Determining the composition of physical structures from boundary measurements, including the composition of subscriber loops
View Patent ↗A method for the direct estimation of configuration parameters defining the make-up of a physical system, such as cable lengths and gauges in the case of telephone subscriber loops, from boundary or end-point measurements of the physical structure, such as the impedance or return loss response of a subscriber loop, due to a probing source.
1. A method for estimating a loop composition of a subscriber loop in terms of loop parameters X 1 , X 2 , . . . , X i , . . . , X N the loop having a frequency-domain response H(ω,X 1 ,X 2 , . . . ,X i , . . . ,X N ) for the loop parameters, the method comprising the steps of
(a) determining a range for each loop parameter X i ;
(b) for each loop parameter X i , generating a frequency-domain loop parameter function F x i (ω) wherein
F
x
i
(
ω
)
=
∫
x
1
∫
x
2
…
∫
x
i
…
∫
x
N
X
i
H
(
ω
,
X
1
,
X
2
,
…
,
X
i
,
…
,
X
N
)
ⅆ
X
1
ⅆ
X
2
…
ⅆ
X
i
…
ⅆ
X
N
,
(c) generating a loop kernel k(ω,β) for all loop parameters wherein
k
(
ω
,
β
)
=
∫
x
1
∫
x
2
…
∫
x
N
H
(
ω
,
X
1
,
X
2
,
…
,
X
N
)
H
(
β
,
X
1
,
X
2
,
…
,
X
N
)
ⅆ
X
1
ⅆ
X
2
…
ⅆ
X
N
,
(d) generating a parameter response function g i (β) for each loop parameter from the integral relation
F
x
i
(
ω
)
=
∫
β
k
(
ω
,
β
)
g
i
(
β
)
ⅆ
β
,
(e) energizing the loop from a measurement end with an energy source,
(f) measuring a response signal H R (ω)=H(ω,X 1 ,X 2 , . . . ,X 1 , . . . ,X N ) for the loop at the measurement end, and
(g) directly determining each loop parameter X i from the integral relation
X
i
=
∫
β
H
R
(
β
)
g
i
(
β
)
ⅆ
β
.
2. The method as recited in claim 1 wherein step (e) includes the step of computing the inverse of k(ω,β).
3. The method as recited in claim 1 wherein step (e) includes the step of computing the inverse of k(ω,β) using singular value decomposition.
4. The method as recited in claim 3 wherein step (f) includes the step of filtering noise from the response signal.