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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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Setting the measurement noise covariance matrix for sensors with different variances

I'm implementing a kalman filter that fuses data from 2 different sensors. Both sensors provide the same data (a 3d position measurement), but the variances for each sensor are different (i.e. one is ...
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Fusing like data from multiple sensors using kalman filter

I'm new to kalman filters and filtering, and I'm working on a personal project where I have multiple readings all providing the same data (3d position in space, provided via computer vision algorithms)...
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How do I derive complicated robotic motion models easily?

I have a filter that tracks a robot. I want it to use a 2D coordinated turn polar velocity motion model (from page 15 here): But I want to expand on this motion model: I want an additional velocity ...
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Kalman Filter State Covariance Matrix

If I have a discrete time process model of the form: $$x_{k+1} = x_{k} + v_{k}\cos(\theta_{k})dt$$ $$y_{k+1} = y_{k} + v_{k}\sin(\theta_{k})dt$$ $$v_{k+1} = v_{k} $$ $$\theta_{k+1} = \theta_{k}$$ ...
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Defining the observation matrix for a Linear Kalman Filter

So I'm working on some content for an exam tomorrow and have hit a logical snag. The question can be seen below: In particular I am referring to 5)c). The questions asks for a measurement model to ...
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Determining position and g-forces from accelerometer and gyroscope data

I'm analyzing gyroscope + accelerometer data acquired from an IMU for a run of a water skiing slalom course, sampled at 100Hz. The double spikes represent spurious ~15G jitter from crossing both ...
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Kalman filter - order of update step?

I have seen some literature where the covariance is updated first, like $(P_k)^{-1} = (P_k^-)^{-1} + H^T R^{-1} H$, where $P^-$ is the a priori estimate of the state covariance $P$. Then, the updated ...
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Finding time-varying coefficients for a VAR model by using the Kalman Filter

I'm posting this again, since after my last post i've been able to advance the code quite alot. I'm still trying to write some code in R to reproduce the model i found in this article. The idea is to ...
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Error with simple Extended Kalman Filter simulation in Python

I am trying to write a Python simulation for a bearing-only EKF tracking problem. I wish to estimate the $x$ and $y$ position and velocity vectors for an object, so my state vector is $$\mathbf{x} = [...
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Trying to create an Extended Kalman Filter for this problem at hand

Currently I have a system that measures the GPS coordinates of an object. The object is first detected and then using trigonometry, the GPS coordinates are determined, as we know of the GPS ...
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Why discretize a continuous transition matrix in Kalman Filter?

In the Kalman filter toolbox at http://becs.aalto.fi/en/research/bayes/ekfukf/cwpa_demo.html the example code shows that a function lti_disc is called, which is essentially a matrix exponential ...
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Modified Bryson-Frazier (MBF) smoother explain

I'm reading about MBF smoother on Wikipedia. I'm confused of the quantity $\hat{\lambda}_k$ and $\tilde{\lambda}_k$. What does they really mean intuitively ? Why the update formula has the form $\...
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Restrict a state value in an Extended Kalman Filter

I am trying to use an EKF to filter/predict a noisy sinusoidal waveform using the states of phase, rate of change of phase and amplitude. I am finding, however, that sometimes the EKF amplitude state ...
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Estimation filter [closed]

Can anybody explain me the basic difference between kalman filter and particle filter? For the process of estimation which is the best filter to be ised among them and why? Please provide some example ...
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Is my Kalman Filter model reasonable? Using for a 3 wheels rover platform

Background: I'm building a 3 omniwheel rover platform that looks something like this: It has 1 IMU sensors on each of the wheels (3 in total). So in theory, I can get gyroscope and accelerometer data ...
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FMCW MIMO radar RX post processing pipe

Currently working on a FMCW MIMO radar RX pipe consisting of the following modules: 2D CFAR – processing the Range Doppler images per Angle. 3D clustering – clustering the 3D cube generated from the ...
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Defining Model in Kalman for Getting Position Using

I am stuck at modeling a system model, i.e. getting my state vector and input vector for navigating just using navaid and ins (tactical). My guess is that position is my only state vector and INS ...
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Matlab 'kalman': why is one input channel disappearing?

Please excuse if this is somewhat Matlab related, but I believe the question is general (and the answer might be very simple...): I have an LTI system: ...
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How to implement discrete extended kalman filter in matlab

I have a nonlinear system, and I need to use the extended kalman filter to estimate it. I know I need the jacobian, but once I get that, is everything else the same as the normal kalman filter? I ...
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Kalman Filter : How measurement noise covariance matrix and process noise helps in working of kalman filter , explain intuitively please?

How noise covariance matrix and process covariance matrix helps in improving the state estimate, can some one explain intuitively without mathematics ?
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Should I pass Kalman Filter absolute or offset-from-mean sensor values?

I'm using Kalman filters to segment the loudness of an acoustic signal from surrounding noise. The problem I've encountered is that muffled or faulty microphones measuring 'silence' (-70dB, -69dB, -...
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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 ...
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Rocketry : Combine two accelerometers to reduce noise?

I am designing an IMU for an experimental rocket. I'll be using the BN055 9DOF that has sensor fusion - orientation quaternion - and gravity compensation. My main goal is speed computation, and I was ...
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1answer
95 views

“Bi Directional” Kalman Filter

I am working on a project in Object Tracking, i.e. need to predict the location of next bounding box. I used a Hungarian algorithm with a Kalman Filter which produced decent results. However, lots of ...
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Question on Wiener Filtering

I have read that a Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process. Now, my doubt ...
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Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

I'm new to Kalman filtering and state estimation and I'd like some guidance on EKFs. Currently, I'm trying to use a linear prediction model coupled with nonlinear measurements to estimate the state ...
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166 views

How to find the probability of Kalman filter states? [OpenCV+Python]

I am working on a video object tracking problem. I am using Kalman filter to predict and correct the object position return by an algorithm such as CamShift. I want to adjust the likelihood ...
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101 views

How to Realize the Sigma Point Sampling Function in Unscented Kalman Filter?

Recently I'm learning the unscented kalman filter (UKF). When designing the unscented kalman filter, it involves a non-linear function to generate the sigma points and then use the system non-linear ...
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1answer
122 views

Unscented Kalman Filter - Multiple Consecutive Measurement Updates

In trying to implement an Unscented Kalman Filter (UKF), I have come across the issue of what to do when my measurement signals come in at a different rate than my control inputs, which I use in the ...
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Kalman filter equations/code to estimate velocity from known position and acceleration

I was reading this post and I have the same problem: I want to estimate the velocity using displacement and acceleration measures. But the problem is that I don't know how I have to code/implement an ...
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2answers
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Question About Kailath's Paper - An Innovations Approach to Least Squares Estimation Part I: Linear Filtering in Additive White Noise

I'm reading the paper at the link below and I was following it for about 2 pages until I hit a road block on the bottom of page 648 where the author says: putting together 9-11, we obtain and ...
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Using the Kalman filter given acceleration to estimate position and velocity

Note : port from this post, until fully merged. 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 ...
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128 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 ...
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1answer
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Naive Kalman filter for 3D position

I looked at posts that discusses 3D kalman filter. Kalman Filter to estimate 3D position of a node Help with Kalman Filter implementation for estimating 3D position Both from my understanding, both ...
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Basic questions related to Kalman filter

Since I'm a newbie to Kalman filter, so, I had some confusions that I needed to clarify. What is the difference between measurement and state? Can they be of different dimensions? All the ...
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282 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. )....
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IMU speed tracking through known path

new to signal processing and KFiltering here. Thanks for your help. I working with an IMU for a tracking project where the IMU moves throw a known path but at an unknown speed (within limits), the ...
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146 views

A State space model for discrete Sine wave Using kalma filter

I'm looking to apply an optimal LQR filter to a discrete signal of the form $$ x[n]=A\sin(\omega_0n+\phi)+v[n] $$ The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate using ...
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EKF smoothing for prediction at t=0 when no there is no measurement

I have a simple first-order reaction batch system for which I have some discrete measurements ($0<t_{k}\le t_{endbatchsample}$). I have an initial guess for $x_0$ and $P_0$ and from here I ...
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Help with Kalman Filter implementation for estimating 3D position

I wrote a kalman Filter implementation using the Eigen Library in C++ and also using the implementation at this link to test my filter: My prediction step looks like this: ...
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177 views

Extended Kalman Filter for linear systems with non-linear measurements

I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates. ...
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1answer
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Handling a number of simultaneous measurements in Extended Kalman Filter?

If I have a number of sensors whose measurements arrive at the same time - how can I handle them properly in the Kalman filter? P.S. The measurements are not necessarily taken at the same time but I ...
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3answers
783 views

How to use Kalman filter for altitude prediction based on barometer data?

I have barometer noisy data with known variance. I studied Kalman filter but I did not find an answer to this problem: My process model is: altitude is changed because of velocity that is changed ...
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2answers
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What is the value of $0.01\log_{10}$?

I have posted this question in math.stackexchange.com, [can be found here], which I originally thought it is a math question. I now believe this would fit more to the Signal Processing community. For ...
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3answers
187 views

Kalman Filter Sensor Processing

Kalman filter achieves convergence of state vector by using sensor observations. Assuming a sensor such like velocity sensor, giving two axis velocity information in X-axis as well as Y-axis(see edit ...
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In kalman Filter why Q discrete is defined as $\int_0^Te^{\mathbf{A}\tau} Q e^{\mathbf{A}^T \tau} d\tau$?

I would like to ask, why in the transformation to the discretization, $\mathbf{Q}$ is obtained from the expression containing the integral (image attached), what is the theory behind it?
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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} =...
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Image Restoration using kalman filter

I have been trying to restore an image that was blurred with a known Point Spreading Function and corrupted with noise using a kalman filter. I have looked at theory and have a basic understanding of ...
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931 views

[Python ]How can I improve my 1D Kalman Filter estimate?

I have written the following code to smooth an (almost) linear function: ...
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Unscented Kalman Filter - estimation of two parameters

I am working with Unscented Kalman Filter (UKF) in thermal modelling of a box. I have 3 state variables ($T$ temperature, heating $h_h$ and cooling rates $h_c$) in my model and I am observing just ...