System and method for identifying a preferred sensor

1. A system for identifying a preferred sensor from among the plurality of sensors for trustworthy sensing of a target, the system comprising:

a plurality of sensors, each detecting a plurality of objects by receiving signals from the plurality of objects, wherein one or more of the received signals are not from to the target; and

a processing circuit, configured to:

identify a preferred sensor from among the plurality of sensors for trustworthy sensing of the target, the identifying comprising:

calculating, for each of the plurality of sensors, the product of:

a reward function for the sensor; and

a Bayesian conditional probability of the sensor correctly identifying the target from among the plurality of objects detected by the sensor, given an association event between the plurality of sensors, wherein the Bayesian conditional probability is a Bayesian probability of the sensor correctly identifying the target from among the plurality of objects,

the association event between the plurality of sensors comprising, for each of the plurality of sensors:

a plurality of objects detected by the sensor, and

an identification, by the sensor, of one of the plurality of objects as the target, wherein the association event includes, for each of the plurality of sensors: a data structure for a plurality of objects detected by the sensor, and a data structure for an identification, by the sensor, of one of the plurality of objects as the target, and wherein the processing circuit transmits data from the preferred sensor to a guidance system for tracking the target.

2. The system of claim 1 , wherein the plurality of sensors consists of a first sensor and a second sensor, and the processing circuit is further configured to calculate the conditional probability of the first sensor correctly identifying the target from among a plurality of objects detected by the first sensor, given an association event, according to the proportionality relation

p ( X 1 =1| A )∝ p 1 ( p 2 p A +(1 −p 2 )(1 −p A )),

wherein:

p 1 an estimated prior probability of the first sensor correctly identifying the target from among a plurality of objects detected by the first sensor,

p 2 is an estimated prior probability of the second sensor correctly identifying the target from among a plurality of objects detected by the second sensor, and

p A is an estimated probability of:

the sensors both correctly identifying the target, or

the sensors both incorrectly identifying the target.

3. The system of claim 2 , wherein the processing circuit is further configured to calculate the estimated probability of:

the sensors both correctly identifying the target, or

the sensors both incorrectly identifying the target according to the equation

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each θ is an association hypothesis between the plurality of objects detected by the first sensor and the plurality of objects detected by the second sensor,

Θ is a set of all possible association hypotheses, and

L(θ)=exp Σ (i,j)∈θ l ij , wherein l ij is a log likelihood score corresponding to a measure of similarity between the i-th object detected by the first sensor and the j-th object detected by the second sensor.

4. The system of claim 2 , wherein the processing circuit is further configured to calculate a log likelihood score l ij according to the equation

l ij =log p ( z i ,w j ) ,

wherein:

p ( z i ,w ij )=(1 +d ij 2 exp(− d ij 2 ),

d ij 2 =( z i −w j ) T Σ −1 ( z i −w j ),

Σ= U i +V j ,

z i is a vector of features of the i-th object detected by the first sensor,

w j is a vector of features of the j-th object detected by the second sensor,

U i is a covariance matrix of the first sensor,

V j is a covariance matrix of the second sensor,

p(z i ,w j ) is a chi-square distribution, and

d i,j is a Mahalanobis distance.

5. The system of claim 4 , wherein the processing circuit is further configured to substitute for the calculated log likelihood score l ij a value of negative infinity when the square root of d ij 2 falls below a threshold.

6. The system of claim 4 , wherein both the numerator and the denominator of the estimated probability of:

the sensors both correctly identifying the target, or the sensors both incorrectly identifying the target are calculated using a depth-first search.

7. The system of claim 4 , wherein both the numerator and the denominator of the estimated probability of:

the sensors both correctly identifying the target, or the sensors both incorrectly identifying the target are calculated using a Murty algorithm.

8. A method for identifying a preferred sensor from among the plurality of sensors for trustworthy sensing of a target with a plurality of sensors, the method comprising:

receiving a plurality of signals from the plurality of sensors, each sensor detecting a plurality of objects, wherein one or more of the received signals are not from to the target;

identifying a preferred sensor from among the plurality of sensors for trustworthy sensing of the target, the identifying comprising:

calculating, for each of the plurality of sensors, the product of:

a reward function for the sensor; and

a Bayesian conditional probability of the sensor correctly identifying the target from among the plurality of objects detected by the sensor, given an association event between the plurality of sensors, wherein the Bayesian conditional probability is a Bayesian probability of the sensor correctly identifying the target from among the plurality of objects,

the association event between the plurality of sensors comprising, for each of the plurality of sensors:

a plurality of objects detected by the sensor,

an identification, by the sensor, of one of the plurality of objects as the target, wherein the association event includes, for each of the plurality of sensors: a data structure for a plurality of objects detected by the sensor, and a data structure for an identification, by the sensor, of one of the plurality of objects as the target, and

transmitting data from the preferred sensor to a guidance system for tracking the target.

9. The method of claim 8 , wherein the plurality of sensors consists of a first sensor and a second sensor, and the method further comprises calculating the conditional probability of the first sensor correctly identifying the target from among a plurality of objects detected by the first sensor, given an association event, according to the proportionality relation

p ( X 1 −1| A )∝p 1 ( p 2 p A +(1 −p 2 )(1 −p A )),

wherein:

p 1 an estimated prior probability of the first sensor correctly identifying the target from among a plurality of objects detected by the first sensor,

p 2 is an estimated prior probability of the second sensor correctly identifying the target from among a plurality of objects detected by the second sensor, and

p A is an estimated probability of:

the sensors both correctly identifying the target, or

the sensors both incorrectly identifying the target.

10. The method of claim 9 , further comprising calculating the estimated probability of:

the sensors both correctly identifying the target, or

the sensors both incorrectly identifying the target according to the equation

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wherein:

each θ is an association hypothesis between the plurality of objects detected by the first sensor and the plurality of objects detected by the second sensor,

Θ is the set of all possible association hypotheses, and

L(θ)=exp Σ (i,j)∈θ l ij , wherein l ij is a log likelihood score corresponding to a measure of similarity between the i-th object detected by the first sensor and the j-th object detected by the second sensor.

11. The method of claim 9 , further comprising calculating a log likelihood score according to the equation

l ij =log p ( z i ,w j ),

wherein:

p ( z i ,w j )=(1 +d ij 2 )exp(− d ij 2 ),

Σ= U i +V j ,

z i is a vector of features of the i-th object detected by the first sensor,

w j is a vector of features of the j-th object detected by the second sensor,

U i is a covariance matrix of the first sensor,

V j is a covariance matrix of the second sensor,

p(z i ,w j ) is a chi-square distribution, and

d ij is a Mahalanobis distance.

12. The method of claim 11 , further comprising substituting for the calculated log likelihood score l ij a value of negative infinity when the square root of d ij 2 falls below a threshold.

13. The method of claim 11 , wherein both the numerator and the denominator of the estimated probability of:

the sensors both correctly identifying the target, or the sensors both incorrectly identifying the target are calculated using a depth-first search.

14. The method of claim 11 , wherein both the numerator and the denominator of the estimated probability of:

the sensors both correctly identifying the target, or the sensors both incorrectly identifying the target are calculated using a Murty algorithm.