# Tagged Questions

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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### Kalman Filter with single input?

Is a Kalman Filter still a Kalman filter if there are no inputs that explicitly predict the next state of the system? For instance, if I have a signal where I know it has characteristics of a first ...
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### Estimate $s$ from $y=s+n$

Thank you in advance. My question is: Now I receive $y=s+n$, $s$ is the signal and $n$ is the white guassion noise. Everytime $s$ will be change irregularly, have some methods to get a estimation ...
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### Extended Kalman filter (EKF)

I am working on the localization problem of an underwater vehicle. However the problem is still in very simple and it does not matter that it is about underwater. How can I use the EKF when I have ...
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### Structuring Kalman filter for tracking problem where only position is known

I'm new to Kalman filters and my extensive web search about them has helped me understand the majority of it (or so I think). However I still need some light shed on my problem formulation. I have a ...
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### Non-zero mean of Kalman innovation

I am using a Kalman filter to fuse gyro and inclinometer data. The prediction step is given by: $\hat{\alpha_{i}}^- = \hat{\alpha}^+_{i-1} + \omega_{i}$ Where $\hat{\alpha_{i}}^-$ is the prediction ...
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### Will an unscented Kalman filter be “as good” as other optimisation algorithms for this problem?

I want to calibrate a tri-axis magnetometer when a tri-axis gyroscope is also available. I am fairly certain I can solve this problem using various optimisation algorithms, but I would prefer to use ...
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### Can a (vanilla) Kalman Filter's Observation Matrix $H_k$ depend on the state vector $x_k$?

A vanilla Kalman Filter allows for a time varying observation matrix $H_k$. Is it allowable for $H_k$ to be a function of the system state $x_k$ in a vanilla Kalman filter? First, am I correct that ...
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### Why Runge-Kutta for Quaternion integration in Kalman filter?

I'm reading up on Kalman filtering at the moment. In particular, I'm interested in using the "extended" and "unscented" variants for IMU sensor fusion and calibration. In A comparison of unscented ...
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### Kalman filter : simple code example

I read lots of things about Kalman filtering, but in order to fully understand it, I would probably need to see it working on some data. Would you have a minimal example (Python code or any other ...
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### Implementing a 1-D Kalman Filter Regression, Missing the smoothing action (getting the opposite)

I am implementing the 1D Kalman Filter in Python on a fundamentally noisy set of measurement data, and I should be observing a large amount of smoothing...but, instead, my Kalman Filter is doing the ...
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### Tracking position and velocity using a kalman filter

I am using a kalman filter (constant velocity model) to track postion and velocity of an object. I measure x,y of the object and track x,y,vx,vy . Which works but if a add gausian noise of +- 20 mm to ...
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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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### Combining Kalman Filters

Say I want to use Kalman filters for predicting the price of items at a supermarket. I have a Kalman filter for each item (apple/beef/brooms/etc). I notice that some items are sort of related, like ...
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### Kalman Filter for estimating position with nonconstant velocity & acceleration

I am trying to estimate the position & head direction of a rodent going through a 2D environment (a circular surface of 1m radius). Above his head is an overhead camera which records 4 LEDs ...
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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 ...
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I've been trying to understand the concept of the Kalman Filter. I came across this great article which makes the concept sufficiently clear. However I could not understand the concept of the matrix $... 0answers 49 views ### What f() for unscented kalman filter for stock trading? I am trying to estimate to "next" price of a stock, based on a group of 5 other correlated stocks. I believe this is a 6 state unscented Kalman problem. However, I do not know how to describe ... 1answer 51 views ### Why does my GAIN remain constant after a few cycles? [closed] I am assuming that GAIN is the matrix P? From this example: ... 0answers 65 views ### Kalman Filter initial Q values I have a 6 state Kalman Filter (Unscented). When I use a diagonal matrix only for Q (i.e only the diagonal has covariances), I get a "smooth" plot of estimate against actual. If I use the entire Q ... 2answers 144 views ### Is the Kalman Filter a Best Linear Unbiased Estimator (BLUE) for Heteroscedastic Noise? According to the Gauss-Markov Theorem, a ordinary least squares estimator is BLUE if the noise entering a system is uncorrelated with zero mean and is homoscedastic (has a constant finite variance). I ... 1answer 34 views ### Can I model process noise as a known “error” in my dynamics while designing a Kalman Filter? Consider I am modelling the dynamics of a robot and using a Kalman filter to obtain estimates of some state. I have certain terms in my equation which correspond to data not accessible to this robot ( ... 0answers 50 views ### Optimality of Kalman Filter for Process Noise dependent on magnitude of state Consider I have a dynamical system$\dot{x} = Ax + w(t)$,$x \in \mathbb{R^2}$where$w(t)$is a Gaussian random variable with mean$E(w(t)) = C\|x\|^2$where$C \in R^2$is a constant and covariance ... 1answer 292 views ### Kalman Filter - Velocity [Matlab] I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a ... 0answers 23 views ### Convergence analysis and Kalman Gain I have a general question in regard to stability and convergence analysis of filtering algorithm like Kalman filter and its non-linear version - Extended and Unscented for parameter estimation. In ... 1answer 193 views ### Kalman Filter to estimate 3D position of a node Code given on this link works for 1D: More on: Kalman filter for position and velocity In my problem I need to estimate 3D position.What is the criteria ? How F, G ,H,Q and R change in 3D case. ... 2answers 107 views ### Q matrix and updating times in a Kalman filter The context of the problem is that I have several robots located remotely which give their position (x,y coordinates) every x seconds and send it to a centralized remote server. The value of the ... 2answers 97 views ### Kalman filter restricted by areal constraints I'm developing a device for tracking pets in a room with several motion detectors. I use a Kalman filter to estimate the position, which is based on the active outputs of the motion detectors. If an ... 0answers 71 views ### Purple noise modeling / Differentiated white noise (Kalman Filtering) I am designing a Kalman Filter for a signal which features a certain kind of noise and I do not know how to model it properly in the filter. The noise is constructed from a white noise source, called$...
In this paper: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf in eqns 3,5 the state eqn has the mean removed. $(z_t-\mu)=A(z_{t-1}-\mu) + \epsilon_t$ $y_t=C z_t + \delta_t$ ...