9
votes
Accepted
What are the advantages and disadvantages of Kalman filter compared with FIR, IIR and low pass filter to filter data with noise?
Kalman filters really aren't that special, and you seem to be missing the point of a Kalman filter. A Kalman filter is really just a generally time-varying, generally IIR, generally multi-input ...
- 12.9k
8
votes
Accepted
Kalman filter after lowpass filter: bad idea?
The Kalman filter is the optimal filter under various assumptions. You need to check whether those assumptions hold in your case:
a) the model perfectly matches the real system,
b) the entering noise ...
- 25.9k
7
votes
Accepted
Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter
We can build a non linear dynamic model in order to estimate the parameters of a sine signal.
Let's model the signal as $ a \sin \left( \phi \right) $ where $ \phi $ is the instantaneous phase. So the ...
- 20.2k
7
votes
Kalman Filter on Sinusoidal Signal
This isn't quite what you're asking, because it neglects the amplitude, $A$, but it's a relatively straightforward example of application of an extended Kalman filter to the frequency tracking problem....
- 25.9k
7
votes
Accepted
What sensors can be fused using the Kalman Filter framework
Remark: I will answer this using the Linear framework of the Kalman Filter but the idea is the same.
The Kalman Filter basically propagate and fuses Gaussian Distributions in order to calculate the ...
- 20.2k
6
votes
Accepted
Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?
Well, in continuous time, a sinusoid with a bias can be seen as the output of the linear system
\begin{align*}
\begin{bmatrix}\dot x_1\\\dot x_2\\\dot x_3\end{bmatrix} &= \begin{bmatrix}0 & 1 ...
- 768
6
votes
Kalman Filter Motion model with moving sensors
I find the discussion of the "Converted Measurement Kalman Filter" in "Multitarget-Multisensor Tracking: Principles and Techniques", 1995, by Yaakov Bar-Shalom and Xiao-Rong Li to ...
5
votes
Why Does the Kalman Filter Remove Only Gaussian Noise?
First of all let us assure that a Kalman filter (estimator) does not only remove Gaussian noise, but can remove (with certain success) any other type of noise as long as it's designed accordingly.
...
- 28.4k
5
votes
Layman Description of the Kalman Filter
Simple Description
Imagine you're in a car that is traveling at 70MPH with cruise control. Because the cruise control isn't perfect, your actual speed might vary slightly. This imperfection is called ...
- 902
5
votes
Kalman Filter: Why do we decrease the state uncertainty regardless of the current measurement?
The Kalman filter is one of those interesting algorithms which are completely impenetrable if you don't have the underlying math background (multivariate statisics, in this case), but become utterly ...
- 12.9k
5
votes
Accepted
Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)
We each have different life experiences to fuel our intuition, but try this one out:
Let $\mathbf A = 1$ and $\mathbf Q = 0$, and $\mathbf C = 1$ -- i.e., the actual state variable just doesn't change,...
- 12.9k
4
votes
What Is the Relationship Between a Kalman Filter and Polynomial Regression?
I suggest this reference regarding the comparison between least-squares and Kalman filters :
Fundamentals of Kalman Filtering: A Practical Approach by P. Zarchan & H. Mussof
Especially Chapter 3 ...
- 41
4
votes
What Is the Relationship Between a Kalman Filter and Polynomial Regression?
A lot has been said already, allow me to add some comments:
Kalman filters are an application of Bayesian probability theory, which means that "a priori information" or "prior uncertainty" can (and ...
4
votes
Removing drift from integration of accelerometer data
I can say a couple of things about this problem since I have been working on a similar one for a few weeks. First thing to note is that you should subtract the mean of a section of noise from your ...
- 41
4
votes
Accepted
Kalman filter for tracking sinusoidal motion
Assume that the amplitude remains constant as well as the angular frequency $\omega$. The phase will be predicted using $\phi_k=\phi_{k-1} + \omega T_s$
The measurement matrix usually denoted as H ...
- 618
4
votes
Accepted
How to choose the "best" measurment (from a given set) as input for a kalman filter?
Question: Which parameter is suitable to indicate how "good" the
measurement fits to the Kalman filter?
To estimate a quality of association you can use likelihood function. The likelihood ...
- 388
4
votes
Accepted
Unscented Kalman Filter Equations for Constant Turn Rate and Velocity Process Model
From a statistical point of view, the noise parameters are zero mean gaussian distribution and that does not mean that at all times the value of noise would be zero. All it says is that if you were to ...
4
votes
Kalman Filter Sensor Processing
As with any question like this, the answer is: It depends.
What does it depend on? Your signal model.
If your signal model generates $X$ and $Y$ axis velocities independently from each other so that ...
- 25.9k
4
votes
What is the value of $0.01\log_{10}$?
Differences in log scales correspond to ratios of the underlying values. Saying you are within .01 on a $\log_{10}$ scale means the true value is within $10^{-.01}$ and $10^{.01}$ of the stated value,...
- 7,590
4
votes
Layman Description of the Kalman Filter
KF is actually a mixture of a deterministic state propagator and a statistical estimator.
Despite it's name including the term filter, Kalman filter is not a simple frequency selective one. It's ...
- 28.4k
4
votes
How to Reduce Phase Lag Caused by Kalman Filter
Have you considered trying a constant jerk model as opposed to a constant acceleration model? Perhaps a higher order model would capture the acceleration better. See, for instance:
K. Mehrotra and P. ...
- 41
4
votes
Accepted
How to Reduce Phase Lag Caused by Kalman Filter
What you're experiencing is the transient lag of the Kalman Filter.
The Kalman Filter, using the Measurement and Process Noise balances between begin very adaptive to being an aggressive smoother.
In ...
- 20.2k
4
votes
Accepted
How to handle a logarithmic term in Kalman filter?
First of all, you're trying to evaluate the derivative of an exponential. If the base of the exponential is positive, the derivative exists. However, if the base is negative, the derivative does not ...
- 3,787
4
votes
Recommendation for courses / studies on digital signal processing
I've kind of grouped your subjects into larger overall subjects.
Note that there's a lot of overlap here, with the possible exception of actually making it work in a microprocessor (except -- in my ...
- 12.9k
4
votes
Accepted
Kalman Filter on Sinusoidal Signal
I'm copying my answer to Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter which solves a more general problem with example code:
We can build a non linear ...
- 20.2k
4
votes
What sensors can be fused using the Kalman Filter framework
Are there types of measurements that are not compatible for sensor fusion? Can any measurement be fused to better inform the underlying model?
Any sensor that gives you more information about the ...
- 12.9k
3
votes
Removing drift from integration of accelerometer data
Double integration amplifies any offsets, non-linearities and noise. These can't be removed without the use of some type of external reference point measurements (e.g. not from the accelerometer) or ...
- 35.6k
3
votes
Accepted
Where to get transtion matrix for Kalman filter?
Simple: if you do not have a model, you cannot apply the Kalman filter. Or you could and make up a model, but you cannot expect any of the optimality properties of the filter to hold. Based on that ...
- 25.9k
Only top scored, non community-wiki answers of a minimum length are eligible