C. Biomechanics of a Human Walking (4) For M^z0,L...,L,
The 3-D biomechanics of a human movement compute a,(n) » (m 212,..., M)
were discussed, center of body gravity, velocity,
accerelation, torque, inertia, work etc. In this and o^(M )
study, metabolic energy of knee joint is discussed.
The sum of metabolic energy C during waling by the following recursive procedure:
sequence is defined as follow.
M
ay, (M *1) 2 (o(M) (C, (M +1) = Y a, (m)(C,, (M €1-m)
C= > (0.8V +0.5) (2.C.1) & (2.D4)
where V is accerelation. Ay. (m) 2 a (m) = 4,4, (M *1)a, 4M *1- m)
(m 1/2,..., M)
(2.D.5)
D. Spectral Analysis utilizing Auto Regressive
Modeling (AR modeling) OM +1)=0"(M)(1 -ay.(M +1) @Ds)
Observed data, stationary time series,
{x0s}s = 1,2, Ni
is given, by subtracting the portion that can be
expressed as a linear combination of M past values
(5) At the same time, also compute
FPE(M)- (N (M * D(n-(M «1) ! o^(M)
(2.D.7)
x(s - 1),..,x(s - M) and adopt a, (m) corresponding to the M
the series of residuals, univariate Auto Regressive that gives the minimum of FPE( M)
Model is given. OM m, seen)
M
e(s)= x(s)- Wa(m)xGs — m) (2.D.1)
i=1 (6) The estimate of the power spectral density
Assume that the data set is given.
7.48) is given by
(X SAT) m. 2,2]
m o*(M)
(1) Subtract the mean value, i.e.,calculatandby q,:(2) = 2 (2.D.8)
END hun 1- S'a,(m)exp(-i2xgm)
== — f s
x = = x(sAÂt) (2.D.2) 1
and defined x(s) by restoring the sampling interval Af
the estimate of p : AL) is
x(s) = x(sAt) - X(s 2 1,2,..., N) pd
(2) For 1 =0,1,...,L. compute by PG ND » qu CATAL
1 1
IN (sf s)
C E S x(s * lD)x(s) (2.D.3) 2 At 2 At
N s=1
The formula that defines the best predict is
Put a,(m) = 0m = 1,2,..., M) given, the power spectral density is gotten, which
o?(0) » C,,(0) express the characteristics of a sequential system
concisely, decomposing into periodic components.
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
A. Ac
New
accura
distor
veloci
shows
B. Bic
