**4. Simulation results**

where, *G*ð Þ*<sup>t</sup>* represents gravitational constant at time *t*, *M*ð Þ*<sup>t</sup>*

*Fd t*ð Þ

*<sup>i</sup>* <sup>¼</sup> <sup>X</sup> *N*

> *acc d t*ð Þ *<sup>i</sup>* <sup>¼</sup> *<sup>F</sup>d t*ð Þ *i Ma*ð Þ*<sup>t</sup> ii*

*<sup>i</sup>* <sup>¼</sup> *CF*ð Þ*<sup>t</sup>*

*m*ð Þ*<sup>t</sup>*

where *CF* represents the cost function of the candidate *i*.

*M*ð Þ*<sup>t</sup>*

two candidates *i* and *j* and *ε* is a small constant. Then *G*ð Þ*<sup>t</sup>* is calculated as [19].

where, *G*<sup>0</sup> represents the initial value of gravitation constant, *α* is descending coefficient, the current iteration is represented by *itr*, and *maxitr* represents the

Then the total force that acts on candidate *i* in dimension *d* is calculated as

*j*¼1, *j*6¼1

where *Maii* represents the mass of the candidate *i*. The inertial mass and the

*pi* <sup>¼</sup> *<sup>m</sup>*ð Þ*<sup>t</sup> i* P*<sup>J</sup>*

*best*ð Þ*<sup>t</sup>* <sup>¼</sup> *min <sup>j</sup>* <sup>∈</sup>ð Þ *<sup>I</sup>::<sup>J</sup> CF*ð Þ*<sup>t</sup>*

*worst*ð Þ*<sup>t</sup>* <sup>¼</sup> *max <sup>j</sup>*∈ð Þ *<sup>I</sup>::<sup>J</sup> CF*ð Þ*<sup>t</sup>*

Then the position and the velocity of candidates are given by [19].

dð Þ *t*þ1

*d t*ð Þ þ1 *<sup>i</sup>* ¼ *x*

*<sup>i</sup>* ¼ *randi* � *v*

where *randi* represents a random number. Finally, the position and velocity of

*position* : *x*

*velocity* : *v*

the candidate are obtained.

**138**

*<sup>i</sup>* � *worst*ð Þ*<sup>t</sup>*

*<sup>j</sup>*¼<sup>1</sup>*m*ð Þ*<sup>t</sup> j*

> *d t*ð Þ *<sup>i</sup>* þ *v*

> > *d t*ð Þ *<sup>i</sup>* þ *acc*

*d t*ð Þ þ1

*d t*ð Þ

*best*ð Þ*<sup>t</sup>* � *worst*ð Þ*<sup>t</sup>* (31)

*<sup>j</sup>* (33)

*<sup>j</sup>* (34)

*<sup>i</sup>* (35)

*<sup>i</sup>* (36)

where *rand <sup>j</sup>* is a random number. As reported to the motion's law, the accelera-

passive gravitational mass related to candidate *i*, *M*ð Þ*<sup>t</sup>*

tional mass related to candidate *j*, *R*ð Þ*<sup>t</sup>*

*Innovations in Ultra-WideBand Technologies*

maximum number of iterations.

tion of candidate *i* is given as

gravitational mass are updated as follows [19].

The best and worst value are given by

*pi* represents the

*aj* represents the active gravita-

*ij* (29)

(30)

(32)

*ij* represents the Euclidian distance between

*<sup>G</sup>*ð Þ*<sup>t</sup>* <sup>¼</sup> *<sup>G</sup>*<sup>0</sup> � exp ð Þ �*<sup>α</sup>* � *itr=maxitr* (28)

*rand jFd t*ð Þ

In this section, simulation results are discussed and analyzed. All the simulation results are carried out in MATLAB environment. The same control parameters for PSO, CSA and GSA have been selected for appropriate comparison of optimization algorithms. The lower and upper limits of the optimized coefficients are set to be 10 and 150 for functional realizability. Absolute magnitude error (AME), phase response, pole-zero plot, convergence rate and improvement rate are taken into account in assessing the performance of the proposed SOMI magnitude response.
