The absolute and relative errors between regularized and exact solutions are estimated.
Table 5 gives a discussion as regards the impact of bound E on the relative error of the regularized approximation for Example 2, and we also see that a wrong constant E may lead to bad regularized solutions.
Since the relative performance of the regularized estimation with respect to the standard least squares will be shown in terms of MSE, it is necessary to use synthetic networks with the known Euler vector components.
In this paper, an approach named regularized robust filter algorithm is proposed to control the relative installation error of star tracker in the attitude measurement data.
For a better illustration, we define the relative error estimate between exact solution and regularized solutions as follows: σ i, ϵ ( y ) = ∑ k = 1 I | u i, ϵ ( x k, y ) − u ( x k, y ) | 2 ∑ k = 1 I | u ( x k, y ) | 2. Table 2 shows the relative error estimations between the exact solution and the first regularized solution ( σ 1, ϵ ) and by the second regularization solution ( σ 2, ϵ ).
For instance, at P T = 30 dBW the regularized channel inversion in the feed space generates a 111% relative throughput increase with respect to the reference scenario, and 17% with respect to the same processing in the beam space.
(5.18) Tables 1 and 2 show the absolute and relative error estimates between the exact solution and its regularized solution for both, the a priori and the a posteriori, parameter choice rules in the numerical examples.
A modified regularized robust filter is proposed for spacecraft attitude determination in the presence of relative misalignment of attitude sensors.
This is borne out through several numerical examples wherein the relative performance of the proposed recursion scheme vis-à-vis a regularized Newton strategy is compared.
This paper examines periodic solutions and most notably stick slip, on a simple one-degree-of-freedom system (mass, spring, damper, and belt), with Coulomb's friction law, and with a regularized friction law (i.e. the friction coefficient becomes a function of relative speed, with a stiffness parameter).
