Kalman filter for crawler robot?

Question

data mining

Good day
, I smoked literature on this issue for a long time (mostly bourgeois articles), but there are many questions left
(there will be many formulas written in text form, who don’t want to torture themselves - at the end of the text there will be a link to a screenshot of Matkadov’s sheet, there are formulas look clearer)
we have:
a caterpillar platform on which an accelerometer and a gyroscope are installed
received the following filter:
State vector X (6x1):

x	x-coordinate
y	y-coordinate
φ	robot rotation angle
V	linear speed of the robot
ω	robot angular velocity
a	tangential acceleration of the robot

Observation matrix Y(2x1):

ya	accelerometer readings
yg	gyroscope readings

system model (t - time step):

x = x + cos(φ) * (V * t + a * t^2/2)

y = y + sin(φ) * (V * t + a * t^2/2)

φ = φ + ω * t

V = V + a * t

ω = ω

a = a

matrix F(6x6):

one	0	-sin(φ) * (a * t^2 / 2 + V * t)	t*cos(φ)	0	t^2 * cos(φ) / 2
0	one	cos(φ) * (a * t^2 / 2 + V * t)	t*cos(φ)	0	t^2 * sin(φ) / 2
0	0	one	0	t	0
0	0	0	one	0	t
0	0	0	0	t	0
0	0	0	0	0	t

Matrix H(2x6):

0	0	0	0	0	one
0	0	0	0	one	0

Matrix I (6x6) - single
Matrix N (2x2) - single
Matrix V (2x2) - single
Matrix R (2x2) - single
Matrix W (2x2) - single
Matrix Q (6x6): - selected empirically, tried to calculate based on random sampling based on variance (for diagonal elements) and covariance for all others
Matrix P(6x6) - initially equal to matrix Q
[xT] - transposed matrix, (x[-1]) - inverse matrix
of the filter itself:
K = P* [HT] ((HP[HT] + VR[VT])[-1])
P=(I - KH)P
x = x + K(y - h(x))
P=FP[FT] + WQ[ WT]
x = f(x,y)
what I ended up with:
acceleration
graph rotation angle graph
in general and in general, for acceleration, the graph is more or less similar to the truth, but for the angle of rotation, complete anarchy occurs.
it was noticed that the Q matrix has a very big influence on the behavior of the filter,
so I have two questions:
1) how close am I to the correct compilation of the filter itself (do not judge strictly if I got into a puddle, but rather indicate)
2) how the matrix is ​​\u200b\u200bcalculated Q? there was even such a thing - I picked up the matrix Q - everything works perfectly, changed the behavior of the system (suppose it changed the acceleration) - and the filter stopped working.
all calculated moments on the matkad sheet:

Answer 1

Where does speed come from? From the readings of the acceleration sensor, the speed cannot be calculated (too rough + an additive error accumulates).
The coordinates from the readings of the accelerometer and the angular sensor, all the more impossible to calculate - complete nonsense will turn out. And also imagine what the accuracy of determining the coordinates will be if, say, the angle sensor is 16-bit, and the robot traveled only a couple of kilometers (I suggest: 10cm for each km if the robot was driving in a straight line, and this is if the speed is calculated perfectly) ...
Of course, the noise depends on the capacity of the sensors: for example, if you have 128-bit sensors, then you won’t notice much error in the first hour or two of work.