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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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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:...
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Why is the concept of a “state covariance matrix” necessary in estimation?

I'm currently taking a course in optimal estimation (and it's still very early in the course). Much of our work is based around the idea of a measurement model $y=Hx + v$ This model assumes our ...
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Coordinate frame in IMU/GPS Error-state kalman filtering

I just read this really nice paper "Quaternion kinematics for the error-state Kalman filter", according to this book "Principles-Multisensor-Integrated-Navigation-Applications" we have following ...
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Kalman Filter - How to combine data from sensors with different measurement rates?

I'm trying to implement a Kalman filter for tracking the position of a vehicle with the help of position data from GPS and Odometry measurements. The GPS data (WGS84 format collected from an app on an ...
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Kalman Filter Parameter Definition for Vehicle Position Estimation in Python

I'm relatively new to Kalman filter concepts and I would like to use it for estimating and tracking the accuracy of the position of a vehicle with GPS measurements (As a first step). However, I am not ...
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Error in using Kalman Filter for 2D Position Estimation in Python

This is my first question on DSP Stack exchange, so I apologise if it is poorly worded. I have some positioning data from a vehicle (GPX Format, collected through Strava) and want to use a Kalman ...
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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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Position Kalman Filter fails to track a constant-acceleration path

I'm trying to build a discrete Kalman Filter that fuses accelerometer (acceleration) and GPS (position, velocity) measurements. However, I'm finding that my filter can't properly track a constant-...
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Using Kalman filter vs Extended Kalman filter for differential drive robot with IMU

I have an IMU that provides me with a heading that is pretty accurate and accurate encoders on the wheels of my differential drive robot which provides me with pretty accurate velocity but has ...
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Have you ever seen logarithmic burn-in on a Kalman filter before?

I'm reviewing a paper that uses a multiplicative factor $\ln i$ where $i$ is the number of steps since the Kalman filter was initialized. The idea is to slowly build confidence as the filter sees ...
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Kalman Filter Process Noise - Model Where It Vanished

I am trying to use the Kalman filter (the scalar version) to estimate the steady state of a set measurements which is a random process. I have used a constant dynamic model as the state equation, $$ ...
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Can Kalman filter remove 50 Hz noise?

I'm dealing with a brain stimulation. My EEG contains large spikes (>3 mV) when stimulation occurs. I want to remove the 50 Hz noise, but I can't use notch filter because it creates large artifacts. ...
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Model-based Kalman filtering a noisy signal

In a healthcare application, I need to calculate urine flow by differentiating the mass of urine emitted by a person over time. The measuring instrument consists of a load-cell under a fluid container,...
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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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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: (i) Which model to use? CV ...
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Weight update in particle filters

For particle filtering weight update, often the transitional prior is used for the proposal density, in which case the weight update simplifies to just the likelyhood function. However, in one ...
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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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Kalman filter with polar measurements: is the innovation a geometric difference of vectors?

I'm debugging someone else's implementation of a Kalman filter and it uses a cartesian state space and takes observations in polar coordinates. When looking at the mathematical description of the ...
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Discrete Kalman filter for a continuous system

The question is related to the implementation of a discrete kalman filter given a description of the system model in continuous time. I will give an example. Suppose we have a mass, spring and damper ...
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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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“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 is a common method in this domain) which ...
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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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220 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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158 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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201 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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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 ...