# 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### Kalman filter in practice

I have read the description of the Kalman filter, but I am not clear on how it comes together in practice. It appears to be primarily targeted at mechanical or electrical systems since it wants linear ...
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### Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

I'm new to Kalman filtering and state estimation and I'd like some guidance on EKFs. Currently, I'm trying to use a linear prediction model coupled with nonlinear measurements to estimate the state ...
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### How to Determine Covariance Matrix $Q$ and $R$ in Kalman Filter

I am implementing getting orientation from smartphone. I want to use Kalman filter and should determine process noise covariance matrix $Q$ and measurement noise covariance matrix $R$. (newbie to ...
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### Why Does the Kalman Filter Remove Only Gaussian Noise?

What and where in the derivation of the Kalman filter is the assumption of Gaussian noise? Why and how does this assumption help?
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### Derivation of the LMMSE (Linear Minimum Mean Squared Error) Estimate and the MMSE Under Gaussian Prior

I am learning estimation theory through Steven M. Kay - Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory. In the ...
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### Estimating a Signal Given a Noisy Measurement of the Signal and Its Derivative (Denoising)

I have a signal and its derivative simultaneously measured, both including additive noise. The measurement is completed before the analysis, so it can be looked ahead. Now I want to reconstruct a less ...
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### Question on Wiener Filtering

I have read that a Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process. Now, my doubt ...
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