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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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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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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 ( ...
sid's user avatar
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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 $...
Elarion's user avatar
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Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): \begin{align} X_{t+1}&=FX_t + V_t\\ Y&=HX_t+W_t\\ V_t &\sim \mathcal N(0,Q)\\ W_t &\sim \...
Bazman's user avatar
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Velocity estimation knowing acceleration and displacement from measurements using Kalman filter

I am having a hard time in trying to use a Kalman filter to obtain velocity from acceleration and position measurements. I think the main reason is that I am not familiar with Kalman filters (I had ...
Rhei's user avatar
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Correct Kalman Filter for Gaussian State Space Model

I am trying to follow a paper where they say they apply the Kalman filter, but don't give the forumulation for the Kalman filter! Moreover I have looked at two references Wikipeadia and Durbin and ...
Bazman's user avatar
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Extended kalman filter for accelerometer data on shaking table

I am using an accelerometer to record the motion of a shake table (a rocking table) which moves forward and backward in one direction. The signal is very noisy and decided to use Extended Kalman ...
ukg's user avatar
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Kalman Filter: continuous state space, discrete observations

This is just an idea. How can we model the kalman filter to get the state representation in continuous space when the observations to the system are actually from the discrete space. The discrete ...
Rex Roy's user avatar
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Extended Kalman Filter - how do I get transition functions

I am measuring position and velocity, both have some noise in them. Velocity is defined as derivative of position. The system is apparently non-linear so I need to use EKF. Model: \begin{align} X&...
c0dehunter's user avatar
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301 views

Estimate process error for Kalman filter on financial data

I'd like to apply a Kalman filter, using Octave, to financial data but due to the nature of the data it will be difficult to impossible to specific the process error in advance of applying the filter. ...
babelproofreader's user avatar
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What is the value of $0.01\log_{10}$?

I have posted this question in math.stackexchange.com, [can be found here], which I originally thought it is a math question. I now believe this would fit more to the Signal Processing community. For ...
shashashamti2008's user avatar
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Intuition for $\mathbf{P} = \mathbf{0}$ in steady-state when $\mathbf{Q} = \mathbf{0}$ (Kalman filter)

Consider the following discrete-time system: \begin{equation} \mathbf{x}(k+1) = \mathbf{A}_d \mathbf{x}(k) + \mathbf{B}_d \mathbf{u}(k) \end{equation} \begin{equation} y(k) = \mathbf{C}_d \mathbf{x}(k)...
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What is the difference between Kalman filter algorithm and stationary Kalman filter algorithm?

I want to compute the stationary Kalman filter algorithm but I haven't found any information about that algorithm ( not even the pseudo code ) so, I wonder what is the difference between the Kalman ...
andrestoga's user avatar
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Can the Kalman filter estimate a factor of the model? Product of two state variables

I've written down a discrete state-space model for a simple pendulum, with the state variables angle, angular velocity and angular acceleration. This can be easily plugged into a simple Kalman filter ...
Anna's user avatar
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The Stability of the RLS Algorithm for Equalization

I am reading in the litterature that LMS is more stable than RLS. But RLS is far more faster in convergence. So my concern is how to be sure that my RLS algorithm will be stable when I am doing ...
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1 answer
707 views

Getting Vario (m/s) from a bmp180

I am building a variometer as a hobbie, this could be a duplicate from an existing question: How to use Kalman filter for altitude prediction based on barometer data? . Details follow: I have a ...
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Discrete Kalman filter for a continuous system

The question is related to the implementation of a discrete kalman filter given a description of the system model in continuous time. I will give an example. Suppose we have a mass, spring and damper ...
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Should I pass Kalman Filter absolute or offset-from-mean sensor values?

I'm using Kalman filters to segment the loudness of an acoustic signal from surrounding noise. The problem I've encountered is that muffled or faulty microphones measuring 'silence' (-70dB, -69dB, -...
Petrus Theron's user avatar
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1 answer
3k views

Using Kalman Filter to fuse two sensor readings of the same type

I have always used Kalman Filter to smooth a signal comes from one sensor only. I would like to know if Kalman Filter could be used to fuse data coming from two different sensors that provide the ...
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Apply Kalman filter to remove process noise, given zero measurement error

I have a recording, corrupted by environment noise. The measurement noise is zero. How can I use Kalman filter to remove environment noise? I tried this Matlab code here but if the measurement error ...
Max's user avatar
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Kalman filter, defining the measurement model

I would like to implement a Kalman filter to estimate the velocity and position of an object. I have an accelerometer, therefore the acceleration is known. The approach is same as: Kalman filter for ...
user3506463's user avatar
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2 answers
2k views

about Kalman gain

Hi everybody. I'm very new in Kalman filter. Today I try to design Kalman filter to get estimated postion, velocity and acceleration from measurement position (by linear encoder). I don't use optimal ...
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How to generate ground truth in constant velocity Kalman simulation?

I'm trying to simulate a particle going from (-3,0) to (3,0) with a constant velocity and some noise (e.g. the particle is a quadcopter trying to fly at constant velocity, but may be pushed by gusts ...
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Finite Difference Estimation for error propagation

For a complex system where symbolic computation of the jacobian is challenging, is estimating the jacobian via finite difference a viable option? To be explicit I'm mostly interested in playing around ...
FourierFlux's user avatar
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1 answer
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IMU state estimation Covariance updating

EKF filter normally has a predict + update step, I am curious - how do you evolve the covariance of the state without one of the steps? In essence I want to evolve the state of an object using an IMU ...
FourierFlux's user avatar
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1 answer
253 views

EKF: IMU vs State Transition Model

Suppose you have an object you're interested in estimating the state of, ex position. Suppose you don't have a state transition model but you do have an IMU. Can the IMU be used to simulate a state ...
FourierFlux's user avatar
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1 answer
86 views

How does sampling jitter affect state estimation?

Suppose I have some process which is governed by: $$ \vec{x_{k+1}} = A\vec{x_k} + B\vec{u_k} + w_k$$ where $u_k$ is the input, and $w_k$ is process disturbance. This process is continuous time in ...
fpf3's user avatar
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Does a gyroscope get impacted by gravity?

When processing IMU data, does the gyroscope get impacted by gravity? Linear accelerometers need to have gravity compensation but nothing is said of IMU.
FourierFlux's user avatar
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950 views

If there are state variables in the Kalman filter that aren't being measured, is their output just rubbish?

I've been learning about the Kalman filter on this website: https://www.kalmanfilter.net/multiExamples.html As you can see there is a numerical example regarding a car that is traveling in a 2 ...
user1477107's user avatar
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301 views

Kalman filter continues to update position even though speed is zero

Background I set up a conventional Kalman filter that makes use of smartphone GPS only (no inertial sensors). That is, it uses the position, doppler speed, and course, in order to create positions ...
William Grand's user avatar
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1 answer
98 views

Is Kalman Filter for LTV systems applicable on Hybrid systems?

As all of us know Kalman Filter is designed for LTV (Linear Time Variant) systems. But nobody in the literature applies that on Hybrid systems. In my opinion Linear Hybrid systems are a subset of ...
Navid Hashemi's user avatar
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1 answer
152 views

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

When applying Kalman filtering to estimate the position of a car, there are several different vehicle dynamics models that you could use. One of the simplest is "constant velocity" or CV, ...
Kerrick Staley's user avatar
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1 answer
64 views

Can a Kalman Filter Be Applied Using Measurement-Space Dependent Sensors?

I'm currently attempting to apply a Kalman filter to track the angular position, velocity, and acceleration of a bike wheel, and I'm having a lot of trouble, so I want to check if I'm even applying ...
sgbrown's user avatar
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Why is the concept of a "state covariance matrix" necessary in estimation?

I'm currently taking a course in optimal estimation (and it's still very early in the course). Much of our work is based around the idea of a measurement model $y=Hx + v$ This model assumes our ...
Izzo's user avatar
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Learner level information on Kalman filtering for different input kinds

I am learning Kalman filters and have seen example on data as state varaibles that have real values / numeric. However, in digital communication the information is in digital - bits. So, can Kalman ...
Ria George's user avatar
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1 answer
1k views

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 ...
Chris's user avatar
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kalman filter with time-varying noise?

in regular discrete-time (1 dimensional) kalman filter, it is assumed that we have white gaussian noise affecting the transitions and the observations: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
user24823's user avatar
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Relation between Kalman filter and Sequential linear MMSE estimation

Are the results of applying Kalman filter and recursive linear MMSE estimation process the same ?
triomphe's user avatar
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Gyroscope Error Propagation: Why not use Euler Angles?

Looking at the EKF formulation for Gyroscopes in more depth I'm wondering, why can't we use Euler Angles in the Error State EKF framework for error and covariance propagation instead of Quaternions? ...
FourierFlux's user avatar
1 vote
1 answer
439 views

Kalman Filter - Comparing the Static Kalman gain and the Dynamic/Recursively updating Kalman Gain

I studied Kalman filters some time ago, and recently came to realize I do not understand some parts on them. Specifically related to the difference between using a static Kalman-gain, found by ...
Chris_abc's user avatar
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1 answer
70 views

What are the Kalman filter capabilities for the state estimation in presence of the uncertainties in the system input?

I have a question regarding the capabilities of the discrete Kalman filter for estimation of the unmeasurable state variables of a dynamic system. In the time being I have been using a discrete ...
Steve's user avatar
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1 answer
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What's the best way of modeling 3d target motion with only 2d angle observations?

A maneuvering target is flying in 3d cartesian space, but a sensor (passive infrared or mic array, etc.) can only observe it in polar coordinate with 2d orientations (azimuth, elevation). For ...
Steven Ding's user avatar
1 vote
1 answer
235 views

Kalman filtering with dynamic covariance/variance

What is the appropriate way to implement KF if your sensor confidence is time and observation dependent? Ex, you asses the quality of camera tracking by the percentage of features correctly matched by ...
FourierFlux's user avatar
1 vote
1 answer
668 views

How to initialize observation Matrix in Kalman Filter when there is no clear relationship between measurement and state?

I am try to use Linear Kalman to do time series prediction. I understand that I have to define a model process matrix which indicate how system state evolve, and a measurement matrix H which convert ...
Xiaolong Wu's user avatar
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2 answers
1k views

Kalman filtering for position using GPS,accelerometer and speed sensors

I am working on tracking a vehicle under tunnel when GPS is lost. Whenever the vehicle in on the road, the GPS works fine and gives good accuracy but when the vehicle is under tunnel, the GPS is lost ...
230490's user avatar
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1 answer
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Tracking movement of audio speaker driver using images

I have a speaker emitting low-frequency sinusoidal wave and I have physically marked a curved edge on the speaker driver as shown in red in the image below, which I would like to track: I detect the ...
Abhijith Bagepalli's user avatar
1 vote
1 answer
790 views

Reduce Jitter in Live Kalman Filter

I have a stream of data over time that I have fed into a Kalman filter. This data represents the vertical displacement in time of a vehicle's rearwheel as it travels over a bump in the road. The ...
Andrea's user avatar
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1 answer
528 views

why does DFE feedback filter matters?

I recently came across an article on the inventor of adaptative equalizer Robert Lucky, In this article : An Oral History by Robert Lucky (http://www.ieeeghn.org/wiki/index.php/Oral-History:...
Abby_DSP's user avatar
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Fuse two sources of linear acceleration with a Kalman filter

How would I fuse two different sources of linear acceleration with a Kalman filter (perhaps linear acceleration readings from an IMU and from a dedicated accelerometer)? My state is defined by ...
HackNode's user avatar
1 vote
1 answer
403 views

Kalman Filter Process Noise - Model Where It Vanished

I am trying to use the Kalman filter (the scalar version) to estimate the steady state of a set measurements which is a random process. I have used a constant dynamic model as the state equation, $$ ...
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