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I have been reading more about EKF and I am a bit confused on how you handle predictions with multiple sensors.
Ex, I have IMU, GPS, Odom and Stereo Camera.
Each can be used to predict location, how do you combine them?
My understanding of EKF fits in the basic framework of predict, act, measure, fuse prediction with sensor.
But it's not clear how multiple sensors that measure the same thing is used.
You can have only one (or no) primary sensor which is used in the prediction process. All other sensors are secondary and only used for corrections. Each correction takes the current state and a measurement from one of the secondary sensors and outputs the corrected state. You can run corrections as often as you want, typically each time one of the secondary sensors produces a new measurement. There is no need to run corrections at a fixed interval.
The new state is predicted from the model matrices F and B and from the old state x and primary sensor data (or control input) u. $$x_{k+1} = Fx_k + Bu_k$$
The corrected state is calculated from the kalman gain matrix K, observation matrix H and secondary sensor data z. Each secondary sensor has its own observation matrix. $$x_{k,corrected} = x_k + K_k(z_k-H_k x_k) $$
You have to designate one primary sensor each for orientation and position. Alternatively, you can go without primary sensors if system dynamics allow. The primary sensors should be extremely reliable, accurate in the short term, and support a high update rate. Long term drift is not a concern here.
In a car navigation system, the primary sensors are usually steering angle and odometer, the secondary sensor is GPS. In an attitude and heading indicator for aircraft, the primary sensor is a three-axis gyro and secondary sensors are accelerometer and magnetometer.
There can be an arbitrary number of secondary sensors. Their purpose is to provide long term accuracy, which the primary sensors lack. The secondary sensors have other shortcomings, like unreliability (no GPS in tunnels), poor short term accuracy (apparent gravity vector disturbed by g-forces from maneuvering), or incomplete information (gravity vector provides pitch and bank, but not heading). If you have a sensor that can take both roles - a sensor that is reliable, provides enough information to uniquely deduce orientation or position, and is accurate both in the short and long term, then you don't need a Kalman filter in the first place.
The prediction stage of the Kalman filter runs at a fixed and high rate and continuously updates the current estimates for position and orientation based on the old estimates and measurements from the primary sensors. If you operate the Kalman filter without primary sensors, it turns into a simple model-based extrapolator. Needless to say, extrapolating from the last known GPS position using steering and odometer data is much more accurate than a simple constant-speed extrapolation.
The correction stage of the Kalman filter becomes active whenever a measurement from a secondary sensor arrives. Each correction handles the measurement from only one sensor and updates the current estimates for position and orientation. There can be an arbitrary number of corrections with arbitrary or even irregular update rates (still no GPS in tunnels, therefore no corrections for several minutes).
