Recursive Least Squares Adaptive Filter (RLS)

Category: trend

An adaptive FIR filter that uses the Recursive Least Squares algorithm to minimize the squared error between the input and the filtered signal, offering faster convergence than LMS.

Formula

\begin{aligned}e(n) &= s(n) - w^T(n-1)x(n) \\ k(n) &= \frac{P(n-1)x(n)}{\lambda + x^T(n)P(n-1)x(n)} \\ w(n) &= w(n-1) + k(n)e(n) \\ P(n) &= \lambda^{-1} [P(n-1) - k(n)x^T(n)P(n-1)] \end{aligned}

Inputs

• Filter Order (taps) (default: 16)
• Forgetting Factor (λ) (default: 0.99)
• Source (default: close)

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