Robust Estimation for Discrete Markov System with Time-Varying Delay and Missing Measurements

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="321935.fig.005a" src="https://static.hindawi.com/articles/mpe/volume-2013/321935/figures/321935.fig.005a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b><svg height="12.9375" id="M252" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 17.0875 12.9375" width="17.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> and estimation <svg height="16.8375" id="M253" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 17.0875 16.8375" width="17.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="321935.fig.005b" src="https://static.hindawi.com/articles/mpe/volume-2013/321935/figures/321935.fig.005b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="12.9375" id="M254" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 17.0875 12.9375" width="17.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> and estimation <svg height="16.8375" id="M255" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 17.0875 16.8375" width="17.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,2.238,11.95)"><path d="M470 557l-12 -25q-103 25 -223 64q-128 -41 -223 -64l-12 25q172 77 224 109h22q57 -35 224 -109z" id="xF5C01"></path></g><g transform="matrix(.017,-0,0,-.017,.625,12.125)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
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</svg></td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="321935.fig.005c" src="https://static.hindawi.com/articles/mpe/volume-2013/321935/figures/321935.fig.005c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b><svg height="13.0875" id="M256" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 17.0875 13.0875" width="17.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> and estimation <svg height="16.975" id="M257" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 17.0875 16.975" width="17.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,2.238,11.95)"><path d="M470 557l-12 -25q-103 25 -223 64q-128 -41 -223 -64l-12 25q172 77 224 109h22q57 -35 224 -109z" id="xF5C01"></path></g><g transform="matrix(.017,-0,0,-.017,.625,12.125)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
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<g transform="matrix(.012,-0,0,-.012,10.125,16.213)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
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</svg></td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="321935.fig.005d" src="https://static.hindawi.com/articles/mpe/volume-2013/321935/figures/321935.fig.005d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>signal <svg height="17.174999" id="M258" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 48.375 17.174999" width="48.375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.625,12.475)"><path d="M475 445l-64 -69q-119 -128 -289 -280q27 6 81 -15q66 -26 102 -26q48 0 111 93l23 -19q-41 -84 -75.5 -116.5t-73.5 -32.5q-37 0 -147 53q-43 21 -63 7q-22 -15 -38 -41q-4 -7 -11 -7q-8 10 -8 26q0 38 47 83l292 273q-32 -5 -67 -1q-63 7 -105 7q-32 0 -53.5 -22
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<g transform="matrix(.012,-0,0,-.012,9.087,16.55)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
<g transform="matrix(.017,-0,0,-.017,19.2,12.475)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,34.312,11.95)"><path d="M470 557l-12 -25q-103 25 -223 64q-128 -41 -223 -64l-12 25q172 77 224 109h22q57 -35 224 -109z" id="xF5C01"></path></g><g transform="matrix(.017,-0,0,-.017,32.95,12.475)"><path d="M475 445l-64 -69q-119 -128 -289 -280q27 6 81 -15q66 -26 102 -26q48 0 111 93l23 -19q-41 -84 -75.5 -116.5t-73.5 -32.5q-37 0 -147 53q-43 21 -63 7q-22 -15 -38 -41q-4 -7 -11 -7q-8 10 -8 26q0 38 47 83l292 273q-32 -5 -67 -1q-63 7 -105 7q-32 0 -53.5 -22
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<g transform="matrix(.012,-0,0,-.012,41.425,16.55)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></td></tr></table></td></tr></table>

<table>Original signal and estimation signal.</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Robust Estimation for Discrete Markov System with Time-Varying Delay and Missing Measurements 