Identification of target primitives with multiple decision-making sonars using evidential reasoning

598

Identification

of

_Target

Primitives with

Multiple

Decision-Making

Sonars

_Using

Evidential

Reasoning

Birsel

_Ayrulu

Billur Barshan

Department

of Electrical and Electronics

_Engineering

Bilkent

_University

Bilkent 06533 Ankara,

Turkey

Abstract

In this

_{study, physical}

models are used to model

_{reflections from}

target

primitives commonly

encountered in a mobile robot’s

envi-ronment. These _targets are

_{differentiated}

_{by employing}

a multi-transducer

_pulse/echo

system that relies on both

time-of-flight

data and

_amplitude

in the

_{feature-fusion}

process,

allowing

more robust

differentiation. Target features

are

generated

as

_{being evidentially}

tied to

_{degrees of belief,}

which are

_subsequently

_{fused by}

employ-ing

multiple logical

sonars at

_{geographically}

distinct sites. Feature

datafrom multiple logical

sensors

_arefused

with

_Dempster’s

rule

_of

combination to

_improve

the

_performance

_{of classification}

_by

reduc-ing perception uncertainty. Usreduc-ing

three

_sensing

nodes,

improvement

in

_{differentiation}

is between 10% and 35%

_{withoutfalse decision,}

at

the cost

_{of additional computation.}

The method is

_{verified by}

exper-iments with a real sonar _system. The evidential

_approach

_employed

here

_helps

to overcome the

_{vulnerability of}

the echo

_amplitude

to

noise, and enables the

_{modeling of nonparametric uncertainty}

in real time.

1. Introduction

There is no

_single

sensor that

_perfectly

detects, locates,

and identifies

_targets

under all circumstances.

Although

some

sensors are more accurate at

_locating

and

_{tracking objects,}

they

may not

_provide

_identity

information,

or vice versa,

pointing

to the need for

combining

data from

_multiple

sensors

via data-fusion

_techniques.

The

_primary

aim of data fusion is to combine data from

_multiple

sensors to

_perform

inferences

that may not be

_possible

from a

_single

sensor. Data-fusion

applications

span a wide

domain,

including

automatic

_target

recognition,

mobile-robot

_navigation,

_target

_tracking,

aircraft

navigation,

and

_{teleoperations}

_(Steinberg

1987;

Blackman

The International Journal of Robotics Research,

Vol. 17, No. 6, June 1998, pp. 598-623,

© 1998 _Sage Publications, Inc.

and Broida

_1990;

Hall

_1992;

_Murphy

_1993).

In robotics

applications,

data fusion enables

_intelligent

sensors to be

in-corporated

into the overall

_operation

of robots so that

_they

can interact with and

_operate

in unstructured

environments,

without the

_complete

control of a human

_operator

_(Luo

and

Lin

1988).

Data fusion can be

_{accomplished by using geometrically,}

geographically,

or

_physically

different sensors at different

levels of

_{representation,}

such as

_{signal-level, pixel-level,}

feature-level,

and

_symbol-level

fusion. In this

_study,

phys-ically

identical sonar sensors are

_employed

to combine in-formation when

_they

are located at

_{geographically}

differ-ent

_sensing

sites. Feature-level fusion is used to

_provide

a

_system

_performing

an

_{object-recognition}

task with

addi-tional features that can be used to increase its

_recognition

capabilities.

One mode of

_sensing

that is

_potentially

useful and cost ef-fective for mobile-robot

_applications

is sonar. Since

acous-tic sensors are

light,

robust,

and

inexpensive

devices,

they

are

_widely

used in

_applications

such as

_navigation

of

au-tonomous vehicles

_through

unstructured environments

_(Kuc

and

_Siegel

1987;

Kuc and Viard

1991),

map

building

(Crow-ley

1985;

Leonard and

_{Durrant-Whyte}

1991 ),

target

tracking

(Kuc 1993),

and obstacle avoidance

_(Borenstein

and Koren

1988).

Although

there are difficulties in the

_{interpretation}

of

sonar data

_owing

to

_{multiple specular}

_reflections,

_{the poor}

angular

resolution of sonar, and the need to establish

cor-respondence

between

_multiple

echoes on different receivers

(Peremans,

Audenaert,

and

_Campenhout

1993;

Kleeman and

Kuc

_1995),

these difficulties can be overcome

_by

employ-ing

accurate

_physical

models for the reflection of sonar.

Sensory

information from a

_single

sonar has _poor

angu-lar resolution and is not sufficient to differentiate the most

commonly

encountered

_target

_primitives

_(Barshan

and Kuc

1990).

Therefore,

many

applications

require

multiple

sonar

configurations.

The most

_popular

sonar

_ranging

_system

is

599

time

_elapsed

between the transmission of a

pulse

and its

re-ception.

Since the

_amplitude

of sonar

_signals

is prone to

en-vironmental conditions and since the standard electronics for the

_commonly

used Polaroid transducers

(Polaroid 1990)

do

not

_provide

the echo

_{amplitude directly,}

most sonar

_systems

exploit only

the TOF information. Differential TOF models of

_{planes, edges,}

comers, and

_cylinders

have been used

_by

several researchers in

_{map-building,}

robot-localization,

and

target

tracking applications.

In Bozma

_(1992),

_using

a

sin-gle

mobile sensor for map

_{building, edges}

are differentiated

from

_planes

and corners from a

_single

location. Planes and corners are differentiated

_by

_scanning

from two

_separate

lo-cations

_using

TOF information from

_complete

sonar scans of

the

_targets.

In Leonard

₍₁₉₉₀₎

and Peremans et al.

_(1993),

similar

_approaches

have been

_proposed

to

_identify

these

tar-gets

as beacons for mobile-robot localization.

_Manyika

has

applied

differential TOF models to

_target

_{tracking (Manyika}

and

_{Durrant-Whyte}

1994).

For

_improved

_{target classification,}

multitransducer

pulse/echo

systems

that

_rely

on both TOF and

_amplitude

information can be

_employed.

In earlier work

_by

Barshan and

Kuc,

a

_methodology

based on TOF and

_amplitude

in-formation is introduced to differentiate

_planes

and corners

using

a statistical error model for the

_{noisy signals}

(Barshan

and Kuc

_1990).

Here,

this work is extended to

_develop

algo-rithms that cover additional

_{target types}

and fuse the decisions

of

_{multiple sensing}

_agents

_using

evidential

_reasoning.

Un-certain environmental data

_{acquired by multiple}

sonars at dis-tinct

_geographical

sites is used for

_target

_recognition.

First,

the ultrasonic reflection _{process from}

_commonly

encountered

target

primitives

is modeled such that sonar

_pairs

become

evi-dential logical

sensors.

Logical

sensors, as

_opposed

to

physi-cal sensors that

_{simply acquire}

real

data,

process real sensory data to

_generate

_perception

units that are

_{context-dependent}

interpretations

of the real data

(Nazhbilek

and Erkmen

1993).

By

processing

the real

data,

logical

sensors

classify

the

tar-get

primitives.

An automated

_perception

_system

for mobile robots

_fusing

_{uncertain sensory information} must be reliable in the sense that it is

_predictable.

Therefore,

quantitative

approaches

to

_uncertainty

are needed. These considerations favor measure-based methods for

_handling

sensory data

(both

physical

and

_logical)

at different levels of

_granularity

related

to the resolution of the

data,

as well as the time constants

of the different sensors. The

_{sensor-integration problem}

can

be abstracted in a

_conceptual

model where

uncertainty

about

evidence and

_knowledge

can be measured and

systematically

reduced. To overcome the

_{vulnerability}

of echo

_amplitude

to

noise,

multiple

sonar sensors are used in the

decision-making

process. Decisions of these

sensing

agents

are then

_integrated

using Dempster’s

rule of combination.

Section 2

_explains

the

_{sensing configuration}

used in this

study,

and introduces the

_target

_primitives.

A differentiation

algorithm

that is

_employed

to

_identify

the

_target

_primitives

is also

_provided

in the same section. In Section

3,

the

belief-Fig.

1. A

_typical

echo of the ultrasound

_ranging

_system.

assignment

process is

described,

which is based on both TOF

and

_amplitude

characteristics of the data. Also included is

a

_description

of feature and location fusion when

_multiple

sonar-sensing

nodes are used. Consensus of

_multiple

sen-sors at different sites is achieved

_{by using}

_Dempster’s

rule of

combination,

and the

_sensitivity

to different levels of

ampli-tude noise is

_{investigated.}

Simulation results are

_provided

in

Section 4. In Section

_5,

the

_methodology

is verified

experi-mentally by assigning

belief values to the TOF and

_amplitude

characteristics of the

_target

_primitives,

based on real data. Further

_experiments

are conducted in an uncluttered

rectan-gular

room where feature and location fusion _processes are

demonstrated

_{by employing}

one to three

_sensing

nodes. In the last

section,

concluding

remarks are made and directions

for future research are motivated.

2. Sonar

_Sensing

and

_Target

Differentiation

Algorithm

In this

_section,

basic

_principles

of sonar

_sensing

are reviewed. The

_{sensing configuration}

and the

_target

_primitives

that are

used in this

_study

are described. A differentiation

_algorithm

is

_developed

to

_identify

and locate the

_target

_primitives

from the measurements of a

_{single logical}

sensor.

2.1.

_{Physical Reflection}

Models

_of

Sonar

_{from Different}

Target

Primitives

The most

_popular

sonar

_ranging

_system

is the TOF

_system.

In

this

_system,

an echo is

_produced

when the transmitted

pulse

encounters an

_object

and a _range value r is

produced

when

the echo

_amplitude

waveform first exceeds a

_preset

threshold level T, as shown in

_Figure

1:

Here,

to is the TOF of the echo

_signal

at which the echo

Fig.

2.

_{Sensitivity region}

of an ultrasonic transducer

pair.

of sound in

air.

I

Assuming

additive Gaussian-distributed

noise,

T is

_usually

set

_equal

to 4 to 5 times the value of the noise standard

deviation,

which is estimated based on

experimental

data.

In this

_study,

the far-field model of a

_piston-type

transducer

having

a circular

_aperture

is used

_{(Zemanek 1971 ).}

The

am-plitude

of the echo decreases with inclination

_angle

B,

which

is the deviation

_angle

of the

_target

from normal

incidence,

as

illustrated in

_Figure

2. The echo

_amplitude

falls below the

threshold level when

₁₈₁

>

_0.,

where

0.

is the beam

_angle

that

_depends

on the

_aperture

size and the resonant

_frequency

of the transducer as

Here,

a is the transducer

_{aperture radius,}

and

f

is

the

resonant

_frequency

of the transducer

(Zemanek 1971).

With a

_single

_transducer,

it is not

_possible

to estimate the azimuth of a

_target

with better resolution than the

angular

resolution of sonar, which is

approximately

290.

In the

present system,

two identical acoustic transducers a and b

with center-to-center

_separation

d are

_employed

to

_improve

the

_angular

resolution,

as illustrated in

Figure

2. Each

trans-ducer can

_operate

both as transmitter and receiver

_by

con-struction. The

_{typical shape}

of the

_{sensitivity region}

of an

ultrasonic transducer

_pair

is shown in

_Figure

2. The extent

of this

_region

is in

_general

different for each

_{target type,}

since

geometrically

or

_physically

different

targets

exhibit different reflection

_properties.

The word

_target

is used here to refer to

any environmental feature that is

capable

of

being

observed

by

a sonar sensor.

In this

_study,

the

_target

_primitives

modeled are

plane,

cor-ner, acute comer,

edge,

and

cylinder,

whose horizontal cross

sections are illustrated in

_Figure

3. These

_target

_primitives

constitute the basic

_building

blocks for most of the surfaces

likely

to exist in an uncluttered robot environment. Since the

wavelength

of sonar

(À ~

8.6 mm at 40.0

kHz)

is much

_larger

than the

_{typical roughness}

of

_object

surfaces encountered in

laboratory

environments, targets

in these environments

re-flect acoustic beams

_specularly,

like a mirror

_(Morse

and

Ingard

1968).

Hence,

while

_modeling

the received

_signals

from these

_targets,

all reflections are considered to _be

specu-lar. This allows transducers both

_transmitting

and

_receiving

to be viewed as a

_separate

transmitter T and virtual receiver R in all cases

_(Kuc

and

_Siegel

_1987).

Detailed

_physical

reflection models of these

_target

primi-tives with

_{corresponding echo-signal}

models are

_provided

in the

_Appendix.

2.2.

_Target

_{Differentiation Algorithm}

In the differentiation of the

_target

_primitives

discussed in this

section,

both TOF and

_amplitude

characteristics are used.

In

_Figures

4 and

_5,

TOF characteristics of various

_target

primitives

are

_given

over the

range 9

E

_{[-60°, 60°]}

for a

wide-beam transducer. The TOF characteristics of

_plane,

comer,

_edge,

and

_cylinder

have almost the same form as

il-lustrated in

_Figure

4.

However,

Figure

5 indicates that the TOF characteristics of the acute corner are

significantly

dif-ferent than those of other

_targets.

Let

_{tab( 0)}

denote the TOF

reading

extracted at

_{angle 9}

from

_Aab(r,

_{0, d, t),}

which is the

signal

transmitted

_by

a and received

_by

b,

modeled in the

Ap-pendix.

The difference in the TOF characteristics of the acute

comer is

_exploited

_by

the

_{following algorithm}

to differentiate

the acute comer from the other

_targets.

Acute corner

_{differentiation algorithm}

then acute comer;

then

_plane,

corner,

_edge,

or

cylinder.

In this

_algorithm,

0’ is the standard deviation of the TOF

es-timate,

which is in

_{general nonlinearly}

related to the additive

noise on the

_{signal amplitude.}

This

_relationship

is

inves-tigated

in

_(Ayrulu

_1996).

A

_multiple

of ot,

A;t<7t,

is used to

_improve

the robustness of the differentiation

_algorithm

to

noise

_(Ayrulu

1996).

Note that if a new decision on the

_{target type}

is to be made at each value of 9 as

_proposed

in the

_algorithm,

an acute

comer and a corner cannot be differentiated over a ±1’ °

in-terval around 0 = 0° . This is because the

qualitative

TOF

1. c =

331.4&radic;T/273

m/s, where T is absolute _temperature in Kelvin. At room _{temperature (T} = 293 K), c = _{343.3 m/s.}

601

Fig.

3.

_Target

_primitives

modeled and differentiated in this

_study.

Fig.

4. The TOF characteristics of

targets

when the

_target

is at r = 2 m:

_(a)

_plane;

(b)

corner;

(c)

_edge

with

0,

=

90’;

and

(d)

cylinder

with rc = 20 cm.

characteristics of a comer are the same as that of an acute

corner in this

interval,

as illustrated in

_Figures

4b and 5.

However,

after

_{mistakenly identifying}

a comer as an acute corner, the

wedge

angle

of the acute comer will be

computed

as 90° in this small

_interval,

as verified

experimentally

in

Section 5.

Hence,

if the differentiation

_{algorithm initially}

detects an acute comer but calculates the

_{wedge angle}

to

be around

90°,

the final decision will be a corner. For 6

values outside the interval

[-20°, 20°],

an acute corner of

0c

= 60° _cannot be differentiated from the other

_target

prim-itives,

since its TOF characteristics resemble those of other

target

primitives

for these 0 values.

_Similarly,

acute comers

of

0c

= 45° and

0c

= 30° _cannot be differentiated when 0

is outside the intervals

[-45°, 45°]

and

[-55°, 55°],

respec-tively.

Therefore,

acute corners of

_{wedge angle}

less than 60°

can be

_reliably

differentiated from the rest of the

_target

prim-itives when 0 E

[-20°, 20°]. If 0,

>

60°,

the differentiation

is not

_reliable,

since the TOF characteristics are very similar

to those of other

_targets.

The azimuth 0 and

_angle

0,

of the acute corner can be estimated as

Fig.

5. TOF characteristics of acute corner at r = 2 m with

_{(a) 0c}

=

_{30° (b) 0,}

=

45°

_{(c) 0.}

=

60°

and

_{(d) 0,}

= 90°.

where the

_geometry

for raa and r66 are

_provided

in the

Ap-pendix.

For () = 00,

To estimate _{the range} r

for 0 #

0°,

a second-order

poly-nomial

_equation

must be solved:

The coefficients of this

_polynomial

are:

For the identification of the rest of the

_targets,

_amplitude

characteristics of the return

_{signals, given}

in

_Figure

6,

must

be

_used,

since their TOF characteristics have the same form.

Based on the

_amplitude

characteristics,

the

_following

algo-rithm is used to differentiate the

_planar

_target

from the rest

of the

_target

_primitives.

Plane

_{differentiation algorithm}

then

_plane

with

then corner,

_edge,

or

_cylinder.

Here,

Aaa(0), Aab(O),

and

_{A66(B), respectively,}

denote the maximum values of

_{Aaa(r, 0, d,}

_t),

_Aab(r,

0, d, t),

and

603

Fig.

6.

_Amplitude

characteristics at r = 2 m when the

_target

is a

_(a)

_plane;

_(b)

corner;

(c) edge

with

_6e

=

90° ;

(d)

cylinder

Abb(r,

0, d,

t)

over time at

_angle

0. Functional forms of the latter are

provided

in the

Appendix.

The ra and rb are _the

per-pendicular

distances of the

_respective

transducers from the

target,

whose

_geometries

are also included in the

_Appendix.

To differentiate a comer

_target

from an

_edge

or

_cylinder,

amplitude

characteristics over the

_{range 9}

E

_{[ - 0., 0. j}

are

studied. The

_{distinguishing}

feature is that the maxima of

Aaa(8), Aab(B), A6b(B)

over 0 E

[-90, 80]

are

_equal

for a

right-angle

corner, whereas this is not so for the

_edge

and the

cylinder,

as shown in

_Figure

6.

Hence,

the differentiation

algorithm

follows.

Comer

_{differentiation algorithm}

. _If

[max{Aaa(8)} -

max{Abb(8)}

<

_kAoA]

and

[max{Abb(8)} -

max(Aab(0))

<

kAO&dquo;A]

then comer with

else

_edge

or

_cylinder.

In the above

_algorithm,

_max{Aaa(9)}

_corresponds

to the maximum

_amplitude

over 0 for 9 E

[ - 00 , 80],

With the

_given

number of measurements, it is not

_possible

to determine the orientation of the two

_{planes forming}

the corner.

_Only

the

orientation of the line where the two

_planes

intersect can be

found with

_respect

to the line of

_sight.

To find the orientation

of the

_planes,

measurements that include reflections from the

two constituent

_planes

are _necessary.

In the above

_algorithms,

noise

_multiplicity

factors

_kA

and

kt

provide

robustness for the differentiation process.

Simu-lation results for

_integer

values of

_{kA and kt}

between 0 and 6 are

_provided

in

_{Ayrulu (1996),}

which indicate that for the

desired level of

_robustness,

it is

_appropriate

to set these

_equal

to one. In situations where a

_greater

level of robustness is

desired,

larger

values may be

employed.

Referring

to

_Figure

_6,

_edge

and

_cylinder

_targets

can be

distinguished

over a small interval near 0 = 0’. At 0 =

0°,

Aaa(0)

=

Aab(0)

=

Abb(0)

for _an

edge,

but this

equality

is not true for a

_{cylinder. Depending}

on the radius of the

cylinder,

it may be

possible

to differentiate

_edge

and

_cylinder

with this

_{configuration}

of transducers. An

_edge

is a

_target

with zero radius of curvature. For an

_{edge, expressions}

for

range r and azimuth 0

given

in eqs.

(12)

and

(13)

are the same as in the case of a corner. In the case of a

_cylinder,

in addition to _{range and}

azimuth,

the radius of the

_cylinder

can be estimated. The radius of curvature has two limits of interest: As re ~

0,

the characteristics of the

cylinder

approach

those of an

edge.

On the other

hand,

as _y-e -> oo, the characteristics are more similar to those of a

_plane.

By

assuming

the

_target

is a

_cylinder

first and

_estimating

its

radius of curvature

_{(Barshan 1996),}

_{it may be}

_possible

to

distinguish

these two

_targets

for

_{relatively large}

values of r,.

Approximate expressions

for the

_{r, 0}

and re estimates are

given by

The ratio of transducer

_separation

to the

_operating

range

(d/r)

is an

_important

_parameter

in the differentiation of

_target

primitives, directly affecting

how well these

_target

_primitives

can be differentiated

_by

their TOF and

_amplitude

character-istics. The further

_apart

are the

transducers,

the

_larger

are

the differentials in TOF and

_amplitude

as

_long

as the

_target

remains within the

_sensitivity

_patterns

of both

transducers,

as

in

_Figure

7a. If this is not the case, as in

_Figure

_7b,

some or all

four of the

_signals

_may not be detected. In the

_{limit d}

_{-> 0,}

which

_corresponds

to either the transducers

_being

too close

together

and/or the

_target

_being

too

far,

the two transducers behave as a

single

transducer and the differential

_signals

are

not reliable. This situation is

_equivalent

to the case of

try-ing

to differentiate the

_targets

_using

a

single

transducer at a

fixed

location,

which is not feasible

_(Barshan

and Kuc

1990;

Bozma

_1992).

A detailed

_study

on the effect of transducer

separation

d and range r on the maximum differentials is

provided

in

_Ayrulu

(1996).

3.

Feature

and Position Fusion

_{by Multiple}

Logical

Sensors

This section focuses on the

_development

of a

_{logical sensing}

module that

_produces

evidential information from uncertain

and

_partial

information obtained

_{by multiple}

sonars at

geo-graphically

distinct

_sensing

sites. The formation of such evi-dential information is

_accomplished

with

_reasoning

based on

belief functions. Belief values are

_{generated by}

each

_logical

sensor and

_assigned

to the detected features. These features and their evidential metric obtained from

_multiple

sonars are

then fused

_using

_Dempster’s

rule of combination.

A belief function is a

_mapping

from a class of sets to the interval

_{[0,1 that}

_assigns

numerical

_degrees

of

_support

based

on evidence

_{(Shafer 1976).}

This is a

_{generalization of}

proba-bilistic

_approaches,

since one is allowed to model

_ignorance

about a

_given

situation. Unlike

_{probability theory,}

a belief

function

_brings

a metric to the intuitive idea that a

_portion

of

605

Fig.

7. A

_planar

_target

falls

_(a)

within the intersection of the

_sensitivity

_patterns

of both transducers and

_(b)

outside the intersection of the

_sensitivity

_patterns

so that

_{cross-signals}

are not detected.

committed to its

_complement.

In the

_target

classification

problem, ignorance corresponds

to not

_having

_any

informa-tion on the

_type

of

_target

that the transducer

pair

is

scanning.

Dempster-Shafer

theory

differs from the

_{Bayesian approach}

by allowing

support

for more than one

_proposition

at a

_time,

allowing

lack of data

_(ignorance)

to be

_represented.

With this

approach,

full

_description

of conditional

_(or

_prior)

probabili-ties are no

_{longer required,}

and incremental evidence can be

easily incorporated.

Several researchers have

_recently

started

using

evidential

_reasoning

in

_applications

such as

landmark-based

_{navigation (Murphy}

₁₉₉₆₎

and map

building

(Pagac,

Nebot,

and

_{Durrant-Whyte}

1996).

To differentiate the

_target

_primitives,

differences in the reflection characteristics of these

_targets

are

exploited

and

formulated in terms of basic

_probability

masses. This

_logical

sensor model of sonar

_perception

is novel in the sense that it

models the uncertainties associated with the

_{target type,}

its range, and its

azimuth,

as detected

by

each sensor

_pair.

The

uncertainty

in the measurements of each sensor node is

rep-resented

_by

a belief function

_having

_{target type}

(or

feature)

and

_target

location rand 0 as focal

elements,

with basic

prob-ability

masses

_m(.)

associated with them:

3.1. Feature Fusion

_{from Multiple}

Sonars

The focus of this section is feature

fusion;

fusion of

target-location estimates will be handled in the next section.

_Logical

sensing

of the

_target

_primitives

is

_{accomplished through}

a

metric as

_degrees

of belief

_assigned

to the

_target

_primitives,

according

to the TOF and

_amplitude

characteristics of the received

_signals

described in Section 2.

_According

to the method used in this

_study,

a new decision on the

_{target type}

is made on-line at each discrete value of

9,

based on the

differentiation

_algorithm.

Since

_{complete amplitude}

sonar

scans that cover _{the whole range} of 0 E

_[-00,00]

must be

interpreted

to differentiate

_edge

and

_cylinder

from corner, it is

possible

to differentiate

_{only plane,}

corner, and acute corner

with on-line data

_processing.

However,

once

_complete

TOF

and

_amplitude

characteristics are obtained for all values of

0,

all five

_targets

can be differentiated. Based on TOF and

amplitude

characteristics of the received

_signals

from

_plane,

comer, and acute corner, basic

_{probability assignment}

to each feature is made as follows:

where

_Aab(0)

denotes the maximum value of

_{Aab(r, 9,}

d,

t)

(the

signal

transmitted

_by

a and received

by

b),

and

tab(0)

de-notes TOF extracted from

_Aab(r,

9,

d, t)

at inclination

_angle

0

_{by thresholding.}

The definitions of

_{Aaa(8), Abb(O), taa(9),}

and

_tbb(0)

are similar.

1,, I2, 13,

and

14

are the indicators of

The

_remaining

belief is

_assigned

to an unknown

target type,

representing ignorance

or undistributed

probability

mass, as

Dempster’s

fusion rule

_applies

where

_{independent opinion}

sources are to be combined

_(Shafer

_1976).

This is the case

in the

present

application.

Given two sources with belief

functions

and

consensus is obtained as the

_orthogonal

sum

which is both associative and

commutative,

with the

_resulting

operation being

shown in Table 1. The

_sequential

combina-tion of

_multiple

bodies of evidence can be obtained for n

sensor

_pairs

as

Using Dempster’s

rule of

combination,

where

_L

_Lhk=f.n9,=o

_~t(A)~2(~)

is a measure of

con-flict.

’ ’

The consensus belief function

representing

the

feature-fusion process has the metrics

Disagreement

in the consensus of two

_logical

_sensing

units is

_represented

_by

the &dquo;conflict&dquo; term above. The conflict

measure is

expressed

as

After

_discounting

this

conflict,

the beliefs can be rescaled and used in further data-fusion processes, such as in the

se-quential

combination of

_multiple

bodies of evidence

_(Murphy

1996).

3.2. Fusion

_{of Range}

and

Azimuth

Estimates

Assignment

of belief to _{range and}

_angle

measurements is

based on the

simple

observation that the closer the

_target

is

to the face of the

transducer,

the more accurate _{is the range}

reading,

and the closer the

_target

is to the line of

_sight

of the

transducer,

the more accurate is the

_angle

estimate

_(Barshan

1991 ).

This is due to the

_{physical properties}

of sonar:

signal

amplitude

decreases with r and

with

181.

At

large

_{ranges and}

larger

angular

deviations,

the

_{signal-to-noise}

ratio is smaller. The most accurate measurements are obtained

_along

the line

of

_sight

₍₉

=

0°)

and _at

nearby

ranges to the sensor

_pair.

Therefore,

belief

_assignments

to _{range and} azimuth estimates derived from the TOF measurements are made as follows:

Note

that,

belief of r takes its maximum value of one when

r = _r~.~,zn and its minimum value of _zero when r = _rmax- ·

Similarly,

belief of 9 is one when 0 = 0° and _zero when

8 =

tB°.

Since each sensor

_pair

takes measurements in its own

sensor-centric coordinate

_frame,

_{the beliefs of range and}

az-imuth information need to be first

_projected

onto a common

coordinate

_system

where

_they

can be

_integrated.

_{This is} rep-resented in

_Figure

8,

where erroneous estimates are assumed

for r and 9. Then the metric of the fusion _{process is}

_computed

based on these

projected

values. Due to the noise on _the

sys-tem, estimated range and azimuth values are different than

the true values.

_{Suppose n}

transducer

_pairs

are

employed

and each

_pair

_{estimates the range and azimuth of the}

_target

as

607

Table 1.

_Target

Differentiation

_{by Dempster’s}

Rule of Combination

Fig.

8. Common coordinate

_system

for n

_pairs

of sonar sensors.

Fig.

9.

_Projected

range and azimuth for transducer

pair

i.

in each sensor’s own coordinate

_frame,

while the

_target

is

within its

_sensitivity

_region.

The

_projected

_{range and azimuth}

are

_represented

in

_Figure

9 as

Although typically logarithmic relationships

are used to

re-late

_uncertainty

and belief

_{(Pearl 1988),}

here a

simpler

linear

relationship

is chosen to facilitate the

_analysis:

where p

corresponds

to either _{the range} or azimuth of the

target.

Since _{the range and azimuth} estimates are transformed

onto a common coordinate

_frame,

uncertainties in the

esti-mated range and azimuth must be

_represented

as uncertainties

in the transformed _range and azimuth with the transformation

below:

where (7~ and

_ug

represent

uncertainties in the range and azimuth measurements,

respectively,

and

_4>i

is the

_angle

be-tween

_f,

and

_r’’.

Since the

_position

of the

ith

transducer

_pair,

rs, , is

known,

4>~

can be found from the

_geometry

_by

_using

the cosine theorem:

where rs, is the distance of the

ith

sensor

_pair

from the

ori-gin.

After

_projecting

the range and azimuth estimates onto

a common coordinate

_system,

they

are fused into a

single

range and a

_single

azimuth estimate as follows:

where the new belief value in the common coordinate

_system

can be found

_{by solving}

_eq.

_{(41 )}

for

_m(p).

Beliefs to these combined range and azimuth estimates

Fig.

10. Position of a

plane

with

_respect

to each sensor

_pair.

is noiseless and the location of the

_target

in the common

coordinate

_system

is

(r,

0),

all estimated _{range and} azimuth

values are

_equal

to their true values:

Then the

_projected

and fused range and azimuth estimates

are all

_equal:

For the

_planar

_target

case, which is illustrated in

Figure

10,

fusion of range and azimuth estimates needs to be

modified,

because each sensor

_pair

detects the

_plane

at a different

posi-tion. For this case, a line that

_represents

the

_plane

in 2-D can

be estimated

_using

the estimated

_positions

of the

_{plane by}

all sensor

_pairs

in the common coordinate frame. Then the

perpendicular

distance between this line and the

_origin,

and the orientation of this line with

_respect

to the

_origin

must be found which

_yield

the fused _{range and azimuth of} this

_plane.

In

_2-D,

a

_planar

_target

can be

_represented

as a line with the

equation

If range and azimuth measurements from n sensors are

avail-able,

a

_{weighted least-squares}

solution

_{(Bar-Shalom 1990)}

is

sought

for a and b where the

_weights

and

_uncertainty

are

in-versely

related. The

_{weighted least-squares}

solution can be

found

_{by minimizing}

the

_{following expression:}

Here,

and the

_weights

that minimize the _mean-square error can be

found as

_(Barshan

and Kuc

₁₉₉₀₎

where ()&dquo; x. and oy. are found

_{by transforming}

the uncertainties

in

_{r’ and 0§}

_as

Note that here there is no need to normalize the sum of the

weights

to one. The

_{weighted least-squares}

solution is

and the fused range and azimuth estimates are

4.

Simulation

Results

4.1. Feature Fusion

_for

Plane-Corner

_{Identc; fication}

In the simulation

studies,

it is assumed that a

_{decision-making}

unit

_consisting

of a

_pair

of sonars with

_separation

d = 24.0 cm

is

_available,

mounted on a

_stepper

motor with

_step

size 0.9°.

Signals

are simulated

_according

to the models

_presented

in the

Appendix

for the Panasonic

_transducer,

which has a resonant

frequency

of

₁₀

= 40 kHz and

0.

= 54°.

Temporally

and

spatially

uncorrelated zero-mean additive Gaussian noise of standard deviation <y~ is added to the echo

_signals.

At each

step

of the motor, a

_pulse

is

transmitted,

and four TOF and

four

_amplitude

measurements are recorded. The unit scans an uncluttered area which is a 1.4 m x 1.0 m

_rectangular

room

for 0

E

_{[-180°,180°]}

_in

order to detect corners and

_planar

walls.

The results of the belief

_assignment

_{process for} a

_single

transducer

_pair

located at the center of the room are

_given

in

_Figure

11. In this

_figure,

m(1n)

clearly

indicates that the

plane

feature is

_recognized

with

_high

beliefs at

_{right angles}

around

0°, ::1::900,

::I:: 1800,

and with

_highest

_{beliefs in range} than comer, since

_planes

lie at closer

_proximity

to the sensor

609

Fig.

11. Belief

_assignment

with information from a

_single

transducer

_pair.

than corners. For

_larger

inclination

_angles,

these four

_planes

are confused with corners, because the tails of the

amplitude

characteristics of a

_plane

and corner are similar. The belief

m(c)

shows that the four corners of the room are identified

with

_highest

belief values around :f:45° and :f: 1350. The be-lief

_chop

in the middle of each corner belief curve reflects a

_pin-type

rise in

_uncertainty

at these locations. This is due

to the

_amplitude

characteristics of the corner. At +E, me

degrees

to the left or to the

_right

of this

line,

higher

beliefs

are

_generated

in the

recognition

of a corner. In the

_angular

interval between the identification of

_plane

and that of comer,

there exists a

_region

of

_{high uncertainty}

in

m(u)

due to no

re-turn

_{signal being}

available. In this case,

neglecting

multiple

reflections of third and

_higher

orders,

all transmitted

wave-forms bounce off the room

boundaries,

and no return

_signal

is recorded.

Thus,

m(r)

=

m(6)

= 0.

Further simulation studies were

_performed

with three

iden-tical

_logical

sensors located at different

_positions

in the 1.4 mx 1.0 m

_rectangular

room. The decisions of the three

pairs

are combined so as to

_perform

the feature fusion

by

employing Dempster’s

rule of combination. The locations of these transducer

_pairs

are

_{(0.0, 0.0), (-0.1, 0.1 ),}

and

_{(0.1, 0.1 )}

in meters, where the

origin

is taken as the center of the room.

All transducer

_pairs

are assumed to rotate on

_stepper

mo-tors with

_step

size 0.9’. These units scan the room for

0

E

[-180°,180°].

At each

_step,

transducer

_pairs

collect data from the

_target

at the same

_step

_angle

_0,

and the decisions

of all

_pairs

at this

_angle

are fused. To calculate

_{probabilities}

of correct

_{classification, misclassification,}

and lack of

_target

identification,

data is collected

_{for 0}

E

[-180°, 180°] three

times,

which

_corresponds

to about

1,200

decisions.

The classification results for each transducer

_pair

and the data fusion

_using

three transducer

_pairs

are

_given

in

_Figure

12. For a maximum

_{echo-amplitude}

value of

_0.3,

_amplitude

noise

standard deviation of 0.02

_corresponds

to 50% of the

max-imum

_{signal-amplitude}

differences. For

u A >

0.03,

differ-ential

_signal

levels are

_comparable

to the noise

level,

and it becomes

_impossible

to detect these differences. In

Fig-ure

12b-12d,

the

probability

of misclassification with one

pair

is almost zero for all the noise standard deviation

values,

owing

to the inclusion of a A in the classification

algorithms.

The

_probability

of correct classification with the fusion of three

_pairs

can be seen in

_Figure

12e. The

_improvement

in

the

_probability

of correct classification is shown in

_Figure

12f.

Here,

the

_probability

of correct classification is derived from the consensus of three

logical

sonars,

_illustrating

how fusion

provides

an increase in evidential

_support

that raises the

prob-ability

of correct classification when

_compared

to that of a

single

transducer

_pair.

The

improvement

is between 10% and 35% for a A <

0.03,

becoming

smaller for

_larger

values of

a A. Of course, this is at the increased cost of time to collect

more data and do the necessary

computations

to fuse the data from three

_pairs

of sensors.

When O’A is excluded from the differentiation

algorithm

by

replacing

it with zero, the

algorithm

becomes less robust

and the

_probability

of misclassification

increases,

as shown

in

_Figure

13. In this case, when

u A >

0.02,

the

performance

of the classification is

_comparable

to the

_performance

of a

randomized decision rule

_(Berger

_1988),

where 50% of the time the

_target

is

_randomly

guessed

to be a

_plane,

and 50% of the time it is

_guessed

to be a comer,

_{by completely ignoring}

the information carried

_by

the data.

4.2. Acute Corner Simulations

Acute comers are less

_frequently

encountered in

comparison

to the other

_target

_primitives.

One

_example

where

_they

com-monly

occur is in orchestra shells for auditoriums and opera

houses.

In the acute-comer

simulations,

the same

sensing

configu-ration as in the

_previous

subsection is used. An acute corner

with

_{wedge angle}

0c

is

_placed

in front of the sensor

_pair

at r = 2 _{m, as} shown in

Figure

14. Each time a

_pulse

is

transmitted,

four TOF and four

_amplitude

measurements are

collected. The

_stepper

motor is

rotated,

and the

_target

is

scanned for 9 from -60° to 60’. While

_obtaining

classifi-cation results for each

_angular

step,

the unit scans the

_target

from 0 = -60° to 9 =

60°,

eight

times. As _a

result,

the

log-ical

_sensing

unit makes about

1,072

decisions for each

_pair

of at and a A values.

For the

_region

in which an acute comer can be

reli-ably

differentiated with the classification

_algorithm

(9

E

[-20°, 20°]),

the results of belief

_assignments

_by

a

logi-cal sensor unit for different values of

0c

are

_obtained,

and

the result for

0c

= 60° is

provided

in

Figure

15 as an

exam-ple. According

to the

_results,

for all

Or

values,

the maximum belief of

_being

an acute corner is obtained at 0 = 0° when

the

_system

is noiseless.

Moreover,

the belief of

_being

a

_plane

or a comer is zero for all

0,

9~,

and a A values. The values of a A used in this

study

are 0.002 and 0.003.

_Although

the

decrease in the belief of acute corner with

_increasing

101

is

sharper

for

_larger

_9~,

the belief of acute corner is

_greater

than

the belief of unknown

target

for all 0 and QA values. Belief values are between 0.8 and 1.0 for

Or

=

30°,

between 0.7

and 1.0 for

_0c

=

45°,

and between 0.6 and 1.0 for

Oc

= 60’.

The range,

azimuth,

and

0c

are estimated for acute comers

with

_0c

=

30°, 45°,

and 60° at r = 2 _m, for different _{a A}

values. The results for a A = 0.002 _are

provided

in

_Figure

16. For a A =

0.002,

the maximum _{range error} is 5.7 _cm, and

the maximum error in azimuth is

1.8°,

which occurs with the

acute corner of

_0c

=

30°,

and the maximum error in

0c

is

1.4°,

occurring

for the acute comer of

0,

= 60°.

The classification results for these acute corners are

il-lustrated in

_Figure

17. In this

_figure,

the

_probability

of

correct classification is

_higher

than both the

_probability

of

misclassification and the

_probability

of unknown

_target

up to ut = 160 J.Lsec for

0c

=

30°,

_ut = 100

psec for

Be

=

45°,

and ut = 40 ilsec for

0,

= 60’. The

probability

of

misclas-sification is

_always

less than both the

_probability

of correct

classification and the

_probability

of unknown

_target.

5.

_Experimental

Verification

In this

_study,

an

_experimental

_setup

is

_employed

to

_assign

belief values to the

_{experimentally}

obtained TOF and

am-plitude

characteristics of the

_target

_primitives,

and to test

the

_proposed

fusion method for

_target

classification. Data

was collected at Bilkent

_University

Robotics and

_Sensing

Research

_Laboratory.

Three sensor nodes are

_placed

in a

small, uncluttered,

rectangular

room with

_specularly

reflect-ing

surfaces. Panasonic transducers are

_used,

which have much wider beam width than the

_commonly

used Polaroid transducers. The

aperture

radius of the Panasonic transducer is a = 0.65 _cm, and its _resonant

frequency

is

10

= 40

kHz;

therefore

_{00 E#}

54° for these transducers

_{(Panasonic 1989).}

Since Panasonic transducers are manufactured with distinct

characteristics for

_transmitting

and

_receiving,

two transmit-ter/receiver

_pairs

_{with very small vertical}

_separation,

as

il-lustrated in

_Figure

18,

are used as a

single logical

unit. The

horizontal center-to-center

_separation

between the

transduc-ers is d = 24.0 _cm. This

sensing

unit is mounted _{on a} small

6-V

_stepper

motor with

_step

size 0.9’. The

_stepping

action is

controlled

_through

the

_parallel

_port

of an IBM-PC

486,

with

the aid of a microswitch. The sensor data is

_{acquired using}

a

DAS-50 A/D card with four

channels,

12-bit

resolution,

and 1 MHz

_{sampling frequency.}

The echo

_signals

are

_processed

on an IBM-PC 486

_using

a C

_language

_{program. From the}

time of

transmission, 10,000

samples

of each echo

_signal

are

collected and thresholded. The

_amplitude

information is

ex-tracted

_{by finding}

the maximum value of the

_signal

after the

threshold value is exceeded. The

_targets

_employed

in this

study

are:

_cylinders

with radii

1.5, 2.5, 5.0,

and 7.5 cm; a

planar

target;

a comer; and an acute corner of

_Oc

= 60° .

All of the

_experiments

are conducted on

_large

sheets of

millimetric paper to allow accurate _{calibration. In the}

exper-iments,

each

_target’s

surface distance r to the center of the transducer

_system

is varied between 20 cm to 140 cm at 10

cm intervals. At each

_position,

the

_target

is scanned while it is

_stationary

at 0 = 0° . The

typical

differential TOF between

the transducers varies between 0 cm and 14 cm,

depending

on the

target type,

curvature, and distance for the fixed

sep-aration of d = 24.0 _cm

(Ayrulu

1996).

As the

range of the

target increases,

the differential

signal

becomes less reliable for

target

classification.

Belief-assignment

results to the TOF and

_amplitude

char-acteristics of a

plane

at r = 50 _cm when scanned with the

sensing

unit are

_given

in

_Figure

19. In this

_figure,

belief of

_being

a

_planar

_target

primitive

is

_greater

than zero for

611

Fig.

12.

_(a)

The simulated room;

(b)

classification results: sensor at

_{(0.0, 0.0); (c)}

sensor at

_{(-0.1, 0.1); (d)}

sensor at

_(0.1,

0.1 ); (e)

all three sensors;

(f)

improvement

in the

_probability

of correct classification.

Fig.

13. Classification with a

_single

transducer

_pair

without the _{(j A} term in the classification

_algorithm.

Fig.

14. Position of the transducer

_pair

and the acute comer.

0 E

_{[-20°, 20°].}

Belief of

_being

a

_plane

and the belief of

being

an unknown

_target

oscillate around 0.5 for

101

<

10°,

and the belief of

_being

an unknown

_target

is

_greater

than

the belief of a

_plane

outside this

_region.

Moreover,

belief of

_being

a corner or an acute corner is zero for all 0 values.

Estimated range and azimuth values are

_given

in

_Figure

20.

Referring

to this

_figure,

_{maximum range} error is 0.5 cm and

maximum error in the azimuth estimate is 0.7°.

Beliefs are

_assigned

to the TOF and

_amplitude

character-istics of a corner at r = 80 _cm, as shown in

_Figure

21 when scanned with the

_sensing

unit.

_Although

the

target

is a

cor-ner, for the interval 0 E

_{[-5°, 2°],}

_highest

belief is

_assigned

to the acute comer. This is due to the

_similarity

of the TOF characteristics

(for

small

9 ~ )

of corners and acute comers

with

_large

8e,

as

_explained

in Section 2.2. Belief of corner

becomes

_larger

than belief of acute corner for

101

>

_5°,

as

expected.

Since the TOF characteristics are

significantly

dif-ferent for

₁₀₁

>

_5°,

the correct decision is reached. Belief of

plane

is zero for all 0 values

except

at 0 = -9°.

Estimated range and azimuth values are

_given

in

_Figure

22.

Referring

to this

_figure,

maximum range error is 0.3 cm,

and the maximum error in azimuth is 3.6° in the

_region

0 E

_{[-4°, 4°].}

In

_Figure

22c,

estimated

_{wedge angle}

of the acute corner is shown.

_Although

the belief for an acute

corner is around one for

101

< 5°,

estimated

_{wedge angle}

is

around 90° in this

_region.

Therefore,

the final decision is a

comer, as discussed in Section 2.2.

Beliefs

_assigned

to the TOF and

_amplitude

characteristics of an acute corner

_{of 8}

= 60° _{at r} = 40 _cm, which is scanned

with the same

_system,

are

_given

in

_Figure

23. In this

_figure,

belief of

_being

an acute corner is

_always

_greater

than the belief

of

_being

an unknown

_target,

and belief of

_being

a

_plane

or a comer is

_always

zero. Estimated range,

_azimuth,

and

_wedge

angle

of acute comer are

_given

in

_Figure

24.

_Referring

to this

figure,

maximum range error is 2.0 cm, maximum azimuth

error is

3.0°,

and maximum error in estimated

_angle

of the

acute comer is 4.2’ for 9 c

[-6°, 6°].

The fusion method is tested

_{experimentally}

in an

unclut-tered

_rectangular

room

measuring

1.4 m x 1.0 m with

specu-larly reflecting

surface,

created

_{by partitioning}

off a section

of a

_laboratory.

The test area is scanned

_by

three sensor units

located at

_{(0.0, 0.0), (-0.1, 0.1),}

and

_{(0.1, 0.1)}

in meters,

which are same as the

_{positions employed}

in the simulation

studies. The

_physical

limitations of the hardware

_prevent

the

sensors from

_covering

the entire

_angular

range

0.

Instead,

rotation is over the

_{range 0}

E

[0°, 284°].

As an

_example,

the

range

readings

of the sensor located at

_{(-0.1, 0.1)}

are

_given

in

_Figure

25.

Feature beliefs are

_{assigned by}

the sensors based on

the TOF and

_amplitude

characteristics of the sonar

sig-nals reflected from comers and

_planar

walls. The basic

probability assignments by

individual sensors are shown in

Figure

26a-26c. Note the

_{high degree}

of

_uncertainty,

since

a

_{single logical}

sensor is

_employed.

Each of the sensor

de-cisions on

_{target type}

is referred to the central

_position

for

comparison

and fusion.

_During

a _scan, a sensor estimates the

range and

angle

of the

target

under observation. The values

for a

_target

are

_{weighted by}

the beliefs

_assigned

to the esti-mates, and then referred to

_position

_{(0.0, 0.0).}

The sensors’

determinations of beliefs are fused

_{using Dempster’s}

rule of

combination. Fusion results are shown in

_Figure

26d.

Us-ing

a

_{single sensing}

_node,

the

_percentage

of correct decisions is about 30%. The

_remaining

70% is attributed to incorrect

decisions due to noise and

_{complete uncertainty,}

which oc-curs when the

_target

is not visible to the sensor at certain