Kalman filter with sensors having different sampling rate
$begingroup$
I would like to implement Kalman filter scheme with two different kind of sensors - say 9DOF IMU (gyro/accelerometer/magnetometer) and GPS sensor (position/velocity/altitude).
Problem is, as i understand, classic Kalman and Extended Kalman filter schemes require sensor measurements to be synchronized. But GPS sensor measurements could be obtained ones/two times a second, as opposed to gyro/accelerometer/magnetometer measurements which available 100 times a second.
So my question, how to fuse sensors with different sampling rates together?
data-analysis
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
$endgroup$
add a comment |
$begingroup$
I would like to implement Kalman filter scheme with two different kind of sensors - say 9DOF IMU (gyro/accelerometer/magnetometer) and GPS sensor (position/velocity/altitude).
Problem is, as i understand, classic Kalman and Extended Kalman filter schemes require sensor measurements to be synchronized. But GPS sensor measurements could be obtained ones/two times a second, as opposed to gyro/accelerometer/magnetometer measurements which available 100 times a second.
So my question, how to fuse sensors with different sampling rates together?
data-analysis
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
$endgroup$
$begingroup$
The usage of the tag "filters" is completely incorrect. Also, this is not mathematics.
$endgroup$
– user122283
Feb 28 '14 at 23:32
1
$begingroup$
Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: stats.stackexchange.com/questions/86332/…
$endgroup$
– littleO
Aug 4 '17 at 5:13
add a comment |
$begingroup$
I would like to implement Kalman filter scheme with two different kind of sensors - say 9DOF IMU (gyro/accelerometer/magnetometer) and GPS sensor (position/velocity/altitude).
Problem is, as i understand, classic Kalman and Extended Kalman filter schemes require sensor measurements to be synchronized. But GPS sensor measurements could be obtained ones/two times a second, as opposed to gyro/accelerometer/magnetometer measurements which available 100 times a second.
So my question, how to fuse sensors with different sampling rates together?
data-analysis
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
$endgroup$
I would like to implement Kalman filter scheme with two different kind of sensors - say 9DOF IMU (gyro/accelerometer/magnetometer) and GPS sensor (position/velocity/altitude).
Problem is, as i understand, classic Kalman and Extended Kalman filter schemes require sensor measurements to be synchronized. But GPS sensor measurements could be obtained ones/two times a second, as opposed to gyro/accelerometer/magnetometer measurements which available 100 times a second.
So my question, how to fuse sensors with different sampling rates together?
data-analysis
data-analysis
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
edited Mar 1 '14 at 18:20
HumpfreyJordan
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
asked Feb 28 '14 at 22:36
HumpfreyJordanHumpfreyJordan
212
212
$begingroup$
The usage of the tag "filters" is completely incorrect. Also, this is not mathematics.
$endgroup$
– user122283
Feb 28 '14 at 23:32
1
$begingroup$
Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: stats.stackexchange.com/questions/86332/…
$endgroup$
– littleO
Aug 4 '17 at 5:13
add a comment |
$begingroup$
The usage of the tag "filters" is completely incorrect. Also, this is not mathematics.
$endgroup$
– user122283
Feb 28 '14 at 23:32
1
$begingroup$
Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: stats.stackexchange.com/questions/86332/…
$endgroup$
– littleO
Aug 4 '17 at 5:13
$begingroup$
The usage of the tag "filters" is completely incorrect. Also, this is not mathematics.
$endgroup$
– user122283
Feb 28 '14 at 23:32
$begingroup$
The usage of the tag "filters" is completely incorrect. Also, this is not mathematics.
$endgroup$
– user122283
Feb 28 '14 at 23:32
1
1
$begingroup$
Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: stats.stackexchange.com/questions/86332/…
$endgroup$
– littleO
Aug 4 '17 at 5:13
$begingroup$
Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: stats.stackexchange.com/questions/86332/…
$endgroup$
– littleO
Aug 4 '17 at 5:13
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
So, from my understanding in your motion model will have inputs from some sensors (gyro/accelerometer/magnetometers) and your observer will be only the GPS?
The way I understand, the Kalman Filter should work in the frequency of the observer. In any other configuration you would be accumulating errors from your motion model and at some point your filter may diverge.
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
$endgroup$
add a comment |
$begingroup$
Well indeed, that's much more an engineering problem rather (or better, before) than mathematical.
Whatever manipulation you have to do on the data, first you must consider how much variable in time they are, how much noisy, and how many data of each you can memorize and work with.
That will determine the best trade-off among interpolating the slower sensor / filtering the quicker, in consideration of the advantage to get a more or less frequent output.
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
$endgroup$
add a comment |
$begingroup$
This is pretty much an engineering question, rather than a mathematics one. But fortunately, this is basically already solved in many books like Farrell or Titterton. Bad thing is, the answer is rather long.
To give you a heads up:
1-Magnetometer measurements are rarely used in practice for Aided Navigation, their quality is usually way too poor to fuse directly in a Kalman Filter. They may have other uses that you might want to analyze separately.
2-INS devices, you shouldn't require the user to provide you with estimated acceleration (either linear or angular). Instead, IMU measurements (angular rate and linear acceleration) are generally used directly for propagation of states, with Kalman corrections being used for GPS measurements to avoid divergence.
3-Normally, what you should do when the rate of sensors do not match, is that you should propagate states at a base sample rate (say 10Hz), and depending on your implementation you may propagate covariance only between measurements or all the time. Once a measurement arrives, you perform the Kalman correction, updating your covariance and your state.
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f694504%2fkalman-filter-with-sensors-having-different-sampling-rate%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
So, from my understanding in your motion model will have inputs from some sensors (gyro/accelerometer/magnetometers) and your observer will be only the GPS?
The way I understand, the Kalman Filter should work in the frequency of the observer. In any other configuration you would be accumulating errors from your motion model and at some point your filter may diverge.
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
$endgroup$
add a comment |
$begingroup$
So, from my understanding in your motion model will have inputs from some sensors (gyro/accelerometer/magnetometers) and your observer will be only the GPS?
The way I understand, the Kalman Filter should work in the frequency of the observer. In any other configuration you would be accumulating errors from your motion model and at some point your filter may diverge.
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
$endgroup$
add a comment |
$begingroup$
So, from my understanding in your motion model will have inputs from some sensors (gyro/accelerometer/magnetometers) and your observer will be only the GPS?
The way I understand, the Kalman Filter should work in the frequency of the observer. In any other configuration you would be accumulating errors from your motion model and at some point your filter may diverge.
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
$endgroup$
So, from my understanding in your motion model will have inputs from some sensors (gyro/accelerometer/magnetometers) and your observer will be only the GPS?
The way I understand, the Kalman Filter should work in the frequency of the observer. In any other configuration you would be accumulating errors from your motion model and at some point your filter may diverge.
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
answered Feb 10 '17 at 15:46
Daniel LucenaDaniel Lucena
1
1
add a comment |
add a comment |
$begingroup$
Well indeed, that's much more an engineering problem rather (or better, before) than mathematical.
Whatever manipulation you have to do on the data, first you must consider how much variable in time they are, how much noisy, and how many data of each you can memorize and work with.
That will determine the best trade-off among interpolating the slower sensor / filtering the quicker, in consideration of the advantage to get a more or less frequent output.
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
$endgroup$
add a comment |
$begingroup$
Well indeed, that's much more an engineering problem rather (or better, before) than mathematical.
Whatever manipulation you have to do on the data, first you must consider how much variable in time they are, how much noisy, and how many data of each you can memorize and work with.
That will determine the best trade-off among interpolating the slower sensor / filtering the quicker, in consideration of the advantage to get a more or less frequent output.
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
$endgroup$
add a comment |
$begingroup$
Well indeed, that's much more an engineering problem rather (or better, before) than mathematical.
Whatever manipulation you have to do on the data, first you must consider how much variable in time they are, how much noisy, and how many data of each you can memorize and work with.
That will determine the best trade-off among interpolating the slower sensor / filtering the quicker, in consideration of the advantage to get a more or less frequent output.
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
$endgroup$
Well indeed, that's much more an engineering problem rather (or better, before) than mathematical.
Whatever manipulation you have to do on the data, first you must consider how much variable in time they are, how much noisy, and how many data of each you can memorize and work with.
That will determine the best trade-off among interpolating the slower sensor / filtering the quicker, in consideration of the advantage to get a more or less frequent output.
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
answered May 9 '18 at 1:03
G CabG Cab
18.4k31237
18.4k31237
add a comment |
add a comment |
$begingroup$
This is pretty much an engineering question, rather than a mathematics one. But fortunately, this is basically already solved in many books like Farrell or Titterton. Bad thing is, the answer is rather long.
To give you a heads up:
1-Magnetometer measurements are rarely used in practice for Aided Navigation, their quality is usually way too poor to fuse directly in a Kalman Filter. They may have other uses that you might want to analyze separately.
2-INS devices, you shouldn't require the user to provide you with estimated acceleration (either linear or angular). Instead, IMU measurements (angular rate and linear acceleration) are generally used directly for propagation of states, with Kalman corrections being used for GPS measurements to avoid divergence.
3-Normally, what you should do when the rate of sensors do not match, is that you should propagate states at a base sample rate (say 10Hz), and depending on your implementation you may propagate covariance only between measurements or all the time. Once a measurement arrives, you perform the Kalman correction, updating your covariance and your state.
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
$endgroup$
add a comment |
$begingroup$
This is pretty much an engineering question, rather than a mathematics one. But fortunately, this is basically already solved in many books like Farrell or Titterton. Bad thing is, the answer is rather long.
To give you a heads up:
1-Magnetometer measurements are rarely used in practice for Aided Navigation, their quality is usually way too poor to fuse directly in a Kalman Filter. They may have other uses that you might want to analyze separately.
2-INS devices, you shouldn't require the user to provide you with estimated acceleration (either linear or angular). Instead, IMU measurements (angular rate and linear acceleration) are generally used directly for propagation of states, with Kalman corrections being used for GPS measurements to avoid divergence.
3-Normally, what you should do when the rate of sensors do not match, is that you should propagate states at a base sample rate (say 10Hz), and depending on your implementation you may propagate covariance only between measurements or all the time. Once a measurement arrives, you perform the Kalman correction, updating your covariance and your state.
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
$endgroup$
add a comment |
$begingroup$
This is pretty much an engineering question, rather than a mathematics one. But fortunately, this is basically already solved in many books like Farrell or Titterton. Bad thing is, the answer is rather long.
To give you a heads up:
1-Magnetometer measurements are rarely used in practice for Aided Navigation, their quality is usually way too poor to fuse directly in a Kalman Filter. They may have other uses that you might want to analyze separately.
2-INS devices, you shouldn't require the user to provide you with estimated acceleration (either linear or angular). Instead, IMU measurements (angular rate and linear acceleration) are generally used directly for propagation of states, with Kalman corrections being used for GPS measurements to avoid divergence.
3-Normally, what you should do when the rate of sensors do not match, is that you should propagate states at a base sample rate (say 10Hz), and depending on your implementation you may propagate covariance only between measurements or all the time. Once a measurement arrives, you perform the Kalman correction, updating your covariance and your state.
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
$endgroup$
This is pretty much an engineering question, rather than a mathematics one. But fortunately, this is basically already solved in many books like Farrell or Titterton. Bad thing is, the answer is rather long.
To give you a heads up:
1-Magnetometer measurements are rarely used in practice for Aided Navigation, their quality is usually way too poor to fuse directly in a Kalman Filter. They may have other uses that you might want to analyze separately.
2-INS devices, you shouldn't require the user to provide you with estimated acceleration (either linear or angular). Instead, IMU measurements (angular rate and linear acceleration) are generally used directly for propagation of states, with Kalman corrections being used for GPS measurements to avoid divergence.
3-Normally, what you should do when the rate of sensors do not match, is that you should propagate states at a base sample rate (say 10Hz), and depending on your implementation you may propagate covariance only between measurements or all the time. Once a measurement arrives, you perform the Kalman correction, updating your covariance and your state.
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
answered Oct 29 '18 at 12:23
MefiticoMefitico
926117
926117
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f694504%2fkalman-filter-with-sensors-having-different-sampling-rate%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
The usage of the tag "filters" is completely incorrect. Also, this is not mathematics.
$endgroup$
– user122283
Feb 28 '14 at 23:32
1
$begingroup$
Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: stats.stackexchange.com/questions/86332/…
$endgroup$
– littleO
Aug 4 '17 at 5:13