9

Here is what I experimented with: Use ELSD to generate elliptic contours. You could basically use any edge detector, but since in the following stages I will benefit from circle detectors, it is good to already have some geometrical edges. Here is what the output looks like:               &...


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

I will tell you something, even if it is differntiable, use Unscented Kalman Filter for any non linear case. This flavor of Kalman Filter, based on the Unscented Transform, is almost always superior to the Extended Kalman due to its properties. The main reason is it is able to better predict the mean and variance (Which all Kalman Filter needs) of the ...


3

How to determine the initial position pdf distribution? I have a Bluetooth beacon to detect the starting position. Particle filter requires a cluster of point at the start, right? No, the distribution of a particle filter does not need to be a cluster when it starts. A classic case is for a robot to figure out where it is. At first it does not know where ...


2

Your question is about the resampling step, and let's focus on that. Resampling is used in particle filtering to counteract "sample impoverishment" that is the fact that some particles may have very low weights. This is a waste of resources as you want to describe your probability distribution ate best. You should note that it should not interfere (a ...


1

I implemented many types of particle filter for one sensor. Since your case(i.e sensor fusion) includes multiple sensors, I try to make analogy using KF which I used many times for sensor fusion. In KF you perform time update and measurement update for each upcoming measurement sequentially. And if your measurements are asyncronous you modify your time ...


1

There is a strict difference between KF and ML. Former provides density of the state while the latter provides a point estimate. So, they are not alternative of each others exactly. But, sure you might use ML instead of KF if you need point estimate.


1

why do we need the particle filter? When your model is non-linear there is no analytical solution to obtain the PDF of the state. The Kalman filter/smoother can't be applied in the sense that it is not optimal. The particle filter is one method to obtain an estimate of state PDF in a sequential setup. can't we just do ML estimation Dependent on the ...


1

Let $\mathbf z = [z_1, z_2]^T$ be the observations and $\mathbf x = [x_1, x_2]^T$ be the hidden states, and the observation model is $z_i = x_i + n_i$ for $i=1,2$. Here $n_i$'s are independent (but not identical, since the noise has different distributions). So I would like to know under which restrictions the first step is allowed (I for example know ...


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

The following papers are good resources: Gordon, N. J.; Salmond, D. J. and Smith, A. F. M. (1993). "Novel approach to nonlinear/non-Gaussian Bayesian state estimation". IEE Proceedings F on Radar and Signal Processing 140 (2): 107–113. Arulampalam, M.S.; Maskell, S.; Gordon, N.; Clapp, T.; (2002). "A tutorial on particle filters for online nonlinear/non-...


1

If you can make the assumption that the two observations are independent then the the likelihood function you need is just the product of the two likelihood functions. If for particle x, the likelihood of it in terms of the colour distribution is p(z_c|x) and the likelihood of it in terms of the motion contour is p(z_m|x) then the likeliood of both ...


1

The easiest way to do this is to keep track of the parameters a and h from detection. How did you pick out a car from the scene? a simplified method would be: background subtraction, followed by clustering, data association, find centroid of clusters => x,y. Also store the bounding box of the cluster, easiest way to keep an accurate a,h. But I'm guessing ...


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