IJCSES, Vol. 10, Nos. 1-2, January-June 2016
CSES International © 2016 ISSN 0973-4406
A Novel Total Sum Vector Approach for EmbeddedBased Fall Monitoring System
Sawit TANTHANUCH1, Pornchai PHUKPATTARANONT2 and
Boonchareon WONGKITTISUKSA3
1,2
3
Department of Electrical Engineering, Faculty of Engineering, Prince of Songkla UniversityHatyai
Songkhla 90110, Thailand, E-mail:[email protected], [email protected]
Center of Excellent for Rehabilitation Engineering, Faculty of Engineering, Prince of Songkla UniversityHatyai
Songkhla 90110, Thailand, E-mail: [email protected]
Abstract: The root-sum-square is a common function to compute total sum vectors in the fall monitoring system, where the
vectors are the 3 axis acceleration components. However, the operation is difficult to implement on a microcontroller based
system due to complexity of square root extraction. This paper presents an algorithm for calculating a square root result,
which is adapted from a reciprocal square root operation. The proposed algorithm utilizes the modified Newton-Raphson
iterative method in order to employ basic arithmetic operators such as an adder, a multiplier and a shifter. The operations
are reusable with a sum-square function for optimizing resource. The numerical tests and accuracy of the proposed algorithm
are demonstrated. Results show that the proposed algorithm is highly suitable for fall monitoring based on embedded
system.
Key words: Fall detection, Total sum vector, Square root extraction, Newton-Raphson iteration.
1.
INTRODUCTION
In Thailand, the portion of population over 60 years of age
is growing rapidly. The Thailand Nation Statistical Office
(TNSO) reported that the number of elders will be more than
15 millions (15%) in 2020. This will require more investment
in elderly care services [1].
Balance dysfunction associated with the physical aspects
of agin g is th e prime in ciden ce in gerontology.
Approximately one in every three elders falls each year and
at least one-fifth results in an injury. The injuries include
bone fractures, superficial cuts and abrasions to the skin as
well as connective and soft tissue damage. In addition, falls
are the leading cause of deadly injury with brain trauma.
This is a major problem for the elder’s morbidity and
mortality affecting the overall quality of life (QoL) [2].
The risk of falling is also reduced by the personal
emergency response system (PERS). A computer vision
based on motion tracking was applied; nevertheless the
effectiveness is performed within restricted areas and without
occluding objects [3]. On the other hand, acceleration sensors
as a motion detector are widely used to overcome the
limitation of visual system. However, an accelerometry
perspective has variations as a function of movements. A
number of approaches have been proposed to distinguish
between falling and activities of daily life (ADL), thus nearly
Manuscript received February 9, 2009
Manuscript revised September 20, 2009
all of researches employ wireless transmission of
acceleration signals to a computer because the embedded
device has insufficient resource to process the information.
Therefore, the conventional system is complicated and
confronted with real-time monitoring causing delay time
around wireless link [4-5].
In this paper, we aim to describe the alternative algorithm
to approach a root-sum-square function for the fall monitoring.
The proposed algorithm utilizes Newton-Raphson numerical
method, where the same operation is reused in the iterations.
This method leads to reduce computational resources and is
highly suitable for accelerometry based on embedded devices.
The proposed algorithm is implemented on IAR Embedded
Workbench development tool and is then verified by
ADXL320 accelerometer sensors and MSP430 ultra-lowpower RISC microcontroller.
2.
THEORY
2.1. Acceleration Sensor
Accelerometers are commonly applied as activity monitoring
devices for physical activity assessment because they
respond to both the frequency and intensity of movement.
Furthermore, a measurement of acceleration can provide
velocity and position by single integration and double
integration, respectively.
Recently, the sensors have made tremen dous
advancements in Micro-Electromechanical System (MEMS).
86
IJCSES, Vol. 10, Nos. 1-2, January-June 2016
They are also miniaturized device, low cost and low energy
consumption [6]. Therefore, the ADXL320 dual axis
accelerometer based on MEMS from Analog Device is a
choice, as shown in Figures 1 and 2. The acceleration range
is ±5g, sensitivity is 174 mV/g (@3V), typical noise floor is
250mg/Hz (@ 25°C) and bandwidth ranges from 0.5 Hz to
25kHz.
Figure 3: Sensor Assembled and Associated Coordinate Systems
model [7-8], as shown in Figure 4 and the total sum vector
is calculated as:
m
Figure 1: Function Block Diagram of ADXL320
r
aX2
r
aY2
r
aZ2 .
(1)
Figure 4: ADXL320 Matlab/Simulink Model
Figure 2: Output Response of ADXL320
2.2. Square Root Extraction
Table 1
Definition of Acceleration Signals
Coordinate
X-axis
Y-axis
Z-axis
Earth
Movement
Zero
Front � +
Zero
Left � +
- gravity
Top � +
Figure 3 shows the proposed sensor, which is assembled
using two ADXL320 accelerometers mounted perpendicular
to each other for 3-degree of freedom (3-DOF) orientation.
The axes of accelerometers are aligned with the Cartesian
coordinate system, thereby providing values of acceleration
vectors along the X, Y and Z coordinates. When the sensor
is stationary, the acceleration signals along the X and Y axes
are both zero, hence the acceleration signal along the Z-axis
has the value of 1g due to gravity of the earth. Otherwise,
the acceleration signals are as shown in Table 1.
The acceleration signals are evaluated and calibrated
under various scenarios with ADXL320 Matlab/Simulink
Newton-Raphson iteration is a numerical method often used
for complicated computations. The main purpose of this
method is to find a zero point of the function shown in Figure
5 [9].
The derivation can be carried out by a piecewise first
order Taylor series expansion, as follows:
Figure 5: Newton-Raphson iteration Method
A Novel Total Sum Vector Approach for Embedded-Based Fall Monitoring System
f(xi+1) = f(xi) + f �(xi) (xi+1 – xi),
(2)
th
where xi is the value at the i iteration, f(xi) is the function
value at xi and f�(xi) is the function derivative at xi.
When f(xi+1) is closed to zero, the general form of
Newton-Raphson iteration is given as:
xi
xi
1
f ( xi )
f ( xi ) .
(3)
A conventional square root of an operand r can be
defined as
f (x) � x2 – r = 0
or
x
3.
87
EXPERIMENT AND RESULTS
The 12-bit ADC in MSP430 microcontroller at 16 MHz
clock speed was employed to acquire signals from two
ADXL320 acceleration sensors. The proposed algorithm was
realized with IAR Embedded Workbench development tool
providing that the binary point was in the middle of the
numbers with 16/32- bit fixed point arithmetic. An initial
approximation q0 was estimated by a half of 1/r as a shifter
operation. In order to enhance performance a truncated
Booth’s and Wallace tree multiplicative algorithm was
applied and shared with a square operation. The operation
flow chart is described in Figure 6.
(4)
r.
From Eq. (3) and Eq. (4), the Newton-Raphson iteration
of a square root function can be expressed as:
xi
1
xi
2
1
r
xi .
(5)
Note that Eq. (5) employs a divisor that has a higher
latency required performing a computation. It is tedious in
subsequent operations with arithmetic logic unit (ALU) of
embedded system [10].
In alternative form, a square root result is proposed by
multiplying an operand r with reciprocal square root of an
operand r
r
r / r . A reciprocal square root of an
operand q can be defined as
f (q )
or
q2
1
r
0
q 1/ r .
(6)
Then, the Newton-Raphson iteration of a reciprocal
square root function can be defined as
qi
1
qi
qi
(3 rqi2 )
2
qi
(1 rqi2 )
2
qi 1
pi
,
2
(7)
where pi = 1 – rwi and wi qi2 .
Eq. (7) is more attractive since it does not involve with
a divisor, and the result converges rapidly as quadratic
characterization. Moreover, a bit-complementary and a bit
shifter operation are obtained to enhance computation of pi.
However, a square operation should be revised with
truncated multiplication algorithm for regulating the
overflow, when wi approaches 1/r; and pi is then closed to
zero [11].
Figure 6: The Operation Flow Chart
The result of a square root extraction was obtained after
4 iterations while keeping up with 100 samples of the signals
per second, as shown in Figures 7 and 8.
88
IJCSES, Vol. 10, Nos. 1-2, January-June 2016
ACKNOWLEDGMENTS
This research is carried out under the framework of the Center of
Excellence for Rehabilitation Engineering under the National
Electronics and Computer Technology Center of Thailand
(NECTEC) and Prince of Songkla University.
REFERENCES
[1]
Statistical Yearbook Thailand 2003, Statistical Forecasting
Bureau, Thailand National Statistical Office, 2004.
[2]
Salva A., Bolibar I. and Arias C. “Incidence and
Consequences of Falls among Elderly People Living in the
Community”, Med. Clin., 122(5), 2004, 172–176.
[3]
Fan B. W., and Li W., “A New Rapid Algorithm of Motion
Estimation for H.264”, IJCSEC, 2(1), 2007, 1-3.
[4]
Tanthan uch S., Won gkittisu ksa B., Saejia M. and
Phukpattaranont P., “The Investigation of Tilt Sensors based
Fall Monitoring in the Elder”, in Proc 31 st The electrical
Engineering Conference (EECON31), Nakornnayok,
Thailand, Oct 29-31, 2008, 1233-1236.
[5]
Kan gas M., Konttila A., Winblad I. and J amsa T.,
“Comparison of Low-complexity Fall Detection Algorithms
for Body Attached Accelerometer”, J. Gait & Posture, 28,
2008, 285–291.
[6]
Stephen B., Micheal K. and Niel W., MEMS Mechanical
Sensors, Artech House Inc., Norwood, MA, 2004.
[7]
Grigorie T.L., “Th e Matlab/Simulin k Modeling and
Numerical Simulation of an Analogue Capacitive Microaccelerometer Part1: Open Loop.” , in MEMSTECH’2008,
Polyana, Ukraine, May 21-24, 2008, 105-114.
[8]
Roger R. M., Applied Mathematics Integrated Navigation
System, American Institute of Aeronautics and Astronautics
Inc, Virginia, 2003.
[9]
Montuschi M. and Mezzalama P.M., “Survey of Square
Rooting Algorithms”, IEE Comp and Digital Tech., 137(1),
1990, 31-40.
Figure 7: Comparison of the True and the Estimated Results from
the Proposed Algorithm
Figure 8: Difference between the True and the Estimated Value
4.
DISCUSSION AND CONCLUSIONS
We proposed a novel algorithm for a total sum vector
function. The modified Newton-Raphson iteration of
reciprocal square root operation is introduced in order to
reuse functions in the iterations without a divisor. This allows
minimizing of the programming code size to implement on
embedded devices for the fall monitoring. The proposed
algorithm achieves an efficient total-sum-vector computation
with error less than 0.01g. This method will open up
opportunity for the development of wearable sensors and
hence clinically acceptable devices that incorporate
accelerometer.
[10] Wang L. K. and Schute M. J., “Decimal Floating-point
Square Root using Newton-Raphson Iteration”, in Proc 16th
Intl Conf on Application Specific System, Architecture and
Processors (ASAP’05), Samos, Greece, Jul 23-25, 2005,
84-95.
[11] Venkat K., “Efficient Multiplication and Division using
MSP430”, Application Report SLAA329, Texas Instrument,
Texas, Sept. 2006.