Enhancing the Performance of Pedometers Using a Single Accelerometer

8/11/2019 Enhancing the Performance of Pedometers Using a Single Accelerometer

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APPLICATION NOTEOneTechnologyWayP.O.Box9106Norwood,MA02062-9106,U.S.A.Tel:781.329.4700Fax:781.461.3113www.analog.com

Enhancing the Performance of Pedometers Using a Single Accelerometerby Jim Scarlett

Rev. 0 | Page 1 of 16

The AN-602 application note examined the use of an Analog

Devices, Inc. accelerometer to make a simple but relatively

accurate pedometer. However, newer devices have been

introduced that allow the use of accelerometers in more cost-

sensitive applications. Thus, applications such as pedometers

are finding themselves in many consumer devices such as

cellular handsets.

Given this trend, a closer examination was made of pedome-

ters using a single accelerometer. The AN-602 technique was

implemented in an attempt to duplicate its results. Though thealgorithm performed well, the same accuracy was not duplicated.

In particular, there was greater variation than expected from

person to person, as well as when one person used a different

pace and stride length. This led to an investigation of potential

improvements to the algorithm used in AN-602.

The tests were done using two different pedometer test boards,

both utilizing an ADuC7020 ARM7 controller. One setup was

a combination of the ADuC7020 microcontroller and ADXL322

accelerometer evaluation boards, with an added 16 2 char-

acter LCD display. The other was a custom board using the

ADuC7020 and an ADXL330 3-axis accelerometer, again with

a 16 2 character LCD display. See Figure 5for the customboard schematic.

AN-602 METHOD

The underlying reasoning in the AN-602 method is based on

the principle that the vertical bounce in an individuals step is

directly correlated to that persons stride length (see Figure 1).

Because the angles and are equal, the stride can be shown to

be a multiple of the maximum vertical displacement. Differences

in an individuals leg length are accounted for, given that for the

same angles the vertical displacement would be greater or

smaller for taller or shorter people.

Using an accelerometer, however, gives changes in acceleration

rather than displacement. These acceleration measurements must

be converted to a distance before they can be used. With the

limited computing power available in the AN-602 setup, a

simple formula was used to approximate the double integralneeded for the conversion. With plenty of processing power

available, an attempt was made to do the discrete integrals

directly for this experiment.

A simple method was chosen to calculate the integrals. After

each step was determined, all of the acceleration samples

within that step were added to obtain a set of velocity samples.

The velocity samples for each step were normalized such that

the final sample was zero. They were then added together to

get a value for the displacement.

This technique looked promising initially, because measured

distances were relatively consistent for one subject walking

a course multiple times. However, the variance problem fromperson to person was exacerbated, as was the variance for one

subject at different paces. This led to an investigation of

whether the problem is with the model itself.

06617-001

BOUNCE

RIGHT

LEG

LEFT

LEG

LEFT

LEG

HIP

RIGHT

LEG

Figure 1. Vertical Movement of Hip While Walking


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UNDERSTANDING THE MODEL

This model has two primary conditions. First, it assumes that

the foot actually makes contact with the ground at a single

point. Second, it assumes that the impact of each foot on the

ground is perfectly elastic. Of course, neither of these is the

case. The question arose of whether this can explain the largevariations encountered. Based on this experiment, it is safe to

state that it does explain much of the variation.

To understand this, it helps to look at the measured acceleration

values over several steps, shown in Figure 2. Different sources of

spring in one persons step are shown on the data.

340

290

240

190

140

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HEEL-TO-BALL BALL-TO-TOE

TOE UP

HEEL DOWN ACCEL

ACCELLERATION

Figure 2. Acceleration Graph for Subject 1 at a Normal Pace

Figure 2demonstrates the problems encountered trying to

translate acceleration measurements into an accurate distance

calculation. Methods that take into account the peak-to-peak

change (or even those that integrate the data) run into troublewith this type of data. The cause of this difficulty is the variation

in spring in the steps of different people, or in the steps of one

person using different paces from one measurement to another.

Figure 3shows the same subject with a longer and faster stride.

The peak-to-peak acceleration difference is larger, and the

various spring points look different. Thus, the amount of data

representing spring data vs. the amount representing real data is

different compared with Figure 2. However, the algorithm only

sees a set of acceleration measurements and does not note the

context of those measurements. The problem, therefore, is how

to remove the effect of the spring in a subjects step without

removing useful data.

1

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ACCELERATION

500

0

1

450

400

350

300

250

200

150

100

50

ACCEL

Figure 3. Acceleration Graph for Subject 1 at a Fast Pace

There are some important differences between the two plots.

The bottom part of the curve for each step is slightly narrower

in Figure 3and the tops of the curves are more consistent (fewer

distinctive peaks). These differences result in a higher averagevalue of the samples compared to the minimum and maximum

sample values.

For comparison purposes, review the data plot for a different

individual in Figure 4. The stride length is very similar to that of

Subject 1 in Figure 2. However, the data itself looks very different.

1

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ACCELERATION

50

1

400

350

300

250

200

150

100

SERIES 1

Figure 4. Acceleration Graph for Subject 2 at a Normal Pace

The stride of Subject 2 has a great deal more spring in it than

that of Subject 1 (shown in Figure 2). Yet both sets of data

represent roughly the same distance walked. Calculating distance

solely on the peak values gives widely varying results. Using asimple double integration suffers from the same problem.


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SOLVING THE PROBLEM OF SPRING

All efforts to come up with a decent solution to this problem

using straightforward calculations had the same problems.

This led to a series of attempts to normalize the data in a way

that eliminated the spring, but all these attempts proved unsuc-

cessful. The main reason seemed to be that they required someknowledge of the context of the data. In actual use, however,

the system has no idea what is going on outside; all it has are

data points. The solution needs to be able to operate on the

data without context.

A possible solution to this problem began to emerge. It was

noted earlier how the data changed when going from a slower

to faster pace. There is less apparent variation due to the spring

with a longer, quicker stride. The result was a higher average for

the sample points, with respect to the data minima and maxima.

Visually, it is a little difficult to be sure of this, given the amount

of bounce in the steps shown in Figure 4. But calculations showed

that the average-vs.-peak values are very similar to those inFigure 2. Therefore, a possible simple algorithm was used to

determine the distance walked. It is

)(

)(

minmax

minavgkd

= (1)

where:

dis the distance calculated.

kis a constant multiplier.

maxis the maximum acceleration value measured within this step.

minis the minimum acceleration value.

avgis the average acceleration value for the step.

Equation 1 is completed for each step, as determined by a

different step-finding algorithm. The step-finding algorithm

uses an 8-point moving average to smooth the data. It searches

for a maximum peak, followed by a minimum. A step is counted

when the moving average crosses the zero point, which is the

overall average for the step. The data used in the distance algo-

rithm takes into account the 4-point latency of the moving

average.

This simple solution held up well for Subject 1 over various

stride lengths. It also did reasonably well with additional subjects.

But some subjects produced distances that varied as much as

10% from the average measured distance for the group. This

was not within the 7.5% error band that was targeted for an

uncalibrated measurement. Another solution was needed.

The ratio used in the last test seemed to reflect the differences

in the spring of different subjects steps. It made sense to try

combining the two methods examined here. Going back to

the original idea of using a double integral, this ratio was used

as a correction factor to remove the spring data from the calcu-

lation. The resulting formula is therefore

= )(*

)(

)(avgaccel

minavg

minmaxkd (2

where accelrepresents all measured acceleration values for

the step.

This algorithm held up well for a variety of subjects and paces,

with all variation within approximately 6%. The algorithm lends

itself to easy calibration for a specific individual/pace by adjusting

the Multiplier k. There is also provision within the listed code

to perform an average on the stride length to smooth out step-

to-step variation. The results noted here did not include the use

of this averaging.

In this experiment, only the X- and Y-axes were used. The

3-axis accelerometer was chosen for flexibility, and two axes

were found to be adequate for the task. An ADXL323 could

be used in place of the ADXL330. The same layout can be used

for both because the pin configuration is identical except for the

Z-axis output.

These experiments concentrated on achieving good results for

the pedometers distance measurement. There was no extensive

work done on the step-counting algorithm beyond ensuring it

works well while walking (and running), with measured steps

within 1 to 2 steps of the actual number over hundreds of steps

taken. However, it is possible that a simple algorithm can be

fooled with nonwalking motions. Improvements can be made

in that area, such as the time-window function described in

AN-602. The object is to ignore steps that are outside the

expected time window, while retaining the ability to adapt

when the subject changes pace.

SUMMARY

This application note represents the results of a single set of

experiments attempting to gain decent performance from a

simple pedometer that uses a single accelerometer. Some of

the barriers to gaining that performance have been reviewed.

The final results have met the stated accuracy goals, with the

added possibility of improved accuracy with calibration. Although

greater accuracy can be obtained with a more complex system

(for instance, with multiple accelerometers), the algorithm

provided in this application note is an excellent starting point

for simple, low cost applications.


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06617-005

Figure 5. Custom Board Schematic


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06617-006

Figure 6. Custom Board Schematic (Continued)


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ADuC7020 C CODE

The following three files contain the code used to implement this algorithm on the test boards using an ADuC7020 microcontroller.

MAIN.C

The file main.cis used to initialize the device:

/ *********************************************************************

Aut hor : J Scarl et t

Dat e : Nov 2006

Fi l es : mai n. c, di spl ay.c, ped. c

Har dwar e : ADuC7020

Descr i pti on : I mpl ement s a si mpl e pedometer based on appl i cati on not e AN- 602

*********************************************************************/

#i ncl ude

/ / Functi on Prot ot ype wi t h requi red f uncti on at t ri but e.

ext ern voi d Moni t or_Functi on( voi d) ;

extern voi d Di spl ay_I ni t (voi d) ;

/ / *********************************************************************

/ / Mai n Funct i on f or ADuC7020 Pedometer essenti al l y per f orms st art up f unct i ons

/ / *********************************************************************

i nt mai n ( voi d)

{

POWKEY1 = 0x01;

POWCON = 0x06; / / set t o 653kHz cor e cl ock

POWKEY2 = 0xF4;

REFCON = 0x2; / / use ext ernal r ef erence

/ / ( connect ed to VDD)

/ / *********************************************************************

/ / I ni t i al i ze Per i phera ls

/ / *********************************************************************

/ / GPI O Conf i gur ati on

GP4DAT = 0x04000000; / / P4. 2 conf i gur ed as an out put .

/ / LED i s t ur ned on

GP0CON = 0x00000000; / /

GP0DAT = 0xE0000000; / / 0. 7, 0. 6, and 0. 5 are out put s

/ / 0. 7 = E, 0. 5 = R/ W*, 0. 6 = RS

GP1DAT = 0xFF000000; / / Al l P1 pi ns are out put s

ADCCON = 0x20; / / Turn ADC on but do not enabl e

Di spl ay_I ni t( ) ; / / f ound i n F i l e di spl ay. c

Moni t or_Functi on( ) ; / / f ound i n Fi l e ped. c/ / *********************************************************************

/ / Mai n Loop

/ / *********************************************************************

whi l e( 1)

{

}

} / / mai n( )


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DISPLAY.C

The file display.ccontains all functions that access the display:

/ / F i l e "di spl ay. c"

/ / perf orms al l LCD di spl ay i nt erf ace f uncti ons

#i ncl ude

ext ern char st epbcd[ 6] ; / / f ound i n Fi l e ped. c

ext ern char di stbcd[ 6] ; / / t hi s t oo

voi d Di spl ay_I ni t( voi d);

voi d di spl ay_dat a( voi d) ;

voi d di spl ay_dat a_cl ear( voi d) ;

voi d char_l oad( i nt RS, i nt dat a) ;

voi d del ay( unsi gned i nt cycl es);

i nt r everse_data(i nt dat a) ;

voi d Di spl ay_I ni t( ){

/ / used once t o i ni t i al i ze di spl ay and wri t e

/ / t he "St eps" and "Di st ance" headers

i nt r s , data;

/ / Di spl ay i ni t i al i zat i on

rs = 0; / / no RAM access yet

dat a = 0x30; / / f uncti on set : 2- l i ne mode, di spl ay off

char_ l oad( rs, dat a);

dat a = 0x38; / / f uncti on set : 2- l i ne mode, di spl ay off


data = 0x08; / / di spl ay of f , cursor of f , bl i nk of f


dat a = 0x01; / / cl ear di spl ay


del ay( 49) ; / / ~1. 5 ms addi t i onal del ay i s r equi r ed

data = 0x06; / / i ncr ement mode, no shi f t


data = 0x0C; / / di spl ay on, cursor of f , bl i nk of f


data = 0x80; / / set dat a addr ess t o home, j ust t o be sure


r s = 1; / / now wr i t i ng t o data RAM

data = 0x53; / / st art of sequence t o send

char_l oad(r s, data); / / "Steps Di stance" f or t i t l e l i ne

data = 0x74; / / "t "


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char_l oad( rs, data);

dat a = 0x65; / / "e"


dat a = 0x70; / / "p"


dat a = 0x73; / / "s"


data = 0x20; / / " " t i mes 3




data = 0x44; / / "D"


dat a = 0x69; / / " i "


dat a = 0x73; / / "s"


dat a = 0x74; / / "t "


dat a = 0x61; / / "a"


dat a = 0x6E; / / "n"


dat a = 0x63; / / "c"


dat a = 0x65; / / "e"


} / / Di spl ay_ I ni t ( )

voi d di spl ay_data()

{

/ / di spl ays t he data contai ned i n stepbcd[ ] & di st bcd[ ]

/ / begi nni ng at t he f i r st and ni nt h charact ers

/ / on r ow 2 of t he di spl ay

i nt i , r s , data, zero;

r s = 0; / / want t o set addr ess, not data

dat a = 0xC0; / / st art of second l i ne



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r s = 1;

zero = 0;

f or ( i =5; i >=0; i - - ) / / di spl ay steps

{

i f ( ( stepbcd[ i ] > 0) | | ( zero ==1) ) / / suppress l eadi ng zeroes,

{ / / but not embedded zer oes

zero = 1;

data = 0x30 | st epbcd[ i ] ; / / numbers on di spl ay character t abl e

/ / begi n at 0x30

char_l oad ( rs, dat a) ;

} / / i f

} / / f o r

rs = 0; / / set address

data = 0xC8; / / ni nth character of second l i ne


r s = 1;

zero = 0;

f or ( i =5; i >=0; i - - ) / / di spl ay di stance

{

i f ( ( di stbcd[ i ] > 0) | | (zero ==1))

{

zero = 1;

data = 0x30 | di stbcd[ i ] ;

char_l oad ( rs, dat a) ;

} / / i f

} / / f o r

} / / di spl ay_dat a( )

voi d di spl ay_dat a_cl ear( voi d)

{

/ / used t o cl ear di spl ay dat a f i el d

/ / bef or e new measur ement

i nt i , r s , data;

rs = 0; / / want t o set address

dat a = 0xC0; / / start of second l i ne


r s = 1;

data =0x20;

f or ( i =0; i


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/ / si gnal t i mi ng assumes a cor e cl ock < 4MHz

/ / del ay at end i s ~61us, t o al l ow wr i t e to compl ete

data = r everse_data(dat a); / / boar d l ayout di ctat ed r eversi ng MSB/ LSB

GP1CLR = 0x00FF0000; / / ensure cl ean sl ate f or next charact er

GP1SET = dat a


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PED.C

The fileped.ccontains those functions used by the pedometer algorithm:

/ / f i l e "ped. c "

/ / per f orms pedometer and mi sc f unct i ons

#i ncl ude

#i ncl ude

#i ncl ude

/ / Functi on Protot ype & var i abl es

char st epbcd[ 6];

char di stbcd[ 6] ;

char st epf l ag;

f l oat str i de, avgstr i de, accel _dat[ 50];

f l oat maxavg, mi navg, accel _avg, vel oci t y, di spl ace;

f l oat di stance;

i nt steps;

voi d Moni t or_Functi on( voi d) ;

voi d get_sampl e(unsi gned i nt *xdat, unsi gned i nt *ydat, unsi gned i nt *zdat ) ;

char I sSt ep( f l oat avg, f l oat ol davg) ;

voi d di spl ay_prep( voi d) ;

l ong i nt bi n_t o_bcd( l ong i nt bi n_no) ;

ext ern voi d di spl ay_dat a( voi d) ; / / f ound i n Fi l e di spl ay.c

ext ern voi d di spl ay_dat a_cl ear( voi d) ; / / f ound i n Fi l e di spl ay.c

/ / f uncti ons

voi d Moni t or_Functi on( )

{

char f l ag;

unsi gned i nt xdat, ydat, zdat;

i nt i , cycl e_count , t ot _sampl es, avgconst = 1, l at ency = 4, avgl en = 8;

f l oat r ssdat , newmax, newmi n, ol davg, newavg, avgt hresh=1. 0;

f l oat wal kf udge = 0. 0249;

f l ag = 0;

T1CON = 0; / / t urn of f i nt er val t i mer and cl ear any I RQ

T1CLRI = 0;

whi l e (1)

{

i f ( I RQSI G & XI RQ0_BI T) / / XI RQ0 but t on has been pressed

{

whi l e(GP0DAT & 0x00010); / / wai t f or XI RQ t o be l ow agai n

i f ( ! f l ag)

{

T1CON = 0; / / t urn of f i nt er val t i mer

T1CLRI = 0; / / cl ear any t i mer I RQ

stepf l ag = 2;


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maxavg = - 10000. 0;

mi navg = 10000. 0;

newmax = - 10000. 0;

newmi n = 10000. 0;

ol davg = 0. 0;

newavg = 0. 0;

cycl e_count = 0;

t ot_sampl es = 0;

steps = 0;

di st ance = 0. 0;

accel _avg = 0. 0;

vel oc i ty = 0. 0;

di spl ace = 0. 0;

avgstr i de = 0. 0;

di spl ay_data_cl ear( ); / / c l ear ol d data f romdi spl ay

f l ag = 1;

T1LD = 1092; / / ~30 Hz sampl e r at e

T1CON = 0x2C0; / / 32. 768 kHz cl ock, t i mer on,

/ / peri odi c mode

} / / i f not runni ng, start .

} // l ook f or st op but t on

i f ( GP2DAT & 0x01)

{

whi l e( GP2DAT & 0x01) ;

f l ag = 0;

} / / i f runni ng, stop

i f ( ( ( I RQSI G & GP_TI MER_BI T) && ( f l ag) ) ! = 0) / / wai t f or ti meout

/ / and f l ag

{T1CLRI = 0;

i f ( t ot_sampl es > 7) / / subt ract f i rst sampl e i n sl i di ng boxcar avg

{

ol davg = newavg;

newavg - = accel _dat [ cycl e_count - avgl en] ;

} / / i f

get_ sampl e(&xdat, &ydat, &zdat ) ; / / get data f r omaccel erometer

xdat - = 8192; / / subt r act Zero g val ue

ydat - = 8192;

rssdat = sqrt (( f l oat) (xdat*xdat + ydat *ydat) / 16. 0); / / vector sum

accel _dat [ cycl e_count ] = r ssdat; / / pl ace cur r ent sampl e data i n buf f er

newavg += r ssdat ; / / add new sampl e t o sl i di ng boxcar avg

i f ( ( abs( newavg- ol davg) ) < avgt hresh)

newavg = ol davg;

i f ( r ssdat > newmax)

newmax = r ssdat;

i f ( r ssdat < newmi n)

newmi n = r ssdat ;


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t ot _sampl es++;

cycl e_count ++; / / i ncrement count of sampl es i n cur r ent st ep

i f (t ot_sampl es > 8)

{

i f ( I sSt ep( newavg, ol davg) )

{

f or ( i = l at ency; i < (cycl e_count - l atency); i ++)

accel _avg += accel _dat [ i ] ;

accel _avg /= ( cycl e_count - avgl en) ;

f or ( i = l at ency; i < (cycl e_count - l atency); i ++)

{

vel oci ty += (accel _dat[ i ] - accel _avg);

di spl ace += vel oci t y;

} / / create i nt egr ati on and doubl e i nt egr ati on

/ / cal cul ate str i de l ength

st r i de = di spl ace * ( newmax - newmi n) / ( accel _avg - newmi n);

st r i de = sqrt (abs(str i de)) ;

/ / use appr opr i ate const ant t o get st r i de l engt h

str i de *= wal kfudge;

/ / generat e exponent i al average of st r i de l ength t o smoot h data

i f ( s teps < 2)

avgstr i de = str i de;

el se

avgstr i de = ( ( avgconst - 1) *avgstr i de + str i de) / avgconst ;

st eps++;di st ance += avgst r i de;

/ / need al l data used i n cal cul ati ng newavg

f or ( i = 0; i < avgl en; i ++)

accel _dat[ i ] = accel _dat[ cycl e_count + i - avgl en];

cycl e_count = avgl en;

newmax = - 10000. 0;

newmi n = 10000. 0;

maxavg = - 10000. 0;

mi navg = 10000. 0;

accel _avg = 0;vel oc i ty = 0;

di spl ace = 0;

di spl ay_prep( ) ;

di spl ay_dat a( ) ;

/ / t emporar y

i f ( GP4DAT & 0x04) / / t oggl e LED t o r ef l ect st ep

GP4CLR = 0x040000;

el se


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GP4SET = 0x040000;

} / / we have a new st ep

} / / enough sampl es t o st art checki ng f or st ep ( need at l east 8)

} / / i f t i meout

} / / cont i nual l oop

} / / Moni t or_Functi on( )

voi d get_ sampl e(unsi gned i nt *xdat, unsi gned i nt *ydat, unsi gned i nt *zdat )

{

/ / gets new sampl es f or x, y, z axes

/ / sums t oget her 4 measurments t o get average

i nt i ;

*xdat = 0;

*ydat = 0;

*zdat = 0;

f or ( i =0; i > 16) & 0xFFF) ; / / dat a i s i n bi t s 16 - 27, so shi f t i s necessar y

ADCCP = 1; / / y axi s

i ++;ADCCON = 0xA3;

whi l e ( ! ( ADCSTA) ) ;

*ydat += ( ( ADCDAT >> 16) & 0xFFF) ;

ADCCP = 2; / / z axi s

i ++;

ADCCON = 0xA3;

whi l e ( ! ( ADCSTA) ) ;

*zdat += ( ( ADCDAT >> 16) & 0xFFF) ;

} / / f o r

} / / get_sampl e()

char I sSt ep( f l oat avg, f l oat ol davg)

{

/ / t hi s f unct i on att empt s t o deter mi ne when a st ep i s compl ete

f l oat step_t hresh = 5. 0; / / used t o prevent noi se f r om f ool i ng t he al gori t hm

i f (st epf l ag == 2)

{


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i f ( avg > (ol davg + step_thresh))

stepf l ag = 1;

i f ( avg < ( ol davg - st ep_t hresh) )

stepf l ag = 0;

return 0;

} / / f i rst t i me t hrough t hi s functi on

i f ( stepf l ag == 1)

{

i f ( ( maxavg > mi navg) && ( avg >

( ( maxavg+mi navg)/ 2) ) &&

( ol davg < ( ( maxavg+mi navg/ 2)) ) )

ret urn 1;

i f ( avg < ( ol davg - st ep_t hresh) )

{

stepf l ag = 0;

i f ( ol davg > maxavg)

maxavg = ol davg;

} / / sl ope has t urned down

return 0;

} / / sl ope has been up

i f ( stepf l ag == 0)

{

i f ( avg > (ol davg + step_thresh))

{

stepf l ag = 1;

i f ( ol davg < mi navg)

mi navg = ol davg;

} / / sl ope has t urned up

return 0;} / / sl ope has been down

return 0;

} / / I sStep()

voi d di spl ay_prep( )

{

i nt i ;

l ong i nt t emp;

/ / conver t st eps t o BCD val ues f or sendi ng t o di spl ay

t emp = st eps;

t emp = bi n_t o_bcd( t emp) ; / / f unct i on t o conver t bi nary

f or ( i =0; i > 4;

} / / f o r

/ / conver t di st ance t o BCD val ues f or sendi ng t o di spl ay


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temp = (l ong i nt )( di stance); / / convert f l oat to l ong i nt

t emp = bi n_t o_bcd( t emp);

f or ( i =0; i > 4;

} / / f o r

} / / di spl ay_prep( )

l ong i nt bi n_t o_bcd( l ong i nt bi n_no)

{

i nt i ;

l ong i nt di vi sor , mul t i pl i er, bcd_no, t emp;

di vi sor = 100000;

mul t i pl i er = 1048576;

bcd_no = 0;

t emp = 0;

i f ( bi n_no > 999999)

bi n_no = 999999;

f or ( i =0; i > 4;

} / / f o r

r etur n bcd_no;

} / / bi n_t o_bcd( )

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AN06617-0-7/07(0)

Enhancing the Performance of Pedometers Using a Single Accelerometer

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