Gaussian Intro - Artificial Intelligence for RoboticsYouTube↗  IA↗(long shot)
Education  8.9K views 8 likes 1 dislikes   29 May 2012
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Вы помните нашу модель Маркова, когда мир был разделен на дискретные сетки,
You remember our Markov model where the world was divided into discrete grids,
и мы назначали для каждой сетки определенную вероятность.
and we assigned to each grid a certain probability.
Такое представление вероятности над пространствами называется гистограммой
Such a representation of probability over spaces is called a histogram
в том, что она делит непрерывное пространство на конечное число ячеек сетки
in that it divides the continuous space into a finite many grid cells
и приближается к заднему распределению гистограммы по сравнению с первоначальным распределением.
and approximates the posterior distribution by a histogram over the original distribution.
Гистограмма представляет собой простое приближение для непрерывного распределения.
The histogram is a mere approximation for this continuous distribution.
В фильтр Калмана распределения дается то, что называется гауссовым.
In Kalman filters the distribution is given by what's called a Gaussian.
Гауссова непрерывная функция на пространстве мест,
A Gaussian is a continuous function over the space of locations,
и площадь под сумм до 1.
and the area underneath sums up to 1.
Вот наша гауссова снова.
Here's our Gaussian again.
Если мы называем пространство х, то гауссова характеризуется двумя параметрами -
If we call the space x, then the Gaussian is characterized by two parameters--
средний, часто сокращенно с греческой буквой μ, а ширина гауссовой,
the mean, often abbreviated with the Greek letter μ, and the width of the Gaussian,
часто называется дисперсией, в причины этого я не хочу вдаваться
often called the variance, and for reasons I don't want to go into,
он часто в виде квадратичной переменной σ ^ 2.
it's often written as a quadratic variable σ^2.
И гауссово в 1D, означает, что пространство параметров здесь 1 мерная,
And Gaussian in 1D, which means the parameter space over here is 1 dimensional,
характеризуется μ и σ ^ 2.
is characterized by μ and σ^2.
Вместо того, чтобы оценить весь дистрибутив в виде гистограммы,
Rather than estimating the entire distribution as a histogram,
Наша задача фильтров Калмана является поддержание μ и σ ^ 2, что является нашей лучшей оценкой
our task in Kalman filters is to maintain a μ and a σ^2 that is our best estimate
расположения объекта, которого мы пытаемся найти
of the location of the object we're trying to find.
Точная формула является экспоненциальной квадратичной функции, где мы берем
The exact formula is an exponential of a quadratic function where we take
показателем этого сложного выражения здесь.
the exponent of this complicated expression over here.
Квадратичное отличие нашего запроса точки х относительно среднего μ
The quadratic difference of our query point x relative to the mean μ
деленное на σ ^ 2 умноженное на -1 / 2.
divided by σ^2 multiplied by -1/2.
Теперь, если х = μ, то числитель становится 0,
Now, if x equals μ then the numerator becomes 0,
и у нас есть х 0, что 1.
and we have x of 0, which is 1.
мы должны нормализовать этой постоянной
It turns out we have to normalize this by a constant--
1 за квадратный корень из 2πσ ^ 2 -
1 over the square root of 2πσ^2--
но для всего, что мы будем говорить сегодня, эта постоянная не имеет значения, так что можете игнорировать его.
but for everything we'll talk about today, this constant won't matter, so ignore it.
Главное, у нас есть экспоненциальный квадратичной функции здесь
What matters is we have an exponential of a quadratic function over here.
Позвольте мне нарисовать вам пару функций, а вы мне, какие из них вы считаете,
Let me draw you a couple of functions, and you tell me which ones you believe
гауссовыми, установив флажок на правой стороне.
are Gaussian by checking the box on the right side.
Пожалуйста, простите мои бедные навыки рисования .
Please excuse my poor drawing skills here.
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