1st International Conference on Sensing Technology
November 21-23, 2005 Palmerston North, New ZealandGlobal Calibration Based on Local Calibration for an
Ultrasonic Location Sensor∗
Akifumi Nishitani

Yoshifumi NishidaToshio Hori

Tokyo University of Science
2641, Yamazaki, Noda-shi, Chiba,278-8510, Japana-nishitani@aist.go.jp

Digital Human Research Center, AIST
& CREST, JST
2-41-6, Aomi, Koto-ku, Tokyo,
135-0064, Japany.nishida@aist.go.jp

Digital Human Research Center, AIST
& CREST, JST
2-41-6, Aomi, Koto-ku, Tokyo,
135-0064, Japant.hori@aist.go.jp

Takeo Kanade

Hiroshi Mizoguchi

Digital Human Research Center, AIST
& CREST, JST
2-41-6, Aomi, Koto-ku, Tokyo,
135-0064, Japant.kanade@aist.go.jp

Tokyo University of Science
2641, Yamazaki, Noda-shi, Chiba,278-8510, Japanhm@rs.noda.tus.ac.jp

Abstract— The ability to quickly construct a human activity
observation system is required in order to conduct fieldresearch on human activities. The authors have developed
an ultrasonic location system, which is a type of location
sensing system for observing human activities. The present
study attempts to establish a systematic method for quickly
constructing an ultrasonic location system in various environments. A calibration function that can be used invarious environments is one of the basic functions of theultrasonic location system. In the present paper, we propose
a new calibration method, “global calibration based on local
calibration (GCLC),” for calibrating the 3D positions of ultrasonic receivers placed arbitrarily in a daily-use environment.
The proposed method requires a relatively small number oftransmitters and is independent of room size. In addition, we
describe two constraints that can be used in conjunction with
the GCLC method. The performance of the GCLC method
was investigated in an experimental room (4.0×4.0×2.7 m),
in which 80 ultrasonic receivers were attached to the ceiling.
A portable system based partly on the proposed method is
also presented herein.
Keywords— human activity obervation, ultrasonic location
sensor, calibration.

I. I NTRODUCTION
Recently, human-centered information processing services have been attracting increasing attention. The goal of
the present research is to establish a technique by which
to recognize both human activity and the state in a living
space. Therefore, it is necessary to observe human activity
in real time and with high accuracy, without the presenceof constraints that prevent natural human activities.
As a method for efficient and robust recognition ofactivities in a daily environment, the concept of objectbased activity recognition has been proposed. The behaviorof handling objects in an environment such as an office orhome can be recognized based on the motion of the objects[1]. We have developed a three-dimensional (3D) ultrasonic∗ This study was supported in part by a Grant-in-Aid as part of theSpecial Coordination Fund for Promoting Science and Technology from
the Ministry of Education, Culture, Sports, Science and Technology ofJapan.

11

location system as a fundamental system for robustly
tracking objects and have verified that the observation ofhuman activity based on object tracking is possible [2],[3]. However, like other location sensors, the developed
ultrasonic location sensor has a disadvantage in that lackof portability makes it difficult to collect activity data inthe various environments in which actual human activities
occur.
In the present paper, we propose a rapid calibration
method, “global calibration based on local calibration,” thatenables users to quickly calibrate the positions of ultrasonicreceivers of an ultrasonic location system and observe thesystem for field research on human activities.
II. R ELATED W ORK
Several types of ultrasonic location systems have been
proposed. The Bat Ultrasonic Location System [4–7] developed by AT&T, and the MIT Cricket Indoor Location System [8] are well known. Although a calibration
method using a robot [9] has been proposed, the required
calibration device is too large for use in a number ofenvironments. An auto calibration method was consideredin the DOLPHIN system [10], which can calibrate thepositions of receivers/transmitters using a small numberof reference receivers/transmitters having known positions.
However, the system has only been tested in narrow areas
having dimensions of approximately 2.5 m × 2 m. Bristol
University proposed another auto calibration method, inwhich the positions of n transmitters and m receivers can becalculated given n×m distance data among the transmittersand receivers and that the condition, 3(n + m) − 6 < n · m,
is satisfied [11]. However, the scalability of this method islimited.
In contrast, the present study proposes and examinesa new calibration method, “global calibration based on
local calibration,” that requires a relatively small numberof transmitters and is independent of room size. Using
the proposed method, the calibration problem becomesa similar to a fitting problem in object modeling withmultiple range images [12], [13] after local calibration. The

1st International Conference on Sensing Technology
November 21-23, 2005 Palmerston North, New Zealandpresent paper describes the method for global calibration
based on local calibration and the constraints that are usedin conjunction with the method for reducing the error of
the calibrated receiver positions.

between the spheres as
AP =
where

B,


P =

III. Q UICK C ALIBRATION M ETHOD
In the present paper, in addition to the ”global calibration
based on local calibration (GCLC)” method, we propose
two constraints that can be used in conjunction with the
GCLC method, as described below.
The procedure for GCLC is described below.
1. Move the calibration device arbitrarily to multiple positions (A, B, and C in Fig. 1).
2. Calculate the positions of the receivers in a local
coordinate system, with the local origin set at the positionof the calibration system.
3. Select receivers for which the positions can be calculated
from more than two calibration system positions.
4. Select a global coordinate system from among the
local coordinate systems and calculate the positions of thecalibration device in the global coordinate system using thereceivers selected in Step 3. Then, calculate transformation
matrices (M1 and M2 in Fig. 1).
5. Calculate the receiver positions using the receiver positions calculated in Step 2 and the transformation matrices
calculated in Step 4.

(4)
For the case of four or more transmitters that are notcoplanar, the rank of A becomes 3. The position (x,y,z)
can be calculated by the least squares method as
P = (AT A)−1 AT B.

n

n

E=

Place Ci=0 j=i+1

M1

(5)

(i,j)

||Mi Pi(i,j) 2

− Mj Pj|| ,(6)

where Mi is the transformation matrix from the local
coordination system i to the global coordination system,(i,j)
and Pjdenotes points in the local coordination systemj for the case in which the points can be calculated in both
local coordination systems i and j.

M2

Fig. 1.

(2)⎞
2(x2 − x1 ) 2(y2 − y1 ) 2(z2 − z1 )⎜ 2(x3 − x1 ) 2(y3 − y1 ) 2(z3 − z1 ) ⎟
⎟
⎜
..
..
..
⎟
⎜
.
.
.
(3)
A =⎜
⎟,
⎜ 2(x − x ) 2(y − y ) 2(z − z ) ⎟
i
1
i
1
i
1
⎠
⎝
..
..
..
.
.
.
⎛ 2
⎞
l1 − x21 − y12 − z12 − l22 + x22 + y22 + z22
2
2
2
2
2
2
2
2
⎜ l1 − x1 − y1 − z1 − l3 + x3 + y3 + z3 ⎟
⎜
⎟
..
⎜
⎟
B=⎜
.
⎟.
⎜ l2 − x2 − y 2 − z 2 − l2 + x2 + y 2 + z 2 ⎟
⎝ 1
1
1
1
i
i
i
i ⎠
..
.

0

Calibration device(Transmitters),

This method calculates position by solving plane equations derived from the equations of intersecting spheres.
Reference [2] presents a detailed description for the casein which the rank of A is 2.
2) Calculating the positions of the calibration device inthe global coordinate system (Step 4): The error function
E can be defined as follows:

Receivers

Place A(1)

⎛

A. Proposal of a rapid calibration method

Place Bxyz

Quick calibration method 1

Steps 2 and 4 are described in detail in the following.
B. Linear method for rapid calibration∂E∂Mi1) Calculating the 3D positions of receivers in a local
coordinate system based on distance data (Step 2): The
receiver position (x,y,z) is calculated by a multilateration
algorithm, such as that used in the Global Positioning
System [14]. Trilateration or multilateration algorithms
have been proposed in the field of aerospace [15], [16]. The
present paper briefly describes a multilateration algorithm
based on simultaneous linear equations [2] that is applicable to a more general case, in which multiple ultrasonicreceivers are placed in arbitrary positions. This is explained
in detail below.
Here, l1 , l2 , · · ·, li denote the distances from the ultrasonic receiver at (x,y,z) to the ith ultrasonic transmitter at
position (xi ,yi ,zi ). Using the spherical equations, we obtain
simultaneous linear equations for the intersecting planes

=

12

=

∂
∂Mi

n

(i,j)
(i,j)
Mi P
− Mj PijTrj=0(i=j)
n

T

(i,j)
(i,j)
Mi P
− Mj Pij(i,j) T(i,j)(i,j) T(i,j)−(Mj P) Mi P− (Mi P
) Mj Pjiijj=0(i=j)(i,j) T(i,j)(i,j) T(i,j)+(Mi P) Mi P+ (Mj P
) Mj P
i
i
j
j
∂
∂Mi

Tr



(i,n)
(i,n) T(i,i−1)(i,i−1) T= −2M0 P(P) − · · · − 2Mi−1 P
(P
)
0
i
i−1
i−1
n
(i,j)
(i,j) T
P
(P
)
+2Mi
i
i
j=0
(i=j)(i,i+1)(i,i+1) T(i,n)(i,n) T
−2Mi+1 P(P) − · · · − 2Mn Pn
(P
) .
i+1
i
i

(7)

If we select the local coordinate system 0 as the global
coordinate system, M0 becomes an identity matrix. From

1st International Conference on Sensing Technology
November 21-23, 2005 Palmerston North, New ZealandIn case of Pb1 are constrained
as the basis for Pb0 .

Eq. (7), we can obtain simultaneous linear equations andcalculate Mi using Eq. (8),(Pb1 − Pb0 )⋅ n = l1 − l0

Global coordinate

M1( M1 M2 · · · Mn ) =(0,1)(0,1) T(0,2)(0,2) T(0,n)(0,n) T
×
P
(P
)
P
(P
)
··· P
(Pn
)
0
1
0
2
0
n
(1,i)
(1,i) T
(1,2)
(1,2) T(1,n)(1,n) T
P
(P
)
−P
(P
)
· · · −P
(Pn
)
1
1
1
2
1
i=0
n
(1,2)
(1,2) T(2,i)(2,i) T(2,n)(2,n) T
−P
(P
)
P
(P
)
· · · −P
(Pn
)
2
1
2
2
2
i=0

⎛

⎞−1

⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝

⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠

.
.
.

.
.
.

(1,n)
(1,n) T
−Pn
(P
)
1

(2,n)
(2,n) T
−Pn
(P
)
2

.

.

.

n

···

.
.
.
(n,i)
(n,i) T
Pn
(Pn
)

M2

l0
n

Wall, floor, or ceiling of building

boundary constraints is as follows:

Regarding the GCLC method as presented above, theerror of calibration will accumulate as the space in which
the ultrasonic receivers are placed becomes larger. Therefore, the number of moving calibrating devices becomeslarger. For example, if we place receivers on the ceiling ofa corridor of size 2 x 30 m, the accumulated error may belarge. This section describes the boundary constraint withwhich we can reduce the error accumulation.
In most cases, the ultrasonic location system will beplaced in a building or on the components of a building,such as on a wall or ceiling. If we can obtain CAD dataof the building or its components or if we can measure
the size of a room inside the building to a high degreeof accuracy, then we can use the size data as a boundary
condition for calibrating the receiver positions.
Here, let us consider the boundary constraint shown in
Fig. 2. We can formulate this problem using the Lagrange’s
undecided multiplier method as follows:3

M1 M2 · · · Mn=(0,1)(0,1) T(0,n)(0,n) T
P
(P
)
P
(Pn
)
0
1
0
ni
nn
×
··· ···
T
λn,i nn,i PT−1/2
λ1,i n1,i P
−1/2
n,i
1,i
i=0
i=0
n
(1,i)
(1,i) T
(1,2)
(1,2) T(1,n)(1,n) T
P
(P
)
−P
(P
)
···
−P
(Pn
)
1
1
1
2
1
i=0
i=1
n
(2,i)
(2,i) T(2,n)(2,n) T
(1,2)
(1,2) T
P
(P
)
···
−P
(Pn
)
−P
(P
)
2
2
2
2
1
i=0
i=2



⎛

⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
.
.
⎜
.
⎜
(1,n) T⎝ −P(1,n)(P)
n1i=0 j=i+1.

(2,n)(2,n) T
−Pn
(P
)
2

⎛

(0,1)
(0,1) T
P
(P
)
1
1
(1,2)
(1,2) T
+P
(P
)
1
1

⎜
⎜ (1,2) (2,1) T⎝ −P2 (P1 )0(1,2)(1,2) T
−P
(P
)
1
2
(1,2)
(1,2) T
P
(P
)
2
2
(2,3)
(2,3) T+P(P)22(2,3) T
(2,3)
(P
)
−P
3
2

×
0

(2,3)
(2,3) T
−P
(P
)
2
3

M3

Pb2

Pb0

l3

Pb1

l0

l1

l5

M2

l2

l4

n1

⎞−1
⎟
⎟
⎠

(13)

Global coordinaten2( M1 M2 M3 ) =

i=0
i=n

Fi,j = (Mi Pi,j −Pb0 ) · ni,j − ∆li,j = 0,

where λ denotes a Lagrange’s undecided multiplier. By
solving this equation, we can obtain the following equations:
0 −1/2λnPT
b1

.

···

(12)

M1

(0,1)
(0,1) T
P
(P
)
0
1

.

⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
.
.
⎟
.
⎟
n
(n,i)
(n,i) T ⎠Pn
(Pn)

where λi,j , ni,j , and Pi,j denote the j-th undecided multiplier, the j-th constraint vector, and the j-th constrained
point in the i-th local coordinate system, respectively. In
this case, the boundary constraints are as follows:

(9)
(10)

F (M3 ) = (M3 Pb1 − Pb0 ) · n + l0 − l1 = 0

.
.
.

⎞−1

where ∆li,j denotes a distance constraint. The above
GCLC method with boundary constraints is applicable to,for example, the case in which more complex boundary
conditions exist, as shown in Fig. 3.


2

(i,j)
(i,j) − Mj Pj  + λF (M3 ),Mi Pi3

Example of a boundary condition as the basis for the building

(8)





l1

.

C. Considering the environment boundary condition

E =

Pb1

Pb0

Fig. 2.

i=0M3. (11)

Wall, floor, ceiling of building

Fig. 3. Example of a greater number of boundary conditions as the basisof the building(2,3)(2,3) TP(P)
3
3

By substituting M3 into Eq. (10), we can solve λ andeliminate it from Eq. (11).
The general case of the GCLC method with multiple

13

D. Consideration of ultrasonic damping1) Error due to ultrasonic damping: The authors discovered a phenomenon whereby the measured distance
between receivers and transmitters appears longer than,

1st International Conference on Sensing Technology
November 21-23, 2005 Palmerston North, New Zealand60

1517[mm]1735[mm]
1940[mm]
2122[mm]2325[mm]2539[mm]50

Error ∆ L [mm]the actual distance due to ultrasonic damping. This phenomenon causes an increase in the error. The damping
is caused by the directivities of the transmitter and thereceiver. This section describes a method that considers
the directivities in order to reduce this effect.
The newly developed ultrasonic location system measures the distance from the time-of-flight of the ultrasonicpulse. The time at which the ultrasonic wave exceeds thethreshold is the arrival time of the ultrasonic pulse at
the receiver, as shown in Fig. 4. However, in the caseof damping of the ultrasonic wave, due to the effects ofdirectivity and distance, the error of the measured distanceincreases as a result of the delay in the ultrasonic pulse
arrival time expressed by ∆T.
2) Approach to the damping problem: There are two
approaches to this problem: a hardware approach and asoftware approach. In the hardware approach, the highest
point of the ultrasonic wave, for example, can be assumed
to be the ultrasonic pulse arrival time, as determined bysampling and analyzing the ultrasonic wave, which requires
expensive equipment. Therefore, in the present paper, weconsider the software approach.

40
30
20
10

y = -61.323x + 58.205
0
0

0.2

0.4

0.6

-10

Fig. 6.

0.8

1

1.2

cos θ
Relationship between transmitting angle and error

Here,∆Lij = −61.323 cos θij − 75.622 cos φij + 131.662(16)was obtained experimentally.
IV. E XPERIMENTS

Voltage

A. System configuration
wave shapeThreshold∆T
Arrival time
Fig. 4.

Time

Measurement of ultrasonic pulse arrival time3) Method for dealing with the damping problem: The
distance between the receivers and transmitters is|Pri − Ptj | = Lij ,(14)

where Pri are the positions of the receivers, Ptj are
the positions of the transmitters, and Lij are the actual
distances. The ultrasonically measured distances Lm,ij arelonger than the actual distances Lij . The actual distances
Lij are described by
Lij = Lm,ij − ∆Lij ,up to 127 devices
PIC

PIC

up to 2032 devices

C&
YN
ID

Ultrasonic receiver & amplifierRadio Ultrasonicreceiver transmitter
40kHz
PIC

Battery

Ultrasonic 3D tag 28x20x13mm

Pt
Transmitter

Fig. 5.

PIC

dS

φ

θ
z

Measure time of flight RS485(921.6kbps,1km)

PIC

Sen

L

Collect data
SYNC signal
dataRadio transmitter& SYNC generator
VHF 314.9MHz
wireless RS232

Receiver
Pr
n

L

PC
RS232(9.6k to 921.6kbps)(15)where ∆Lij is the error of the distance.
ReceiverPr

Figure 7 shows the system configuration for the proposed 3D ultrasonic tag system. The system consists ofan ultrasonic receiving section, an ultrasonic transmitting
section, a time-of-flight measurement section, a network
section, and a personal computer. The ultrasonic receiving
section receives ultrasonic pulses emitted from the ultrasonic transmitter and amplifies the received signal. The
time-of-flight measurement section records the travel timeof the signal from transmission to reception. The network
section synchronizes the system and collects time-of-flightdata from the ultrasonic receiving section. The positions ofobjects are calculated based on more than three time-offlight measurements.

Pt
Transmitter

Fig. 7.

System configuration

Angle and distance

The experimentally obtained relationship between thetransmitting angle of a transmitter and the error and thatbetween the receiving angle of a receiver and the error are
shown in Figure 6.

14

B. Experimental results
1) Method for error evaluation: Errors are defined as
the distances between the calculated receiver positions andthe true receiver positions and are denoted by e1 , e2 , · · · ,1st International Conference on Sensing Technology
November 21-23, 2005 Palmerston North, New Zealanden . The average error is defined by
n

E=

1
ei .
n i=1

(17)

2) Accuracy evaluation: Calibration was performed ina room (4.0×4.0×2.5 m) having 80 ultrasonic receivers
embedded in the ceiling. Figure 8 shows the experimental
results obtained using the GCLC method without any
constraints. The authors performed calibration at 16 points
in the room. Seventy-six receivers were calculated. In
the figure, the red spheres indicate calculated receiver
positions, the black crosses indicate the true receiver positions, and the blue spheres indicate the positions of thecalibration device. Figure 9 shows the experimental results
for the GCLC method considering directivities. Seventy-six
receivers were calculated. Table I shows the average error
E, maximum error, and minimum error for these methods.
The above results show that using the GCLC method we
can calibrate the position of receivers placed in a spaceof average room size and that the error can be reduced
significantly by considering directivity.
Another calibration was performed in a rectangular space(1.0×4.5) having a longitudinal length that is much longer
than its lateral length. Seventy-six ultrasonic receivers wereembedded in the space. Figure 10 shows the experimental
results obtained using the GCLC method without any
constraints. Seventy-five receivers were calculated. Figure
11 shows the experimental results obtained using the GCLC
method directivity consideration and a boundary constraint.
Table II shows the average error E, maximum error, andminimum error for these methods. The above results showthat with the GCLC method with directivity consideration
and boundary constraint has a significantly reduced error.

TABLE IE RRORS ( MM ) OF THE PROPOSED METHOD FOR THE CASE OF A
SQUARE - LIKE SPACE

GCLC
GCLC
with directivity consideration

Ave.
error
195
mm

Max.
error
399 mm

Min.
error
66 mm

75 mm

276 mm

9 mm

2000
1800
1600
1400
1200
1000
800
600
400
200
0

Origin of global coordinate system

0
1000
2000
3000
4000
2000

Fig. 10.

1500

1000

500

0

Experimental results obtained by the GCLC method

Reference point

Constrained point

1800
1600
1400
1200

calculated receiver positions
true receiver positions
positions of the calibration device

1000
800
600

[mm]

Origin of global coordinate system

400

1500

200

1000

Directions of constraint

0

500
x

0

0

y

1000

0
-1000
-2000
-3000

-1000

[mm]

Fig. 8.

0

1000

2000

2000

[mm]

3000
2000

Experimental result obtained by the GCLC method

1500

1000

500

0

Fig. 11.
Experimental results obtained by the GCLC method withdirectivity consideration and a boundary constraint
calculated receiver positions
true receiver positions
positions of the calibration device

TABLE IIE RRORS ( MM ) OF THE PROPOSED METHOD FOR THE CASE OF A
RECTANGULAR SPACE HAVING A LONGITUDINAL LENGTH THAT IS

[mm]
1000

MUCH LONGER THAN ITS LATERAL LENGTH

500
z
x

0

y

0
-1000

[mm]

-1000
0

GCLC

-2000

1000
2000

-3000

[mm]

Fig. 9. Experimental result obtained by the GCLC method considering
directivity

15

GCLC
with directivity consideration
and boundary constraint

Ave.
error
236
mm

Max.
error
689 mm

Min.
error
17 mm

51 mm

121 mm10 mm

1st International Conference on Sensing Technology
November 21-23, 2005 Palmerston North, New Zealand

V. A DVANTAGES OF THE GCLC M ETHOD
The advantages of the GCLC method are listed below.
• The method requires a relatively small number oftransmitters, at least three transmitters, so that the user
can calibrate the ultrasonic location system using asmall calibrating device having at least three transmitters.
• The method can calibrate the positions of the receivers
independent of room size.
• The error can be reduced by considering the directivity
constraint. The constraint is useful for cases in which
the ultrasonic location system adopts a method inwhich the time-of-fight is detected by thresholding theultrasonic pulse.
• The error can be reduced by considering the boundary
constraint. The constraint is useful for cases in which
the receivers to be calibrated are placed in a rectangular space having a longitudinal length that is muchgreater than the lateral length, such as a long corridor.
VI. R EALIZED U LTRASONIC P ORTABLE 3D TAG
S YSTEM
The GCLC method enables a portable ultrasonic 3D
tag system. Figure 12 shows a portable ultrasonic 3D tag
system, which consists of a case, tags, receivers, and a calibration device. The portable system enables measurementof human activities by quickly installing and calibrating thesystem on-site, at the location where the activities actuallyoccur.

Ultrasonic sensors

Portable case
Calibration device
built in sections

Fig. 12.

Developed portable ultrasonic 3D tag system

VII. C ONCLUSION
In the present paper, we proposed a new calibration
method, “global calibration based on local calibration(GCLC)”, for an ultrasonic location system so that users
can quickly calibrate a system and observe human activity

16

in various environments where the activities actually occur. One of the advantages of the GCLC method is therequirement for a relatively small number of transmitters.
In addition, the GCLC method is not dependent on room
size. We also described two constraints that can be usedin conjunction with the GCLC method: the directivity
constraint and the boundary constraint.
In addition, a portable ultrasonic location sensor basedon the proposed method was realized. The portable systemallows human activities to be measured in the area where
the activities actually occur with quick installation andcalibration.
Further studies will examine the refinement of themethod in order to measure the 3D positions with higher
accuracy, systematization of calibration methods, and theuse of the portable 3D ultrasonic tag system in a living
space.
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[3] Y. Nishida, K. Kitamura, T. Hori, A. Nishitani, T. Kanade, H.
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