18

Roughly speaking, they are the amount of noise in your system. Process noise is the noise in the process - if the system is a moving car on the interstate on cruise control, there will be slight variations in the speed due to bumps, hills, winds, and so on. Q tells how much variance and covariance there is. The diagonal of Q contains the variance of each ...


7

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 model could be also written as $ a \sin \left( \omega t + \psi \right) $. Then the model can be: $$ {a}_{k} \sin \left( {\omega}_{k} {t}_{k} + \psi \right) = {...


6

So this is just the start of an answer. I'll have to keep updating it as I go. The first attempt is to say that the quantities you are interested in are the location of the center of the four LEDs, and the roll, pitch, and yaw (rotation angles) of the LEDs. That means your Kalman FIlter state will be: $$ \mathbf{x}_k = \left[x_k\ y_k\ \alpha_k\ \beta_k\ \...


5

To track a frequency ramp with a Phase lock loop, with zero steady state error requires a type 3 PLL Loop; which means three integrations (DC Poles) in the open loop gain (your NCO would be one of the integrators and your loop filter needs to provide the other two). Stabilizing such a system becomes more challenging but here is one reference paper detailing ...


5

In addition to Peter's answer, if you have a nonlinear system that is well-behaved in a sense of being only mildly nonlinear or at least exhibiting no discontinuities, special variants of the Kalman filter can still be applied. Extended Kalman Filter This filter linearizes the system at the current state of the system using a first order Taylor Series ...


5

Well, let's look at the two issues: 1) linearity and 2) Gaussianity. Linearity If you're imaging moving 3D objects (people) with a single camera, then you're working with a 2D projection of those 3D objects. That dimensionality reduction can cause non-linearities to appear. Take a 2D to 1D example: an object moving in a circle in 2D. The object is ...


4

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 considers not only residual but also uncertainty and represented as scalar value: $$\mathcal{L} = \frac{1}{\sqrt{2\pi S}}\exp [-\frac{1}{2}\mathbf y^\mathsf T\mathbf S^...


3

This is exactly where the Dynamic Model comes into play. The whole idea of the Kalman Filter is that you have a model which connects between variables which are measured to those which are not measured (Estimation) or measured differently (Fusion). Since the velocity is the derivative of the location over time you have a model which connects them both. Once ...


3

You should parameterize the path as a parameter of time. You can do that off line with accurate measurements of the path. Then use Non Linear Least Squares to find the best match between the reads of the IMU to the model. From there you'd be able to match the speed.


3

In general, a kernel is a function that acts as a parameter to some algorithm. Filtering: For example, it's possible to call the impulse response of a filter $h[n]$ a kernel, so that it is the parameter that defines the filter operation: $$ y[n] = h[n] * x[n]. $$ The use of the term kernel in the filtering context is much more common in 2D filtering or ...


3

From my understanding of the linked answer which you base your algorithm on I would conclude that the FT will detect all the edges in the frame domain, so all the moving objects. If you want to localize the transform information, I suggest you use a wavelet transform with a complex wavelet. Instead of correlating the signal with $e^{i2\pi fx}$ as FT does it ...


2

From my experience, I have successfully utilized Leo Grady's Random Walks method for this. The code is also available here. It works very well and can easily be made to run in real-time depending on the contour and image size. You could watch the video from my implementation here. Note that though, it might perfom differently than the original.


2

Main thing is that in the first frame it will be required to select the object of detection because it is obvious that the algorithm will not know automatically which object you want to track if a number of things will be moving in the video scene.Lucas-Kannade method is one of the methods which can detect moving objects in a given video frame . If you do ...


2

I don't think you have any choice other than to use the same number of bins for each observation. Otherwise not only will you not be able to average the histograms, you will also not be able to compare them. And you definitely need to change the histogram slowly, i. e. $$h = (1 - \alpha)h + \alpha h_{obs}$$ where $h$ is your "moving average" histogram, $h_{...


2

The short answer is: use your optical flow algorithm to get the best-fit warping of some number of previous images into your current image. Then assume that your object is moving on a line through the images, and do some kind of robust best-fit to that line. When the object reappears it is more likely to be near the predicted projection of the line than ...


2

To better deal with occlusions, my idea would be to separate this problem into detecting if: the 1st door is in position fully opened (1) the 1st door is in position fully closed (2) the 2nd door is in position fully opened (3) the 2nd door is in position fully closed (4) To tackle either of these problem, I would apply the following algorithm let's say ...


2

I think the magic acronym is CHCV, "constant heading constant velocity". This returns at least a few results on Google.


2

For $y\approx y_0$ you have $$\begin{align}\sqrt{p_m(y)q_m}&\approx\sqrt{p_m(y_0)q_m}+\frac{p_m(y)-p_m(y_0)}{2\sqrt{p_m(y_0)}}\sqrt{q_m}\\&=\frac12\sqrt{p_m(y_0)q_m}+\frac12 p_m(y)\sqrt{\frac{q_m}{p_m(y_0)}}\tag{1}\end{align}$$ So the function you're approximating is $f(x)=\sqrt{x}$, with $x=p_m(y)$, and you do this in the vicinity of the value $a=...


2

Every system will be different, so it’s impossible to make a blanket statement that applies to everything, but IFF systems can be used to accomplish the task. The signal processing here can be as basic as looking for a predetermined pulse pattern, or require demodulation/decryption of some “special” signal. The Wikipedia article I linked covers the topic in ...


1

One reason is that higher frequencies are envisioned. With higher frequencies, the path loss grows (cf. Friis equation). Also, the wavelength is reduced and thus, $\lambda/2$ radiators start becoming quite small. The power you can radiate from a small aperture is limited as well so overall our power budget suffers. The only way out is directivity (cf. Friis ...


1

There are lots of examples on the web for GPS signal tracking at baseband. Look for "SoftGNSS" on GitHub. As far as converting from complex baseband to real IF, it's the opposite as what receivers normally do. You can certainly modulate a signal from complex baseband to real IF by multiplying the real part by and the imaginary part by and then ...


1

I think tracking motion of something like corner or handle of the window would work. Consider following procedure: 1. Track the corner of the windwo 2. If position of the corner changes more than X pixel(you determine X), change the STATE I suggest to use object tracking algorithms. I think the best candidate point would be corners of the window. For ...


1

Search for radar plot to track association. There's a lot of algorithms on this subject. To your question: The residual itself will not give you information without its associated covariance matrix Try a chi-squared test on it. Putting a threshold on this scalar is called gating and it's a first step of plot to track association.


1

I didn't read the paper but let me provide some intuition about object detection and tracking. When you try to track a target in a video, object detection algorithms might not be enough and you need to support the algorithm with target tracking methods in bayesian framework. It could be Kalman filter or particle filter. In particle filter or any Bayesian ...


1

First I would recommend filling in the contour of the toy - in case it looks like the one in the second image. You could do this by analyzing the hierarchy output from findContours: make white all regions having a parent or by using an iterative morphological operations (not directly implemented in OpenCV). Once the toy is nice and fat (not just the edge),...


1

However, in Matlab it seems that to implement this I would need to assume either constant acceleration or velocity which is not the case since the rodent is freely moving. First of all you can choose any dynamic model not only constant acceleration or velocity. Secondly, In Kalman filter you don't need to have exact dynamic model. consider state dynamic ...


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