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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Intertial navigation on android phone with Kalman filter

Ok, so suppose I've got a phone with gyroscope, compass and 3-d accelerometer. I wanted to track position of the moving phone for about 1 minute with let's say 50 mm accuracy. Actually let's say that ...
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79 views

How do you apply Kalman Filter to track a signal?

The example that I've seen on state estimation involves deriving the ABCD matrix of a physical system (i.e. falling object) and tracking that object. I would like to use Kalman Filter for signal ...
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Is there a standard way for modeling a Kalman filter where the measurements are obtained from differences?

Consider for simplicity a Kalman filter applied to the one-dimensional state space model $x_{n}=f_{n}x_{n-1}+q_{n}$ $y_{n}=h_{n}x_{n}+r_{n}$ with white noise errors. Assume that $r_n=e_n-e_{n-1}$ ...
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Particle filter Tracking

I am tracking a car using particle filter by making a rectangle around it, and I am using the state vector $[x, y, u, v, a, h]$, where: $x$, $y$ is the position of the body $u$ and $v$ are velocity ...
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31 views

simulating range-bearing sensor with Matlab with Gaussian noise

I would like to simulate a sensor that provides range and direction of a beacon. This is for EKF localization, so the noise must be Gaussian (i.e. $\mathcal{N}(0, \sigma^{2})$. Also, I would like to ...
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Kalman Filtering with Restrictions

A question on this topic has been asked before: Combining a linear Kalman Filter with additional linear constraints? and I checked out some of the references given: ...
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41 views

Variance of an Implicit Function of Kalman State Vector

Given a state vector given by $ x = {[r, v, a]}^{T} $ (Range, Velocity, Acceleration) the Time to Hit is the the time which holds the following: $$ r + v {T}_{tth} + \frac{a {T}_{tth}^{2}}{2} = 0 $$ ...
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Identifiability for Time Invariant State Space Models

Kevin Murphy's Kalman Filter toolbox (for Matlab) contains an example where it's the fact that the state space system in not identifiable causes problems. I include the example in it's entirety but ...
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EKF-Localization Correction Step (implementation)

I'm trying to implement EKF-Localization algorithm with known correspondences, given in this book "Probabilistic Robotics". I've got confused with the correction step. In the book, the correction step ...
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26 views

Correct Implementation of Kalmand Filter to Gaussian state space model?

I am simulating a time series from a state space model, I then want to estimate the state space model parameters from the simulated time series using a kalman filter: I have already posted my code ...
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28 views

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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16 views

Observation initialization Kalman Filter

I'm designing a Kalman Filter in Matlab, However I want to set initial values. I have set following matrices and finding a way to set initialize observation. ...
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14 views

IMM Kalman Filter for Non Linear State and Measurement Function

Has anyone encountered an article or implementation of IMM Kalman Filter for non linear transformations? Even for the most trivial case, measurements are in Polar Coordinate System ($ R, \Theta $) ...
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27 views

Kalman filter for GPS tracking. How to use lat and lon?

Summary - I know how a kalman filter works - I use this as a reference: http://www.mathworks.nl/help/dsp/examples/estimating-position-of-an-aircraft-using-kalman-filter.html - I don't know how to use ...
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166 views

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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42 views

Edge following using Hough transform

Im trying to improve an edge following algorithm developed by some students who did a projekt at my work. The algorithm is supposed to make an robot follow a line with use of an camera. Their approch ...
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1answer
66 views

Analogous filter to Kalman that maximizes mode (as opposed to minimizing variance)

I may have a potential application where maximizing the mode (as opposed to typically minimizing the variance) would be useful for state estimates. The situation may arise from skewed distributions ...
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52 views

Queries on Kalman Filter

I am trying to apply kalman filter for video processing , i am studying about it from different sources but it take me towards question that if i don't know that where my object come in frame mean i ...
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156 views

Kalman filtering in image processing, resources?

I'm looking for a good resource (book, tutorial, lesson etc.) that explains the usage of Kalman filtering in image processing applications. I'm aware of the fact that Kalman filtering is an optimal ...
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31 views

Kalman Filter Properties with Biased (By Constant) Measurements

Assuming I have a filter with the following form: $$ \begin{bmatrix} {r}_{k} \\ {\dot{r}}_{k} \end{bmatrix} = {F}_{k} \begin{bmatrix} {r}_{k - 1} \\ {\dot{r}}_{k - 1} \end{bmatrix} + {v}_{k} $$ $$ ...
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42 views

Incorporating delayed data in Kalman filter

my guide has told me to get familiarized with state estimates and kalman filter ....the problem is that: 1) I am totally new to this topic and finding it really difficult to understand due to lack of ...
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715 views

Re-implementing the “spectrogram” function from matlab

I am trying to make a spectrogram viewer without using the spectrogram command. For this purpose, I used a sin function. I broke up the input signal into 256 segments, multiplied each segment with the ...
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193 views

Kalman filter with accelerometer with DC offset

Goal: For a particle moving uniaxially, to estimate position ($d$) and velocity ($v$) from noisy acceleration ($a$) and very noisy position (GPS) measurements using a Kalman filter. Catch: The ...
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39 views

2-D Distance for Kalman measurements

I have designed a simple 3-state $[x\ \dot{x}\ \ddot{x}]$ Kalman filter which is updated by measurements for $x$ and $\dot{x}$. The filter is tracking a peak on a surface in the $x/\dot{x}$ plane. At ...
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54 views

Estimating Position Based on Range Measurement

I want to present Kalman Filter problem. For simplicity I'd assume the simplest dynamic model - Piece Wise Constant Velocity. The state vector and dynamic model are given by: $$ \begin{bmatrix} ...
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84 views

Applying Kalman filter to a data set

I went through the answer Kalman filter in practice and it seems we must know all the first and second order properties of random variables to apply the Kalman filter. But when I only have a set of ...
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98 views

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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65 views

Kalman filter for random observation matrix $G_t$

I have a problem that is similar to the state space model in Kalman filter but the observation matrix $G_t$ of $$y_t=G_tx_t +w_t,$$ is random. The elements of $G_t$ are i.i.d. random variables with a ...
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172 views

Kalman filter covariance

I've recently started playing with the Kalman filter for a simple 2D (x,y,dx,dy) tracking toy problem. But I seem to have some misunderstanding on what I can expect from the filter. I'm interested in ...
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1answer
263 views

Kalman Filter - Position/Velocity from Accelerometer and periodic position measurements

I am trying to implement an EKF to estimate my position and velocity states by using accelerometer measurements as well as periodic GPS (position) measurements. Basically I want to use the constantly ...
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256 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 ...
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106 views

Why is the Kalman gain constant when position and velocity change?

I used the measured position to estimate the velocity using a Kalman filter. But in simulations, the Kalman gain changes quickly and then remains constant when position and velocity continue to ...
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Can a state space model have changing state size over time?

I have worked with state space models in relation to Kalman estimation. Here I have always seen state space models with fixed state size over time, i.e. the state transition matrix is square. Let us ...
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581 views

How to model the noise in Kalman Filter?

Background: I am a newbie in DSP. I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope. My Understanding: I ...
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2answers
109 views

Situations where complexity is too big to exceed linearity and gaussianity

I'm studing about Kalman Filter and Particle Filter in multiple target tracking in computer vision (tracking pedestrians). Reading sientific papers I'm colliding with a lot of sentences like: The ...
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99 views

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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have position, want to calculate velocity and acceleration

This is simple i thought, but my naive approach led to a very noisy result. I have this sample times and positions in a file named t_angle.txt: ...
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2answers
251 views

Extended Kalman Filter linearization of non-linear functions

I have more general question about the extended Kalman filter usage. What is not clear to me is why the EKF uses non-linear functions $f$ and $h$ for state prediction and estimate, while in other ...
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69 views

(Unscented) Kalman Filter with variable state dimensions

i have to estimate a process which changes over time, not with respect to the system-evolution or the measurement-function, but regarding the number of objects that have to be estimated. So every ...
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Smoothing data by using Kalman filter

I would like to ask about smoothing data by using Kalman filter. Due to quantization, I have data that is not smooth. How can I smooth this data by using Kalman Filter. For your information, the data ...
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More on: Kalman filter for position and velocity

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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1answer
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Implementing a Kalman filter for position, velocity, acceleration

I've used Kalman filters for various things in the past, but I'm now interested in using one to track position, speed and acceleration in the context of tracking position for smartphone apps. It ...
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109 views

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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293 views

information filter instead of kalman filter approach

I read many sources about kalman filter, yet no about the other approach to filtering, where canonical parametrization instead of moments parametrization is used. So I would like to learn on examples ...
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144 views

Sequential processing of uncorrelated measurements in Kalman Filter

I'm starting to brush up on the Kalman Filtering I learned a couple decades ago. From what I remember, if you have a measurement vector $$ z=H x + v $$ and the $n$ components of the measurement ...
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1answer
184 views

Is Kalman smoother symmetric in time?

Suppose my model is reversible in time (e.g. GPS + accelerometers for a vehicle), so that I can run Kalman filter forwards or backwards. Kalman filter, of course, cannot be symmetric, because it is ...
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110 views

How to combine a perfect signal with a limited dynamic range with a poor one with high dynamic range?

I have two sensors that measure speed $v(t)$ of a moving vehicle. The first sensor produces a signal $f(t)$ which is a very accurate estimation of speed. However, it only works for slow to moderate ...
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309 views

Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ ...
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90 views

estimation of the position of the magnetic source

I have a flying robot with magnetic coil as a sensor. An output from the coil is measured every second in different position. I know the position of the coil and its angles. I need to estimate the ...
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Optimal inference for nonlinear state space models

When considering a linear-Gaussian state space model, it is often referred that, optimal inference is tractable which is very rare in state space models. When considering a nonlinear state space ...