Information Technology Reference
In-Depth Information
3
Video Traffic Prediction Based on Wavelet Packet
As mentioned above, frequency division of real-time video signal can be determined
if we can find the optimal orthogonal wavelet packet basis in
LR
. This section gives
video traffic prediction algorithm based on optimal wavelet packet decomposition.
2
()
LMS algorithm is a linear filtering method; it uses a linear combination of historical
data to predict. This algorithm is more adaptive, simple and effective, does not need to
know the autocorrelation structure of time series and able to achieve satisfactory online
prediction results of real-time signal [13]. Real-time prediction accuracy of the LMS
algorithm is close to the long memory model prediction accuracy when the signal has
lower Hurst parameter and do not show very long correlation [14].
For prediction problem in the wavelet domain, LMS algorithm can be described as
follows : there exists two sets of variables
di
and ( )
( )
pi
, where
di
is a known set
( )
of wavelet coefficients,
pi
is a set of wavelet coefficients need to be predicted,
( )
namely,
pi
is a function with an input set { ( ), (
( )
di di
−
1),
, (
di M
−
+
1)}
. As-
sume that this function is linear and we have:
M
−
1
pn k
(
+=
)
wl d n l
( )
⋅
(
−
)
(4)
l
=
0
Where,
T
are coefficients of the prediction filter,
Www
=
[(0 , (1 , , (
wM
−
1
1)]
T
is the input sequence and
pn k
(
+
)
is the
Dn
() [ (), (
=
dn dn
−
1), , (
dn M
−
+
estimates of
k
step. Prediction error is given as follows:
T
en
( )
=+−+=+−
pn k
(
)
d n k
(
)
pn k
(
)
W Dn
( )
(5)
Optimal linear prediction on mean squared error sense should make the mathemati-
cal expectation of mean square error
2
[( ]
ξ =
Ee n
to obtain the minimum. LMS algo-
rithm is a gradient search algorithm, the prediction coefficients
W
alters over time, of
which the adjustment process depends on the feedback of error
en
. When prediction
initiate, we first estimate to set the coefficient of the initial value (0
w
, then update
coefficient
W
using equation (6) and use the updated coefficients for the next predic-
tion.
( )
β ⋅
en k
(
−⋅
)
Dn k
(
−
)
(6)
Wn
(
+=
)
Wn
( )
+
2
Dn k
(
−
)
2
Where
<<
, if
β
is greater, the prediction convergence is quicker and response to the signal changes
is more rapid, but the fluctuations after the convergence is greater too. On the con-
trary, if
⋅
,
β
is step adjustment factor meet
0
Dn k
(
−=−
)
Dn k
(
)
Dn k
(
−
)
2
T
β
is smaller, the prediction convergence is slower, but the fluctuations after
