# 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?
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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 ...
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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 ...
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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 ...
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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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### 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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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 ...
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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 ...
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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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### 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 ...
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### 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 ...
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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 ...
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