APPLICATION OF EVIDENCE ACCUMULATION BASED ON

ESTIMATION THEORY AND HUMAN PSYCHOLOGY FOR

AUTOMOTIVE AIRBAG SUPPRESSION

Michael E. Farmer

University of Michigan-Flint, 303 East Kearsley St. Flint, Michigan, U.S.A.

Keywords: Sensor fusion, Dempster-shafer, Kalman filtering, Belief updating.

Abstract: The traditional D-S conditioning is based on a collection of ‘experts’ inputting their evidence and

accumulating the beliefs. Researchers have often adopted this same mechanism for integrating evidence

from single sources of evidence over time, such as seen in sensor networks. The traditional D-S

conditioning ensures the order of inputs does not matter. While this is sensible for a collection of experts we

propose that it is not suitable for a single input providing streams of evidence. Research in psychology show

order of integration of evidence does matter, and depending on the application humans have a preference for

recency or primacy. Estimation theory provides frameworks for analyzing data over time, and recently some

researchers have proposed integrating evidence in an estimation-inspired manner. We then propose a

Kalman-filter based approach for integrating temporal streams of evidence from a single sensor. We then

propose the system uncertainty be modeled by the conflict defined by Dempster. We then define a real-time

evidence accumulation system for airbag suppression and demonstrate that the Kalman filter-based

approach indeed out-performs Dempster-Shafer based evidence accumulation.

1 INTRODUCTION

It has been recognized in cognitive psychology

research that a key aspect of belief updating is its

sequential nature. There has likewise been

significant research in the artificial intelligence

community with respect to evidential reasoning,

with the most common approaches being Bayesian

and Dempster-Shafer (D-S), but other methods such

as Transferrable Belief Model, Possibility Theory,

Fuzzy Logic, etc. also playing critical roles. This

paper will use Dempster-Shafer as its foundation.

There are three key areas where the existing research

in evidential reasoning has differed significantly

from the findings in human cognition, (i) order

effects, (ii) evidence impact reduction in long

evidence streams, and (iii) evidence evaluation

versus estimation. As high performance real time

sensors, particularly imaging sensors become more

pervasive, it is time to relook at the mechanisms of

evidence accumulation and belief updating from

temporal streams of sensor data.

The first issue, namely that of order

independence is not found to exist in human

reasoning, and there are definite situations when

order-effects are present, either in the form of

recency preference or primacy preferences (Hogarth

and Einhorn, 1992); (Wang et al., 1999); (McKenzie

et al., 2002); (Baratgin and Politzer, 2007). Most

traditional approaches such as Dempster-Shafer

ensure order independence, and there is no

mechanism to support when order dependence is

important.

The second issue which demands another look is

that of how to integrate evidence over long streams

of data. In human cognition there is clear research

evidence that the impact on new information should

reduce as more evidence is gathered, whereas the

common approaches of Bayes and D-S weight the

entire history equally with the most recent input.

The third issue related to human cognition is based

on what cognitive researchers call encoding

(Hogarth and Einhorn, 1992). In human evidential

reasoning there are two approaches, evaluation and

estimation. Evaluation is a process in which the

reasoning tasks tend to be formulated into a true-

false framework and evidence in encoded positive

or negative with relation to a hypothesis (it either

supports or refutes). Evaluative reasoning is

identical to the Bayes formulation for combining

470

E. Farmer M..

APPLICATION OF EVIDENCE ACCUMULATION BASED ON ESTIMATION THEORY AND HUMAN PSYCHOLOGY FOR AUTOMOTIVE AIRBAG

SUPPRESSION.

DOI: 10.5220/0003650004700476

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ANNIIP-2011), pages 470-476

ISBN: 978-989-8425-74-4

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

evidence. Estimation tasks, however, are additive in

nature and assess ‘how much evidence is to be

allocated to a belief’(Hogarth and Einhorn, 1992).

Cognitive researchers have found that ‘estimation

may be more frequently used than evaluation’,

whereas artificial reasoning systems tend to rely on

the evaluative approaches.

A final issue in addition to the three related to

human cognition is that of the meaning of data

independence in evidence combining. The clarity of

when data is independent is different when

integrating evidence across sensors or experts

compared to when integrating evidence temporally

from individual sensors. Liu and Hong recall that

Dempster was very clear where he stated: “Different

measurements by different observations on different

equipment would often be regarded as independent”

(Liu and Hong, 2000). Thus there should be a

distinction between these two types of integration

yet the distinction has generally not been widely

recognized or exploited in the literature to date. We

propose there is a need for a distinction between

traditional statistical independence and the stronger

independence proposed by Dempster, which we

term Evidential Independence. For temporal

integration of data within single sensors, statistical

independence is to be expected, however evidential

independence should not be expected. This

distinction in the types of independence requires

different a approaches for integrating evidence over

time from a single sensor.

The purpose of this paper is to review evidence

combination approaches and show the need for an

alternative approach that provides for temporal

integration of information from a single sensor. We

then propose a framework for such a system devised

from first-principles of Kalman filtering where the

concept of evidence conflict defined by Dempster

plays a critical role in managing the adaptive filter

gain. We then apply the algorithm to an interesting

real-world automotive airbag suppression problem

and demonstrate that the Kalman approach has

superior performance to a traditional discounted

Dempster-Shafer approach.

2 EXISTING APPROACHES TO

COMBINING TEMPORAL

STREAMS OF EVIDENCE

Dempster’s Rule of Combination has been extended

to process a temporal stream of sensor inputs by

viewing m2(a) “not as sensor Sj’s observation, but

instead as the previously combined observations.

Wu et al. propose extending Dempster-Shafer by

weighting the masses in the computation

accordingly (Wu et al., 2003):



 















ZYX

YmwXmw

Zmm

2211

(1)

where the weights are computed according to:

  

pTntctw 





0

(2)

and c

(t) is either 0 or 1 depending on whether the

sensor estimate is correct or not,



is the

incoming data sampling rate, and p controls the

decay rate of samples being considered.

Unfortunately for many classification systems, there

is no knowledge of whether the incoming sensor

data is correct or note.

Farmer has likewise proposed an extension to

Dempster-Shafer based on pre-processing the

incoming sensor data based not on reference to

correctness, but rather on its credibility in relation to

past system beliefs, where incoming probability

masses are discounted using (Farmer, 2006):











  































A,pAmp

A,PAAmp

for 11

and

where

(3)

where the probability p of the evidence being valid

is determined by:











last

temp

Bel

BelBel

p 1

(4)

and

temp

Bel

is the beliefs assuming the new

information has been integrated, and

last

Bel

is the

beliefs prior to the inclusion of the new information.

Once the incoming masses are discounted they

are integrated using Dempster’s standard rule of

combination.

Integration of temporal streams of data sources,

such those found in signal processing systems

typically employ estimation techniques.

One estimation framework has been developed

by Premaratne, et al. where they define belief

updating according to (Premaratne et al., 2007):









ABBelBBelBBel

kkkkk

1111















(5)

where the weights are constrained by

1



The weight selection controls the relative

importance of new versus historical evidence,

APPLICATION OF EVIDENCE ACCUMULATION BASED ON ESTIMATION THEORY AND HUMAN

PSYCHOLOGY FOR AUTOMOTIVE AIRBAG SUPPRESSION

471

thereby providing a mechanism to support primacy

and recency; however, the authors did not address

the task of weight selection and evolution. We will

specifically address these two key aspects of

evidence filtering (weight selection and weight

evolution) in our proposed approach in Section 5.

Equation (5) exhibits some of the behavior we

tend to expect when processing temporal streams of

evidence, namely: “…when encountered with the

same streaming information continuously, the belief

converges to a value decided solely by this incoming

information” (Premaratne et al., 2007).

Benferhat, et al. developed an analogy to the

Kalman filter for qualitative belief revision within

Possibility Theory, where they assume a prediction

equation of the simple form,



1





where



is the belief state at time t. The estimated possibility

for state



at time t+1 is then (Benferhet et al.,

2000):

 

























)(

max

(6)

and the estimate update is(Dubois & Prade, 1997):

  



 









AAA

|1,|max,|











(7)

where A is the new information provided by the

sensors, and



is the necessity measure of the input

A (a measure of its certainty or error). The









term reduces the plausibility value







, and

hence the rankings.

3 BELIEF REVISION IN HUMAN

PSYCHOLOGY STUDIES

Hogart and Einhorn (Hogarth and Einhorn, 1992)

suggest that the recency effect is more important

when messages are inconsistent. This result was also

verified by Wang et al. for an interesting Combat

Information Center application (Wang et al., 1999).

Baratgin and Politzer recently address the issue of

updating (dynamic environment) in human decision

making and confirm by reviewing numerous studies

that “a message has greater contextual effects when

it is learnt in the last position” (Baratgin & Politzer,

2007).

For example, in response to their order effect

results Hogarth and Einhorn proposed an anchoring

and adjustment model to explain these order effects.

They developed the following model for belief

adjustment (Hogarth and Einhorn, 1992):







RxsRxsSSS

kkkkk





for



(8)

and















RxsRxsSSS

kkkkk











for 1



(9)

where

is the current level of belief,

1k

is the

belief at the last update,





is the new evidence

input into the system, and



and



are weights to

enforce sensitivity towards negative or positive

evidence, relative to a reference level of support R.

This model also supports decaying impact of

evidence through the mechanism where “as

information accumulates and as people become

more firmly committed to their beliefs, values of



and



would decline in a long series of evidence

items” (Hogarth and Einhorn, 1992).

Hogarth and Einhorn noted that the values for the

constants of evidence integration,



and



, would

change over time to modify the changing impact of

new evidence in relation to the aggregated body of

evidence up to that point in time (Hogarth and

Einhorn, 1992).

4 VIDEO-BASED AIRBAG

SUPPRESSION AS A MODEL

PROBLEM

Farmer and Reiman developed an interesting system

application which can be used to demonstrate the

application of evidential stream processing (Farmer

and Reiman, 2006). They developed a monocular

vision system which viewed the occupant in a

passenger vehicle and disabled the airbag if the

occupant was a infant or child, or in the case of an

adult, if the occupant was leaning too close to the

bag for a safe deployment. A diagram of the system

concept is provided in Figure 1. The image

processing for this system consisted of two parallel

paths, one for classification processing and one for

track processing. The classification system provided

a result at a 0.2 Hz rate.

Figure 1: System concept for airbag suppression system.

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472

There are four classes of occupants which comprise

the Frame of Discernment:



= {infant, child,

adult, empty}. Example images for these classes are

shown in Figure 2. As the vehicle drives through the

world, the occupant is moving, and there are

shadows and light bands moving across the camera

field of view that will continuously change the scene

the camera is processing. The classification system

must integrate this temporal stream of perceived

classifications and determine the best candidate

class in order to disable the airbag in case of a child

or an infant seat.

(a) (b) (c) (d)

Figure 2: Examples of each of the classes: (a) infant, (b)

child, (c) adult, and (d) empty seat.

One unique condition that is experienced by this

system is that there are times when the occupant’s

behavior can dramatically change the perceived

class of the occupant. For example if an adult

occupant reaches down to tie their shoe they can

appear like an infant seat (see Figure 3), and a child

that stands in the seat can appear to be an adult. We

then need to be able to change the system beliefs as

the evidence is gathered based on this changing

world view.

(a) (b)

Figure 3: Demonstration of need for temporal evidential

combining: (a) adult seated normally and (b) adult leaning

forward and appearing to system to be an infant seat.

Figure 4

and Figure 5 provide a series of frames

across the entire image sequence for a 5

percentile

male passenger and a 5

percentile female

passenger where they are moving and performing a

number of hand and arm gestures to intentionally try

to fool the system. These video sequences are ideal

for demonstrating the real-world issues regarding

integration of temporal streams of evidence, and

clearly shows the roles temporal-based Kalman-

filter can play.

Figure 4: Every 65 frames from sequence 1.

Figure 5: Every 25 frames from sequence 2.

5 PROPOSED STRUCTURE FOR

A KALMAN FILTER FOR

EVIDENCE FILTERING

Consider the estimate of a basic evidential state at

some time increment k, to be



and an incoming

measure of such a state to be



obs

. Assume an

initial estimate of the uncertainty in that state is

defined to be:



and the known uncertainty in the

measurements to be



. For simplicity we will also

assume the state transition matrix and the

measurement matrix are simply the identity matrix

for the sake of clarity of the derivations.

The basic estimate update equation is (Gelb,

1974):

















ˆˆ











kxkxkGkxkx

EobsEE

(10)

After each update of the filter we compute a new

estimate for the estimate uncertainty (Gelb, 1974):













 kkGk



(11)

APPLICATION OF EVIDENCE ACCUMULATION BASED ON ESTIMATION THEORY AND HUMAN

PSYCHOLOGY FOR AUTOMOTIVE AIRBAG SUPPRESSION

473

where the gain term is (Gelb, 1974):







 









(12)

Equations (10) through (12) represent the simplest

form possible for the Kalman filter. In these

equations, the value for



can be computed from

either the signal-to-noise ratio of the sensor source,

or in the case of a classifier such as for the above

airbag application, it can be the overall probability

of correct classification for the system or it can

capture the local decision surface for a particular

classification result. Note however, that the gain

term defined in Equation (12) does not include the

desired System Covariance which captures the

uncertainty in the system model. To add this term

we need to note that if there is an added system error

h introduced at time k, and then the state for that

time would actually be:

   

khkxkx

 1

(13)

This would then result in the covariance for the state

estimate to be:

  

kkk

hEE

222

ˆˆ





(14)

There are two key questions we must address: (i)

what behavior do we want from an evidential

filtering viewpoint as







varies, and (ii) what

does the term





correspond to in the evidential

reasoning domain.

To address these questions we will begin with

this interesting point by Schubert, who mentions that

“A high degree of conflict is seen if there is a

representation error in the frame of discernment;

while a small conflict may be the result of measuring

error” (Schubert, 2008). Recall the conflict between

two sources of evidence is defined to be (Shafer,

1976); (Schubert, 2008):

 









YmXm

2112

(15)

If we substitute a term based on this conflict into

Equation (15) we get:

  

kKkk

recEE 12

ˆˆ





(16)

where

rec



is the recency factor which will serve to

bias the resultant state estimate towards either

recency or primacy. The resultant behavior of using

the conflict in this manner will be that evidence will

not be discarded or reassigned as in Dempster’s rule,

but rather will be added to the system at a reduced

level. As this conflicting evidence continues to come

into the system (assuming it is a sustained change in

environment), it will become less and less

conflicting as the masses evolve, and the gain will

continue to increase as the belief system evolves

from this evidence.

6 CONCLUSIONS AND FUTURE

WORK

Figure 6 provides a graphical view of the incoming

classification results from the sequence shown in

Figure

Figure 6: Incoming classifications (adult- class 3 is the

correct class).

The classification result for the adult 50% male

sequence (Figure 4 and Figure 6) is roughly 64%

correct as is shown in Table 1. Note the Dempster-

Shafer approach provides an improvement to

roughly 76%. The four different entries for the

Kalman filter are based on the relative nominal gain

of the filter which depends on the recency factor

defined in Equation (16). The high gain filter

performance is quite poor due to the fact that with a

higher gain, the filter is more heavily weighting the

most recent classifier results. The ultra-low gain

filter provides superior performance and more

closely mimics human reasoning where: ‘as

information accumulates, beliefs are expected to

become less sensitive to the impact of new

information because this represents an increasingly

small proportion of evidence already processed”

(Hogarth and Einhorn, 1992). The improved

performance of lower recency factors can most

readily be seen in Figure 7 where the peak in

classifier performance occurs for a recency factor of

roughly 0.005.

One other parameter that must be initialized is

the estimation uncertainty:



. Figure 8 shows that

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

474

fortunately, the performance of the system is not

particularly sensitive to this value, however, a value

below 0.1 provides the optimal classification

performance.

Table 1: Classification Results for Adult Male Sequence.

Method Correct Classification

Raw Data .6375

Discounted Dempster-Shafer .7667

Kalman (High Gain) .6778

Kalman (Medium Gain) .7001

Kalman (Low Gain) .8096

Kalman (Ultra-low Gain) .9142

Figure 7: Classification results versus recency factor.

Figure 8: Classification results versus initial estimation

uncertainty.

Figure 9 provides the incoming classifications

for the sequence in Figure 5 where the initial

classification was roughly 73% correct. The results

for the 5

percentile female were also very

encouraging for the Kalman filter-based approach,

as can be seen in Table 2. Once again the ultra-low

gain Kalman outperformed the discounted

Dempster-Shafer algorithm. Thus for both datasets

the ultra-low gain Kalman filter which heavily

weights primacy of data similar to human reasoning

outperformed the Dempster-Shafer approach.

While a very low gain filter is optimal for

limiting change, we must analyze whether this bias

against change can limit performance when change

is required. To test this case, we started the data

integration system at a point in the classification

sequence where there was an extended period of

false classifications, as can be seen in Figure 10,

where the adult male occupant was leaning forward

and appeared as an infant seat.

Figure 9: Raw incoming classifications for sequence 2.

Table 2: Classification Results for Female Sequence.

Method Correct Classification

Raw Data .7297

Discounted Dempster-Shafer .9369

Kalman (High Gain) .7477

Kalman (Medium Gain) .8063

Kalman (Low Gain) .9820

Kalman (Ultra-low Gain) .9820

The raw incoming classification result for the data

set that begins on an extended epoch of mis-

classifications is roughly 63%. .

Table

3 provides the results for the Dempster-

Shafer approach compared to the various Kalman

filters of varying gain. Even in this dataset, the

Kalman filter achieved 86% classification accuracy

versus the Dempster-Shafer’s 75%.

Figure 10: Incoming classifications (adult- class 3 is the

correct class) with starting at epoch where classification

begins incorrectly.

APPLICATION OF EVIDENCE ACCUMULATION BASED ON ESTIMATION THEORY AND HUMAN

PSYCHOLOGY FOR AUTOMOTIVE AIRBAG SUPPRESSION

475

Table 3: Classification Results for Adult Male Sequence

Starting at Epoch with Extended Wrong Classification.

Method Correct Classification

Raw Data .6291

Discounted Dempster-Shafer .7549

Kalman (High Gain) .6725

Kalman (Medium Gain) .6920

Kalman (Low Gain) .7961

Kalman (Ultra-low Gain) .8568

In summary, the proposed Kalman filter-based

temporal evidence accumulation algorithm

outperformed the traditional Dempster-Shafer

algorithm on all three of the datasets in this real-

world application from an automotive airbag

suppression system.

7 CONCLUSIONS AND FUTURE

WORK

We have introduced the notion that when integrating

evidence from a temporal stream of sensor inputs, an

approach based on estimation theory and human

reasoning provides superior performance to a

traditional evidential reasoning approach based on

Dempster-Shafer. We posited that this is due to the

fact that the Dempster-Shafer approach is based on

the concept of evidential independence which

mandates the data be derived from different sensors

(as originally envisioned by Dempster) and that for a

single sensor a weaker statistical independence is all

that can be assured.

We reviewed various approaches for evidence

accumulation. We then developed an alternative

Kalman filter representation from first principles and

identified the key uncertainty terms as being: the

estimate uncertainty:





, the measurement

uncertainty:



, and the system uncertainty:







We proposed that the concept of conflict in the

incoming evidential states can be used as a means of

estimating the system uncertainty. The approach was

tested on a real-world automotive airbag suppression

application which consisted of a high resolution

camera providing real-time classification inputs to

our evidence accumulation system. An ultra-low

gain Kalman filter out-performed the traditional

Dempster-Shafer algorithm, which parallels the

findings from human cognition where long term

accumulation of evidence is best considered an

estimation technique and recent evidence is highly

discounted in favour of the historical accumulation

of evidence.

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