# 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 Motion model with moving sensors

Suppose I have an object that I am tracking with moving sensors using a basic Kalman Filter (for example, think of a ship being tracked by satellites). In the simplest case where the sensors are ...
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### Removing drift from integration of accelerometer data

I am trying to get a positional data from the accelerometer data using the following steps: Re-zero the accelerometer value Removing mean from accelerometer value First integration of accelerometer ...
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### How to model the noise in Kalman Filter?

Background: I am a newbie in DSP. I am implementing a simple Kalman Filter that estimates the heading direction of a robot. The robot is equipped with a compass and a gyroscope. My Understanding: I ...
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### Tracking a Sine Wave with Kalman Filter - How to Account for Offset (DC Signal)?

I am attempting to create a Kalman filter to track a sine wave (I am using a linear Kalman filter example assuming I already know the frequency of the sine wave) - the example I am using is derived on ...
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### 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 ...
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### 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 ...
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### Explain the Adaptive Part of Adaptive Algorithms - Kalman Filter and Least Mean Square / Constant Modulus

General questions: Is the Kalman filter (they have used Unscented Kalman Filter) adaptive or not? Is the Unscented Kalman Filter used in the paper an adaptive algorithm? Adaptive algorithms such as ...
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### Frequency tracking with huge noise

I'm working on a frequency tracking problem with noise, where the amplitude of the noise is orders of magnitude higher than the amplitude of my signal (~1000x). Some details: The signal is roughly ...
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### Combining Kalman Filters

Say I want to use Kalman filters for predicting the price of items at a supermarket. I have a Kalman filter for each item (apple/beef/brooms/etc). I notice that some items are sort of related, like ...
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### Discrete Sinusoidal to State Space

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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### Is Kalman smoother symmetric in time?

Suppose my model is reversible in time (e.g. GPS + accelerometers for a vehicle), so that I can run Kalman filter forwards or backwards. Kalman filter, of course, cannot be symmetric, because it is ...
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### 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 ...
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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 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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### Kalman filter restricted by areal constraints

I'm developing a device for tracking pets in a room with several motion detectors. I use a Kalman filter to estimate the position, which is based on the active outputs of the motion detectors. If an ...
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### Particle filter Tracking

I am tracking a car using particle filter by making a rectangle around it, and I am using the state vector $[x, y, u, v, a, h]$, where: $x$, $y$ is the position of the body $u$ and $v$ are velocity ...
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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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### Can Kalman Filter be used to track Randomly Moving Target?

i want to track random moving object with a camera using kalman filter...i have the following questions... Randomly moving target means $Corelation(t) = E[ x(T)x(T+t) ]$ is very low...where $x(T)$ is ...
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### 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 ...
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### Kalman Filter for estimating position with nonconstant velocity & acceleration

I am trying to estimate the position & head direction of a rodent going through a 2D environment (a circular surface of 1m radius). Above his head is an overhead camera which records 4 LEDs ...
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### 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 $R$. ...
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### 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 ...
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### How to include phase in a sinusoidal Kalman Filter

I start with the equation for sinusoidal motion with an offset and differentiate to get the 2nd order ODE describing the motion of the object. \begin{align} x &= A\sin(\omega t + \phi) + O\\ \dot{...
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### Kalman Filter - Updating the Covariance Matrix Step

I am trying to simulate the Kalman Filter. I have the covariance matrix P_{0|0}. Tell me please, how can I get the predicted (a priori) estimate covariance matrix ...
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### Estimation of accelerating target using position measurements only

I am currently thinking about approaches to estimating the position and velocity of an accelerating target. At this time, I have tried a few approaches that work alright. I have tried two variations ...
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### Smoothing data by using Kalman filter

I would like to ask about smoothing data by using Kalman filter. Due to quantization, I have data that is not smooth. How can I smooth this data by using Kalman Filter. For your information, the data ...
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### Understanding an adaptative single neuron PID controller

I only know the "vanilla" use of a Kalman filter and I am currently trying to understand an article available here (the algorithm is presented in the 6 first pages) : Adaptive Single Neuron ...
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### Application of UKF on quaternions

I'm trying to perform a state estimation on quaternions to predict the future orientation of a human head. The only sensor data I can obtain (from the AR headset) is the current orientation of the ...
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### IMU Speed Tracking Through Known Path

I am new to signal processing and Kalman Filtering 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 ...
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### Filtering difference of correlated measurements

I have an application with two separated GPS receivers giving live positions and I'm deriving a heading/displacement from the vector between them. Each set of position measurements is noisy and has ...
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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?
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### How to Find the Probability of Kalman Filter States?

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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### 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. )....