# 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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### Least Square Error Estimation: Conditions for $(A^TA)^{ -1} = A^{-1}(A^T)^{-1}$?

I am new to linear algebra and have this simple question... in least sqaure estimation...the best estimation of the equation $Ax = b$ is $x_{Estimated} = A (A^t A )^{-1} A^t b$...the projection of $b$ ...
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### Kalman Filtering with Unknown State Transition Matrix

I'm currently studying the use of Kalman filters for estimating linear systems. My current State Transition Matrix (STM) is the identity since so far I've been dealing with non time-varying systems. ...
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### Kalman Filter with Accelerometer with DC Offset

Goal: For a particle moving uniaxially, to estimate position ($d$) and velocity ($v$) from noisy acceleration ($a$) and very noisy position (GPS) measurements using a Kalman filter. Catch: The ...
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### In Kalman filters why is it necessary to transform the systems dynamics matrix to the state transition matrix?

Previously when I have implemented Kalman filters I have used the transformation $$\mathbf{A(t)} = \mathcal{L}^{-1} \left( s \mathbf{I} - \mathbf{F} \right) ^{-1}$$ to calculate the state ...
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### Why is the Kalman gain constant when position and velocity change?

I used the measured position to estimate the velocity using a Kalman filter. But in simulations, the Kalman gain changes quickly and then remains constant when position and velocity continue to ...
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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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### Capture legitimate huge increase/drop in fuel level from noisy measurements

I have a fuel sensor installed in a lorry fuel tank. The sensor measures the current fuel level (in percentage) of the tank. However, due to the fact that the fuel is sloshing in the tank, the fuel ...
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### The role of GPS in INS/GPS navigation systems

Ideally, a gyroscope and an accelerometer would be enough for a complete navigation solution (attitude + position), using dead reckoning. This comprise the Inertial Navigation System, INS. In non-...
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### Interpreting sensor noise data

Introduction :I am trying to create an EKF for an autonomous vehicle, and i need to model the error of the sensors. (I am a mechanical engineer so my knowledge on electric signals is limited). The ...
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### How to determine covariance matrices $\mathbf P$, $\mathbf Q$, and $\mathbf R$ in Extended Kalman Filter

I am implementing an Extended Kalman-Filter and an Unscented Kalman-Filter for state and parameter estimation of a conveyer belt system. The problem is that I don't really know how to determine the ...
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### Alternatives to offline Kalman filtering

Recently I got into vehicle models and filtering in general and immediately faced with the following question. I have the recorded GPS data from car driving on a highway. However, there is a ...
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### Image Restoration using kalman filter

I have been trying use a Kalman filter to restore an image that was blurred with a known Point Spreading Function and corrupted with noise. I have looked at theory and have a basic understanding of ...
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### Improving Velocity Estimation Using Multiple Sensors in a Dynamic System

I have a sensor reduction model which gives me a velocity estimate of a suspension system(velocity 1) . This suspension system estimate velocity is used to calculate another velocity(velocity 2) via ...
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### Kalman Filter Algorithm for Unknown Process and Measurement Noise

I want to be use kalman filter for the state estimation but I don't know about process and measurement noise. How can I estimate process and measurement noise and use this information for kalman ...
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### When is it necessary to use a Kalman Filter, and not a simple estimation method?

I know its a stupid question, but I got understand this very fundemental point. Say we have a sinousodial signal, which we want to extract from a noisy (known variance and mean) measurement. It is ...
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### Kalman Filter - Deriving state transition function

I am relatively new to using Kalman Filtering. Currently I am trying to understand it and how to implement it in Matlab. I found a website with some nice examples that I would like to rewrite in ...
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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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### 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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### 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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### Simulating Range Bearing Sensor with MATLAB with Gaussian Noise (Generating Gaussian Colored Random Vector)

I would like to simulate a sensor that provides range and direction of a beacon. This is for EKF localization, so the noise must be Gaussian (i.e. $\mathcal{N}(0, \sigma^{2})$. Also, I would like to ...
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### Questions on Weighted Least Square Estimation

This is a page from the book linear algebra,geodesy and gps by Gilbert Strang.... the page explains about the justification of the inverse of the of the co variance matrix of measurement vector $b$ in ...
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### Gyroscope sensor drift problem at speed

I have an iPhone mounted on a bike to measure the slope of the road in real-time. This works pretty well at first but as soon as I speed up, the reported pitch starts to drift. I'm using CoreMotion ...
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### Kalman filter with multiple sensors

I have been reading more about EKF and I am a bit confused on how you handle predictions with multiple sensors. Ex, I have IMU, GPS, Odom and Stereo Camera. Each can be used to predict location, how ...
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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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### If a Kalman filter can only receive information on $(x, y)$ position, is there any reason to have acceleration as part of the model?
I'm new to working with Kalman filters. I have a Kalman filter that's working well for modelling the 2D position of an object. The model at the moment holds information on position ($x$ and $y$) and ...