Stable composite clock
Apparatus and method for producing a composite clock signal with optimized stability characteristics from individual clocks which have different stabilities or variances. The composite clock signal includes weighted individual clock signals. In a first (PPN) case, an optimum composite clock is a scale-factor-weighted linear combination of clock signals. In another (non-PPN) case, the optimum stable composite clock is the output of a linear filter of the input clocks signals. Both the phases and frequencies of the individual clocks over time are estimated.
1. A composite clock, comprising:
a plurality of individual clocks, each producing a clock signal, and the i th clock having known Allan variance curve give by a standard curve times a constant λ i ;
reading means coupled to said plurality of individual clocks, for simultaneously reading said clock signals; and
means coupled to said reading means and to a source of said variance information, for generating a composite clock signal according to
x
->
c
(
t
)
=
∑
i
=
1
n
K
i
*
x
->
i
(
t
)
(
57
)
where
{right arrow over (x)} c =Composite clock state (estimate of phase and/or frequency produced by the composite clock mechanism);
* represents multiplication;
{right arrow over (x)} i =Individual clock states read out by the hardware
K i =the gain chosen to optimize the stability of the composite clock, such that
K
i
=
(
1
/
λ
i
)
/
(
∑
j
=
1
n
1
/
λ
j
)
.
(
58
)
2. A clock according to claim 1 , wherein the gains add to unity (1) in accordance with
1
=
∑
i
=
1
n
K
i
(
t
)
.
(
59
)
3. A composite clock comprising:
a plurality of individual clocks, each producing a clock signal, and the i th clock having known Allan variance curve given by a standard curve times a constant vector
λ
→
i
=
[
λ
x
i
λ
y
i
]
;
λ
x
i
=
scale factor for short term (phase random walk) stability errors,
λ i y =scale factor for long term (frequency random walk) stability errors,
reading means coupled to said plurality of individual clocks, for simultaneously reading said clock signals; and
means coupled to said reading means and to a source of said variance information, for generating a composite clock signal, the vector
[
x
c
y
c
]
according to
[
x
.
c
y
.
c
]
=
[
y
c
+
u
v
]
(
60
)
where
[
x
c
y
c
]
is the phase and frequency;
x c is phase; and
y c is the frequency,
u is the estimate of the composite clock phase noise,
v is the estimate of the composite clock frequency noise, and u and v are given by
[
u
v
]
=
∑
j
=
1
n
K
→
j
*
[
x
.
j
-
y
j
y
.
j
]
(
61
)
where
[
x
i
y
i
]
are phase and frequency estimates of the ith clock,
the optimized gains are given by
K
→
i
=
[
K
x
i
K
y
i
]
(
62
)
K
x
i
=
(
1
/
λ
x
j
)
/
(
∑
j
=
1
n
1
/
λ
x
j
)
(
63
)
K
y
i
=
(
1
/
λ
y
j
)
/
(
∑
j
=
1
n
1
/
λ
y
j
)
.
(
64
)