Kalman filters and matrix inverses

Started by Rune Allnor in comp.dsp13 years ago 4 replies

Hi all. I'm reading about Kalman filters in Durbin & Koopman: "Time series analysis by state space methods". The filtering equations are ...

Hi all. I'm reading about Kalman filters in Durbin & Koopman: "Time series analysis by state space methods". The filtering equations are y[t] = Z[t]a[t] + e[t] a[t+1] = T[t]a[t] + R[t]n[t] where e[t] ~ N(0,H[t]) n[t] ~ N(0,Q[t]) a[1] ~ N(A[1],P[1]). A bit into the derivations, a matrix F appears as F[t] = Z[t]P[t]Z'[t] + H[t]. The inverse of F is used as a[...


Kalman filter with accelerometer

Started by blackmangoes in comp.dsp14 years ago 26 replies

I only have an 2d accelerometer availabe but it is noisy, so I want to do better than just doing low pass filtering. I am wondering if it...

I only have an 2d accelerometer availabe but it is noisy, so I want to do better than just doing low pass filtering. I am wondering if it is possible to do kalman filtering with just an accelerometer. Let's say I am just concerning in position and velocitly in 1d space for now. I am a little confused what ithe input u in x(t+1) = Ax(t) + Bu(t) + w equation and what the output y in y(x) = Cx(t) ...


Norm of Covariance Matrix

Started by WalkyTalky in comp.dsp11 years ago 1 reply

Hi to all, I have been also confused about the covariance matrix of the Kalman filter. I have a Kalman filter which has 9 states and therefore...

Hi to all, I have been also confused about the covariance matrix of the Kalman filter. I have a Kalman filter which has 9 states and therefore 9 X 9 error covariance matrix which is updated at the every time step. My question is; How can i be sure that the Kalman filter works properly by using the error covariance matrices. Should the norm of the error covariance matrix converge to ze...


How many scalar equations for 4-state Kalman filter

Started by fl in comp.dsp6 years ago 1 reply

Hi, I read a paper it said that "For a 4-state Kalman filter, all the Kalman filter equations can be expressed as 30 scalar...

Hi, I read a paper it said that "For a 4-state Kalman filter, all the Kalman filter equations can be expressed as 30 scalar equations." Because 30 is not an integer multiples of 4, I do not know how it get 30 scalar equations. Could you help me on that? Thanks,


Q matrix tuning - Kalman filtering

Started by res in comp.dsp12 years ago

Hi there, I am using a Kalman filter to determine trajectory and attitude of a terrestrial vehicle, with the measurements of an INS/GPS...

Hi there, I am using a Kalman filter to determine trajectory and attitude of a terrestrial vehicle, with the measurements of an INS/GPS system. I have some difficulties in choosing the right values of the Q matrix. Are there any methods to choose them? I heard about Bartlett's method but I don't know how to make it work properly... Thanks a lot for your help and sorry for my English! ...


How did you learn to use kalman filters?

Started by Sven in comp.dsp13 years ago 2 replies

Hello I wonder which path I should take to learn about Kalman filtering and how to se them practically. What do I need to...

Hello I wonder which path I should take to learn about Kalman filtering and how to se them practically. What do I need to learn? How did you do?


Help, want to learn about and use Kalman filtering

Started by Beginner in comp.dsp12 years ago 8 replies

I would want to learn to use and understand Kalman filtering. Which books should i read to achieve that? My algebra math skills are at...

I would want to learn to use and understand Kalman filtering. Which books should i read to achieve that? My algebra math skills are at elementary linear algebra level.


Very small time step in Discrete Kalman filter

Started by OKH in comp.dsp13 years ago 1 reply

Dear all, I thought to post the message here, because I asked everybody whom I could ask and looked in the books I could find and ... because...

Dear all, I thought to post the message here, because I asked everybody whom I could ask and looked in the books I could find and ... because I just want to talk about it. :) If you encountered a similar problem, I would really appreciate any discussion. I'm working on implementing Kalman filter in the the numerical code (fortran). I have a very large linear system (thousands of equatio...


Calculating noise covariance matrix in Kalman filtering.

Started by chammidhan in comp.dsp10 years ago 2 replies

Hello all.. I am developing a vehicle acceleration pattern capturing device using accelerometers. I intend to use a Kalman filter for noise...

Hello all.. I am developing a vehicle acceleration pattern capturing device using accelerometers. I intend to use a Kalman filter for noise reduction in the accelerometer data. I saw elsewhere the following model for the state of the system for a similar problem. s(k+1)=s(k)+T*v(k)+0.5*T^2*a(k) v(k+1)=v(k)+T*a(k) a(k+1)=a(k) My first question is, is this model correct regarding the acce...


EKF for a basic underwater navigation situation

Started by elspeth in comp.dsp13 years ago 4 replies

Hello, I am new to Kalman filters but know the basics fairly well. I have a device that will be pulled behind a boat (in the y direction) with...

Hello, I am new to Kalman filters but know the basics fairly well. I have a device that will be pulled behind a boat (in the y direction) with several accelerometers and a few gyros - I implemented the linear discrete Kalman filter but got a terrible integration offset because obviously I have to integrate the accelerometers twice and the gyros once with the transition matrix A, state vector xk, ...


Kalman Assumption

Started by Cagdas Ozgenc in comp.dsp9 years ago 22 replies

Hello, In Kalman filtering does the process noise have to be Gaussian or would any uncorrelated covariance stationary noise satisfy...

Hello, In Kalman filtering does the process noise have to be Gaussian or would any uncorrelated covariance stationary noise satisfy the requirements? When I follow the derivations of the filter I haven't encountered any requirements on Gaussian distribution, but in many sources Gaussian tag seems to go together. Thanks


Kalman Filter Post processing of IMU data

Started by Kiwi23 in comp.dsp11 years ago 3 replies

Hello All I'm quite a newbie to the Kalman Filter. I'm using a 3 axis accelerometer and gyroscope data to calculate angle, and from this 3D...

Hello All I'm quite a newbie to the Kalman Filter. I'm using a 3 axis accelerometer and gyroscope data to calculate angle, and from this 3D position (I also have a magnetometer, but its outputs are too unreliable). I'm still trying to understand how to apply the data I'm getting to the filter equations (if you feel like explaining that it would be great :D). Anyway, I have the advantage in...


Kalman filter tutorial for the Dummy's dumber cousin?

Started by roschler in comp.dsp9 years ago 5 replies

I'm a veteran computer programmer with a Math background that came to a screeching halt at about the 1st semester of Calculus. However, I think...

I'm a veteran computer programmer with a Math background that came to a screeching halt at about the 1st semester of Calculus. However, I think I'm wasting time implementing filtering solutions that could be better served by a Kalman filter. Here's a recent example. I am interfacing with a Gyroscope, that for some enigmatic reason seems to put out, via the API call I make to its interface ...


Kalman Filtering

Started by mj in comp.dsp11 years ago 2 replies

Hi My final year project on Inertial navigation system using Gyro and Acclerometer. for filtering i calculate the bias,angular random walk and...

Hi My final year project on Inertial navigation system using Gyro and Acclerometer. for filtering i calculate the bias,angular random walk and RRW variance from Allan variance, But i dont know how to use it in Kalman filter equation. Can anybody tell me How to write the matrix x(k+1) = Ax(k)+ bu(k)+w(k) y(k) = cx(k)+z(k) i am measuring acceleration from that i have to calculate the velocity a...


kalman filter - python implementation

Started by grzegorz g. in comp.dsp9 years ago 24 replies

Hi, I try to implement kalman filter (Python 2.6), and I have a problem with covariance matrix, which in some time start to have crazy...

Hi, I try to implement kalman filter (Python 2.6), and I have a problem with covariance matrix, which in some time start to have crazy values (going to minus infinity) and in effect my estimations are also crazy. For example: observation: [[ -0.21369917] [ 1.76860362] [ 5.57973197] [ 12.32486812] [ 20.49270401] [ 31.83940345] [ 41.51642446]] X_estimate = [ 0.00000000e+00 ...


Kalman filtering...

Started by gino in comp.dsp13 years ago 9 replies

I am looking for Matlab codes for using Kalman filters to estimate unknown parameters, which, I hope, can be an alternative to the maximum...

I am looking for Matlab codes for using Kalman filters to estimate unknown parameters, which, I hope, can be an alternative to the maximum likelihood estimate of the parameters... How to do that? And could anybody point me to some samples, tutorials, resources, examples, Matlab codes? Thanks a lot!


Kalman filter

Started by mik in comp.dsp14 years ago 5 replies

I have a simple question (with a complex answer i suppose): is it possible to decouple gravity and inertial acceleration, or better filter out...

I have a simple question (with a complex answer i suppose): is it possible to decouple gravity and inertial acceleration, or better filter out gravity from measures taken ONLY with a triaxial accelerometer (without using other sensors as gyroscopes ecc); if it is, can a Kalman filter minimize effect of gravity? This message was sent using the Comp.DSP web interface on www.DSPRelated.com...


Kalman Filter for predicing the center of a filter

Started by Mat in comp.dsp13 years ago 39 replies

X-N-Archive:yes I'm interested in methods useful for predicting the center of a simple moving average with window length of 20 to 40...

X-N-Archive:yes I'm interested in methods useful for predicting the center of a simple moving average with window length of 20 to 40 periods. If a Kalman filter or some other dsp method is not useful for this what other math or statistical related newgroup might know? I'm looking for sources, referrences or someone who actually used an algorithm that is helpful in predicting the smooth...


signals applied to a kalman filter or other estimator

Started by Kai in comp.dsp11 years ago 1 reply

Hello, I'm using a Kalman-filter for state estimation issues. My question is dealing with the signals that I apply to the filter. Let's...

Hello, I'm using a Kalman-filter for state estimation issues. My question is dealing with the signals that I apply to the filter. Let's think of an analog sensor with a changeable low-pass filter at its output. I could think of tuning the RC-elements to a bandwith of let's say 40 Hz or 400 Hz. When I measure the noise levels and variances I can use these values in both cases to feed my K...


Unscented kalman filter math question

Started by hagai_sela in comp.dsp9 years ago 5 replies

Hi, I am trying to implement an unscented kalman filter, as described here: http://cslu.cse.ogi.edu/nsel/ukf/node6.html My problem is with...

Hi, I am trying to implement an unscented kalman filter, as described here: http://cslu.cse.ogi.edu/nsel/ukf/node6.html My problem is with equation 18 - What does the multiplication mean? As far as I understand, the first (Yi - y^) is a row vector, and the second one is a column vector, therefore this is a dot product. But then the result of the expression inside the sigma is a scalar, and ...