Input Noise Variance Estimation for Adaptive Filtering Without Prior Information

In adaptive filtering, input noise degrades the performance of standard algorithms by introducing bias into the weight estimate. This paper presents a bias-compensated adaptive filtering method that estimates the input noise variance without requiring any prior information. By exploiting the orthogonality between the estimated weight vector and the error vector, the proposed Prior-Free Noise Variance Estimator (PFNVE) obtains a reliable noise variance estimate that is independent of the output noise characteristics and the input-to-output noise ratio. System identification experiments show that the PFNVE achieves steady-state accuracy comparable to existing techniques while offering noticeably faster tracking when the system undergoes abrupt changes. Since the PFNVE does not require any structural modification to the underlying filter, it can be directly applied to other adaptive filters, including MS-PNLMS. Performance is evaluated through simulations on dense and sparse systems under various conditions, including colored input and time-varying noise.