Tracking Analysis of Minimum Kernel Risk-Sensitive Loss Algorithm Under General Non-Gaussian Noise

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 66; no. 7; pp. 1262 - 1266
• Main Authors: Rastegarnia, Amir, Malekian, Parnian, Khalili, Azam, Bazzi, Wael M., Sanei, Saeid
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Adaptive filter; Adaptive filters; Algorithms; Circuits and systems; Computer simulation; Cost function; Energy conservation; Energy distribution; Error analysis; Gaussian distribution; Kernel; Kernel risk-sensitive loss; Kernels; Noise; Noise measurement; non-stationary; Nonstationary environments; Normal distribution; Random noise; Risk analysis; Steady state; Tracking; tracking analysis
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2018.2874969

In this brief, the steady-state tracking performance of minimum kernel risk-sensitive loss in a non-stationary environment is analyzed. In order to model a non-stationary environment, a first-order random-walk model is used to describe the variations of optimum weight vector over time. Moreover, the measurement noise is considered to have non-Gaussian distribution. The energy conservation relation is utilized to extract an approximate closed-form expression for the steady-state excess mean square error (EMSE). Our analysis shows that unlike for the stationary case, the EMSE curve is not an increasing function of step-size parameter. Hence, the optimum step-size which minimizes the EMSE is derived. We also discuss that our approach can be used to extract steady-state EMSE for a general class of adaptive filters. The simulation results with different noise distributions support the theoretical derivations.