19 votes
Accepted

Kalman filter - understanding the noise covariance matrix

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 ...
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9 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 ...
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  • 40.4k
6 votes

Kalman Filter for estimating position with nonconstant velocity & acceleration

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, ...
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  • 22.3k
5 votes

How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?

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 ...
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  • 40.4k
5 votes
Accepted

Transfer function of a PLL Loop Filter that can support a linearly increasing (chirping) frequency

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 ...
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5 votes

IMU Speed Tracking Through Known Path

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 ...
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  • 40.4k
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 ...
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  • 388
4 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 ...
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3 votes
Accepted

What does "kernel based" mean?

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 ...
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  • 22.3k
3 votes

Is it possible to do single vehicle tracking using Fourier transform?

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 ...
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2 votes
Accepted

Tracking a Predefined Curve in a Series of Images

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 ...
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  • 5,207
2 votes

How to reliably detect the state (opened or closed) of sliding doors from a statically-positioned video stream

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 ...
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2 votes

What is the name for a constant-heading Kalman filter model for vehicle tracking?

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

GPS signal tracking

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 ...
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  • 172
2 votes
Accepted

Taylor series expansion in mean shift tracking

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{...
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  • 80.2k
2 votes

Friendly target identification in radar

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 ...
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2 votes
Accepted

How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?

But what does the overall covariance matrix of the measurements look like where velocity is unmeasured? That's a meaningless question -- if you're really not measuring velocity, then by definition it ...
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  • 8,240
2 votes

Kalman Filter Motion model with moving sensors

If the paths of the sensors are unknown and unknowable, and if a set of sensor readings does not let you determine enough about the sensor's position to get sufficient information about the position ...
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  • 8,240
2 votes

Detecting & tracking an arbitrary object in a video

If all you want to do is to isolate* and track objects that have some contrast against the background, then the key phrase you want to search on is "object tracking", "video tracking&...
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  • 8,240
1 vote

GPS | Retain Signal Tracking after Noise Bound

Now that the OP has clarified in the comments that this is an IF file for beginners I understand the issue. The point is to not be able to demodulate or recognize the individual chips of the GPS PRN ...
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1 vote

How is a Particle Filter used to Estimate Parameters of a State Transition Function?

I suppose I can treat the parameters of the state transition function as the space in which I want to generate the particles ... Is this how it's done with a particle filter? More or less, yes. You'...
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  • 8,240
1 vote
Accepted

Why is beamforming needed in 5G?

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 ...
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  • 2,288
1 vote

How to reliably detect the state (opened or closed) of sliding doors from a statically-positioned video stream

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 ...
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  • 1,906
1 vote

Kalman Filter for estimating position with nonconstant velocity & acceleration

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 ...
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  • 21
1 vote

How to choose the "best" measurment (from a given set) as input for a kalman filter?

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 ...
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  • 580
1 vote

Object Tracking with Improved Detector of Objects Similar to Target

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 ...
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