Skip to main content

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
2 votes
2 answers
174 views

Gyroscope sensor drift problem at speed

I have an iPhone mounted on a bike to measure the slope of the road in real-time. This works pretty well at first but as soon as I speed up, the reported pitch starts to drift. I'm using CoreMotion ...
5 votes
5 answers
606 views

Layman Description of the Kalman Filter

I want to know about Kalman Filter but i tried searching different links including Electrical Engineering StackExchange but the information available there was hardly digestible. All I am able to ...
3 votes
2 answers
732 views

Alternatives to offline Kalman filtering

Recently I got into vehicle models and filtering in general and immediately faced with the following question. I have the recorded GPS data from car driving on a highway. However, there is a ...
21 votes
3 answers
1k views

Should the input of a Kalman filter always be a signal and its derivative?

I always see the Kalman filter used with such input data. For example, the inputs are commonly a position and the correspondent velocity: $$ (x, \dfrac{dx}{dt}) $$ In my case, I only have 2D ...
0 votes
0 answers
19 views

Kalman filters which only update a subset of variables?

What is the general approach to updating a subset of variables with a kalman filter? IE sensor X only updates variable Y. What I'm a little bit confused on is how the covariance would be propagated.
1 vote
1 answer
677 views

Getting position data from 9-axis IMU

I want to track the movement of a person in a 2D plane using a 9-axis IMU. The size of the plane in which the movement is not bigger than 6 by 6 meter. The IMU is mounted on the head of the person and ...
0 votes
0 answers
47 views

PLL Phase Error Detectors for non-bandpass-communication type signals

I'm quite familiar with PLLs for bandpass signals (e.g., GPS) which operate on IF or complex baseband signals. However, I now have a phase tracking problem where the signal is not necessarily ...
1 vote
2 answers
209 views

Kalman Filter in Vision - Constant Velocity Model - Units

Let's assume we have series of frames with a known object. I want to track the object using Kalman filter using constant velocity / acceleration models. My questions are: Which model to use? CV or CA?...
1 vote
1 answer
179 views

Initial Process Covariance in 1-D Kalman Filter

Having a bit of confusion about what the initial process covariance (P) should be. Assume a 1-D tracking problem where I am measuring the distance/position of a static object. Would P not just be ...
0 votes
1 answer
98 views

SAR and ISAR sampling time

This is a repost of a question that I've previously asked in the EE section of SE. Unfortunately, I've not solved my problem. I'm seeking insight into the typical values of sampling times or refresh ...
1 vote
1 answer
105 views

Time fusion Kalman filter

Suppose I have a set of estimators, $$\{S^1, S^2, S^3, S^4,\ldots,S^n\}$$ that output at each timestep $t$ a measurement representing an estimate of the true signal $y$, however the output of each ...
4 votes
1 answer
162 views

How to regularize the latent variables of a kalman filter to be small?

This is perhaps a bit of a weird idea but suppose I want the latent variables of a Kalman filter to be small (like as if the states were being regularized). This is kind of like putting an extra prior ...
5 votes
1 answer
1k views

Kalman Filter on Sensor Fusion

Assume I have 2 sensors capable of measuring distance to an object of known distance. If I apply a Kalman filter to these 2 sensors, I would have 2 correction and prediction equations. If I have 2 ...
2 votes
1 answer
76 views

Kalman Filter - Gaussian representation

I'm trying to understand well the kalman filter, as a result i'm having this question : Why do we represent noise with a Gaussian ? what does this really mean intuitively ?
4 votes
1 answer
506 views

Deriving a Kalman Filter Equation for a Linear Gaussian Filtering Model with Non Zero Mean Noise

I am trying to answer an exercise question from the book Simo Sarkka - Bayesian Filtering and Smoothing. The question is: Does anyone know if there is a resource that has the solutions for this book?
0 votes
0 answers
22 views

Fusing multiple IMUs in EKF framework

What is the approach to fuse multiple IMUs in EKF framework? Normally you take the IMU as the motion model and the sense step to consist of other sensors but when have multiple IMUs operating, what is ...
3 votes
1 answer
91 views

How to define Q matrix (covariance matrix for process noise) in EKF

I am implementing an Extended Kalman Filter (EKF). I have developed the model for my system and I know must find the Q matrix. I have searched all over the web and noone explains how to define this ...
2 votes
1 answer
65 views

How to simulate the synthetic data for 2 pole low pass filter for Kalman application?

I was trying to simulate data for a 2 pole low pass filter inorder to solve with kalman filter to estimate the true states. With the below code I was unable to generate true states that look like sin ...
1 vote
0 answers
39 views

Implementing signal processing techniques for consistent RSSI signal reception

I've tried to optimize the LoRa setup using Arduino IDE libraries to ensure accurate or acceptable RSSI measurements and for distance estimation between multiple nodes and a master in an outdoor ...
1 vote
0 answers
30 views

Temperature estimation via Kalman filter

Based on the recommendation I would like to ask you for your opinion regarding my question I have asked on different forum.
0 votes
0 answers
36 views

Does it make sense to have diverging Kalman gain and covariance when system accuracy worsens over time?

I've developed an UKF for a system, whose dynamics change slowly over time. The state & measurement equations are quadratic and linear equations fitted to experimental data in the following form: $...
1 vote
0 answers
61 views

Wiener Filter for Noise Reduction in GPS Sensor Measurement

I am getting position and velocity measurements out of a GPS sensor and I want to filter these data, so I can have a better, less noisy, estimation of the true measurements. I thought of doing this ...
0 votes
0 answers
20 views

Kalman filter for multiple data sources, measurements from which have different characteristics of Gaussian noise

I am trying to use the Kalman filter for my task: During the time, I receive data from different sensors. The state of the model may change over time according to the Const Velocity model, or the ...
2 votes
0 answers
83 views

What happens when Kalman filter is applied on a memoryless system?

I'm trying to set up a Kalman filter for my system $$ x_{k+1} = f(u_k) $$ $$ z_{k+1} = g(x_{k+1}) $$ and found that while the filter "works" (able to reduce rmse from 1.5% in the open loop ...
7 votes
2 answers
5k views

What are the advantages and disadvantages of Kalman filter compared with FIR, IIR and low pass filter to filter data with noise?

It is known that the Kalman filter can filter the data with noise. I also find it works well after using it compared with FIR, low pass filter,etc. Now, I have a couple of questions about the ...
2 votes
0 answers
33 views

When is the Kalman Filter state (un)observable?

In Rudolf Kalman's seminal paper, the problem of filtering is defined as below (p. 2): We are given signal $x_1(t)$ and noise $x_2(t)$. Only the sum $y(t) = > x_1(t) + x_2(t)$ can be observed. ...
1 vote
0 answers
31 views

Can the Kalman Filter process covariance be estimated from measurements?

I'm looking for the simplest possible method for estimating the process noise covariance $\mathbf{Q}$ and measurement noise covariance $\mathbf{R}$ for a Kalman Filter. This is assuming a time-...
6 votes
3 answers
856 views

How to Deal with Outliers in Measurement of a Simple Model of Kalman Filter

I am trying to find the one-dimensional velocity of a car based on position measurements, similar to the Wikipedia article. The car moves at almost constant speed and I am mostly interested in ...
4 votes
2 answers
1k views

Sample Dataset for Kalman Filter

I'm a newbie to Kalman filter. I have found the code online but I was wondering if there is any sample dataset available online to get hands-on with it (for example: CIFAR-10 for classification etc. )....
1 vote
0 answers
66 views

Which filter is suitable for reducing noise in feature detection?

I have a feature detection algorithm that is called FAST - Feature Accelerated Segmented Test. It's a very fast algorithm for finding feature points, e.g "corners" inside an image. Here is ...
1 vote
0 answers
39 views

Is it possible to reformulate a Kalman Filter as a Gaussian Markov Random Field?

The generic formulation of a KF uses a set of transitition equations, while the GMRF is typically specified through its mean and precision. However, a simple KF involves Gaussianity and Markov ...
0 votes
0 answers
36 views

Extended Kalman Filter - Jacobian Computation

I have the following problem. I have the following Kalman filter: $ \boldsymbol{x}_k=\boldsymbol{x}_{k-1} + \boldsymbol{w}_k$ $ \boldsymbol{y}_k=h(\boldsymbol{x}_{k}, \boldsymbol{v}_k)$ where $\...
1 vote
0 answers
123 views

average after Kalman filter and how to deal with drift

This is in the context of mobile device localization. The mobile device does not move. All I have is the delay estimated from the signal sent by the mobile device ('measure' in blue). With a simple ...
5 votes
1 answer
2k 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 $R$. ...
1 vote
0 answers
55 views

Phase rotation compensation in AOA

We are using $4 \times 4$ corehw antenna array with nrf52833 mcu as the receiver and nrf52833 as transmitter. When working on AOA Direction Finding, we found that each element in the antenna array has ...
3 votes
0 answers
608 views

Unscented Kalman Filter for Parameter Estimation (Tracking) of Amplitude Frequency and Phase of a Multi Component Harmonic Signal

I'm trying to implement an Unscented Kalman Filter that tracks the amplitude, frequency, and phase of a multi-component oscillatory signal. Below is an attempt using the ...
6 votes
2 answers
9k views

Using the Kalman filter given acceleration to estimate position and velocity

I am reading data from an accelerometer. I want to use this data to estimate velocity and position. Originally, I performed a double integration of acceleration to read this data, and as confirmed by ...
1 vote
0 answers
43 views

2nd order EKF covariance propagation equation (hessian)

[cross-post on MathExchange] I am trying to implement a 2nd-order EKF and am having some issues with the propagation equation for covariance. From the literature (see end of post for references), if $...
3 votes
1 answer
254 views

Kalman Filter Algorithm for Unknown Process and Measurement Noise

I want to be use kalman filter for the state estimation but I don't know about process and measurement noise. How can I estimate process and measurement noise and use this information for kalman ...
1 vote
1 answer
101 views

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? ...
0 votes
1 answer
213 views

Confusion on Error State Kalman Filter reset

I have been reading about kalman filters for IMU and I am confused on the error state formulation. Reading this paper, starting on page 63 and going onto 64 the paper addresses the reset of the error ...
0 votes
1 answer
129 views

Deriving equations for IMU Kalman Filter

I am trying to model a Kalman Filter for an IMU (inertial measurement unit) with the method described by Zhou (2004) and Filippeschi (2017, pp.11-12). In this method, the state vector is: $$ X = \...
4 votes
2 answers
405 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 ...
4 votes
2 answers
318 views

Forward problem of Kalman filter causing NaN values during recursion?

\begin{eqnarray} X_k &=& F X_{k-1}+ \omega_k \nonumber \\ Z_k &=& H X_k + \nu_k \end{eqnarray} The first equation is state exploration equation and second one measurement ...
1 vote
0 answers
372 views

Kalman Filter Under Non-Gaussian Noise

I know that Kalman filter is optimal filter under some assumption like process and measurement noise are Gaussian. But if the process and measurement noise is non-Gaussian, the estimation of the ...
0 votes
1 answer
150 views

What is the intuitive meaning of selecting high or low Q value in Kalman filter?

I am working on experimental data, where I need to choose Q in Kalman filter. How to intuitively understand: What does selecting low value of Q indicates in Kalman filter? What does selecting high ...
1 vote
0 answers
59 views

Non-linear external effect in Kalman filter

Let's say I have a Kalman filter with this simple state model: $$\begin{pmatrix} x^0_{k+1}\\ x^1_{k+1}\\ \end{pmatrix} = \begin{pmatrix} 1 & \Delta t\\ 0 & 1\\ \end{pmatrix} \begin{pmatrix} x^...
1 vote
2 answers
124 views

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 ...
5 votes
2 answers
2k views

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 ...
0 votes
1 answer
237 views

Kalman filter in data fusion

I am very new to Kalman filter. I am doing a project using one sensor the track the sensor's position. I developed 2 methods to solve the position, one in better accuracy and one is less accurate. I ...

1
2 3 4 5
9