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Измерения параметров сигнала. Структура оптимального измерителя (реферат)

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БЕЛОРУССКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ИНФОРМАТИКИ И РАДИОЭЛЕКТРОНИКИ

кафедра ЭТТ

РЕФЕРАТ на тему:

«Измерения параметров сигнала. Структура оптимального измерителя»

МИНСК, 2008

Сущность, условия решения и критерий оптимальности задачи измерения
параметров сигнала

Измеряемые параметры сигнала (время запаздывания, доплеровское смещение
частоты, наклон и кривизна волнового фронта) изменяются во времени.
Поэтому задача измерения по существу сводится к наиболее точному
воспроизведению этих параметров, во времени. Для систем радиолокационных
систем это означает наиболее точное воспроизведение во времени
дальности, скорости и угловых координат объекта наблюдения. Для
радиосистем передачи информации это означает наиболее точное
воспроизведение во времени передаваемого информационного сообщения.

Постановка задачи измерения параметров сигнала, как и всякой другой
задачи, предполагает формулировку некоторых условий ее решения. К числу
таких условий относятся следующие исходные предположения, выступающие в
роли постулатов:

– самостоятельность задачи измерения,

-независимость измерения искомого параметра от других, считающихся
известиями.

Самостоятельность задачи измерения воспринимается с некоторой степень»
условности.

В действительности, решая задачу обнаружения, т.е. принимая решение о
наличии или отсутствии сигнала по каждому элементу разрешения
пространства наблюдения, мы тем самым вместе с решением о наличии
сигнала в данном элементе разрешения формируем оценку о параметрах
сигнала с точностью до элемента разрешения (по дальности, скорости,
угловым координатам). Однако для задачи измерения параметров сигнала
характерны принципиально другие» более высокие, точности. Поэтому
процесс обнаружения сигнала и измерения его параметров целесообразно
рассматривать раздельно. Предполагается наличие обнаружителя, с помощью
которого достоверно (D =1; F =0) устанавливается факт наличия сигнала в
каком-либо элементе пространства наблюдения и осуществляется
первоначальное грубое определение параметров сигнала (с точностью до
элемента разрешения), позволяющее перейти к точному измерению.

Итак, согласно первому постулату о самостоятельности задачи измерения и
достоверности обнаружения источником информации и объектом обработки
(анализа) при решении задачи измерения параметров сигнала является
аддитивная смесь принятого полезного сигнала и помех:

f(t)=m(t,,)+n(t)

Принятый полезный сигнал зависит от некоторого числа измеряемых (1,
2,…k) параметров (время запаздывания, доплеровское смещение частоты,
наклон и кривизне волнового фронта) и некоторого числа неизменяемых (1,
2,… l) или паразитных параметров (случайные амплитуда и фаза).
Измеряемые параметры 1, 2,…k в общем случае являются функционально или
статистически зависимыми. Это обстоятельство приводит к необходимости
совместного измерения взаимозависимых параметров, что сильно усложняет
решение задач синтеза и анализа измерителей параметров сигнала. Поэтому
в дальнейшем рассматривается лишь случай независимого от других
измерения одного параметра, когда все остальные параметры предполагаются
известными. В случае малых ошибок измерения, когда справедливы линейные
приближения, раздельный синтез и анализ измерителей отдельных параметров
вполне допустим.

Под упомянутой выше ошибкой измерения параметра подразумевается разность
между измеренным значением параметра и его истинным значением ц,
закодированным в принятом сигнале:

ц= — ц.

В общем случае ошибка измерения является функцией времени и представляет
собой разность

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f001000008000000320ae001e20a01000000d60015000000fb0220ff0000000000009001
010000000402001054696d6573204e657720526f6d616e0000a3040000002d0100000400
0000f001010008000000320ae0012e0201000000550010000000fb0280fe000000000000
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0000320a8001bc0901000000610008000000320a8001e70501000000610008000000320a
8001230101000000610010000000fb0280fe000000000000900100000002000200105379
6d626f6c0002040000002d01000004000000f001010008000000320a8001b50801000000
2d0008000000320a8001e004010000003d0008000000320a80013a000100000044000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01010004000000f0010000030000000000

где ц(t – изменявшийся во времени измеряемый параметр, закодированный в
принятом сигнале (задающее воздействие измерителя);

(t) – измеренное значение параметра, т.е. результат воспроизведения
задающего воздействия.

Естественным критерием качества измерения параметра является минимум
ошибки измерения ц. Однако формулировка критерия качества в такой форме
не позволяет обеспечить осознания преемственности основных задач
радиосистем (обнаружения, распознавания-различения и измерения) с точки
зрения единства центрального звена решения этих задач –
пространственно-временной и поляризационной обработки сигнала на фоне
помех.

Действительно, в результате пространственно-временной и
поляризационной обработки принятого сигнала на фоне помех формируется
отношение правдоподобия (или любая однозначно связанная с ним величина).
При этом фактически происходит сопоставление принятого сигнала и его
прообраза по измеряемым параметрам.

Если характеристики и параметры принятого сигнала и его прообраза
согласованы, то отношение правдоподобия максимально.

Факт согласованности характеристик и параметров привитого сигнала и его
прообраза, устанавливаемый по максимуму отношения правдоподобия, может
быть использован для формулировки критерия оптимальности в форме,
удовлетворяющей сформулированному выше требованию: оптимальный
измеритель должен обеспечить или минимум ошибки измерения, или максимум
отношения правдоподобия.

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000000000000e4e31200040000002d01000004000000f0010100030000000000

Сформировав отношение правдоподобия и подобрав тем или иным способом
такое значение измеряемого параметра, при котором отношение
правдоподобия максимально, можно тем самым измерить с минимальной
ошибкой тот или иной параметр сигнала. В зависимости от способа выбора
измеряемого параметра различают измерители, классификация которых
излагается ниже.

Классификация измерителей

Измерители различаются по следующим классификационным признакам;

– по степени участия человека (эргатические – с участием человека в
системе “индикатор-оператор” и автоматические – без участия человека),

– по используемому времени (с формированием разовой оценки, т.е. с
оцениванием по результатам

одного обращения к объекту наблюдения Ta = Tн << Tob и с формированием объединенной оценки, т.е. оцениванием по результатам нескольких обращений к объекту наблюдения Ta >> Tн >> ), Tн Tob

– по наличию или отсутствию обратной связи (следящие или замкнутые
измерители и неследящие или разомкнутые измерители).

Неотъемлемой частью эргатических измерителей является система
“индикатор-оператор”. Человек-оператор, наблюдая за экраном индикатора,
используя либо неподвижные калибрационные метки (механические или
электронные), либо подвижные метки, осуществляет максимально
правдоподобную оценку координат или параметров движения целей. При этом
оценивание измеряемого параметра возможно как по результатам одного
обращения к цели ( Та = Тн << Тоб ), что характерно для РЛС кругового обзора с большим периодом обзора (единицы секунд), так и по результатам нескольких обращений к цели (Та >> Тоб >> Тн), что характерно для РЛС
секторного обзора с высокой частотой обзора (десятки герц и более).

Эргатические измерители могут находиться как в следящем, так и
неследящем режимах. Неследящий режим измерения (рис. 1) характерен для
систем “индикатор-оператор” с неподвижными калибрационными метками,
когда оценка измеряемого параметра осуществляется оператором
непосредственно по максимуму отношения правдоподобия, т.е. путем выбора
такого значения измеряемого параметра, при котором сигнал на выходе
многоканального обнаружителя, отображаемый на экране индикатора,
максимален.

Следящий режим измерения (рис. 2) характерен для систем
“индикатор-оператор” с подвижными метками (механическими или
электронными). При этом имеет место визуальная оценка величины и знака
рассогласования между истинным значением измеряемого параметра
(положением Метки на экране индикатора) и измеренным его значением
(положением подвижной механической или электронной метки). Наблюдая и
оценивая это рассогласование, оператор с учетом обретенного им опыта
рассчитывает мышечную реакцию (управлявшее воздействие), прикладываемую
к исполнительному устройству (механизму перемещения механической или
электронной метки) для того, чтобы ликвидировать наблюдаемое им
рассогласование.

Автоматические измерители работающие без участия человека (рис. 3),
могут формировать как разовую (или единичную) оценку измеряемого
параметра заодно обращение к цели – время наблюдения (Та = Тн << Тоб), так и объединенную оценку за несколько обращений к цели ( Та >>
Тоб >> Тн).

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040000002701ffff030000000000
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Рис. 1 Эргатические неследящие измерители:

а) с формированием разовой оценки:

б) с формированием объединенной оценки
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fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7ffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffffffffffffffffffffffffffffff7eff7ffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffff00ffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffff7eff7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7eff7ff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffffffffffffff7eff7ffffffffffffffffffffffffffffffffffffff
fffffffffffffffffffffffffffffffffffffffffff7ffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffff00ffffffffffffffffffffffff
f7f7f7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffefefeffffffffff7fffffffffffffffffffffffffffffffff7f7f7
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffe7e7e7ffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffff00ffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
fffffffffffffffffffffffffffffffffffffffffffffffffffffffff7eff7ffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff000c000000
40092900aa000000000000006500090100000000040000002701ffff030000000000

picscalex57010009000003d800000001009600000000009600000026060f002201574d4
643010000000000010095910000000001000000000100000000000000010000010000006
c0000000000000000000000ffffffffffffffff00000000000000007d1b00006f0a00002
0454d46000001000001000009000000010000000000000000000000000000007f1200007
71a0000c80000001f010000000000000000000000000000000f030058600400160000000
c000000180000000a00000010000000000000000000000009000000100000007d0600007
a020000250000000c0000000e00008046000000280000001c0000004744494302000000f
fffffffffffffff7e0600007b02000000000000460000001400000008000000474449430
3000000250000000c0000000e0000800e000000140000000000000010000000140000000
400000003010800050000000b0200000000050000000c025b00f000040000002e0118001
c000000fb020200010000000000bc02000000cc0102022253797374656d0000000000000
000000000000000000000000000000000000000040000002d010000040000002d0100000
30000000000

Рис. 2 Эргатические следящие измерители:

а) с формированием разовой оценки

б) с формированием объединенной оценки

Д(picscalex1000100090000039d00000002001c00000000000500000009020000000005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,picsc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)=picscalex126010009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picscalex1420100090000030202000002008a01000000008a01000026060f000a03574d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Рис 3 Автоматические слядящие (а) и неследящие (б) измерители с
формированием разовой и объединенной оценок

При этом автоматические измерители могут быть следящими (замкнутыми) и
неследящими (разомкнутыми). В следящих измерителях присутствует
техническое устройство, называемое дискриминатором, на выходе которого
формируется сигнал ошибки D(t,ц), пропорциональный (в определенных
пределах) рассогласованию u=-ц между истинным значением измеряемого
параметра ц и его измеренным значением :
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В неследяших автоматических измерителях присутствует устройство выбора
максимума сигнала на выходе многоканального обнаружителя, фиксирующее
номер канала с максимальным выходом и преобразующее номер канала в
дискретное значение измеряемой координаты (с возможностью последующего
объединения за несколько циклов обращения к цели).

Уравнение оптимальной оценки, структура оптимального измерителя.

Согласно сформулированному выше критерию оптимальности следует считать
измеренным с максимальной точностью такое значение параметра , при
котором отношение правдоподобия (или его логарифм) максимально.
Используя для определения максимума функции математический метод,
следует найти производную этой функции по измеряемому параметру и
установить такое его значение, при котором эта производная становится
равной нулю. Таким образом, оптимальной оценкой параметра является
корень уравнений
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,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Эти уравнения носят название уравнений оптимальной оценки. Они отражают
структуру и алгоритм работы оптимального измерителя параметра.
Реализующий операцию получения оптимальной оценки измеритель состоит из
двух устройств (рис. 4):

– устройства, вычисляющего по принятому сигналу производную логарифма
отношения правдоподобия по измеряемому параметру;

-устройства, определяющего сглаженную оценку, при которой эта
производная равна нулю.
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Рис. 4. Оптимальная структура измерителя (автоматического следящего)

picscalex10001000900000374d701000000b502010000001610000026060f002220574d
46430100000000000100e767000000000e00000000200000ac860100aca6010001000000
6c000000000000000000000048010000850000000000000000000000a6250000550f0000
20454d4600000100aca601000c0000000100000000000000000000000000000000040000
000300002c010000e1000000000000000000000000000000e0930400e86e030046000000
2c00000020000000454d462b014001001c000000100000000210c0db0100000060000000
6000000046000000584b00004c4b0000454d462b224004000c000000000000001e400900
0c00000000000000244001000c000000000000003040020010000000040000000000803f
214007000c0000000000000008400005a44a0000984a00000210c0db0100000000000000
0000000000000000000000000100000089504e470d0a1a0a0000000d4948445200000149
0000008608060000005043787d00000001735247420240c07dc500000009704859730000
0ec400000ec401952b0e1b0000001974455874536f667477617265004d6963726f736f66
74204f66666963657fed3571000049fc4944415478daed9d099c8dd51bc743c95676b294
25099152112544b2b428e95f69435a6c69534a2a4b8414510829d94b4976a2947ddf97ec
7bf6194b963afffb7dee3c6f77ae3bd7bd337766eebd737c9ccfccdcfb2ee73def39bff3
7bf64b4ec59e32e1d04ec69c34c78f1c0fe9f58e1e3a6af6edde97e031a74f9c365b366e
317b76ee31f7d6bed7142a58c84c9d3c55fe0ee4fabb77ec3687ff3a6c7efae12793374f
5ef3d8a38fc9dfbe8e3fb8ffa099f3cb1c932d6b36f361d70fcdf1c3c7a57f1cff49ef4f
4c87b73bc87dc77f37de5c72c92566f386cd26e6684c58bc9be47adf3cdfb1c3c7a2f619
6d8b8e7649b43ed8df27ff36d5eeaa9620e09d387e421ac0fccc53cf985f66fc62325e9a
d1fcfedbefe6afbd7f05748f1d5b7798df66ff662e4d7fa9005fdedc79cdd9d367057c9d
e362dc3ff7eedc6bca972f6f162d5864766edd2920c1fd572c5d61325e96d16cfb739b80
eede5d7b4db1a2c54cffcffa9bd863b1513bf100489e75df9e7d7621da664132b5405218
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