May 19, 2013

## How do you implement a basic Kalman filter in this specific situation?

I’m supposed to implement a basic Kalman Filter of a bolas weapon in flight. The Bolas has 2 balls on a string, and after thrown assume the overall system has constant velocity. Your state should have 3D position of 2 balls and their velocities (i.e. 12 variables). (For simplicity ignore the string constraint in the model). I have to make up some fake observations/measurements, where each observation should be one line of data with x1 y1 z1 x2 y2 z2 (positions of each ball). Using Matlab, I read the points, and use a Kalman filter to estimate the state after each observation, and plot them (in 3D), after each update, showing the raw measurements as one symbol and the estimated position as another. I have no idea how to do this!!! This is for my Computational Algebra class, so all I need is a clear example to base it off of. Thanks!

See the tutorial here: http://www.cs.cmu.edu/~motionplanning/papers/sbp_papers/integrated3/kleeman_kalman_basics.pdf

## How do you show norm1 and norm2 are equivalent?

Let x = (x1, x2, …, xn) which is an element of Rn (n-dimensional Real space)

norm 1 of x is
||x||1 = |x1| + … + |xn|

and norm2 of x is
||x||2 = sqrt ( |x1|^2 + … + |xn|^2)

If anything is not clear please let me know and I’ll edit it in the details.

You need to show that there exists positive constants p and q such that for any x:

p ||x||1 <= ||x||2 <= q ||x1||1

Let's compare the square of both norms:

||x||2^2 = x1^2 + x2^2 + …+xn^2

||x||1^2 = x1^2 + x2^2 + …+xn^2 + 2|x1||x2| + all other cross products.

Clearly all the cros products larger than or equal to zero, so we have:

||x||2^2

||x||2<= ||x||1

So, we can take the constant q to be 1.

You can do the other part by applying the convex inequality (a.k.a. Jensen's inequality) to the function f(z) = z^2:

http://en.wikipedia.org/wiki/Jensen's_inequality

The function f(z) = z^2 is clearly convex in the interval ranging from zero to infinity. So, the square of the average of positive numbers must be smaller than or equal to the average of the squares of these numbers:

[(|x1| + |x2| + ...+|xn|)/n]^2 <=

[|x1|^2 + |x2|^2 + ....|xn|^2]/n

We can write this as:

1/n [(|x1| + |x2| + ...+|xn|)]^2 <=

[|x1|^2 + |x2|^2 + ....|xn|^2]

Take the square root of both sides:

1/sqrt(n) (|x1| + |x2| + …+|xn|) <=

sqrt [|x1|^2 + |x2|^2 + ....|xn|^2]

Or:

1/sqrt(n) ||x||1 <= ||x||2

So, we can take the constant p to be 1/sqrt(n)

## What is the success rate of clomid while trying to concieve?

Iam now on another higher dose of clomid 2 X1 ( two tablets a day for five days )anyone tell me about the success rate.We have tried to have a baby and it’s getting us frustrated any advice