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Traditional 'Design of Experiment' (DOE) approaches focus on minimization of parameter error variance.
Next, an index named Modal Parameter Error Index (MPEI) is introduced.
The a priori parameter error σ gives a constraint on the strength of the velocity perturbation.
The uncertainties in the input parameters into the forward model cause the model parameter error.
The adaptive laws are driven by appropriate parameter error information derived by applying filter operations on the output measurements.
Output error dynamics can thus be derived as a stable first-order filter driven by parameter error vectors.
The other criterion is the 2-norm of the parameter error covariance matrix ( P k + 1 2 ).
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The idea is the following: assume for simplicity the noiseless case and consider the parameter-error vector (tilde {{mathbf {w}}}_{k-1}).
The concept was to evaluate not only the mean of the parameter-error vector (tilde {mathbf {w}}_{k}={mathbf {w}}-{mathbf {w}}_{k}) (also known as weight error vector) but also the mean-square of it, typically in terms of the parameter-error vector covariance matrix (Eleft [tilde {{mathbf {w}}}_{k}tilde {{mathbf {w}}}_{k}^{textsf {H}}right ]).
We split the entire parameter-error vector into two parts, say g and h, and correspondingly we use two partitions, say u k and x k, as regression vectors.
A consequence of the l 2−stability property is that an energy-bounded input sequence (noise v k and initial parameter-error vector (tilde {{mathbf {w}}}_{0})) causes a bounded output of undistorted errors e a,k.
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