Fdtxjr

Multi tool use

Implement the Thanos sorting algorithm

How to safely derail a train during transit?

How to get regions to plot as graphics

When did Lisp start using symbols for arithmetic?

How do spells that require an ability check vs. the caster's spell save DC work?

What can we do to stop prior company from asking us questions?

Term for the "extreme-extension" version of a straw man fallacy?

Can the Reverse Gravity spell affect the Meteor Swarm spell?

Where to find order of arguments for default functions

% symbol leads to superlong (forever?) compilations

MAZDA 3 2006 (UK) - poor acceleration then takes off at 3250 revs

WOW air has ceased operation, can I get my tickets refunded?

Too much space between section and text in a twocolumn document

How do I go from 300 unfinished/half written blog posts, to published posts?

Should I tutor a student who I know has cheated on their homework?

How can I get through very long and very dry, but also very useful technical documents when learning a new tool?

Is it my responsibility to learn a new technology in my own time my employer wants to implement?

What is the point of a new vote on May's deal when the indicative votes suggest she will not win?

Does it take more energy to get to Venus or to Mars?

What's the point of interval inversion?

Why doesn't a table tennis ball float on the surface? How do we calculate buoyancy here?

I believe this to be a fraud - hired, then asked to cash check and send cash as Bitcoin

Does the Brexit deal have to be agreed by both Houses?

Why is there a PLL in CPU?

Kalman filter: the bayesian approach derivation some clarifications

1

$begingroup$

I'm reading the book Methods and algorithms for signal processing from Moon Stirling at page 592 there is a derivation of Kalman filter using the Bayesian approach. I have some issues in understanding the propagate step which is the following:
$ p(textbfx_k|textbfz_1:k-1) = inttextbfx_k-1)p(textbfx_k-1$.
The book says under some assumption:
$ x_k-1 | z_1:k-1 sim mathcalN(m_k-1), P_k-1)$ and
$x_k|x_k-1 sim mathcalN(F_k x_k-1, Q_k)$
And inserting these in the prediction step and performing the integration (which involves expanding and completing the square) we find that $x_k$ is a Gaussian with mean $F_k m_k-1$ and variance $F_k P_k F_k ^T + Q_k$.
I don't understand when I insert that two gaussian in prediction formula how is possible to get that mean and that variance, there we have the product of two gaussian distribution but with different random variables maybe that's a gaussian? but then we have an integral of the resulting distribution. Can someone clarify me this?
Thank you

gaussian-integral kalman-filter

share|cite|improve this question

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61

$endgroup$

add a comment | 

1

$begingroup$

I'm reading the book Methods and algorithms for signal processing from Moon Stirling at page 592 there is a derivation of Kalman filter using the Bayesian approach. I have some issues in understanding the propagate step which is the following:
$ p(textbfx_k|textbfz_1:k-1) = inttextbfx_k-1)p(textbfx_k-1$.
The book says under some assumption:
$ x_k-1 | z_1:k-1 sim mathcalN(m_k-1), P_k-1)$ and
$x_k|x_k-1 sim mathcalN(F_k x_k-1, Q_k)$
And inserting these in the prediction step and performing the integration (which involves expanding and completing the square) we find that $x_k$ is a Gaussian with mean $F_k m_k-1$ and variance $F_k P_k F_k ^T + Q_k$.
I don't understand when I insert that two gaussian in prediction formula how is possible to get that mean and that variance, there we have the product of two gaussian distribution but with different random variables maybe that's a gaussian? but then we have an integral of the resulting distribution. Can someone clarify me this?
Thank you

gaussian-integral kalman-filter

share|cite|improve this question

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61

$endgroup$

add a comment | 

$begingroup$

I'm reading the book Methods and algorithms for signal processing from Moon Stirling at page 592 there is a derivation of Kalman filter using the Bayesian approach. I have some issues in understanding the propagate step which is the following:
$ p(textbfx_k|textbfz_1:k-1) = inttextbfx_k-1)p(textbfx_k-1$.
The book says under some assumption:
$ x_k-1 | z_1:k-1 sim mathcalN(m_k-1), P_k-1)$ and
$x_k|x_k-1 sim mathcalN(F_k x_k-1, Q_k)$
And inserting these in the prediction step and performing the integration (which involves expanding and completing the square) we find that $x_k$ is a Gaussian with mean $F_k m_k-1$ and variance $F_k P_k F_k ^T + Q_k$.
I don't understand when I insert that two gaussian in prediction formula how is possible to get that mean and that variance, there we have the product of two gaussian distribution but with different random variables maybe that's a gaussian? but then we have an integral of the resulting distribution. Can someone clarify me this?
Thank you

gaussian-integral kalman-filter

share|cite|improve this question

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61

$endgroup$

share|cite|improve this question

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61

share|cite|improve this question

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61

asked Mar 18 at 11:09

Francesco FisherFrancesco Fisher

61