Physio-associative temporal sensor integration

Physio-Associative Temporal Sensor Integration Erik Blasch and James Gainey, Jr. Air Force Research Laboratory, Sensors Directorate, Avionics Cir. WPAFB, OH 45433-7607

Keywords: Thalamic Gating, Association-Cortex Filter, Association Learning, Sensor Integration, Tracking

ABSTRACT The paper describes the physio-associative temporal sensor integration algorithm which is motivated by the observed function of the thalamus and utilizes signals theory mathematics to model how a human efficiently perceives information in the environment. The algorithm is consistent with that of an aircraft pilot; namely, to estimate, filter, and predict sensed

afferent signals and produce efferent controls under dynamic flight conditions. Dynamic sensor integration under uncertainty requires feature selection which can be formulated as a associative-learning problem in which sensed states are represented as current situational beliefs, and the information either excites or inhibits long-term memory associations. The objective of the learner/observer is to 1) abstract salient signals from the environment, 2) integrate the signal for real-time beliefs, and 3) compare beliefs to learned associations. Biologically, the paper models these processes from the biological systems of the eye, thalamus, and association-cortex; respectively. By selecting the optimal set of mutually non-exclusive sensors and comparing the integrated signal to learned associations, the physio-associative temporal algorithm maximizes the identification oftargets in a simulated dynamic flight situation.

1. INTRODUCTION Human Decision making under uncertainty is a problem of computational intelligence humans face every day. [1,2] For instance, tracking a moving object includes detection and feature selection. In addition to identifying the object, the observer must perform some dynamic analysis to associate the relative movements of the objects as they move through the environment The computation involves saccadic movements to position the eye, visual processing of the image, and feature association between the detected features and known information in working memory. Sequential-decision making under uncertainty is prominent in sensor integration strategies. Sensor integration includes filtering signals, estimating the state and predicting the next sate needed to be sensed. A sensor detection and tracking policy includes a knowledgeable domain representation, a dynamic environment with risks and uncertainties, and complexity arising from many possible sensor actions and outcomes. Such detection problems have been studied for applications in engineering, management science, and operations research which include learning and reasoning strategies [3,4]. Here, we develop our computational algorithm of sensor-integration intelligence.

A common representation between human intelligence and tracking algorithms is information association. In both cases, the sensed measurements are associated with current knowledge. For example, a human would look at an object and process the information using its short-term memory; where the object was at the last time step, the relative directional

movement of the object, and the likelihood of where it is to be next. If any of these characteristics present cognitive dissonance in the working memory, where predicted information is different from measured information, the observer would call long-term memory information to confirm or dis-confirm the current assessment. One example might be to discern the movement of a plane {speed} . When an unclassified plane is observed, its flying characteristics are compared to the movements of previously-observed planes. If an inconsistent association of class-to-performance is determined, a relative

degree of belief may be assigned to the association or the observer might generate a new class with the associated performance. The biological processing of information by a human has been researched for many years. Examples include studies of the saccadic movements of monkeys, pilot tracking studies, and psychology experiments of feature recognition. Many have speculated how the human processes information from the environment, with and without a world representation. [5,6]What has not been studied, or has limited assessment in the literature is possible computational mechanisms on how this process may be conducted. The paper seeks to describe the mechanisms for a human's computational performance. Specifically, we address multitarget-multisensor tracking.

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SPIE Vol. 3390 • 0277-786X198/$1O.00

For the tracking problem, visual information is detected by the retina where some initial filtering is done to help focus the fovea (area of highest resolution of cones) on the object of interest. The visual information is processed individually by rods(peripheral and dim processing) and cones (color processing) of the eye. The information is filtered by pulvinar of the thalamus, Figure 1, where the salient information is sent to the prefrontal cortex. [7, 8] Here, object classification is analyzed by sending the visual information to the primary visual cortex (VI) and distributed to other areas of the brain (V2). The current theory suggests that the analysis is performed by visual streams. Visual information is grouped into clusters which describe features of the objects in the image. For example, one of the first time-detected features is movement. When a feature is compared to the previous representation of the feature in the world model in working memory, it is assumed to be in the same location. A relative displacement causes a cell to fire in the movement-stream association in the brain. Other

primitive features include vertical and horizontal lines. Throughout the process, the clustered data is fed back to the association module of the prefrontal cortex. The key characteristics of the process are: I) visual information from each sensor

is 1) filtered by a thalamic gate, 2) clustered into any non-exclusive combination of information to form features (integration), and 3) feature information is associated with known features for detection and classification (space and time).

Current information theorists are using neural networks to investigate the problem of human intelligence.[9,lO] The limitation of neural networks to describe neuronal processing is that they are essentially a set of linear equations that are trained to retain a weighting value of information that is received from that neuron. Although information feedback is used, time feedback is not usually considered. Figure 2 shows that there is a feedback mechanism (in time) which alters the association of measurements with the information. Our phsyio-temporal model for sensor integration exploits not only the biological structures, such as the thalamus in gating, but also a time element for feedback in association. R.troav. r&,r.J (.nt.dating) of s,b.cvv. s.nory .4peionce 0

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Figure 1. Thalamus Sensor Integration Center.

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Figure 2. Neuronal Processing with Time Feedback..

Figure 3 shows the integration of a variety of biological sensor information sent to the thalamus and the feedback association of intelligent processing. Although a representation is speculated as to the relative areas of the brain that involved, lesions studies have only confirmed that if the structures in the thalamus are inoperative, the sensory information is not distributed to those areas of the brain. Likewise, the hippocampus has only been shown to affect the sending short-term

memory information to the long-term memory. In essence, any current information can not be stored for later use. If however, the hippocampus is lesioned, the person operates with only previous stored information. For instance if a big plane is classified as plane X, then any big plane is classified as plane X even if new information is obtained to indicate that there

are actually two type of big planes {X, Y}. Essential to our computational model of intelligence is the ability to update associations of sensed signals and the filtering of these associations. For instance, faulty measurements and short-time incorrect beliefs. Without the hippocampus, no learning and hence, no association can take place.

The physio-associative temporal model exploits the perceived processing of the brain. Figure 4 shows the computational flow of information through the association cortex and the space-time integration of the information over time. Note, that a working memory of information is the current integration of association is represented with a decision;

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however, a final decision is rendered only when the feedback information confirms or reduces cognitive dissonance below an acceptable threshold. We model this process as a believable association event.

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Figure 3. The Brian Structures, Thalamus.

Figure 4. Neuronal Processing.

The brain contains a massively parallel set of neurons which operates with directional neuronal processing. While research is being conducted to determine intelligence, we investigate a specific domain of intelligence - information correlation - by developing a computational model of the association cortex, Figure 5.

Computational Intelligence

Figure 5. Computation Model of Intelligence.

The paper seeks to describe how multisensor integration (single feature, multiple looks) is conducted in a sequential processing technique. Since the situation is tracking a moving object with human visual systems, measurement uncertainty exists. The key outcome of this research is the development of a filtering technique in which is the most probable association

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- beliefthat is updated in the short-term memory. The thalamic-association filter is based on the filtering of information by the thalamus and association of features by the prefrontal cortex. As sensor information is transferred from the thalamic filter to the visual cortex, excitatory signals are clustered to form feature signals. These signals are sent to the association cortex, where the space and time integration is performed for object classification and inhibition of dissonance. Once a decision or an acceptable belief has been rendered; the output, error of dissonance, and prediction of the next feature state signals trigger the motor cortex to do a next look. [1 1] The signals serve as feedback in time and space and cycle through until a output decision is made.

2. PROBLEM FORMULATION The problem used to demonstrate the computational algorithm is a standard tracking problem of discerning two planes, with measurable features, as they are crossing paths in front of the human observer.[12] Similar analysis of computational algorithms for tracking a single object were assessed in robotic hardware [13, 14] and the derivation is based on the Kalman filter and track fusion principles.[l5] The problem is further complicated in the fact that the planes have many characteristics that are similar and that the visual sensors are not perfect. For instance, two planes may be the same size and the observer is myopic, respectively. An interesting investigation is that when the planes are far off, the human could focus on one at a time

where one plane is in focus and the other plane is located in the periphery. Thus, focused measurements, collecting information at a higher resolution for one plane at a time, could help with classification; but when the planes cross, the observer must track only those features which would discriminate the targets so as to associate a single measured feature with a single plane.

3. COMPUTATIONAL ALGORITHM (THALAMIC-ASSOCIATION FILTER) 3.1 Modeling Assumptions To set up the PATS! algorithm these assumptions exist: 1) The observer has focused on each object individually and has determined the known number targets with known dynamic models (not necessarily the same) 2) Cluttered feature measurements from one target can reside in the validation region of the neighboring target this can happen over several sampling times and acts as apersistent interference 3) Only one feature measurement is associated with a single target (inhibiting cognitive dissonance) 4) The conditional pdf of each object's state given the past measurements states are assumed Gaussian distributed and independent over objects, where the associated means and covariances to objects are available from the previous cycle ofthe filter. 5) Object detection occurs independently over time (batch processing) and from other objects according to a known probability. 6) Previous measurements (in the short term memory) are summarized by an approximate sufficient statistic state estimates (approximate conditional mean), covariances, and association probabilities for each object are computed (only for the latest measurements) jointly across the measurement and the targets. 7) The TAF models all incorrect measurements as random inference, with uniform spatial distribution. The performance ofthe BAF degrades significantly when a neighboring target gives rise to persistent inference. 3.2 Physio-Associative Temporal Sensor Integration Approach 0) Determine the number of known targets and Associated models of the state and measurements which are assumed to evolve in time according to the equations; respectively;

k +1) = F0(k) (k) + (k) 1(k) = H1(k) k)

+ w1(k)

for o = 1, . . ., 0 (Number of objects) for i = 1, . . ., N (Number of sensors)

(1)

where v(k) and w(k) are zero-mean mutually independent white Gaussian noise sequences with known covariances matrices Q(k) and R(k), respectively.

1) For each object track, predict the measurement to form the gate centered at predicted measurement (start at k -1)

(kI k - 1) = F0(k) (k - Ilk - 1) + y..4(k - 1)

(2)

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P0(kl k - 1 ) = F0(k)P0(k - 1 I k - 1 )F(k) + Q0(k)

(kI k - 1) = H0(k) (kJk

- state error covariance

(3)

- 1)

(4)

S0(kI k - I ) = H0(k) P0(kJ k - 1) H'(k) + R0(k)

(5)

2) Thalamic Gating: Simulate the Thalamus by gating the measurements to indicate all the possible sources of each measurement For the purpose of deriving the joint probabilities for intelligent reasoning, no individual thalamic-validation gates are assumed for objects; rather, each measurement is validated for each object. It is assumed are unform1y distributed in the entire thalamic-validation region. To determine the most accurate measurement, consider only the joint events made up of marginal events involving validated measurements, where the measurements within the field are from both ofthe image sensors (the eyes):

forj = 1, . . ., mk

(k)

(Number of measurements)

3) Set up a association matrix A to validate potential sensor measurements Thalamic-Validation gates are used for the selection of the believable joint events, but not in the evaluation of their probabilities. Similar to the data association algorithms for tracking, we define the thalamic-validation matrix:

A = I c0

j = 1, .. . , mk;

0

0,. . . . 0

(Number of Objects)

(6)

with binary elements that indicate ifmeasurementj lies in the validation gate ofobject o. The index o =0 stands for

"none of the objects" and the corresponding column of A has all units since each measurement could have originated from clutter or incorrect associations. The two objects in the proposed example are "coupled" by measurement j = 2 which has been validated for both objects - it lies in the intersection of the two thalamicvalidation regions.

4) Form the believable time-space Association event matrices: A(c1) A believable time-space Association event A, which represents thalamic gating is represented by an event matrix, corresponding to the associations in A

A(,) =

A

I a0(c1)I

where,

A I

cz0(c,)I

= 11

ifc.Ec

(7)

otherwise

where the an evaluation of the conditional probabilities of the joint association events pertaining to the current time k (the time index k is omitted for simplicity) are:

E=

c0

the event that measurement j originated from object o, j = 1 . . . , m; o = 0, object to which measurementj is associated in the event under consideration. where jo

(8)

. . . , N0, o is the index of the

5) For each believable space-time association event A(,): calculate the ö0( ),r(c1), and 4(c1) a) Object detection indicator: 50(c,)

The generation of the believable Association Event matrices A corresponding to believable events can be done by scanning A and picking 1) one unit per row, and 2) one unit per column except for o = 0, where the number of

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incorrect measurement associations is not restricted. The binary variable 60(c) defined above is called the object detection indicator since it indicates whether a measurement is associated with the object o in event e. A bellevable association even! is one whose i) a measurement can have only one source, i.e.

&0(c1) =

ii) at most one measurement can originate from a object:

Vj

1

(9)

&(c1) I

50(c)

i=1

,

N

(10)

b) Measurement Association Indicator t1{c) The measurement association indicator r(c1), a binary variable, determines a possible measurement

t(c) &(c)

(11)

c) Calculate the Number of false measurements 4(c,) for each event. The number of incorrect (un-associated) measurements associations, simulating cognitive dissonance, in event i is:

[ 1 - r(c) ]

4(c) —

(12)

Although the thalamus probably does not keep track of these measurements, they are needed for the for further computation.

Evaluation of the Time-Space Event Probabilities (Probabilistic Belief Reasoning) 6) For each believable space-time association event A(c,) calculate the joint association event probabilities using Bayes' Formula (used for believable decision making): P{c1(k)IZ"} P{cj(k)IZ(k),m(k),Zk

-1

= : p[Z(k) c(k),m(k),Z' ] P{61(k) I Z"

m(k)}

I

= p[Z(k)

-lj P{e1(k) I m(k)}

(13)

where c is the normalization constant and object states conditioned on the past observations are mutually independent.

The likellhoodfunction ofthe measurements in the right hand side ofthe above equation are:

p[Z(k) I c.(k),m(k),Z'

ft p[zj(k) c0(k),Z" I

j

I N0[z,(k)] if r[c,(k)] = 1 -' =1 if'r[c,(k)]

where m(k) is the number of measurements in the union of the validation regions at time k and

N0[,(k)] = N0 [,(k); 4(k 1k -1), S0(kI k - 1)1 =

e

- 0.5[(k) - kj/c-1)] S'(kI k - 1) [,(k) - (ktk-1)] }

cjo

where 0(k 1k -1) is the predicted measurement for object o, with associated innovation covariance S0(k).

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Note, that measurements not associated with a object are assumed uniformly distributed in the perceived region of volume V. Hence, in the above equation, V1 is raised to power 4(c1), the total number of incorrect measurement associations in event c,(k) and the indicators r0(c1) select the single measurement according to their associations in event c.(k). The prior (to time k) probability ofan event c(k), the last term in equation, is: P{E1(k) m(k)}

= P{c1(k),6(c,),4(c,) I m(k)} =

P{c,(k) ö(c1),4(c1),m(k)} P{6(c,),4(e,) m(k)) I

where

the vector of object detection indicators corresponding to event c,(k). and

The first term on the right hand side ofthe above equation is obtained from the following combinatorial reasoning: 1) The event c1(k) the set of objects assumed detected consists of [m(k) - 4(c1)] objects.

2) The number of measurement-to-large! assignment events c.(k) in which these are a set of objects is detected is given by the number ofpermutations ofthe m(k) measurements taken as [m(k) - 4(c1)], the number ofobjects to which a measurement is assigned under the same detection event. Therefore, assuming each such event a prior equally likely, one has P{c1(k) I (c,),4(c,),m(k)}

=

m(k)

( m(k) .

.1

m(k)' .1

Assuming Sand q independent, P{S(c1),4(c1) I m(k)}

=

U (1)o;D)ö0 (1 - o;D)

where 'o;D S the detection probably of object o (the ability of the eye to perceive the object) and t1(q) is the prior probability mass function of the number of Incorrect measurement associations (the clutter model). The indicators 8(:) have been used in above equation to select the probabilities of detection and not detection events according to the event c.(k) under consideration.

Plugging the above equations into Equation 13 yields thepriorprobabiity ofa association event c.(k) as

P{6(c1),(c) I m(k)} =

(k!)

(o;D)8° 0 o;D)

Combining previous equations yields the posteriorprobability ofassociation event c,(k) as:

P{c1(k)IZk}

(cni) '@) V :i {N0(k) [(k)]} [I (PO;D60 (1 o;D)1 o

where 4, 8, and t are all functions ofthe event c,(k) under consideration.

The above still needs the specification of the probability mass function of the number of incorrect measurement associations i(c)• V

With this, the posterior probability becomes, after canceling the constant c, and m(k)!, which appear in each expression

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ft {N(k) [1(k)]} P{c(k)(Z'1') .-— V c j=i

1TI (1)O;D)b0

(1 o;D) 6o

(14)

where c is the appropriate normalization constant. We set c = 1 and normalize later.

Intelligence: Belief Reasoning of Time-Space Association Event Probabilities the Belief in the association of the space-time event probabilities

7. Calculate the

Thalamic-Association Filter Association Cortex

'Ihalamus Seled Believable Event Matrices

—-

1t(k + Ik + I)

;r:: tjc,)

Discern #Targets

Association

k+1k+1)

I

_________

--

-n

TRACK N

Figure 6. Computation Model of The Belief reasoning ofthe Thalamic-Association Filter.

With a priori knowledge, it is assumed object states, conditioned on the past observations, are mutually independent. To assess the object state, one needs the marginal association probabilities, obtained from the joint probabilities by summing over all the joint events in which the marginal event of interest occurs. The bellefassociation probability summation can be written as follows: P{(C,),,o(k)IZk} so 0

P{c1 IZ")&0(e1)

so

j

P{c, IZ"}

1,

..., mk;

o so 0 0

(15)

O:OjEO

where,

c.(k) =

I

{z1(k) is the target orginated measurement)

i1...m(k) 1=0

L {none of the measurements is target originated even)

are mutually exclusive and exhaustive for m(k) 1. Perform a normalization:

a) Sum the rows and normalize

so

rowj

b) Sum up first column and normalize

is! column

13jo

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: col;o [ I1st column

f3 I

C) Normalize over rows and columns 13j0 = 13f0

(16)

col;o

8. Update the State Estimation ofeach object by using the measurements, and innovation The estimate conditioned on measurement i, being correct for object o is

j;o(kIk)

= j;o(kIk _ 1) +

j = 1, ..., m(k)

Wj;o(k)Vj;o(k)

0 = 1, ... , 0

Vj;ø(k) = j;o(k) j;o(kIk 1) Pj;o(kI k) = Pj;o(kI k

1 ) + H(k) R,'(k) H0

where the gain W(k) is the same as in the standard filter Wj;0(k)

Pj;o(klk

1 )Hj;o(k)TSj;o(k)

since, conditioned on c(k)

there is measurement origin uncertainty.

Forj = 0, i.e. ifnone ofthe measurements is correct, or, ifthere is no validated measurement (i.e. m(k) =0), one has 40(klk) = (kIk 1) 9. Combine to form the total integrated space-time association state estimate ofthe state:

Using the total probability theorem, with respect to the events, the conditional mean ofthe state at time k, can be written as:

(kIk) = E[x0(k) I Z'} = =

: E[(k)

I

c.(k) , Zk] P{c1(k) I Zk}

(17)

:: j;o(kIk) f3j;o(k)

where the combined innovation is

k) =

13j;o(k) j;o(k)

The covariance associated with the updated state is: P0(klk) = Fj;o(k)Po(kIk 1) + [1 - 1j;o(k)I P(kIk) + P0(k)

(18)

where the covariance of the state updated with the correct measurement is

P(kIk) = [I - W0(k)H0(k) ]P0(klk- 1) and the spread of the innovations term (similar to the spread of the means term in a mixture) is

I(k)

W0(k)

[

j;o(k) j;o(k) j;o(k)T y0(k) 4k)T) W(k)

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and

!0(k) =

Pj;o(k) Vj;0(k)

10. Finally, repeat the prediction state and measurement to k + 1 done as in the standard filter:

(k + 1 k) = F(k) (k)k)

(19)

(k+ lIk)=H(k+ 1)(k+ Ilk) P(k + 1 1k) = F(k)P(kjk)F(k)' + Q(k).

(20)

(21)

4. RESULTS Simulations were performed in MATLAB to experiment with the thalamic-association filter. From the above analysis, the

two planes were simulated as crossing from the upper right to the lower left. The dynamic model for the targets is X = 1T with the initial values X1(O) = [ 2000 m , 15 mIs, 10700 m , -5 m/s} ' and X2(O) = [ 200 m , 15 mIs, 10300 m, 5

[xy5

for target two; Q = diag {O.I,O.1,O.1,O.1}, P = (1,1,100000,1), and v(k) N(O,15000). The area ofthe 1000 x 1000 m2 and the numbers of the validated measurements are between I and 22, i.e. m = 1 detection probability and gate probability are given as follows: D =0.95 and G =

mis] T

V=

gating region is

22. The target

For the simulated cluttered environment with all possible collected data: two simulations are presented 1) each object is sequentially analyzed without an integrated association of information, and b) an association of multiple sensors in space and time - the computationally intelligent approach. x 10

"

Thalamic-Association Filter without Intelligence

LI

X 10

ThalamicAssOCiation Filter ofPosition Estimate

V

3000

3500

x Position Figure 7. TAF without Intelligence.

Figure 8. TAF with intelligence.

5. DISCUSSION AND CONCLUSIONS The model we have shown models human intelligence for sensor integration and the computational aspects of information association, with thalamic gating and a prefrontal association cortex. From the plots above, it is demonstrated that some world knowledge is useful in discerning the objects in the environment. The plot without association of information simulates a person who is trying to observe one plane at a time. The second plot shows that after intelligence is included, where two planes are incorporated into the working memory, the filter better associates measurements from multiple sensors. The next phases of the research are to 1) assess a less computational algorithm that takes advantage of association-learning, 2) gather tracking data from actual research studies to assess human performance, and 3) determine where the computational intelligence of the computer can be combined with a actual human pilot for assisting in tracking a multitude of data in the battlespace environment.

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