On vio's IMU pre integration (the idea when I first started)

         It involves sensor data processing , At present, my biggest feeling is , Originally continuous random variables obey a distribution , This distribution is what we know , But after discretization , This random variable is still a random variable , But its mean and variance may change , And it is related to the sampling frequency during discretization , All we have to do is ： Using the first moment of known continuous random variables 、 Second order moment , The first moment of random variables with discrete characteristics 、 The second moment is estimated .        

         Be specific IMU How to do pre integration , Exactly what it is , What is theoretical derivation , Record that you haven't understood IMU And my inner thoughts when pre integrating .

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        Once the residual function is involved , One thing we need to make clear is , The residual function is absolutely used to form the increment of back propagation , The larger the residual is , It means that the increment of back propagation is larger , The greater the amount of updates ; But all of this , There is a prerequisite , That's it , Your residual calculation is absolutely correct , If not , Then it is likely to produce the wrong amount of updates ; therefore , To measure this correctness , Then this residual is definitely a random variable that obeys a certain distribution , Generally speaking, it is Gaussian distribution , At this time, add the reciprocal of variance to measure , If the variance is large , The reciprocal of variance is very small , Even multiply by a large residual , Neither is much bigger , That means I don't trust this residual , On the contrary, it means that I trust this residual , therefore , The core work is to determine the second-order central moment as the residual of random variables - variance .

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        Currently in VIO There is a priori term in the residual function of... For the time being, I don't know what it is and where it is sacred .

        VIO The residual function is mainly to estimate the state quantity