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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 ...
TimWescott's user avatar
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8 votes
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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 ...
Peter K.'s user avatar
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7 votes
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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 ...
Royi's user avatar
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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....
Peter K.'s user avatar
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7 votes
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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 ...
Royi's user avatar
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6 votes
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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 ...
LJSilver's user avatar
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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 ...
Steve Gilbert's user avatar
5 votes
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How do I choose the parameters of a Kalman filter?

Is this so far a reasonable scenario / approach to the Kalman filter? Answer 1: Yes, your model looks reasonable. You're treating the acceleration as constant, however. If it will change in your ...
Emiswelt's user avatar
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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. ...
Fat32's user avatar
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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 ...
TimWescott's user avatar
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5 votes
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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,...
TimWescott's user avatar
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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 ...
Florian D's user avatar
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 ...
Bart Van Hove's user avatar
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 ...
K Puri's user avatar
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4 votes
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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 ...
Dr. Nir Regev's user avatar
4 votes
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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 ...
Gluttton's user avatar
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4 votes
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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 ...
Kartik Madhira's user avatar
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 ...
Peter K.'s user avatar
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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,...
Cedron Dawg's user avatar
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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. ...
Luezoid's user avatar
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4 votes
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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 ...
Royi's user avatar
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4 votes
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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 ...
Ben's user avatar
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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 ...
TimWescott's user avatar
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4 votes
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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 ...
Royi's user avatar
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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 ...
TimWescott's user avatar
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3 votes

Apply Kalman filter to remove process noise, given zero measurement error

You're misunderstanding how the Kalman filter framework works. Your measurements are a reflection of what the underlying state of the system is at each time instant. If you have zero measurement ...
Jason R's user avatar
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3 votes
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Why is this matrix invertible in the Kalman gain?

Note that $\mathbf{P} _{k\mid k-1}$, just like $\mathbf{R}_k$, is also a covariance matrix, and for this reason it is (at least) positve semi-definite, i.e., $\mathbf{y}^T\mathbf{P}_{k\mid k-1}\mathbf{...
Matt L.'s user avatar
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3 votes
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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 ...
Peter K.'s user avatar
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