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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Why does noise prevent a (kalman) filter from diverging?

I'm using a filter (not exactly kalman) of the following form to estimate angles by fusing gyroscope with accelerometer and gyro with magnetometer: $(1)\quad \hat{\theta}_k = \hat{\theta}^-_{g,k} + \...
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How to derive an expression for the optimal importance distribution?

I'm trying to answer the exercise 7.6 letter b of this book: https://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf page 133 but I'm having some problems in understanding the question ...
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Deterministic method to compute “Process noise covariance matrix, Q” for a Kalman filter when parameter variations of the model is known apriori

I am implementing a Kalman filter (for a linear ODE system for now). My model represents a physical device that has 6 "parameters", i.e. those values of the device do not evolve over time (within a ...
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Unscented Kalman Filter Equations for Constant Turn Rate and Velocity Process Model

I am learning about Unscented Kalman Filters in Udacity's Self-Driving Car Nanodegree. The UKF is designed to track an object moving under the assumptions of constant turn rate $\ddot\psi$ and ...
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Check if I has right: Is this the Extended Kalman Filter

I have learn the Kalman-Buncy filter for the LQG controllers. I know that this is a signal processing forum and not robotics not math forum. But Extended Kalman Filters are daily discussed here. ...
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173 views

Digital filter for sharp impulse in data

I am looking for an algorithm or a filter to remove sharp peaks from my data. I am collecting raw data after every 1 second from an sensor through an ADC. The ADC has an internal FIR filter. I use ...
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Filtering for Wright-Fisher HMM

I am trying to understand what filter may be suitable for the following HMM: The signal is a Wright-Fisher one-dimensional diffusion characterised by the SDE $$dX_{t}=\frac{1}{2}\left(\alpha(1-x)-\...
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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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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 ...
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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 ( ...
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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 $...
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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 \...
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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 ...
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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 ...
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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 ...
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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 ...
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515 views

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&...
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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. ...
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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 ...
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969 views

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 ...
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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 ...
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1answer
64 views

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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448 views

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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118 views

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, -...
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2k 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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868 views

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 ...
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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 ...
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54 views

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.
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1answer
107 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 ...
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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 ...
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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, ...
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58 views

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 ...
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1answer
579 views

Kalman Filter - How to combine data from sensors with different measurement rates?

I'm trying to implement a Kalman filter for tracking the position of a vehicle with the help of position data from GPS and Odometry measurements. The GPS data (WGS84 format collected from an app on an ...
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1answer
520 views

Error in using Kalman Filter for 2D Position Estimation in Python

This is my first question on DSP Stack exchange, so I apologise if it is poorly worded. I have some positioning data from a vehicle (GPX Format, collected through Strava) and want to use a Kalman ...
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Kalman Filtering with Unknown State Transition Matrix

I'm currently studying the use of Kalman filters for estimating linear systems. My current State Transition Matrix (STM) is the identity since so far I've been dealing with non time-varying systems. ...
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1answer
94 views

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 ...
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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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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: $x(t+1) = Ax + w$ $y(t) = Cx(t) + v$ ...
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Problem with Kalman filtering accelerometer data

I'm having some trouble implementing a Kalman filter in MATLAB. I have an Android phone connected sending data from accelerometer for 10 seconds. After i have the data I take out the x-axis vector. ...
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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 ?
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29 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 ...
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1answer
195 views

Kalman filter with multiple sensors

I have been reading more about EKF and I am a bit confused on how you handle predictions with multiple sensors. Ex, I have IMU, GPS, Odom and Stereo Camera. Each can be used to predict location, how ...
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194 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 ...
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1answer
57 views

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 ...
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1answer
230 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 ...
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357 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:...
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128 views

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 ...
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127 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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