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 [DPRG] how is GPS covariance estimation done? Message index sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: [DPRG] FYI: Roborama video's Belgium May 5, 2007 Next message: [DPRG] how is GPS covariance estimation done? Subject: [DPRG] how is GPS covariance estimation done? From: Chris Jang cjang at ix.netcom.com Date: Sat May 19 18:15:39 CDT 2007 ```Hello, I've been reading about the Kalman filter and wonder where the covariance matrices come from? The theory is interesting. But eventually to use it, the filter requires statistics for both the system process and the measurements. The measurements can be many things - but for most robot builders, they will be GPS position readings. Allow me to provide a concrete example so it makes more sense. If a robot has odometry, then when it drives around, it has a good idea where it is. This location belief will have drift in it. UMBmark is a way of figuring out the systematic and random errors. Ok, let's make this simpler and assume the robot has been tuned so there is no systematic error anymore. So it can drive around in a square (both clockwise and counterclockwise) and on average comes back right to where it started. If these final positions are recorded, we can estimate the covariance experimentally. This is a lot of work. But now there is a statistical representation of uncertainty for the "system process" that is based on odometry readings from the robot's driving. As it drives around, an ever widening Gaussian distribution blob represents the robot position. On average, the robot is really located at the tallest point of the blob. Now say the robot has a GPS receiver. With some assumptions, the Kalman filter combines the odometry based belief as to location with the GPS measurements for an optimal location. To do this, the statistical covariances of the GPS measurement is necessary, just as it was for the odometry. How is this done? I've googled around and notice that as soon as "GPS" and "covariance" are combined, there are more patents. It looks like some methods measure jitter in satellite readings from a fixed position and then try to estimate covariance. But then we know that terrestial GPS is prone to large systematic errors (buildings block the signal). Then there is differential GPS, especially the WAAS corrections common in commercial products. And to make it more complicated, I know the US armed forces has a "GPS weather forecast". Depending on conditions, GPS accuracy can be better or worse. Is this information uploaded into ordnance like the JDAM (GPS guided bomb) on the day it is used? I'm wondering if anyone has experience with real GPS systems to know how this actually works. I have no experience. I'm only reading theory. And it may be that covariance estimation is the really valuable part that no one will reveal. Everyone knows the same theory. But usually in practice, reality decides how things must work. By the way, I'm not using GPS myself. But I do plan on using Kalman filters for computer vision. I'm trying to get my mind around how this will work and hope the GPS case provides some insight. Chris ``` Previous message: [DPRG] FYI: Roborama video's Belgium May 5, 2007 Next message: [DPRG] how is GPS covariance estimation done? Message index sorted by: [ date ] [ thread ] [ subject ] [ author ] More information about the DPRG mailing list