<transcript><audio_19>and now suppose you have a small amount you know some kind of bias like maybe 0.2 meters per second squared you know some amount that's that's left over here and now you integrate that once</transcript><video><caption><image_20>The image shows a man standing in front of a green chalkboard. He is writing on the chalkboard with a marker and appears to be in the middle of a lesson. The chalkboard is filled with mathematical equations and diagrams. The equations are written in white chalk and are arranged in a grid-like pattern. The man is wearing a blue shirt and is focused on the task at hand. The background of the image is a classroom with white walls and a window.</caption><caption><image_21>The image shows a man standing in front of a green chalkboard with white chalk writing on it. The writing on the chalkboard appears to be a mathematical equation or problem related to the concept of Earth's field. 

On the left side of the image, there is a list of equations written in white chalk. The equations are written in black marker and are arranged in a grid-like pattern. On the right side, there are two lines drawn on the blackboard, one representing the equation and the other representing the problem. The equation is written in yellow chalk and the problem is written on a whiteboard.

In the bottom right corner, the man is standing with his back to the camera, looking at the equations. He is wearing a blue shirt and is standing in a room with white walls and a window in the background. The image appears to have been taken in a classroom or lecture hall.</caption><caption><image_22>The image shows a man standing in front of a green chalkboard in a classroom. He is wearing a blue t-shirt and appears to be a teacher or a student. On the chalkboard, there are various mathematical equations written in white chalk. The equations are written in different colors and are arranged in a grid-like pattern. 

On the left side of the image, there is a text that reads "of Earth's field, field" and on the right side, it reads "time and position". On the bottom left corner, it says "elementary filters on SO3". There is also a yellow arrow pointing to the right, indicating the direction of the equations.

In the center of the blackboard is a graph that shows the relationship between the two variables. The graph is labeled "Problem" and "Acceleration". The equation is written in yellow chalk and is accompanied by a yellow line that goes from 0.2m/s.</caption><caption><image_23>The image shows a man standing in front of a green chalkboard. He is wearing a blue t-shirt with a logo on it and appears to be giving a presentation or lecture. The chalkboard is filled with mathematical equations and formulas written in white chalk. The man is gesturing with his right hand as he speaks. He has short dark hair and is looking directly at the camera with a serious expression.</caption></video><caption><image_24>The image shows a man standing in front of a green chalkboard in a classroom. He is wearing a blue t-shirt and appears to be giving a presentation or lecture. On the chalkboard, there are various mathematical equations and formulas written in white chalk. The equations are written in different colors and sizes, and the formulas are arranged in a grid-like pattern. The man is gesturing with his hands as he speaks. He has a serious expression on his face and is looking directly at the camera.</caption><transcript><audio_25>integrate it twice and you take a look at how far your estimate is from reality after 5 or 10 seconds it turns out this grows very fast you may remember that when you integrate a constant once you get a linear</transcript><caption><image_26>The image shows a man standing in front of a green chalkboard with mathematical equations written on it. He is wearing a blue t-shirt and appears to be in a classroom or lecture hall. The equations are written in white chalk and are arranged in a grid-like pattern. The man is pointing to one of the equations with his right hand and is gesturing with his left hand. He has a serious expression on his face and is looking directly at the camera. On the left side of the chalkboard, there is a diagram of a curved line with a point at the end and a line at the top, indicating that the man is explaining the equations. The text on the blackboard reads "Accelerometer to correct your error".</caption><transcript><audio_27>rate and and that's what happens you get a linear drift rate that looks very much like the gyro drift rate but if you integrate twice to get up to position your two derivatives away right or two integrals away from the position then it ends up with a fast quadratic growth rate you know a simple offset</transcript><transcript><audio_28>like this a simple fixed error will help will cause a quadratic growth rate so it's very much as if your head has a fictitious rocket thruster attached to it that's thrusting at this rate and it makes you shoot away and so that's what gets very very bad</transcript> and now suppose you have a small amount you know some kind of bias like maybe 0.2 meters per second squared you know some amount that's that's left over here and now you integrate that once integrate it twice and you take a look at how far your estimate is from reality after 5 or 10 seconds it turns out this grows very fast you may remember that when you integrate a constant once you get a linear rate and and that's what happens you get a linear drift rate that looks very much like the gyro drift rate but if you integrate twice to get up to position your two derivatives away right or two integrals away from the position then it ends up with a fast quadratic growth rate you know a simple offset like this a simple fixed error will help will cause a quadratic growth rate so it's very much as if your head has a fictitious rocket thruster attached to it that's thrusting at this rate and it makes you shoot away and so that's what gets very very bad
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