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I am reading one paper on observability Observability Analysis of Aided INS with Heterogeneous Features of Points, Lines and Planes.

The state vector contains the current IMU state and the feature state. The IMU state consists of a unit quaternion representing the rotation, current IMU velocity and position, and gyroscope and accelerometer biases. The velocity is the derivative of the position with respect to the time, so they are dependent. Do the parameters in the state vector need to be independent? Why are the biases considered as part of the state vector? What are the advantages to do so? Can this result in a better estimation?

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Indeed position, velocity and acceleration (but also the unit quaternion and the angular velocity of the gyroscope) are related to each other. But the word "biases" refers to the measurement of these quantities, for example the gyroscope will measure the angular velocity plus a bias. Including these biases in the state space allows you the estimate the average value of each bias, which would improve your estimate of entire state vector.

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  • $\begingroup$ Acceleration bias and gyroscope bias are modeled as random walk and it means their derivatives are Gaussian distribution. $\dot b = n$. Do it mean their states should not change along time? Is the bias model not correct? Maybe bias states changes very slowly along time, so it is better to add them to state vector. $\endgroup$ – Jogging Song Oct 19 '18 at 3:21
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    $\begingroup$ @JoggingSong You would have to test this to be sure how to model the biases, but from what I remember it can be modeled by a none-zero-mean Gaussian noise. It is also worth mentioning that the biases are temperature dependent. $\endgroup$ – fibonatic Oct 19 '18 at 9:39

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