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.

Filter by
Sorted by
Tagged with
0
votes
1answer
43 views

Are there any general heuristics for Kalman filter noise parameters

Are there any generally applicable heuristics for Kalman filter noise parameters? I am working with a non-linear unscented filter and getting an initial guess for the noise covariances $Q_k$ and $R_k$ ...
1
vote
1answer
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 ...
0
votes
0answers
83 views

Kalman Filter implementation is too slow

I have implemented with a simple code a Kalman Filter for time domain, based on these: KG = error_est / (error_est+error_measurment) estimate = estimate_prev + KG ( measurment - estimate_prev) ...
0
votes
1answer
77 views

Kalman Filter's Correlation Formula

I'm reading a book where the autocorrelation of white noise is expressed as: What is the term $Q(k)$ and why is is expressed as an average value of a dot product ?
2
votes
1answer
95 views

Evaluation of Jacobian for Extended Kalman Filter

For the non-additive noise case, \begin{equation} x_k = f(x_{k-1}, u_{k-1}, \xi_{k-1}) \\ y_k = h(x_k, \nu_k) \end{equation} the EKF takes into account the jacobian wrt to the noise terms $ L_{k-1} =...
0
votes
1answer
39 views

Kalman Filter from 2D LookUp Table

I have two sets of inputs, A (10 values) and B (20 values), and for each point (A,B) I have a measurement to make a (10x20) table of measurements C. Is there a way to use a Kalman Filter to improve ...
4
votes
1answer
63 views

How to linearize this state space model and write it in discrete form?

This might not be trivial nor short so in advance thank you all who read this in attempt to help. I'm building a Kalman filter in matlab and I'm fairly certain the software itself is working correctly ...
2
votes
1answer
472 views

Kalman Filter State Covariance Matrix

If I have a discrete time process model of the form: $$x_{k+1} = x_{k} + v_{k}\cos(\theta_{k})dt$$ $$y_{k+1} = y_{k} + v_{k}\sin(\theta_{k})dt$$ $$v_{k+1} = v_{k} $$ $$\theta_{k+1} = \theta_{k}$$ ...
2
votes
2answers
76 views

In what sense is the Kalman filter optimal?

The Kalman filter is a minimum mean-square error estimator. The MSE is defined as $E\left(||\hat{x}_k-x_k||^2\right)$ where $x$ is the state and $\hat{x}$ is the estimate. When $x$ is a vector, for ...
0
votes
1answer
24 views

Kalman filter for heading estimation with magnetometerv + gyroscope only considers magnetometer

I implemented a Kalman filter to estimate the heading of a robot that is moving in 2D, given the measurements coming from a magnetometer (X, Y) and a gyroscope (Z). The code is the following: ...
0
votes
0answers
12 views

Mixing Constrained Properties in an Interacting Multiple Model Filter

While implementing an Interacting Multiple Model tracking filter with one model being a constant turn rate model, I began questioning how the mix should behave while taking into account that some ...
1
vote
2answers
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.
1
vote
0answers
34 views

I have read multiple sources on the IMM filter but I cannot understand how to implement it

I am working on an image detection and tracking problem and have correctly implemented the Kalman filter. I have two Kalman filters and want to track a maneuvering target. After all the books I have ...
2
votes
1answer
122 views

Kalman Filter for position : introducing acceleration estimates

I want to estimate the position on a 3D environment by introducing only acceleration estimates. Is that possible? If I use the extended Kalman Filter and introduce these estimates will I have the ...
13
votes
1answer
754 views

Will an Unscented Kalman Filter Be "As Good" as Other Optimization 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
91 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 ...
1
vote
1answer
77 views

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 ...
2
votes
2answers
285 views

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 ...
0
votes
0answers
22 views

Is the discrete or continuous-time state-space model most appropriate for implementing an embedded Kalman filter? [duplicate]

I'm writing down a state-space model of a mathematical pendulum, in order to estimate the system parameters in an embedded simple Kalman filter. So far I'm just modeling the system in Matlab and haven'...
0
votes
1answer
324 views

How can a RLS algorithm utilise Wiener filter as FIR (M-tap) block?

I'm currently working with a dataset of $5000$ pulses of $N=15000$ samples each. I managed to implement the RLS algorithms with a FIR M-Tap filter such that $M\leq 15000$ ($150$ seems to achieve the ...
2
votes
0answers
48 views

Why is the prediction step in my Kalman Filter failing?

I am trying to become familiar with state estimation, specifically with the use of an accelerometer. I am simulating the following experiment: a 1D spring-mass system (mass $m = 1$, spring constant $k ...
7
votes
1answer
96 views

Kalman Filter: How to Define Inputs and Outputs of a Model

I'm a software engineer with a CS degree working in machine learning. I'm trying to learn about Kalman Filters. In this short YouTube video from Mathworks, there's a discussion on a Kalman Filter with ...
1
vote
1answer
143 views

Kalman Filter - Deriving state transition function

I am relatively new to using Kalman Filtering. Currently I am trying to understand it and how to implement it in Matlab. I found a website with some nice examples that I would like to rewrite in ...
2
votes
1answer
253 views

Estimate smartphone accelerometer bias

I was planning to develop Android / iOS applications that enable users to measure 3D length using their smartphones. According to this question, you need to know at least the time-varying bias that ...
6
votes
1answer
165 views

Estimate and Track the Amplitude, Frequency and Phase of a Sine Signal Using a Kalman Filter

There is sinusoidally controlled signal, which other than being noisy, can change values for amplitude, frequency, phase and offset. At every new sample a new sine is fitted for the last N samples. ...
0
votes
0answers
117 views

Space-Time Finite Element and Static Condensation for Sensor Fusion

My recent pastime interest deals with the nonlinear sensor fusion of GNSS, barometer, magnetometer, accelerometer and gyroscope data. I had a look at the EKF, UKF and Particle Filters but gave up as ...
8
votes
3answers
12k views

Estimating velocity from known position and acceleration

I am stuck at modeling a system model, i.e. getting my state vector and input vector. My guess is that position and velocity are state vector and acceleration is input vector. My 2nd guess is that all ...
5
votes
1answer
107 views

Variance of an Implicit Function of Kalman State Vector

Given a state vector, $ x $, 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
votes
1answer
192 views

Discretize process noise in Kalman filter

Reading P. Andrews et al. I see that it is very common to do the following approximation of the process noise covariance matrix: $$Q_{k} = G_{k-1}QG_{k-1}^{T}\Delta t$$ so that the propagation ...
3
votes
1answer
43 views

How to determine covariance matrices $\mathbf P$, $\mathbf Q$, and $\mathbf R$ in Extended Kalman Filter

I am implementing an Extended Kalman-Filter and an Unscented Kalman-Filter for state and parameter estimation of a conveyer belt system. The problem is that I don't really know how to determine the ...
4
votes
3answers
114 views

How to Improve the Kalman Filter for Tracking the Periodic Motion of a Car?

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
50 views

Mixing Kalman filter and least-squares

I'm not sure it is the right department. I try my chance I am wondering if there is a way to make a hybrid formulation of a least-square problem and a Kalman filter. Let me explain what I mean: The (...
0
votes
1answer
61 views

Kalman Filter: Why do we decrease the state uncertainty regardless of the current measurement?

I'm struggling with fully understanding the concept behind a Kalman filter. For the sake of simplicity, let's ingore the input variable $u$ and assume constant process $Q$ and measurement noise $R$. ...
7
votes
1answer
14k views

How to Determine Covariance Matrix $Q$ and $R$ in Kalman Filter

I am implementing getting orientation from smartphone. I want to use Kalman filter and should determine process noise covariance matrix $Q$ and measurement noise covariance matrix $R$. (newbie to ...
1
vote
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 ...
4
votes
2answers
119 views

Estimating a Signal Given a Noisy Measurement of the Signal and Its Derivative (Denoising)

I have a signal and its derivative simultaneously measured, both including additive noise. The measurement is completed before the analysis, so it can be looked ahead. Now I want to reconstruct a less ...
32
votes
4answers
39k views

How to understand Kalman gain intuitively?

The Kalman filter algorithm works as follows Initialize $ \hat{\textbf{x}}_{0|0}$ and $\textbf{P}_{0|0}$. At each iteration $k=1,\dots,n$ Predict Predicted (a priori) state estimate ...
1
vote
0answers
83 views

Accelerometer Bias estimation with kalman filter

I have to estimate biases of a 3-axes accelerometer by modyfying an existent kalman filter mounted on a drone. The biases are assumed constant. The filter has 9 states: position (xyz), velocity (xyz) ...
2
votes
2answers
88 views

Recommendation for courses / studies on digital signal processing

I hold a master's degree in mechanical engineering. However at my job I am more and more diving into topics of signal processing and data science. I find it great to discover about new topics and to ...
0
votes
0answers
16 views

Extended Kalman Filter measurment vs input vector

What is difference between measurement and input vector in Extended Kalman Filter? Isn't always input also measurement? If so how to update input vector if I have acceleration or yawrate as input ...
3
votes
1answer
484 views

Kalman Filter EM Estimation of Covariances

The question might be very simple, but I get a strange result from Kalman Filter. Let us consider the simplest state-space model, the random walk plus noise: $$ y_{t} = x_{t} + \varepsilon_{t}\\ x_{t} ...
2
votes
1answer
81 views

How to handle a logarithmic term in Kalman filter?

I am trying to implement a Kalman filter for an echo pulse detection application as similar to this paper. (an open source version is here (pg 16)) The measurement variable is $h(x,t)=A_0 (\dfrac{t-\...
4
votes
2answers
60 views

How Are Unmeasured Properties (Velocity and Covariance of Velocity) Handled with a Kalman Filter?

I'm trying to understand how I can update a Kalman filter with a state variable for position and velocity when I only measure position. I have a covariance matrix of the position measurements. But ...
0
votes
0answers
15 views

Does Kalman Consensus Filter have any public implementations?

I am trying to solve a problem using the KCF described here: https://ieeexplore.ieee.org/document/5399678 Does there exist an implementation of this (preferably in python) which is available openly? I ...
1
vote
1answer
77 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 ...
0
votes
0answers
7 views

Can we combine the application of SIFT with Kalman filter for 3D reconstruction of structural buildings?

This is just a novice question from somebody who just got into this topic. Can the application of Scale-Invariant Feature Transform be combined with extended Kalman Filter?
2
votes
0answers
75 views

How Do Particle Filters Get Velocity When Tracking with Pos Measurements

I am new to particle filtering. I can see when particle filters are used with Ensemble Kalman's, the velocity of the states are taken care of by the Kalman. When tracking using particle filters ...
7
votes
2answers
2k 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 ...
59
votes
6answers
21k views

What Is the Relationship Between a Kalman Filter and Polynomial Regression?

What is the relationship, if any, between Kalman filtering and (repeated, if necessary) least squares polynomial regression?
15
votes
1answer
1k views

Kalman Filter - Optimal Way to Handle "Derived" Measurements?

Ie, if you have as state variables position (p) and velocity (v), and I make low-frequency measurements of p, this also indirectly gives me information about v (since it's the derivative of p). What ...

1
2 3 4 5
8