Ground Balance holes - a solution

[Teleno]

Ground balance (GB) is usually solved by making linear combinations of successive samples such that the sum of the ground signal is null.

Unfortunately, the same linear combinations also null for certain time constants (TC). These are called GB holes. Objects with TC near those holes escape detection if this form of GB is used.

The solution I propose is to use 3 successive samples s1, s2, s3 at times t, 2t and 4t. In the presence of pure ground (thus no targets) and assuming the usual invariant 1/t ground response, the amplitude ratios of successive samples is as follows:

s2/s1 = (1/2t)/(1/t) = 0.5

s3/s2 = (1/4t)/(1/2t) = 0.5

We express this as the point (0.5, 0.5) on a plane. This is the Ground point.

GP = (0.5, 0.5)

A target with TC = tau will have the following ratios:

s2/s1 = exp(-t2/tau)/exp(-t1/tau)
s3/s2 = exp(-t3/tau)/exp(-t2/tau)

We express this as the target point (exp(-t2/tau)/exp(-t1/tau), exp(-t3/tau)/exp(-t2/tau)) on a plane. This is the Target point.
This is a plot of the euclidean distance between the Target and the Ground point. They never meet, which solves the problem of the GB holes.


sqrt((exp(-10/tau)/exp(-5/tau)-0.5)**2 + (exp(-20/tau)/exp(-10/tau)-0.5)**2))

[6666]

Is this something that you will make into a working project ?

[rickb]

Is this something that you will make into a working project ?

The OP should NOT have to commit to a working project on a silver platter in order to propose a possible solution to a problem, nor should he be subjected to criticism for not doing so.

[6666]

The OP should NOT have to commit to a working project on a silver platter in order to propose a possible solution to a problem, nor should he be subjected to criticism for not doing so.

Who asked you, I asked the question to the OP. if he chooses to answer me thats up to him its not for you to stick your nose in, show me where I asked for working project on a silver platter

[Teleno]

The following chart shows how different mixtures of target and ground behave. The TCs vary between 5us and 30us.

The outer (orange) line is 100% target, the next line is a mix of 90% target and 10% ground ... then so on until the last line which is 10% target 90% ground.




in this plot we see the distances to Ground Point of all the above target/ground mixtures:



We see that a distance threshold of about 0.1 can tell a target in a signal that's 70% ground. A threshold of 0.05 works in 90% ground.

Is this something that you will make into a working project ?

It's something I want to experiment with and see if actually works.

gnuplot of the above graphs:

set terminal svg size 400,400 enhanced fname 'arial'  fsize 10 butt solid
set output 'out.svg'
set style fill transparent solid 0.35 noborder
set style circle radius 0.02
set parametric
set xrange [0.2:0.9]
set yrange [0.1:0.7]
unset key
plot [5:30] (1*exp(-10/t)+0/10)/(1*exp(-5/t)+0/5), (1*exp(-20/t)+0/20)/(1*exp(-10/t)+0/10) with lines, (0.9*exp(-10/t)+0.1/10)/(0.9*exp(-5/t)+0.1/5), (0.9*exp(-20/t)+0.1/20)/(0.9*exp(-10/t)+0.1/10) with lines, (0.8*exp(-10/t)+0.2/10)/(0.8*exp(-5/t)+0.2/5), (0.8*exp(-20/t)+0.2/20)/(0.8*exp(-10/t)+0.2/10) with lines, (0.7*exp(-10/t)+0.3/10)/(0.7*exp(-5/t)+0.3/5), (0.7*exp(-20/t)+0.3/20)/(0.7*exp(-10/t)+0.3/10) with lines, (0.6*exp(-10/t)+0.4/10)/(0.6*exp(-5/t)+0.4/5), (0.6*exp(-20/t)+0.4/20)/(0.6*exp(-10/t)+0.4/10) with lines, (0.5*exp(-10/t)+0.5/10)/(0.5*exp(-5/t)+0.5/5), (0.5*exp(-20/t)+0.5/20)/(0.5*exp(-10/t)+0.5/10) with lines, (0.4*exp(-10/t)+0.6/10)/(0.4*exp(-5/t)+0.6/5), (0.4*exp(-20/t)+0.6/20)/(0.4*exp(-10/t)+0.6/10) with lines, (0.3*exp(-10/t)+0.7/10)/(0.3*exp(-5/t)+0.7/5), (0.3*exp(-20/t)+0.7/20)/(0.3*exp(-10/t)+0.7/10) with lines, (0.2*exp(-10/t)+0.8/10)/(0.2*exp(-5/t)+0.8/5), (0.2*exp(-20/t)+0.8/20)/(0.2*exp(-10/t)+0.8/10) with lines, (0.1*exp(-10/t)+0.9/10)/(0.1*exp(-5/t)+0.9/5), (0.1*exp(-20/t)+0.9/20)/(0.1*exp(-10/t)+0.9/10) with lines, (1.38777878078145e-16*exp(-10/t)+1/10)/(1.38777878078145e-16*exp(-5/t)+1/5), (1.38777878078145e-16*exp(-20/t)+1/20)/(1.38777878078145e-16*exp(-10/t)+1/10) with lines



set terminal svg size 400,300 enhanced fname 'arial'  fsize 10 butt solid
set output 'out.svg'
set nokey
set xrange [5:30]
set yrange [0:0.5]
plot sqrt(((1*exp(-10/x)+0/10)/(1*exp(-5/x)+0/5) - 0.5)**2 + ((1*exp(-20/x)+0/20)/(1*exp(-10/x)+0/10) - 0.5)**2) with lines, sqrt(((0.9*exp(-10/x)+0.1/10)/(0.9*exp(-5/x)+0.1/5) - 0.5)**2 + ((0.9*exp(-20/x)+0.1/20)/(0.9*exp(-10/x)+0.1/10) - 0.5)**2) with lines, sqrt(((0.8*exp(-10/x)+0.2/10)/(0.8*exp(-5/x)+0.2/5) - 0.5)**2 + ((0.8*exp(-20/x)+0.2/20)/(0.8*exp(-10/x)+0.2/10) - 0.5)**2) with lines, sqrt(((0.7*exp(-10/x)+0.3/10)/(0.7*exp(-5/x)+0.3/5) - 0.5)**2 + ((0.7*exp(-20/x)+0.3/20)/(0.7*exp(-10/x)+0.3/10) - 0.5)**2) with lines, sqrt(((0.6*exp(-10/x)+0.4/10)/(0.6*exp(-5/x)+0.4/5) - 0.5)**2 + ((0.6*exp(-20/x)+0.4/20)/(0.6*exp(-10/x)+0.4/10) - 0.5)**2) with lines, sqrt(((0.5*exp(-10/x)+0.5/10)/(0.5*exp(-5/x)+0.5/5) - 0.5)**2 + ((0.5*exp(-20/x)+0.5/20)/(0.5*exp(-10/x)+0.5/10) - 0.5)**2) with lines, sqrt(((0.4*exp(-10/x)+0.6/10)/(0.4*exp(-5/x)+0.6/5) - 0.5)**2 + ((0.4*exp(-20/x)+0.6/20)/(0.4*exp(-10/x)+0.6/10) - 0.5)**2) with lines, sqrt(((0.3*exp(-10/x)+0.7/10)/(0.3*exp(-5/x)+0.7/5) - 0.5)**2 + ((0.3*exp(-20/x)+0.7/20)/(0.3*exp(-10/x)+0.7/10) - 0.5)**2) with lines, sqrt(((0.2*exp(-10/x)+0.8/10)/(0.2*exp(-5/x)+0.8/5) - 0.5)**2 + ((0.2*exp(-20/x)+0.8/20)/(0.2*exp(-10/x)+0.8/10) - 0.5)**2) with lines, sqrt(((0.1*exp(-10/x)+0.9/10)/(0.1*exp(-5/x)+0.9/5) - 0.5)**2 + ((0.1*exp(-20/x)+0.9/20)/(0.1*exp(-10/x)+0.9/10) - 0.5)**2) with lines, sqrt(((1.38777878078145e-16*exp(-10/x)+1/10)/(1.38777878078145e-16*exp(-5/x)+1/5) - 0.5)**2 + ((1.38777878078145e-16*exp(-20/x)+1/20)/(1.38777878078145e-16*exp(-10/x)+1/10) - 0.5)**2) with lines

[6666]

It's something I want to experiment with and see if actually works.

Thanks reply, I hope it works for you, good luck with the project.