IMU

 

 

(1) Use IMU to make predictions

Read in a dataset of 10/20 frames, and use the IMU to initially predict the pose and display its path.

Christian Forster, Luca Carlone, Frank Dellaert, Davide Scaramuzza, "IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation," Robotics: Science and Systems (RSS), Rome, 2015. 

 

(2) Use the luminosity difference or something as the update part, calculate the gain through the camera's observation equation, and then update it.

 

A. Filter Initialization 

Equations of motion for error states

2.1 The dynamic equation of the IMU system in continuous time

This involves three quantities, the true value (true-), the nominal value (nominal-), and the error-state value. The true value is a combination of the nominal value and the error value. The nominal value is the "big signal" from the nonlinear equation, and the "small signal" that satisfies the linear Gaussian filter from the linear equation of the error value.

2.1.1 Related variables

• Among the relevant variables here, the input value is the measured value of the IMU, and the local acceleration of gravity.The values ​​of other truth-valued variables are derived from them. The normal value is an abstract variable that represents an ideal value and cannot be estimated. In the fusion, we use the estimated real value as the nominal value to predict.
• The nominal value is a completely ideal value, and we attribute the uncertainty of the true value and the nominal value generated by various factors to the variable representation.
• Here we use the expression method of Hamilton quaternion
• The angular rate here is expressed locally, so that the sensor measurement value under the machine system b can be used directly
• The angle error here is also expressed locally, which is the classic method used by many literatures and algorithms, but it has been proved that the angle error defined by the globally method has better properties.
• acceleration hereThe definition is globally, my understanding is that it is convenient to calculate the speed and position under the navigation system.

2.1.2 True-state kinematics equations

• The equation of motion represented by the true-state variable. The noise of the IMU bias is defined as a random walk.

• Since the initial state and attitude are unknown, this uncertainty is the uncertainty of the gravitational acceleration vector, but in actual engineering, we formulate the initial state, that is, the gravitational acceleration uncertainty no longer exists, and the equation here is also considered to be a constant value.

 

• .IMU error sources are divided into two types, internal bias

• The true value of the IMU here is the value without bias and measurement noise. The acceleration measured by the IMU accelerometer does not include the acceleration of gravity, that is, if the body is in free fall, the reading of the accelerometer is 0 regardless of noise.

 

The true state equation of motion of the system using IMU measurements instead of true values, the state of the equation is, from the noisy measurement of the IMUdriven by white Gaussian noiseinterference.