Least mean squares filter

LMS - algorithm (Least Mean Squares ) algorithm is an algorithm for approximation of the solution of the least mean squares problem, which occurs for example in the digital signal processing. In the neuro- computer science, the algorithm mainly as delta rule or Widrow-Hoff rule is known.

The algorithm is based on the so-called method of steepest descent ( gradient ) and estimates the gradient of the easy way The algorithm works zeitrekursiv, that is, with each new record is the algorithm run through once and updates the solution. The rule was first used in 1960 by Bernard Widrow and Marcian Edward Hoff for the teaching of the Adaline model.

The LMS algorithm is widely used because of its low complexity. Application areas include adaptive filters, adaptive schemes and online identification method.

A major disadvantage of the LMS algorithm is its convergence speed, depending on the input data, that is, the algorithm takes place under adverse circumstances, may not be a solution. Unfavorable circumstances the rapid time change of the input data.

Algorithm

The goal is to determine the coefficients of a FIR filter so that the error between output data of the filter and predetermined reference data y (n ) is minimized target.

The LMS algorithm then has the following form:

Here, y is a vector of input data time points n- (M 1) to n, ( n ) a reference date at the time, the current vector of filter weights of the transversal filter of order M, a factor to adjust the speed and stability of adaptation and the re- defining filter vector of order M. It is therefore determined at each time point, the current error and from the new filter weights are calculated.

Use in the neuro- computer science

The LMS algorithm is one of the supervised learning method. For this purpose, there must be an external teacher who at every moment of entering the desired output, the target knows.

It can be applied to any layered artificial neural network, while the activation function must be differentiated. The back propagation method generalized this algorithm and can be applied to multi-layer networks.