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.

learn more… | top users | synonyms (1)

5
votes
1answer
182 views

How do I choose the parameters of a Kalman filter?

Suppose I want to track the position of a car in 2D. What I get as sensor data is my current position. So my state is $$\mathbf{x} = \begin{pmatrix}x\\y\\\dot{x}\\\dot{y}\end{pmatrix}$$ where $x \in \...
1
vote
1answer
26 views

What are the advantages of higher order Kalman Filters like EKF, UKF?

Kalman Filter provides the optimal estimate of the states of a stochastic dynamical system if the system is linear, the measurements are also linear functions of states and the errors in system ...
1
vote
1answer
16 views

Properties of a Kalman filter of a non controllable system

Let's say I have a standard system \begin{align} x(t+1)&=Ax\\ y(t) &=Cx(t) \end{align} As you can see $B=0$, so the system is not controllable. For the steady state Kalman filter I'd say ...
1
vote
1answer
45 views

Is there a name for this smoothing formula?

Hi: I am reading a book called "lectures on wiener and kalman filtering" by Professor Thomas Kailath. On page 18, it says the following: To carry through this approach, let us first note that a ...
0
votes
0answers
18 views

Tracking quality measurement in recursive Bayesian filtering

I've searching lately to find a method for measuring the quality of tracking in recursive Bayesian framework (Particle, Kalman, etc) but I couldn't find any. My first intuition is to calculate the ...
2
votes
1answer
34 views

Active noise cancellation using kalman filter

I am doing signal processing on audio data sampled at 8Ksps in matlab but it is corrupted with random noise. Therefore, I decided to use LMS and RLS ANC algorithms to remove overlapped frequency ...
0
votes
1answer
31 views

Are the RLS filter and Kalman filter gradient methods?

I would like to extend my previous question What is difference between LMS and gradient-descent adaptation? with this other question. I found out, that RLS and Kalman filter learning seems to be ...
1
vote
1answer
43 views

Good Reference Problem to Test Filtering/Estimation Algorithms

I am looking to figure out if a current filter algorithm I have built could be useful for some problems I am looking into at work. It isn't a Kalman filter, but is instead making estimations using a ...
0
votes
1answer
50 views

Kalman for 3D position and 1D orientation

Is the following state correct for a Constant Acceleration (CA) model KF applied for tracking an object which moves in (x, y, z) and have the freedom of rotation $\phi$ around the $z$ axis? \begin{...
3
votes
1answer
67 views

Estimation of accelerating target using position measurements only

I am currently thinking about approaches to estimating the position and velocity of an accelerating target. At this time, I have tried a few approaches that work alright. I have tried two variations ...
0
votes
1answer
31 views

Derivation of transfer functions for Kalman filter

Hi All: I'm somewhat familiar with the kalman filter from a statistical point of view. But lately I've been trying to familarize myself with the linear systems-EE way of looking at it. So, I've been ...
1
vote
1answer
23 views

Observability for Kalman Filtering?

I wanted to know how observability of a stochastic state space system affects the performance of a Kalman Filter. Do we check for the usual observability matrix involving $\mathbf{C}$ (observation ...
0
votes
1answer
33 views

Extended kalman filter for linear system

I studied about Kalman filter(KF) for about a week. And I understand that Kalman filter(KF) is suitable for linear system and extended Kalman filter(EKF) can be used for nonlinear system. However, I ...
1
vote
1answer
54 views

State Estimation by steady state Kalman Filter

I am working with a discret Kalman filter on a System $x_{k+1}=A_k x_k+B_k u_k+\omega_k$ $y_k=C_k x_k+\upsilon_k$ $E[\omega_k\omega_k^T]=Q$ $E[\upsilon_k \upsilon_k^T]=R$ I have estimated the ...
0
votes
0answers
11 views

Kalman Filtering and space parametrization

I am familiar with Kalman filtering given a linear (time-invariant) state space model. However, the state space parametrization is not unique. Given a controllable and observable state space model (A,...
-1
votes
1answer
37 views

100 samples ahead signal prediction [duplicate]

I have a signal sampled at 100 sample per second. After low pass filtering of 200 order and some calculation such as zero crossing detection, I am getting around 1 second delayed signal. I want it in ...
1
vote
0answers
21 views

RLS Algorithm Convergence

I am looking for some help to understand the concept how RLS converges? If possible to present it graphically that would be best. It is very easy to understand the understanding of convergence in case ...
1
vote
1answer
31 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 ...
0
votes
0answers
23 views

EKF covariance prediction - different methods

I am currently working on a Extended Kalman Filter and found two different versions to predict the covariance matrix $P$. First approach: The time derivative of $P$ is defined as $\dot{P} = FP_k + ...
1
vote
1answer
80 views

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 ...
0
votes
0answers
47 views

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 ...
0
votes
1answer
82 views

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 ...
1
vote
0answers
23 views

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 ...
6
votes
0answers
177 views

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 ...
0
votes
1answer
30 views

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 ...
4
votes
2answers
207 views

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 ...
1
vote
3answers
151 views

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 ...
1
vote
1answer
61 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 ...
0
votes
0answers
76 views

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 ...
1
vote
0answers
68 views

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 ...
4
votes
2answers
78 views

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 ...
5
votes
2answers
158 views

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 ...
1
vote
0answers
38 views

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 ...
3
votes
2answers
113 views

Observation Matrix in Kalman Filter

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 $...
0
votes
0answers
47 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 ...
1
vote
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: ...
1
vote
0answers
60 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 ...
4
votes
2answers
135 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 ...
2
votes
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 ( ...
1
vote
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 ...
1
vote
1answer
261 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 ...
1
vote
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 ...
0
votes
1answer
181 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. ...
1
vote
2answers
92 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 ...
5
votes
2answers
96 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 ...
2
votes
0answers
69 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 $...
0
votes
0answers
27 views

Correct form for State Space Equation for Kalman Filter

In this paper: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf in eqns 3,5 the state eqn has the mean removed. $(z_t-\mu)=A(z_{t-1}-\mu) + \epsilon_t$ $y_t=C z_t + \delta_t$ ...
0
votes
0answers
25 views

Fusing data from multi rate accelerometers

I am working on a project that requires combining multiple accelerometers with different frequencies. What is the best way of combining signals from these accelerometers to obtain dynamic behavior? ...
0
votes
0answers
23 views

reverse engineering - RT frequency estimation

I need to maintain code I inherited. The code is for RT frequency estimation. There is not a single line of comment in the code. I was hoping someone here will recognize which technique is being used ...
1
vote
1answer
43 views

Smoothing process of Kalman filter

I have a question about the smoothing (backward) process of Kalman filter. Is it correct to say $E[x_{t|T}] = x_{t|t}$ where $x_{t|t}$ is the estimated result from forward process? I am struggling ...