# 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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### Proving that the uncertainty can not increase during the update step of a Kalman filter - positive semidefiniteness

I am trying to prove mathematically that the update step in a Kalman filter can not result in a increase in uncertainty. I found the following proof which is based on the inversion lemma and the ...
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### How to use Kalman filter for altitude prediction based on barometer data?

I have barometer noisy data with known variance. I studied Kalman filter but I did not find an answer to this problem: My process model is: altitude is changed because of velocity that is changed ...
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### Real-time oscillation-like noise filtering

I am making real-time measurements, which are affected by some noise. This noise has oscillating pattern, i.e. the total signal tends to oscillate around the mean value. The examples of measurements ...
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### Covariance matrix, Q, for a Kalman filter given the stochastic differential equation for the state of the system?

Given that I have a stochastic differential equation describing the motion of my system like so: $$\ddot{x}(t) + \Omega_0^2x(t) - C\dfrac{dW(t)}{dt} = 0$$ Where $\Omega_0$ and $C$ are constants. I ...
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### Implementing Kalman filter or extended or unscented with only position information

I am new to Kalman filter. Is it possible to use a Kalman filter with just the position information of the target? I am so confused with states and measurement.
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### How to account for multiple signals in the input to a Kalman filter

I am interested in using a Kalman filter to track an oscillating signal due to a physical oscillator in a signal which contains the signal from multiple such oscillators oscillating at different ...
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### Kalman filter - question about matrices

In order to familiarize myself with Kalman filter I decided to see how it work step by step. I would gladly use your help. Let's say I have a falling object with air resistance proportional to its ...
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### Update Sub Set of the State Vector in Kalman Filter

I question about Kalman Filter: If I have system state $$\mathbf{X} = [x_1\ x_2\ x_3\ x_4\ x_5]^T,$$ these state elements are independent. I have measurement from a sensor to correct the ...
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### System Identification: smoothing in E-step of EM algorithm

My question is, do the smoothed values affect the estimates obtained from the Maximization Step? If not then we could eliminate the smoothing. Once the estimates are obtained, they do not change apart ...
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### Iterative Kalman filters and system parameters estimation

i am working recently on a project in which i want to implement a Kalman filter as being an observer, and i couple this observer with a state feedback controller that produces control actions ...
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### Kalman Filter - Gaussian representation

I'm trying to understand well the kalman filter, as a result i'm having this question : Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
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### Kalman filter without model versus RLS

As I found out in my previous question Where to get transtion matrix for Kalman filter?, I need a model for correct usage of Kalman filter. In paper On the Intrinsic Relationship Between the Least ...
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### Kalman filter to filter noise from acceleration data

I would like to apply a Kalman filter to remove noise from my measured acceleration data. The idea is then to compare the results obtained in this way whit the results obtained by applying a low-pass ...
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### Open source GPS+IMU sensor fusion?

Are there any Open source implementations of GPS+IMU sensor fusion (loosely coupled; i.e. using GPS module output and 9 degree of freedom IMU sensors)? -- kalman filtering based or otherwise I see a ...