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Figure 7 Mean weight transient behavior - Linear adaptation case.

Here we give analytical expressions for the mean squared error (MSE), explore the stationary points of the algorithm, evaluate the misadjustment error due to weight fluctuations, and derive recursions for the mean weight transient behavior during the learning process.

The mean weight transient recursions are expressed as: E w jk n + 1 = E w jk n 1 − 2 μ σ x k 2 + 2 μ h jk α k σ x k 2 1 + β k σ x k 2 3 2 199).

The mean weight recursions and the MSE transient behaviors (Figures 6,7) have been estimated over 20 Monte Carlo (MC) simulations and compared to the theoretical derivations (Equations (19) and (41)).

Note the typical behavior of the LMS algorithm: A time constant controls the transient part of the learning curve and the mean weight curve.

Mean weight change was 2.0 ± 1.2 kg.

Mean weight was 2.58 kg.

Mean weight ranged from 73.01 to 95.76 kg.