Adaptive Signal Processing (Newton method, steepest descent method, LMS algorithm)

Source: Internet
Author: User

Textbook: Bernard Widrow's adaptive signal processing
Newton's Method: (One-step iterative, not realistic, but useful for theoretical analysis)
The most important is the correlation matrix, and the transition from the normal coordinate system to the translation coordinate system and finally to the spindle coordinate system.
Figure out what the learning curve is, the performance surface, and the most important weight update formula. Then deduce the performance and calculate the step value.
W (k+1) = W (K)-μxr−1x∇\mu \times r^{-1} \times \nabla, μ\mu as Step

Steepest descent Method: (More practice than Newton's method)
The important point is similar, but the general is compared with Newton's method to learn
W (k+1) = W (K)-μx∇\mu \times \nabla
It can be seen that the weight of the update formula and Newton method is the inverse of the correlation matrix, Newton method (in two performance surface) can learn the best right is because theoretically through the correlation matrix R to the best right, but the actual non-common reason, first, the input signal is the measured value x, In other words, the non-miscible noise generation. Therefore, the correlation matrix can only be estimated, so that the actual weight adjustments can not be one step. And the steepest descent method, in strict accordance with the direction of gradient descent, more easy to operate.

LMS algorithm: (practical)
The abbreviated version of the steepest descent method, which takes only one sample as the current estimate, proves that the LMS algorithm does converge (slightly).

Overall derivation or from the performance surface, the central idea is relatively simple, is the weight update, focusing on the gradient.
Post-book partial exercise result diagram

Detailed Code reference resources:

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