You should use a Kalman Filter. Here are two nice tutorials that explain how Kalman Filter algorithm works and the working principle of IMU/GPS sensors.
The simplest answer to all those questions, is to use an EKF. But since you are not familiar with the mathematical formulas of EKF here are some possible methods which might be useful for your problems. Here I'm trying to explain some steps of the EKF in a simple manner.
Let's start with your second question. Dead Reckoning method can be used to estimate ...
Is it necessary to use any filter to fuse Ublox ZED-F9K's GNSS and IMU/Odometry
My answer is NO, for the following reasons:
(1) GNSS and IMU are independently developed modules with matured software. It is unlikely for the vendor to "fuse" them at the hardware level. A more efficient method is to let the MCU/SBC to talk to ...
This isn't something that can just be answered. There are numerous ways to do this.
You can go low tech with IR emitters and retroflective tape (or retroflectors) with IR sensors.
A more high-tech solution would be to utilize ultra-wide band transceivers. With UWB you can pinpoint your rovers in 3 dimensional space around each other.
I am not sure what you mean by 'displacement value which is acceleration independent'. The conversion of relative positioning you're getting from /dev/input/mouse will always depend on the DPI of the mouse. All you'd have to do is figure out the DPI (either from the specs or from measurements, and hence the conversion between reported dx/dy values, and then ...
An IMU gives you linear acceleration and rotational speed. It doesn't give a position.
You can integrate the output of an IMU to get a linear position and angular orientation (the pose), but you need to choose initial speeds and positions.
Typically, these choices are zero. If you decided to choose zero for your initial/default pose, then returning "home"...
This is another aspect of a longer answer I wrote here. Briefly restated, your problem is that a wheeled robot like this is nonholonomic, which means you can just use absolute encoder counts and get a valid result for position and heading.
You have two axes of control: a left wheel and a right wheel; and you have three degrees of freedom: left/right ...