Inertial navigation system using kalman filter

In summary: I'll look through my notes from my stochastic class a while back for you in a few days.@Cyrus,,,, thanks but i suppose the mathematical model of inertial navigation system can be found in some aerospace subjects,,,thanks in anticipation,,,,,i have read the kalman filter theory and all that..but I am interested in mathematical model(state space model) of inertial navigation system...thanks,,,
  • #1
mehvishanwar
4
0
Hello,

Im working on estimation of inertial navigation system using kalman filtering.
Can anyone help me finding the state space model of inertial navigation system used to estimate the states via kalman filter.

An early response is needed.Thanks in advance.
 
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  • #3
i have read the kalman filter theory and all that..
but I am interested in mathematical model(state space model) of inertial navigation system...
thanks,,,
 
  • #4
I assume what you mean to ask is a state space model of your sensor dynamics. I'd ask DH, he might be able to point you in the right direction.

I'll look through my notes from my stochastic class a while back for you in a few days.
 
  • #5
@ Cyrus,,,, thanks but i suppose the mathematical model of inertial navigation system can be found in some aerospace subjects,,,
thanks in anticipation,,,,,
 
  • #6
Last edited by a moderator:
  • #7
@mughliens,,,, u told me the standard format of the kalman filter but i need the mathematical model of inertial navigation system.
 
  • #8
mehvishanwar said:
Can anyone help me finding the state space model of inertial navigation system used to estimate the states via kalman filter.
This is not an appropriate question for this internet forum, or for any internet forum. The reason it is inappropriate is that it is far too open-ended. You are asking me to write a book. In fact, not just a book, but multiple books, multiple journals, multiple conference proceedings, ...!

What are you trying to do? What is your mathematical background? What have you found in your own research into this subject matter? We do not do people's homework at this site. We help you do your own homework. You need to do some work before we can help you.
 
  • #9
D H said:
This is not an appropriate question for this internet forum, or for any internet forum. The reason it is inappropriate is that it is far too open-ended. You are asking me to write a book. In fact, not just a book, but multiple books, multiple journals, multiple conference proceedings, ...!

What are you trying to do? What is your mathematical background? What have you found in your own research into this subject matter? We do not do people's homework at this site. We help you do your own homework. You need to do some work before we can help you.

I'd personally appreciate any good journal articles you might know on the subject to read in my spare time. I know the theory, but it would be nice to read about some actual applications of KF. It gets to be dense reading very quickly. I have the Hawng book: "Introduction to Random Signals and Applied Kalman Filtering, 4th Ed." I should go back and read that when I have time.
 
  • #10
mehvishanwar said:
@mughliens,,,, u told me the standard format of the kalman filter but i need the mathematical model of inertial navigation system.

The beauty of links to Wikipedia is that the articles include many references from which the information is summarized. In the case of the Kalman Filter article, there are 19 such references. Have you tried printing the references and trying your local library?
 
  • #11
Cyrus said:
I'd personally appreciate any good journal articles you might know on the subject to read in my spare time. I know the theory, but it would be nice to read about some actual applications of KF. It gets to be dense reading very quickly. I have the Hawng book: "Introduction to Random Signals and Applied Kalman Filtering, 4th Ed." I should go back and read that when I have time.
Minor correction: The authors of "Introduction to Random Signals and Applied Kalman Filtering" are Brown and Hwang, and they haven't come out with a 4th edition yet.

Texts
"Introduction to Random Signals and Applied Kalman Filtering" by Brown and Hwang is one of the key texts on the subject. That book has grown in size and scope over the years. The first edition was a nice compact 52 pages. It is now ten times as long. Another good book on the subject is "Applied Optimal Estimation" by Gelb.


Classes
Here is the SIGGRAPH 2001 class on "An Introduction to the Kalman Filter": http://www.cs.unc.edu/~tracker/media/pdf/SIGGRAPH2001_CoursePack_08.pdf

There are lots of commercial classes on Kalman filters as well. Some are boondoggles (the last day is a field demonstration of a Kalman filter in action -- typically on a yacht, cash bar). I never could convince my employer to send me to one of those.


Journals
Almost every issue of AIAA Journal of Guidance, Control, and Dynamics has at least one article on Kalman filters and their application.


Conferences
The following conferences inevitably have multiple papers on Kalman filters and their application:
AAS/AIAA Astrodynamics Specialist Conference
AAS/AIAA Space Flight Mechanics Meeting
AIAA Guidance, Navigation, And Control Conference

The first is sometimes called the GN&Ski conference because it is ofttimes held at a ski resort and has very long lunch breaks (more than enough time to hit the slopes between sessions). Nice boondoggle if you can convince your employer to send you there.
 
  • #12

What is an inertial navigation system (INS)?

An inertial navigation system is a navigation tool that uses a combination of accelerometers, gyroscopes, and other sensors to track an object's position, orientation, and velocity. It is commonly used in aircraft, spacecraft, and submarines, as well as in other applications where precise navigation is required.

How does an inertial navigation system work?

An INS works by measuring the accelerations and rotations of an object in three-dimensional space. These measurements are then integrated over time to determine the object's position, velocity, and orientation. In order to maintain accuracy, the INS must constantly update its measurements and calculations through a process called "dead reckoning."

What is a Kalman filter?

A Kalman filter is a mathematical algorithm that is used to estimate the state of a system by combining measurements with predictions from a mathematical model. In the context of an INS, the Kalman filter is used to combine data from the inertial sensors with other sources of information, such as GPS, to improve the accuracy of the navigation system.

What are the benefits of using a Kalman filter in an inertial navigation system?

The use of a Kalman filter in an INS can improve the accuracy of the navigation system by reducing errors caused by noise, bias, and other sources of uncertainty. It also allows for the integration of different types of sensor data, making the overall system more robust and reliable.

What are some potential limitations of an inertial navigation system with a Kalman filter?

While inertial navigation systems using Kalman filters are highly accurate and reliable, they can be affected by factors such as sensor drift, environmental conditions, and external disturbances. Additionally, the initial calibration and ongoing maintenance of an INS can be complex and time-consuming.

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