# Questions tagged [kalman-filters]

The Kalman filter is a mathematical method using noisy measurements observed over time to produce values that tend to be closer to the true values of the measurements and their associated calculated values.

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### What is the relationship between a Kalman filter and polynomial regression?

What is the relationship, if any, between Kalman filtering and (repeated, if necessary) least squares polynomial regression?
4answers
30k views

### How to understand Kalman gain intuitively?

The Kalman filter algorithm works as follows Initialize $\hat{\textbf{x}}_{0|0}$ and $\textbf{P}_{0|0}$. At each iteration $k=1,\dots,n$ Predict Predicted (a priori) state estimate ...
1answer
47k views

### Kalman filter for position and velocity: introducing speed estimates

Thanks to everyone who posted comments/answers to my query yesterday (Implementing a Kalman filter for position, velocity, acceleration ). I've been looking at what was recommended, and in particular ...
3answers
897 views

### Should the input of a Kalman filter always be a signal and its derivative?

I always see the Kalman filter used with such input data. For example, the inputs are commonly a position and the correspondent velocity: $$(x, \dfrac{dx}{dt})$$ In my case, I only have 2D ...
2answers
9k views

### Is a Kalman filter suitable to filter projected points positions, given Euler angles of the capturing device?

My system is the following. I use the camera of a mobile device to track an object. From this tracking, I get four 3D points that I project on the screen, to get four 2D points. These 8 values are ...
4answers
8k views

1answer
295 views

### Is Kalman smoother symmetric in time?

Suppose my model is reversible in time (e.g. GPS + accelerometers for a vehicle), so that I can run Kalman filter forwards or backwards. Kalman filter, of course, cannot be symmetric, because it is ...
1answer
129 views

### Filtering difference of correlated measurements

I have an application with two separated GPS receivers giving live positions and I'm deriving a heading/displacement from the vector between them. Each set of position measurements is noisy and has ...
1answer
3k views

### Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?

I am attempting to create a Kalman filter to track a sine wave (I am using a linear Kalman filter example assuming I already know the frequency of the sine wave) - the example I am using is derived on ...