A Full-Body Wireless Wearable UWB-Based Human Motion Capture and Gait Analysis System - E-Healthcare Systems and Wireless Communications - page 452

b = d d cos α ( ) (25)

Actual Ranging and Localization
Measurements

ij ki kj

where α is the angle between d ki and d kj Singular
Value Decomposition (SVD): the “scalar prod-
ucts” matrix B formed from the elements b ij is a
symmetric matrix. The SVD of B gives (Zhang-
Xin, He-Wen et al. 2009):

In order to evaluate the system performance based
on actual-data, on-body UWB measurements
were taken at the MPRG 6 labs. The following
equipments were used: HP33120A function gen-
erator, Tektronix CSA8000B Digital Sampling
Oscilloscope, Geozondas pulser (GZ1106DL1,
GZ1117DN-25), and two antennas manufactured
by the Virginia Tech Antenna Group and from Time
Domain Corporation. In practical gait analysis
systems, since the main target is to acquire the
distances among the sensors during movement, the
effect of the probable antenna displacement due
to subject's movement, ought to be considered.
In our case, actual measurements were taken for
the distance between the knee and ankle sensors
at the MPRG labs, and the acquired pulses were
further used in post-processing simulations. This
was done in order to estimate the TOA of the
received pulses, and obtain the corresponding
Euclidean distance. The results are plotted and
compared to a commercial optical tracking system
plotted for the optimal and suboptimal template
based receivers in Figure 6. As can be seen, the
proposed system achieves obvious improvement
as compared to the commercial system, providing
an average ranging accuracy of 1 mm compared
to 11 mm for the commercial optical tracking
system. Further from the results, the same per-
formance of optimal TOA estimators is obtained
using suboptimal templates at the expense of a 2
dB SNR requirement. Specifically, the optimal-
template based detector required an SNR = 20 dB,
whereas the suboptimal-based detector required
an SNR = 22 dB to guarantee the 1 mm ranging
accuracy. Nevertheless, this accuracy is achieved
at low-power consumption.

B = UVU' (26)

where, V=diag{ λ 1 ,λ 2 ,…, λ n } is a diagonal matrix of
eigenvalues of B with λ 1 ≥λ 2 ≥ … ≥λ n ≥0 , and U=[ u 1 .
u 2 ,…,u n ] is an orthogonal matrix with columns
equivalent to the eigenvectors (Zhang-Xin, He-
Wen et al. 2009). Since, B is a symmetric posi-
tive definite matrix, the rank of B is equal to the
dimensionality of D (i.e., the number of positive
eigenvalues) (Zhang-Xin, He-Wen et al. 2009).
Hence,

X = UV 1/2 (27)

Figure 5 (a) shows the estimated positions from
the initialization stage plotted along with the actual
node positions for motion capture (MoCap) data
files representing normal-walking. The achieved
localization accuracy of our proposed system
initialization is 0.247 mm. Moreover, Figure 5
(b) depicts the estimated positions from the core
localization stage also compared to the actual
node positions for MoCap data. The resulting
mean absolute three-dimensional (3D) localiza-
tion error was 0.47 mm with ± 52 μm variations
among the different files. This accuracy is better
than the accuracy for current technologies, with
millimeter and sub-millimeter of up to ≈ 0.8 mm
accuracies reported for the latter (Optotrak 2009;
Vicon 2009).