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Измерение неопределенности в текущем обсервационном месте судна.

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ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 6, ʋ1, 2003 ɝ.
ɫɬɪ.25-28
ɂɡɦɟɪɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ ɜ ɬɟɤɭɳɟɦ ɨɛɫɟɪɜɚɰɢɨɧɧɨɦ
ɦɟɫɬɟ ɫɭɞɧɚ
Ɏ.Ɋ. Ȼɪɚɧɞɬ, ȼ.ɂ. Ɇɟɧɶɲɢɤɨɜ
ɋɭɞɨɜɨɞɢɬɟɥɶɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɌɍ, ɤɚɮɟɞɪɚ ɫɭɞɨɜɨɠɞɟɧɢɹ
Ⱥɧɧɨɬɚɰɢɹ. ɋɨɫɬɚɜɥɟɧɨ ɫɨɨɬɧɨɲɟɧɢɟ, ɩɨɡɜɨɥɹɸɳɟɟ ɨɰɟɧɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɢ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ
ɛɟɡɨɩɚɫɧɨɝɨ ɩɥɚɜɚɧɢɹ ɫɭɞɧɚ ɩɨ ɦɚɪɲɪɭɬɭ. Ɉɩɪɟɞɟɥɟɧɚ ɢɧɮɨɪɦɚɰɢɨɧɧɚɹ ɟɦɤɨɫɬɶ ɬɚɤɨɝɨ ɢɫɬɨɱɧɢɤɚ
ɢɧɮɨɪɦɚɰɢɢ, ɤɚɤ ɨɛɫɟɪɜɚɰɢɨɧɧɨɟ ɫɱɢɫɥɟɧɢɟ ɩɭɬɢ ɫɭɞɧɚ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɝɨ ɦɨɠɧɨ ɞɨɛɢɬɶɫɹ
ɪɟɚɥɢɡɚɰɢɢ ɡɚɞɚɧɧɵɯ ɬɪɟɛɨɜɚɧɢɣ ɩɨ ɨɛɟɫɩɟɱɟɧɢɸ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ.
Abstract. The relation permitting to estimate an amount of information necessary for safe navigation has been given
in the paper. The informational capacity of such resource of information as positioning dead-reckoning of a vessel
route which will help to achieve realization of the specific requirements on the safe navigation has been determined.
1. ȼɜɟɞɟɧɢɟ
Ȼɟɡɨɩɚɫɧɨɫɬɶ ɧɚɜɢɝɚɰɢɢ ɨɞɧɚ ɢɡ ɜɚɠɧɟɣɲɢɯ ɩɪɨɛɥɟɦ, ɫɬɨɹɳɢɯ ɩɟɪɟɞ ɨɬɟɱɟɫɬɜɟɧɧɵɦ ɢ
ɦɢɪɨɜɵɦ ɫɭɞɨɯɨɞɫɬɜɨɦ. Ⱦɨɫɬɚɬɨɱɧɨ ɜɵɫɨɤɢɣ ɭɪɨɜɟɧɶ ɚɜɚɪɢɣɧɨɫɬɢ ɬɪɚɧɫɩɨɪɬɧɵɯ ɢ ɪɵɛɨɥɨɜɧɵɯ ɫɭɞɨɜ,
ɜɨɡɧɢɤɧɨɜɟɧɢɟ ɤɚɬɚɫɬɪɨɮ, ɩɪɢɜɨɞɹɳɢɯ ɤ ɝɢɛɟɥɢ ɥɸɞɟɣ, ɩɨɬɟɪɟ ɡɧɚɱɢɬɟɥɶɧɵɯ ɦɚɬɟɪɢɚɥɶɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ
ɫɪɟɞɫɬɜ, ɷɤɨɧɨɦɢɱɟɫɤɢɦ ɢ ɷɤɨɥɨɝɢɱɟɫɤɢɦ ɩɨɫɥɟɞɫɬɜɢɹɦ ɜɫɟ ɷɬɨ ɩɨɞɱɟɪɤɢɜɚɟɬ ɚɤɬɭɚɥɶɧɨɫɬɶ ɩɪɨɛɥɟɦɵ
ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ ɢ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɟɟ ɞɚɥɶɧɟɣɲɟɝɨ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ.
Ɇɚɫɫɨɜɨɟ ɩɪɚɤɬɢɱɟɫɤɨɟ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɫɪɟɞɫɬɜ ɢɧɮɨɪɦɚɬɢɤɢ, ɨɫɭɳɟɫɬɜɥɹɟɦɨɟ ɧɚ ɨɫɧɨɜɟ ɢɯ
ɜɫɬɪɚɢɜɚɧɢɹ ɜ ɦɨɪɫɤɢɟ ɬɟɯɧɢɱɟɫɤɢɟ ɫɪɟɞɫɬɜɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɛɟɡɨɩɚɫɧɨɫɬɶ ɧɚɜɢɝɚɰɢɢ, ɫɨɫɬɚɜɥɹɟɬ
ɝɥɚɜɧɨɟ ɫɨɞɟɪɠɚɧɢɟ ɬɨɝɨ ɹɜɥɟɧɢɹ, ɤɨɬɨɪɨɟ ɧɵɧɟ ɧɚɡɵɜɚɸɬ ɢɧɮɨɪɦɚɬɢɡɚɰɢɟɣ ɫɭɞɨɜɨɠɞɟɧɢɹ. ȼ ɫɜɨɸ
ɨɱɟɪɟɞɶ, ɢɧɮɨɪɦɚɬɢɡɚɰɢɹ ɫɭɞɨɜɨɠɞɟɧɢɹ ɫ ɨɞɧɨɜɪɟɦɟɧɧɵɦ ɜɧɟɞɪɟɧɢɟɦ ɜ ɦɨɪɫɤɭɸ ɩɪɚɤɬɢɤɭ ɧɨɜɵɯ
ɤɨɫɦɢɱɟɫɤɢɯ ɬɟɯɧɨɥɨɝɢɣ ɩɨɡɜɨɥɢɥɢ ɫɭɳɟɫɬɜɟɧɧɨ ɢɡɦɟɧɢɬɶ ɤɚɤ ɮɨɪɦɭ, ɬɚɤ ɢ ɫɨɞɟɪɠɚɧɢɟ ɫɭɳɟɫɬɜɭɸɳɢɯ
ɩɪɢɟɦɨɜ ɜɨɫɫɬɚɧɨɜɥɟɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ɫɭɞɧɚ.
ɂɦɟɧɧɨ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɟ ɤɨɫɦɢɱɟɫɤɢɟ ɬɟɯɧɨɥɨɝɢɢ ɜɦɟɫɬɟ ɫ ɢɧɮɨɪɦɚɬɢɡɚɰɢɟɣ
ɫɭɞɨɜɨɠɞɟɧɢɹ ɢ ɫɪɟɞɫɬɜɚɦɢ ɨɬɨɛɪɚɠɟɧɢɹ ɧɚɜɢɝɚɰɢɨɧɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨɛɟɫɩɟɱɢɥɢ ɩɟɪɟɯɨɞ ɨɬ
ɤɨɪɪɟɤɬɢɪɭɟɦɨɝɨ ɫɱɢɫɥɟɧɢɹ (ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɩɨ ɞɢɫɤɪɟɬɧɵɦ ɨɛɫɟɪɜɚɰɢɹɦ) ɤ
ɨɛɫɟɪɜɚɰɢɨɧɧɨɦɭ ɫɱɢɫɥɟɧɢɸ (ɜɨɫɫɬɚɧɨɜɥɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɩɨ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɩɪɟɪɵɜɧɵɦ ɨɛɫɟɪɜɚɰɢɹɦ).
Ɍɚɤɨɟ ɢɡɦɟɧɟɧɢɟ ɜ ɫɱɢɫɥɟɧɢɢ ɩɭɬɢ ɫɭɞɧɚ, ɟɫɬɟɫɬɜɟɧɧɨ, ɧɟ ɦɨɝɥɨ ɧɟ ɨɤɚɡɚɬɶ ɜɥɢɹɧɢɹ ɧɚ ɩɪɢɟɦɵ
ɩɨɞɞɟɪɠɚɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ ɧɚ ɡɚɞɚɧɧɨɦ ɭɪɨɜɧɟ ɢ ɞɚɠɟ ɛɨɥɟɟ ɬɨɝɨ ɫɬɢɦɭɥɢɪɨɜɚɬɶ
ɞɚɥɶɧɟɣɲɟɟ ɪɚɡɜɢɬɢɟ ɷɬɢɯ ɩɪɢɟɦɨɜ.
ɉɪɢ ɦɨɞɟɪɧɢɡɚɰɢɢ ɩɪɢɟɦɨɜ ɩɨɞɞɟɪɠɚɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ ɧɚ ɡɚɞɚɧɧɨɦ ɭɪɨɜɧɟ
ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɬɨ, ɱɬɨ ɤɨɧɬɪɨɥɶ ɨɛɫɟɪɜɚɰɢɨɧɧɨɣ ɬɨɱɧɨɫɬɢ ɦɨɠɧɨ ɜɟɫɬɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɫ
ɫɢɫɬɟɦɵ ɨɬɨɛɪɚɠɟɧɢɹ ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɪɟɞɫɬɜɚ ɫɭɞɨɜɨɠɞɟɧɢɹ, ɛɟɡ ɤɚɤɢɯ-ɥɢɛɨ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɪɚɫɱɟɬɨɜ.
ɉɨɷɬɨɦɭ ɪɟɲɟɧɢɟ ɩɪɨɛɥɟɦɵ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɫɥɟɞɭɟɬ ɢɫɤɚɬɶ ɜ ɛɨɥɟɟ
ɷɮɮɟɤɬɢɜɧɨɦ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɬɟɯɧɢɱɟɫɤɢɯ ɫɪɟɞɫɬɜ ɢɧɮɨɪɦɚɬɢɡɚɰɢɢ ɢ ɭɱɟɬɟ ɨɫɨɛɟɧɧɨɫɬɟɣ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɭɞɨɜɨɞɢɬɟɥɹ ɫ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɫɭɞɨɜɨɠɞɟɧɢɹ. ɂɦɟɧɧɨ ɫɪɟɞɫɬɜɚ
ɢɧɮɨɪɦɚɬɢɤɢ, ɜɤɥɸɱɟɧɧɵɟ ɜ ɫɨɫɬɚɜ ɬɟɯɧɢɱɟɫɤɢɯ ɫɪɟɞɫɬɜ ɫɭɞɨɜɨɠɞɟɧɢɹ, ɛɭɞɭɬ ɫɨɡɞɚɜɚɬɶ ɩɪɟɞɩɨɫɵɥɤɢ ɤ
ɡɚɦɟɧɟ ɨɪɝɚɧɢɡɚɰɢɨɧɧɨɣ ɫɢɫɬɟɦɵ ɨɛɟɫɩɟɱɟɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ ɧɚ ɟɟ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɵɣ ɚɧɚɥɨɝ.
ɇɢɠɟ ɮɨɪɦɭɥɢɪɭɸɬɫɹ ɧɟɤɨɬɨɪɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɪɟɡɭɥɶɬɚɬɵ, ɤɨɬɨɪɵɟ, ɜɨ-ɩɟɪɜɵɯ, ɦɨɝɭɬ ɛɵɬɶ
ɩɨɥɨɠɟɧɵ ɜ ɨɫɧɨɜɭ ɨɪɝɚɧɢɡɚɰɢɢ ɩɪɨɰɟɞɭɪɵ ɤɨɧɬɪɨɥɹ ɫɨɫɬɨɹɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ ɫɭɞɧɚ ɩɪɢ
ɨɛɫɟɪɜɚɰɢɨɧɧɨɦ ɫɱɢɫɥɟɧɢɢ, ɚ ɜɨ-ɜɬɨɪɵɯ, ɢɫɩɨɥɶɡɨɜɚɧɵ ɜ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɣ ɫɢɫɬɟɦɟ, ɪɟɚɥɢɡɭɸɳɟɣ ɬɚɤɨɣ
ɤɨɧɬɪɨɥɶ.
2. Ɇɨɞɟɥɶ ɜɡɚɢɦɨɫɜɹɡɢ ɩɨɤɚɡɚɬɟɥɟɣ ɩɥɚɧɨɜɨɣ ɢ ɬɟɤɭɳɟɣ ɨɛɫɟɪɜɚɰɢɨɧɧɵɯ ɬɨɱɧɨɫɬɟɣ
ɉɭɫɬɶ ɫɥɭɱɚɣɧɵɣ ɞɜɭɦɟɪɧɵɣ ɜɟɤɬɨɪ Z ɫ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ f(Z) ɯɚɪɚɤɬɟɪɢɡɭɟɬ
ɚɩɪɢɨɪɧɵɟ ɩɨɝɪɟɲɧɨɫɬɢ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɦɟɫɬɚ ɫɭɞɧɚ, ɤɨɬɨɪɵɟ ɭɱɢɬɵɜɚɸɬɫɹ ɩɪɢ ɩɥɚɧɢɪɨɜɚɧɢɢ
ɛɟɡɨɩɚɫɧɨɝɨ ɧɚɜɢɝɚɰɢɨɧɧɨɝɨ ɦɚɪɲɪɭɬɚ, ɚ ɫɥɭɱɚɣɧɵɣ ɞɜɭɦɟɪɧɵɣ ɜɟɤɬɨɪ W ɫ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ
f(W) ɨɩɪɟɞɟɥɹɟɬ ɫɥɭɱɚɣɧɵɟ ɩɨɝɪɟɲɧɨɫɬɢ, ɫ ɤɨɬɨɪɵɦɢ ɪɟɚɥɢɡɭɟɬɫɹ ɷɬɨɬ ɦɚɪɲɪɭɬ. Ɍɨɝɞɚ ɢɡɦɟɪɢɬɟɥɶɧɵɣ
ɧɚɜɢɝɚɰɢɨɧɧɵɣ ɤɨɦɩɥɟɤɫ (ɫɩɭɬɧɢɤɨɜɚɹ ɧɚɜɢɝɚɰɢɨɧɧɚɹ ɚɩɩɚɪɚɬɭɪɚ), ɨɛɟɫɩɟɱɢɜɚɹ ɨɛɫɟɪɜɚɰɢɨɧɧɨɟ
ɫɱɢɫɥɟɧɢɟ ɩɭɬɢ ɫɭɞɧɚ, ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɜɟɪɨɹɬɧɨɫɬɧɭɸ ɫɜɹɡɶ ɦɟɠɞɭ ɫɥɭɱɚɣɧɵɦɢ ɜɟɤɬɨɪɚɦɢ Z ɢ W, ɤɨɬɨɪɚɹ
ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧɚ ɭɫɥɨɜɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɢɞɚ f(Z/W).
25
Ȼɪɚɧɞɬ Ɏ.Ɋ., Ɇɟɧɶɲɢɤɨɜ ȼ.ɂ.
ɂɡɦɟɪɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ...
Ɂɞɟɫɶ ɢ ɞɚɥɟɟ ɬɟɪɦɢɧ ɫɩɭɬɧɢɤɨɜɚɹ ɧɚɜɢɝɚɰɢɨɧɧɚɹ ɚɩɩɚɪɚɬɭɪɚ (ɋɇȺ) ɩɨɧɢɦɚɟɬɫɹ ɜ ɫɚɦɨɦ
ɲɢɪɨɤɨɦ ɫɦɵɫɥɟ: ɷɬɨ ɜɫɟɜɨɡɦɨɠɧɵɟ ɢɡɦɟɪɢɬɟɥɶɧɵɟ ɫɪɟɞɫɬɜɚ ɫɨɜɦɟɫɬɧɨ ɫ ɢɫɩɨɥɶɡɭɟɦɵɦɢ ɦɟɬɨɞɚɦɢ
ɩɨɥɭɱɟɧɢɹ, ɨɛɪɚɛɨɬɤɢ ɢ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ. ɋɨɫɬɚɜ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɚɩɩɚɪɚɬɭɪɵ, ɨɛɴɟɤɬɵ,
ɫɩɨɫɨɛɵ ɢɡɦɟɪɟɧɢɹ ɢ ɜɢɞɵ ɨɬɨɛɪɚɠɟɧɢɹ ɢɧɮɨɪɦɚɰɢɢ ɜ ɤɚɠɞɨɦ ɤɨɧɤɪɟɬɧɨɦ ɫɥɭɱɚɟ ɦɨɝɭɬ ɛɵɬɶ
ɪɚɡɥɢɱɧɵɦɢ, ɢ ɩɪɢ ɷɬɨɦ, ɟɫɬɟɫɬɜɟɧɧɨ, ɢɡɦɟɧɹɟɬɫɹ ɭɫɥɨɜɧɚɹ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɜɢɞɚ f(Z/W).
ɇɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ W ɢ Z ɨɛɭɫɥɨɜɥɟɧɚ ɫɥɭɱɚɣɧɵɦɢ ɩɨ ɯɚɪɚɤɬɟɪɭ
ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɢɡɦɟɪɟɧɢɣ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ ɬɨɱɧɨɫɬɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɫɚɦɨɝɨ
ɢɡɦɟɪɢɬɟɥɶɧɨɝɨ ɤɨɦɩɥɟɤɫɚ, ɬɚɤ ɢ ɬɨɱɧɨɫɬɶɸ ɜɫɟɣ ɫɢɫɬɟɦɵ ɝɥɨɛɚɥɶɧɨɣ ɧɚɜɢɝɚɰɢɢ (Global Position System
GPS) ɜ ɰɟɥɨɦ. ȼ ɤɨɧɟɱɧɨɦ ɢɬɨɝɟ ɜɫɟ ɷɬɢ ɩɨɝɪɟɲɧɨɫɬɢ ɦɨɝɭɬ ɛɵɬɶ ɫɜɟɞɟɧɵ ɤ ɫɥɭɱɚɣɧɨɦɭ ɟɞɢɧɨɦɭ
ɞɜɭɦɟɪɧɨɦɭ ɜɟɤɬɨɪɭ K ɫ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ f(K).
ȼɨɨɛɳɟ ɝɨɜɨɪɹ, ɩɨɝɪɟɲɧɨɫɬɢ, ɫɬɨɹɳɢɟ ɡɚ ɫɥɭɱɚɣɧɵɦ ɟɞɢɧɵɦ ɞɜɭɦɟɪɧɵɦ ɜɟɤɬɨɪɨɦ K, ɫɥɟɞɨɜɚɥɨ
ɛɵ ɨɩɢɫɵɜɚɬɶ ɭɫɥɨɜɧɨɣ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ f(K/[), ɝɞɟ [ – ɜɟɤɬɨɪ, ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬ
ɮɚɤɬɨɪɵ, ɜɥɢɹɸɳɢɟ ɧɚ ɬɨɱɧɨɫɬɶ ɢɡɦɟɪɟɧɢɣ ɋɇȺ ɜ ɫɢɫɬɟɦɟ GPS. Ɉɞɧɚɤɨ ɜ ɤɨɦɩɥɟɤɫɚɯ ɬɢɩɚ ɋɇȺ ɩɪɢ
ɨɛɪɚɛɨɬɤɟ ɢɡɦɟɪɟɧɢɣ ɷɬɢ ɮɚɤɬɨɪɵ ɜ ɛɨɥɶɲɟɣ ɢɥɢ ɦɟɧɶɲɟɣ ɫɬɟɩɟɧɢ ɭɱɢɬɵɜɚɸɬɫɹ (ɧɚɩɪɢɦɟɪ,
ɢɨɧɨɫɮɟɪɧɚɹ ɢ ɬɪɨɩɨɫɮɟɪɧɚɹ ɪɟɮɪɚɤɰɢɹ ɢ ɬ.ɞ.) ɢ ɩɨɷɬɨɦɭ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɢɯ ɜɥɢɹɧɢɟ ɧɚ
ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ ɨɛɴɟɞɢɧɟɧɢɹ ɫɥɭɱɚɣɧɵɯ ɜɟɤɬɨɪɨɜ W ɢ Z ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɧɟɬ ɧɚɞɨɛɧɨɫɬɢ.
Ʉɨɥɢɱɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɢ, ɤɨɬɨɪɨɟ ɫɨɞɟɪɠɢɬɫɹ ɜ ɫɥɭɱɚɣɧɨɦ ɜɟɤɬɨɪɟ W ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɤɬɨɪɚ Z,
ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫ ɩɨɦɨɳɶɸ ɮɭɧɞɚɦɟɧɬɚɥɶɧɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ, ɢɡɜɟɫɬɧɨɝɨ ɢɡ ɬɟɨɪɢɢ
ɢɧɮɨɪɦɚɰɢɢ
I(W,Z) = ³ ³ f(Z,W)[log2 f(Z,W) / f(Z)f(W)]dZ dW,
(1)
L L
Z W
ɩɪɢɱɟɦ ɷɬɨ ɤɨɥɢɱɟɫɬɜɨ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɨɬɫɱɟɬɚ ɜɟɤɬɨɪɨɜ Z ɢ W. ɉɨɷɬɨɦɭ ɞɚɥɟɟ, ɭɱɢɬɵɜɚɹ ɞɚɧɧɨɟ
ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ, ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɥɶɤɨ ɞɟɤɚɪɬɨɜɭ ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ YɈɏ.
ȼɵɪɚɠɟɧɢɟ (1) ɛɨɥɟɟ ɭɞɨɛɧɨ ɢ ɡɧɚɱɢɦɨ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
I(W, Z) = H(W) – H(W/Z),
(2)
ɝɞɟ H(W) ɢ H(W/Z) – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɚɩɨɫɬɟɪɢɨɪɧɚɹ ɢ ɭɫɥɨɜɧɚɹ ɚɩɨɫɬɟɪɢɨɪɧɚɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ
ɷɧɬɪɨɩɢɢ ɬɟɤɭɳɟɝɨ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɦɟɫɬɚ ɫɭɞɧɚ, ɨɩɪɟɞɟɥɹɸɳɢɟɫɹ ɫɨɨɬɧɨɲɟɧɢɹɦɢ ɜɢɞɚ
H(W) = ³ f (W) log2 f (W) dW,
L
Z
H(W/Z) = ³ ³ f (Z, W) log2 f (W/Z) dZ dW.
L L
Z W
Ⱥɧɚɥɢɡ ɤɨɥɢɱɟɫɬɜɚ ɢɧɮɨɪɦɚɰɢɢ, ɩɨɥɭɱɚɟɦɨɝɨ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɦɟɫɬɚ ɫɭɞɧɚ,
ɫɭɳɟɫɬɜɟɧɧɨ ɭɩɪɨɫɬɢɬɫɹ, ɟɫɥɢ ɩɨɝɪɟɲɧɨɫɬɢ ɢɡɦɟɪɢɬɟɥɶɧɨɝɨ ɤɨɦɩɥɟɤɫɚ (ɲɭɦ ɢɡɦɟɪɟɧɢɹ) ɜ
ɜɟɪɨɹɬɧɨɫɬɧɨɦ ɫɦɵɫɥɟ ɧɟ ɛɭɞɭɬ ɡɚɜɢɫɟɬɶ ɨɬ ɬɟɤɭɳɢɯ ɤɨɨɪɞɢɧɚɬ ɫɭɞɧɚ ɢ ɋɇȺ. Ɍɚɤɨɟ ɞɨɩɭɳɟɧɢɟ, ɤɚɤ
ɩɪɚɜɢɥɨ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɨɜɪɟɦɟɧɧɨɣ ɬɟɯɧɨɥɨɝɢɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɩɭɬɢ ɫɭɞɧɚ.
ȿɫɥɢ ɞɚɥɟɟ ɩɪɢɧɹɬɶ ɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɨɟ ɞɨɩɭɳɟɧɢɟ, ɬɨ, ɫɨɝɥɚɫɧɨ ɬɟɨɪɟɦɟ ɒɟɧɧɨɧɚ
(Ƚɚɥɥɚɝɟɪ, 1974), ɤɨɥɢɱɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɢ, ɩɨɥɭɱɟɧɧɨɟ ɨɬ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɜ ɬɟɤɭɳɟɦ ɦɟɫɬɟ
ɫɭɞɧɚ, ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɬɚɤ
(3)
H(W/Z) = H(W) – H(K),
ɝɞɟ
H(K) = ³ f(K)log2 f(K) dK
L
K
ɹɜɥɹɟɬɫɹ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɷɧɬɪɨɩɢɟɣ ɩɨɝɪɟɲɧɨɫɬɟɣ ɋɇȺ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɣ ɞɟɡɢɧɮɨɪɦɚɰɢɨɧɧɨɟ
ɞɟɣɫɬɜɢɟ ɷɬɢɯ ɩɨɝɪɟɲɧɨɫɬɟɣ.
3. Ɉɰɟɧɤɚ ɤɨɥɢɱɟɫɬɜɚ ɢɧɮɨɪɦɚɰɢɢ ɜ ɬɟɤɭɳɟɦ ɦɟɫɬɟ ɫɭɞɧɚ ɩɪɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɦ ɫɱɢɫɥɟɧɢɢ
ɉɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ f(K), ɤɨɬɨɪɭɸ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɨɛɪɚɛɨɬɤɢ
ɧɚɜɢɝɚɰɢɨɧɧɵɯ ɢɡɦɟɪɟɧɢɣ, ɜɵɩɨɥɧɹɟɦɵɯ ɋɇȺ, ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ, ɩɨ ɫɭɬɢ, ɰɟɧɬɪɢɪɨɜɚɧɧɭɸ
ɚɩɨɫɬɟɪɢɨɪɧɭɸ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɟɤɭɳɟɝɨ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɦɟɫɬɚ ɫɭɞɧɚ. ɉɨɷɬɨɦɭ ɞɥɹ ɬɨɝɨ,
ɱɬɨɛɵ ɜ ɞɚɥɶɧɟɣɲɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɨɨɬɧɨɲɟɧɢɟ (3), ɛɭɞɟɦ ɩɨɥɚɝɚɬɶ, ɱɬɨ f(Z) ɢ f(K) – ɧɨɪɦɚɥɶɧɵɟ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ. Ɍɚɤɨɟ ɞɨɩɭɳɟɧɢɟ ɨɛɳɟɩɪɢɧɹɬɨ ɜ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ, ɤɚɫɚɸɳɢɯɫɹ ɬɨɱɧɨɫɬɢ
ɨɩɪɟɞɟɥɟɧɢɹ ɦɟɫɬɚ ɫɭɞɧɚ, ɢ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ (Ʉɨɜɪɢɝɢɧ, 1974).
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɞɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɞɜɭɦɟɪɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ F(x, y),
ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɨɬɨɪɨɝɨ
26
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 6, ʋ1, 2003 ɝ.
ɫɬɪ.25-28
F(x, y) = 0.5˜S Hx Hy (1k2)0.5 exp{0.5˜(1k2) [(x – x0)2/ Hx2 2k(x – x0)2 (y y0)2/ Hx2Hy2 + (y y0)2 / Hy2]},
ɝɞɟ Hx ɢ Hy – ɫɪɟɞɧɟɟ ɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ x ɢ y, ɚ k – ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ
ɦɟɠɞɭ x ɢ y ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ
H(x, y) = log2[2S e Hx Hy (1 – k2) 0.5].
(4)
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɷɧɬɪɨɩɢɟɣ H(x, y) ɫɥɟɞɭɟɬ ɩɨɥɶɡɨɜɚɬɶɫɹ ɫ ɢɡɜɟɫɬɧɨɣ ɞɨɥɟɣ
ɨɫɬɨɪɨɠɧɨɫɬɢ, ɬɚɤ ɤɚɤ ɨɧɚ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɡɚɜɢɫɢɬ ɨɬ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ, ɜ ɤɨɬɨɪɨɣ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ
(Ƚɚɥɥɚɝɟɪ, 1974). Ɉɞɧɚɤɨ ɞɥɹ ɨɪɬɨɝɨɧɚɥɶɧɵɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ,
ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ, ɩɨɫɤɨɥɶɤɭ ɨɩɪɟɞɟɥɢɬɟɥɶ ɩɨɥɨɠɢɬɟɥɶɧɨ
ɨɩɪɟɞɟɥɟɧɧɨɣ ɤɜɚɞɪɚɬɢɱɧɨɣ ɮɨɪɦɵ ɹɜɥɹɟɬɫɹ ɢɧɜɚɪɢɚɧɬɨɦ. Ƚɟɨɦɟɬɪɢɱɟɫɤɢ ɫɜɨɣɫɬɜɨ ɢɧɜɚɪɢɚɧɬɧɨɫɬɢ
ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɩɥɨɳɚɞɶ ɫɬɚɧɞɚɪɬɧɨɝɨ ɷɥɥɢɩɫɚ ɪɚɫɫɟɢɜɚɧɢɹ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɨɪɬɨɝɨɧɚɥɶɧɵɯ
ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɣ. ɉɨɷɬɨɦɭ, ɪɚɫɫɱɢɬɵɜɚɹ ɜɟɥɢɱɢɧɭ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɣ ɷɧɬɪɨɩɢɢ,
ɦɨɠɧɨ ɫɨɜɟɪɲɟɧɧɨ ɧɟ ɡɚɛɨɬɢɬɶɫɹ ɨɛ ɨɪɢɟɧɬɚɰɢɢ ɤɨɨɪɞɢɧɚɬɧɵɯ ɨɫɟɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ YOX ɢ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɷɬɨɣ ɰɟɥɢ ɜɵɪɚɠɟɧɢɟ
H(x, y) = log2(2S e a b) = log2(2 eS),
(5)
ɝɞɟ a ɢ b – ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɛɨɥɶɲɚɹ ɢ ɦɚɥɚɹ ɩɨɥɭɨɫɢ ɫɬɚɧɞɚɪɬɧɨɝɨ ɷɥɥɢɩɫɚ ɪɚɫɫɟɢɜɚɧɢɹ, ɚ S – ɩɥɨɳɚɞɶ
ɷɬɨɝɨ ɷɥɥɢɩɫɚ ɪɚɫɫɟɢɜɚɧɢɹ.
Ɍɨɝɞɚ, ɟɫɥɢ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɚɹ ɷɧɬɪɨɩɢɹ ɧɨɪɦɚɥɶɧɨɝɨ ɞɜɭɦɟɪɧɨɝɨ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ
ɩɥɨɳɚɞɶɸ ɫɬɚɧɞɚɪɬɧɨɝɨ ɷɥɥɢɩɫɚ ɪɚɫɫɟɢɜɚɧɢɹ, ɬɨ ɤɨɥɢɱɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɢ, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢɡ
ɬɟɤɭɳɟɝɨ ɦɟɫɬɚ ɩɪɢ ɪɟɚɥɢɡɚɰɢɢ ɬɟɯɧɨɥɨɝɢɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ, ɭɱɢɬɵɜɚɹ ɪɚɜɟɧɫɬɜɨ (5) ɢ
ɜɵɪɚɠɟɧɢɟ (3), ɪɚɜɧɨ
I(W) = log2(2eSW) – log2(eSK) = log2(SW / SK),
(6)
ɝɞɟ SW = SaWbW – ɩɥɨɳɚɞɶ ɫɬɚɧɞɚɪɬɧɨɝɨ ɷɥɥɢɩɫɚ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɪɚɫɫɟɢɜɚɧɢɹ ɜɢɞɚ f(W), ɚ SK = SaKbK –
ɩɥɨɳɚɞɶ ɫɬɚɧɞɚɪɬɧɨɝɨ ɷɥɥɢɩɫɚ ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɪɚɫɫɟɢɜɚɧɢɹ f(K).
4. ɍɫɥɨɜɢɹ ɦɟɬɪɢɱɟɫɤɨɣ ɧɟɪɚɡɥɢɱɢɦɨɫɬɢ ɩɥɚɧɨɜɨɣ ɬɪɚɟɤɬɨɪɢɢ ɢ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɦɨɣ ɬɪɚɟɤɬɨɪɢɢ
Ⱦɥɹ ɨɰɟɧɤɢ ɤɨɥɢɱɟɫɬɜɚ ɢɧɮɨɪɦɚɰɢɢ, ɩɪɢɜɥɟɤɚɟɦɨɣ ɩɪɢ ɩɥɚɧɢɪɨɜɚɧɢɢ ɛɟɡɨɩɚɫɧɨɝɨ ɩɥɚɜɚɧɢɹ
ɫɭɞɧɚ ɩɨ ɧɚɜɢɝɚɰɢɨɧɧɨɦɭ ɦɚɪɲɪɭɬɭ, ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɩɨɧɹɬɢɟɦ ɷɩɫɢɥɨɧ-ɷɧɬɪɨɩɢɢ (ɗɧɰɢɤɥɨɩɟɞɢɹ
ɤɢɛɟɪɧɟɬɢɤɢ, 1974). ȼɟɥɢɱɢɧɭ ɷɩɫɢɥɨɧ-ɷɧɬɪɨɩɢɢ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɢɦɟɧɧɨ ɤɚɤ
ɢɧɮɨɪɦɚɰɢɨɧɧɭɸ ɟɦɤɨɫɬɶ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɩɭɬɢ ɫɭɞɧɚ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ, ɜɟɥɢɱɢɧɚ ɷɩɫɢɥɨɧɷɧɬɪɨɩɢɢ ɩɨɡɜɨɥɹɟɬ ɧɚɣɬɢ ɬɨ ɦɢɧɢɦɚɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɢ, ɩɪɢ ɩɨɦɨɳɢ ɤɨɬɨɪɨɝɨ ɷɬɢ
ɬɪɟɛɨɜɚɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɜɵɩɨɥɧɟɧɵ. ɂɫɩɨɥɶɡɭɹ ɪɟɡɭɥɶɬɚɬɵ ɪɚɛɨɬɵ (ɗɧɰɢɤɥɨɩɟɞɢɹ ɤɢɛɟɪɧɟɬɢɤɢ, 1974),
ɜɟɥɢɱɢɧɭ ɷɩɫɢɥɨɧ-ɷɧɬɪɨɩɢɢ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɨɰɟɧɢɬɶ ɦɢɧɢɦɚɥɶɧɨ ɧɟɨɛɯɨɞɢɦɨɟ ɤɨɥɢɱɟɫɬɜɨ
ɢɧɮɨɪɦɚɰɢɢ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɡɚɞɚɧɧɵɣ ɭɪɨɜɟɧɶ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ, ɨɩɪɟɞɟɥɢɦ ɬɚɤ
HH(Z) = In f(K) U{I(W,Z)},
gdH
ɝɞɟ In – ɢɧɬɟɝɪɚɥɶɧɚɹ ɫɭɦɦɚ ɦɟɬɪɢɤ U, I(W,Z) – ɤɨɥɢɱɟɫɬɜɨ ɢɧɮɨɪɦɚɰɢɢ, ɪɚɫɫɱɢɬɚɧɧɨɟ ɩɨ ɮɨɪɦɭɥɟ (1), H
– ɜɟɥɢɱɢɧɚ, ɭɱɢɬɵɜɚɸɳɚɹ ɩɥɚɧɨɜɭɸ ɬɨɱɧɨɫɬɶ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɩɭɬɢ ɫɭɞɧɚ, ɚ g – ɜɟɥɢɱɢɧɚ,
ɤɨɬɨɪɚɹ ɩɪɢ ɜɵɛɪɚɧɧɨɦ ɪɚɫɫɬɨɹɧɢɢ U(Z,W), ɧɚɩɪɢɦɟɪ, ɬɚɤɨɦ ɤɚɤ U(Z,W) = (Z W)2, ɦɨɠɟɬ ɛɵɬɶ ɧɚɣɞɟɧɚ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
g = ³ ³ U(Z,W)f(Z,W) dZ dW.
L L
Z W
ȿɫɥɢ ɬɪɟɛɨɜɚɧɢɹ ɤ ɩɥɚɧɨɜɨɣ ɬɨɱɧɨɫɬɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɡɚɞɚɧɵ ɜ ɜɢɞɟ ɫɬɚɧɞɚɪɬɧɨɝɨ
ɷɥɥɢɩɫɚ ɩɨɝɪɟɲɧɨɫɬɟɣ, ɬɨ ɜɟɥɢɱɢɧɚ ɷɩɫɢɥɨɧ-ɷɧɬɪɨɩɢɢ ɛɭɞɟɬ ɪɚɜɧɚ
HH(Z) = log2(SW/SH),
(7)
ɝɞɟ SH = SaH bH – ɩɥɨɳɚɞɶ ɷɥɥɢɩɫɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨɝɪɟɲɧɨɫɬɟɣ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ, ɩɪɢɧɹɬɚɹ ɧɚ
ɷɬɚɩɟ ɩɥɚɧɢɪɨɜɚɧɢɹ ɛɟɡɨɩɚɫɧɨɝɨ ɧɚɜɢɝɚɰɢɨɧɧɨɝɨ ɦɚɪɲɪɭɬɚ.
Ⱥɧɚɥɢɡ ɜɵɪɚɠɟɧɢɣ (6) ɢ (7) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɭɞɨɜɥɟɬɜɨɪɢɬɶ ɡɚɞɚɧɧɵɟ ɧɚ ɷɬɚɩɟ ɩɥɚɧɢɪɨɜɚɧɢɹ
ɬɪɟɛɨɜɚɧɢɹ ɤ ɬɨɱɧɨɫɬɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɦɨɠɧɨ, ɞɥɹ ɱɟɝɨ ɧɭɠɧɨ ɥɢɲɶ ɜɵɩɨɥɧɢɬɶ ɭɫɥɨɜɢɟ
I(W) t HH (Z).
27
(8)
Ȼɪɚɧɞɬ Ɏ.Ɋ., Ɇɟɧɶɲɢɤɨɜ ȼ.ɂ.
ɂɡɦɟɪɟɧɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɢ...
ɍɫɥɨɜɢɟ (8) ɹɜɥɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɵɦ ɢ ɧɟ ɨɛɥɚɞɚɟɬ ɩɪɢɡɧɚɤɚɦɢ ɞɨɫɬɚɬɨɱɧɨɫɬɢ, ɩɨɫɤɨɥɶɤɭ ɤɨɥɢɱɟɫɬɜɨ
ɢɧɮɨɪɦɚɰɢɢ, ɪɚɫɫɱɢɬɚɧɧɨɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɮɨɪɦɭɥɨɣ (1), ɹɜɥɹɟɬɫɹ ɬɨɥɶɤɨ ɢɧɬɟɝɪɚɥɶɧɨɣ ɨɰɟɧɤɨɣ ɢ ɧɟ
ɭɱɢɬɵɜɚɟɬ ɧɢ ɮɨɪɦɭ, ɧɢ ɨɪɢɟɧɬɚɰɢɸ ɫɬɚɧɞɚɪɬɧɨɝɨ ɷɥɥɢɩɫɚ ɩɨɝɪɟɲɧɨɫɬɟɣ.
ȿɫɥɢ ɞɚɥɟɟ ɩɪɢɧɹɬɶ ɜɨ ɜɧɢɦɚɧɢɟ ɜɵɪɚɠɟɧɢɹ (5, 6 ɢ 7), ɚ ɬɚɤɠɟ ɭɫɥɨɜɢɟ (8), ɬɨ ɢɡ ɧɟɪɚɜɟɧɫɬɜɚ
SH d SK ɫɥɟɞɭɟɬ ɛɨɥɟɟ ɞɨɫɬɭɩɧɨɟ ɤ ɜɢɡɭɚɥɢɡɚɰɢɢ ɢ ɜɨɫɩɪɢɹɬɢɸ ɜ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɤɨɧɬɪɨɥɹ
ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ ɧɟɪɚɜɟɧɫɬɜɨ
H(K) d H(H),
(9)
ɝɞɟ H(H) = log2(2eSH ), H(K) = log2(2eSK) – ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɷɧɬɪɨɩɢɢ ɩɥɚɧɨɜɨɣ ɢ ɬɟɤɭɳɟɣ ɬɨɱɧɨɫɬɢ
ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ ɩɭɬɢ ɫɭɞɧɚ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɭɞɨɜɥɟɬɜɨɪɢɬɶ ɡɚɞɚɧɧɵɟ ɬɪɟɛɨɜɚɧɢɹ ɤ ɛɟɡɨɩɚɫɧɨɫɬɢ ɩɥɚɜɚɧɢɹ ɫɭɞɧɚ ɢ
ɨɛɟɫɩɟɱɢɬɶ ɜɢɡɭɚɥɶɧɵɣ ɤɨɧɬɪɨɥɶ ɡɚ ɷɬɨɣ ɛɟɡɨɩɚɫɧɨɫɬɶɸ ɩɪɢ ɨɛɫɟɪɜɚɰɢɨɧɧɨɦ ɫɱɢɫɥɟɧɢɢ ɩɭɬɢ ɫɭɞɧɚ,
ɧɟɨɛɯɨɞɢɦɨ ɜ ɩɪɨɝɪɚɦɦɧɨɦ ɨɛɟɫɩɟɱɟɧɢɢ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɩɪɨɰɟɞɭɪɭ ɫɛɨɪɚ
ɬɚɤɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɬɟɤɭɳɟɣ ɢɧɮɨɪɦɚɰɢɢ, ɤɨɬɨɪɨɟ ɛɵɥɨ ɛɵ ɧɟ ɦɟɧɶɲɟ, ɱɟɦ ɜɟɥɢɱɢɧɚ ɷɩɫɢɥɨɧ-ɷɧɬɪɨɩɢɢ
H(H), ɡɚɤɥɚɞɵɜɚɟɦɚɹ ɧɚ ɷɬɚɩɟ ɩɥɚɧɢɪɨɜɚɧɢɹ ɧɚɜɢɝɚɰɢɨɧɧɨɝɨ ɦɚɪɲɪɭɬɚ.
5. Ɂɚɤɥɸɱɟɧɢɟ
ɋɨɜɪɟɦɟɧɧɵɟ ɤɨɫɦɢɱɟɫɤɢɟ ɧɚɜɢɝɚɰɢɨɧɧɵɟ ɬɟɯɧɨɥɨɝɢɢ, ɢɧɮɨɪɦɚɬɢɡɚɰɢɹ ɫɭɞɨɜɨɠɞɟɧɢɹ ɢ
ɢɧɬɟɝɪɚɥɶɧɵɟ ɫɢɫɬɟɦɵ ɨɬɨɛɪɚɠɟɧɢɹ ɧɚɜɢɝɚɰɢɨɧɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨɛɟɫɩɟɱɢɥɢ ɩɟɪɟɯɨɞ ɨɬ ɩɪɨɰɟɞɭɪɵ
ɤɨɪɪɟɤɬɢɪɭɟɦɨɝɨ ɫɱɢɫɥɟɧɢɹ ɤ ɩɪɨɰɟɞɭɪɟ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ ɫɱɢɫɥɟɧɢɹ. Ɍɚɤɢɟ ɢɡɦɟɧɟɧɢɹ ɜ ɨɪɝɚɧɢɡɚɰɢɢ
ɫɱɢɫɥɟɧɢɹ ɩɭɬɢ ɫɭɞɧɚ ɩɪɢɜɟɥɢ ɤɚɤ ɤ ɦɨɞɟɪɧɢɡɚɰɢɢ ɫɭɳɟɫɬɜɭɸɳɟɝɨ ɩɪɢɟɦɚ ɩɨɞɞɟɪɠɚɧɢɹ ɛɟɡɨɩɚɫɧɨɫɬɢ
ɧɚɜɢɝɚɰɢɢ ɧɚ ɡɚɞɚɧɧɨɦ ɭɪɨɜɧɟ, ɬɚɤ ɢ ɤ ɪɚɡɪɚɛɨɬɤɟ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɵɯ ɩɪɢɟɦɨɜ.
ɂɫɩɨɥɶɡɭɟɦɵɣ ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɢɧɮɨɪɦɚɰɢɨɧɧɵɣ ɩɨɞɯɨɞ ɤ ɪɟɲɟɧɢɸ ɡɚɞɚɱɢ ɩɨ ɨɛɟɫɩɟɱɟɧɢɸ
ɛɟɡɨɩɚɫɧɨɝɨ ɩɥɚɜɚɧɢɹ ɫɭɞɧɚ ɧɚ ɡɚɞɚɧɧɨɦ ɦɚɪɲɪɭɬɟ, ɩɨɧɢɦɚɟɦɵɣ ɜ ɭɡɤɨɦ ɫɦɵɫɥɟ, ɨɪɝɚɧɢɱɟɫɤɢ ɫɜɹɡɚɧ ɫ
ɫɭɳɟɫɬɜɭɸɳɢɦɢ ɦɟɬɨɞɚɦɢ ɨɰɟɧɤɢ ɛɟɡɨɩɚɫɧɨɫɬɢ ɧɚɜɢɝɚɰɢɢ. Ɉɞɧɚɤɨ ɞɥɹ ɫɥɭɱɚɹ ɨɛɫɟɪɜɚɰɢɨɧɧɨɝɨ
ɫɱɢɫɥɟɧɢɹ ɩɭɬɢ ɫɭɞɧɚ ɬɚɤɨɣ ɩɨɞɯɨɞ ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɜɥɟɱɟɧ ɤ ɨɪɝɚɧɢɡɚɰɢɢ ɩɪɢɧɰɢɩɢɚɥɶɧɨ ɧɨɜɨɣ
ɦɟɬɨɞɢɤɢ ɜɢɡɭɚɥɶɧɨɝɨ ɤɨɧɬɪɨɥɹ, ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɭɠɟ ɜ ɪɚɦɤɚɯ ɢɧɬɟɥɥɟɤɬɭɚɥɶɧɨɣ
ɫɢɫɬɟɦɵ "ɫɭɞɨɜɨɞɢɬɟɥɶ ɬɟɯɧɢɱɟɫɤɨɟ ɫɪɟɞɫɬɜɨ".
ɉɪɚɤɬɢɱɟɫɤɚɹ ɪɟɚɥɢɡɚɰɢɹ ɩɪɨɰɟɞɭɪɵ ɤɨɧɬɪɨɥɹ ɬɪɟɛɭɟɬ, ɱɬɨɛɵ ɜ ɩɪɨɝɪɚɦɦɧɨɦ ɨɛɟɫɩɟɱɟɧɢɢ
ɬɟɯɧɢɱɟɫɤɨɝɨ ɫɪɟɞɫɬɜɚ ɫɭɞɨɜɨɠɞɟɧɢɹ ɛɵɥɚ ɩɪɟɞɭɫɦɨɬɪɟɧɚ ɩɪɨɰɟɞɭɪɚ ɫɛɨɪɚ ɬɚɤɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɬɟɤɭɳɟɣ
ɢɧɮɨɪɦɚɰɢɢ, ɤɨɬɨɪɨɟ ɛɵɥɨ ɛɵ ɧɟ ɦɟɧɶɲɟ, ɱɟɦ ɜɟɥɢɱɢɧɚ ɷɩɫɢɥɨɧ-ɷɧɬɪɨɩɢɢ H(H), ɡɚɤɥɚɞɵɜɚɟɦɚɹ ɧɚ ɷɬɚɩɟ
ɩɥɚɧɢɪɨɜɚɧɢɹ ɧɚɜɢɝɚɰɢɨɧɧɨɝɨ ɦɚɪɲɪɭɬɚ.
Ʌɢɬɟɪɚɬɭɪɚ
Ƚɚɥɥɚɝɟɪ Ɋ. Ɍɟɨɪɢɹ ɢɧɮɨɪɦɚɰɢɢ ɢ ɧɚɞɟɠɧɚɹ ɫɜɹɡɶ. Ɇ., ɋɨɜɟɬɫɤɨɟ ɪɚɞɢɨ, 719 ɫ., 1974.
Ʉɨɜɪɢɝɢɧ Ⱥ.Ȼ. Ɇɟɬɨɞɵ ɨɛɪɚɛɨɬɤɢ ɧɚɛɥɸɞɟɧɢɣ ɜ ɧɚɜɢɝɚɰɢɨɧɧɵɯ ɡɚɞɚɱɚɯ. Ʌ., ɢɡɞ. Ʌɟɧɢɧɝɪɚɞɫɤɨɝɨ
ɭɧɢɜɟɪɫɢɬɟɬɚ, 177 ɫ., 1974.
ɗɧɰɢɤɥɨɩɟɞɢɹ ɤɢɛɟɪɧɟɬɢɤɢ. ȼ 2 ɬ. Ʉɢɟɜ, Ƚɥɚɜɧɚɹ ɪɟɞɚɤɰɢɹ ɭɤɪɚɢɧɫɤɨɣ ɫɨɜɟɬɫɤɨɣ ɷɧɰɢɤɥɨɩɟɞɢɢ, ɬ.2,
618 ɫ., 1974.
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