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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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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 ...
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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 ...
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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?
Econstudent's user avatar
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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 ...
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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 ...
SuperCodeBrah's user avatar
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State estimation in HyperSonic Missiles

I'm curious, what would be the correct approach for state estimation for hypersonic Missiles? Would it be exclusively GPS and IMU? Historically these are what was used, but I have also seen ground ...
FourierFlux's user avatar
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How to compute (in non adaptative way based on MMSE FIR) the feedback and feedword filter for DFE equalization?

System Model Consider the single-input single-output (SISO) communication system in the figure below: where the information bit stream is encoded and mapped such that the output of the encoder is a ...
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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 ...
Maria D.'s user avatar
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Converting an FIR Filter Model to a State Space Model for Kalman Filtering

I want to try and determine the true value of a quantity $\alpha[k]$ from observations of a related quantity $\vartheta[k]$ using a Kalman filter. The observations are of the following FIR filter form:...
the_src_dude's user avatar
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Inconsistant Variation in BLE Beacon RSSI Values for Distance Measurement

I am developing an application to estimate the distance to a BLE Beacon using its RSSi values measured from a Mobile Phone. But when I started to collect data I could see that they varied so much that ...
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Role of Riccati Equations in Kalman Filter Design

I am working on a Kalman Filter (KF) design problem and I am struggling to understand the role of the Riccati equations in the design process of a KF. Some sources discuss the importance of Riccati ...
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(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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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 model,...
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Optimal measurement model for Kalman in Augmented Reality

I am developing an augmented reality SDK that uses Kalman for tracking a planar marker. My state is composed of 3D position, a quaternion, velocity and angular velocity. \begin{bmatrix}{\vec{p}}\\{\...
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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 ...
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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. ...
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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 ...
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Steady-state Kalman filter question

I'm reverse-engineering DSP code and there's a steady-state Kalman filter in it. Because it is a steady-state Kalman filter, the matrix $K$ is fixed. However, I'm a puzzled about the state update ...
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Kalman filter for harmonic oscillator. State variable and Covariance matrix

I've coded a simple damped harmonic oscillator, controlled with a pid. Works fine. I want to use this model to test a kalman filter. So i added a gaussian noise to the position and want to feed the ...
Staufenbache's user avatar
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Choosing Right Type of Filter for time series data

I am working on a temperature time-series data which is very noisy. I am trying to measure true low and ...
Rheatey Bash's user avatar
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230 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 ...
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Estimate standard deviation of random-walk using Kalman filter

I'm new to Kalman filters so this might be a stupid question. I created a Kalman filter that takes in time series observations and estimates the mean of that time series. This is simply modeling a ...
Grant Bartel's user avatar
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493 views

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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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 ...
Dr Krishnakumar Gopalakrishnan's user avatar
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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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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 ...
nema's user avatar
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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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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 ?
Mohamed Benmahdjoub's user avatar
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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 ...
O.K.'s user avatar
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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 \...
Bazman's user avatar
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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 ...
Rhei's user avatar
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140 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 ...
Bazman's user avatar
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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 ...
ukg's user avatar
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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 ...
Rex Roy's user avatar
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2 votes
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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&...
c0dehunter's user avatar
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302 views

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. ...
babelproofreader's user avatar
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 ...
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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.
Steve's user avatar
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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 ...
useeeeer132's user avatar
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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-...
xperroni's user avatar
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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 ...
euraad's user avatar
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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 ...
SCS's user avatar
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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 ...
Rokai's user avatar
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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 ...
user68463's user avatar
1 vote
0 answers
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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 $...
Parker Lewis's user avatar
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381 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 ...
guidolard's user avatar
1 vote
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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^...
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