , wherein each of the plurality of filter weights is based on a minimization of an expected value between the desired output and the filtered signal in the projected signal space by the correntropy function.

9. The nonlinear filter of claim 7 , wherein the lagged discrete signals comprise signals characterized as ergodic signals, and wherein the plurality of filter weights is computed based on an inverse correntropy matrix, correntropy LMS algorithm or correntropy LMS/Newton algorithm.

10. The method of claim 6 , wherein a desired response is a current sample of the input signal, and a filter input of the correntropy filter is delayed by one sample such that the correntropy filter predicts the future values of the signal input.

11. The method of claim 6 , wherein a desired response is a sample of a previously received portion of the input signal, such that the correntropy filter smoothes a noisy component associated with the input signal.

12. A signal processing system, comprising

a nonlinear correntropy-based filter for generating a filter output by filtering a signal; and

a summer for computing a difference between the filter output and a desired signal response.

13. The system of claim 12 , further comprising a plant in electrical communication with the summer, the plant generating the desired signal response based upon a system input signal that is supplied to both the nonlinear correntropy-based filter and the plant.

14. The system of claim 12 , further comprising a delay in electrical communication with the nonlinear correntropy-based filter to supply the signal thereto in response to receiving a random signal, the random signal also defining the desired signal supplied directly to the summer.

15. The system of claim 12 , wherein the signal defines a reference signal, and wherein a primary signal is supplied directly to the summer.

16. A machine-readable storage medium, the medium comprising machine-executable instructions that:

generate a correntropy statistic based on a kernel function that obeys predetermined Mercer conditions, where the correntropy statistic, V is defined as v(t 1 ,t 2 )=E(k(x t 1 −x t 2 )), E being an expected value operator, and k being the kernel function that obeys predetermined Mercer conditions; and

determine a plurality of filter weights based upon the correntropy statistic computed wherein the plurality of filter weights is computed based on an inverse correntropy matrix, correntropy LMS algorithm or correntropy LMS/Newton algorithm.

17. The system of claim 12 , wherein a desired response of the signal processing system is a current sample of the signal, and a filter input of the nonlinear correntropy-based filter is delayed by one sample such that the nonlinear correntropy-based filter predicts the future values of the signal.

18. The system of claim 12 , wherein a desired response is a sample of a previously received portion of the signal, such that the nonlinear correntropy-based filter smoothes a noisy component associated with the signal.