Nuisance alarm filter

[0001] The present invention relates generally to alarm systems. More specifically, the present invention relates to alarm systems with enhanced performance to reduce nuisance alarms.

[0002] In conventional alarm systems, nuisance alarms (also referred to as false alarms) are a major problem that can lead to expensive and unnecessary dispatches of security personnel. Nuisance alarms can be triggered by a multitude of causes, including improper installation of sensors, environmental noise, and third party activities. For example, a passing motor vehicle may trigger a seismic sensor, movement of a small animal may trigger a motion sensor, or an air-conditioning system may trigger a passive infrared sensor.

[0003] Conventional alarm systems typically do not have on-site alarm verification capabilities, and thus nuisance alarms are sent to a remote monitoring center where an operator either ignores the alarm or dispatches security personnel to investigate the alarm. A monitoring center that monitors a large number of premises may be overwhelmed with alarm data, which reduces the ability of the operator to detect and allocate resources to genuine alarm events.

[0004] As such, there is a continuing need for alarm systems that reduce the occurrence of nuisance alarms.

[0005] With the present invention, nuisance alarms are filtered out by selectively modifying sensor signals to produce verified sensor signals. The sensor signals are selectively modified as a function of an opinion output about the truth of an alarm event.

[0013] The present invention includes a filtering device for use with an alarm system to reduce the occurrence of nuisance alarms. FIG. 1 shows alarm system 14 of the present invention for monitoring environment 16. Alarm system 14 includes sensors 18, optional verification sensor 20, alarm filter 22, local alarm panel 24, and remote monitoring system 26.

[0014] Alarm filter 22 includes inputs for receiving signals from sensors 18 and verification sensor 20, and includes outputs for communicating with alarm panel 24. As shown in FIG. 1, sensors 18 and verification sensor 20 are coupled to communicate with alarm filter 22, which is in turn coupled to communicate with alarm panel 24. Sensors 18 monitor conditions associated with environment 16 and produce sensor signals S₁-S_n (where n is the number of sensors 18) representative of the conditions, which are communicated to alarm filter 22. Similarly, verification sensor 20 also monitors conditions associated with environment 16 and communicates verification sensor signal(s) S_v representative of the conditions to alarm filter 22. Alarm filter 22 filters out nuisance alarm events by selectively modifying sensor signals S₁-S_n to produce verified sensor signals S₁′-S_n′, which are communicated to local alarm panel 24. If verified sensor signals S₁′-S_n′ indicate occurrence of an alarm event, this information is in turn communicated to remote monitoring system 26, which in most situations is a call center including a human operator. Thus, alarm filter 22 enables alarm system 14 to automatically verify alarms without dispatching security personnel to environment 16 or requiring security personnel to monitor video feeds of environment 16.

[0015] Alarm filter 22 generates verified sensor signals S₁′-S_n′ as a function of (1) sensor signals S₁-S_n or (2) sensor signals S₁-S_n and one or more verification signals S_v. In most embodiments, alarm filter 22 includes a data processor for executing an algorithm or series of algorithms to generate verified sensor signals S₁′-S_n′.

[0016] Alarm filter 22 may be added to previously installed alarm systems 14 to enhance performance of the existing system. In such retrofit applications, alarm filter 22 is installed between sensors 18 and alarm panel 24 and is invisible from the perspective of alarm panel 24 and remote monitoring system 26. In addition, one or more verification sensors 20 may be installed along with alarm filter 22. Alarm filter 22 can of course be incorporated in new alarm systems 14 as well.

[0017] Examples of sensors 18 for use in alarm system 14 include motion sensors such as, for example, microwave or passive infrared (PIR) motion sensors; seismic sensors; heat sensors; door contact sensors; proximity sensors; any other security sensor known in the art; and any of these in any number and combination. Examples of verification sensor 20 include visual sensors such as, for example, video cameras or any other type of sensor known in the art that uses a different sensing technology than the particular sensors 18 employed in a particular alarm application.

[0018] Sensors 18 and verification sensors 20 may communicate with alarm filter 22 via a wired communication link or a wireless communication link. In some embodiments, alarm system 14 includes a plurality of verification sensors 20. In other embodiments, alarm system 14 does not include a verification sensor 20.

[0019] FIG. 2 shows sensor fusion architecture 31, which represents one embodiment of internal logic for use in alarm filter 22 to verify the occurrence of an alarm event. As shown in FIG. 2, video sensor 30 is an example of verification sensor 20 of FIG. 1. Sensor fusion architecture 31 illustrates one method in which alarm filter 22 of FIG. 1 can use subjective logic to mimic human reasoning processes and selectively modify sensor signals S₁-S_n to produce verified sensor signals S₁′-S_n′. Sensor fusion architecture 31 includes the following functional blocks: opinion processors 32, video content analyzer 34, opinion processor 36, opinion operator 38, probability calculator 40, threshold comparator 42, and AND-gates 44A-44C. In most embodiments, these functional blocks of sensor fusion architecture 31 are executed by one or more data processors included in alarm filter 22.

[0020] As shown in FIG. 2, sensor signals S₁-S₃ from sensors 18 and verification sensor signal S_v from video sensor 30 are input to sensor fusion architecture 31. Pursuant to sensor standards in the alarm/security industry, sensor signals S₁-S₃ are binary sensor signals, whereby a “1” indicates detection of an alarm event and a “0” indicates non-detection of an alarm event. Each sensor signal S₁-S₃ is input to an opinion processor 32 to produce opinions O₁-O₃ as a function of each sensor signal S₁-S₃.

[0021] Verification sensor signal S_v, in the form of raw video data generated by video sensor 30, is input to video content analyzer 34, which extracts verification information I_v from sensor signal S_v. Video content analyzer 34 may be included in alarm filter 22 or it may be external to alarm filter 22 and in communication with alarm filter 22. After being extracted, verification information I_v is then input to opinion processor 36, which produces verification opinion O_v as a function of verification information I_v. In some embodiments, verification opinion O_v is computed as a function of verification information I_v using non-linear functions, fuzzy logic, or artificial neural networks.

[0022] Opinions O₁-O₃ and O_v each represent separate opinions about the truth (or believability) of an alarm event. Opinion O₁-O₃ and O_v are input to opinion operator 38, which produces final opinion O_F as a function of opinions O₁-O₃ and O_v. Probability calculator 40 then produces probability output PO as a function of final opinion O_F and outputs probability output PO to threshold comparator 42. Probability output PO represents a belief, in the form of a probability, about the truth of the alarm event. Next, threshold comparator 42 compares a magnitude of probability output PO to a predetermined threshold value V_T and outputs a binary threshold output O_T to AND logic gates 44A-44C. If the magnitude of probability output PO exceeds threshold value V_T, threshold output O_T is set to equal 1. If the magnitude of probability output PO does not exceed threshold value V_T, threshold output O_T is set to equal 0.

[0023] As shown in FIG. 2, each of AND logic gates 44A-44C receives threshold output O_T and one of sensor signals S₁-S₃ (in the form of either a 1 or a 0) and produces a verification signal S₁′-S₃′ as a function of the two inputs. If threshold output O_T and the particular sensor signal S₁-S₃ are both 1, the respective AND logic gate 44A-44C outputs a 1. In all other circumstances, the respective AND logic gate 44A-44C outputs a 0. As such, alarm filter 22 filters out an alarm event detected by sensors 18 unless probability output PO is computed to exceed threshold value V_T. In most embodiments, threshold value V_T is determined by a user of alarm filter 22, which allows the user to adjust threshold value V_T to achieve a desired balance between filtering out nuisance alarms and preservation of genuine alarms.

[0024] As discussed above, probability output PO is a probability that an alarm event is a genuine (or non-nuisance) alarm event. In other embodiments, probability output PO is a probability that an alarm is a nuisance alarm and the operation of threshold comparator 42 is modified accordingly. In some embodiments, probability output PO includes a plurality of outputs (e.g., such as belief and uncertainty of an alarm event) that are compared to a plurality of threshold values V_T.

[0025] Examples of verification information I_v for extraction by video content analyzer 34 include object nature (e.g., human versus nonhuman), number of objects, object size, object color, object position, object identity, speed and acceleration of movement, distance to a protection zone, object classification, and combinations of any of these. The verification information I_v sought to be extracted from verification sensor signal S_v can vary depending upon the desired alarm application. For example, if fire detection is required in a given application of alarm system 14, flicker frequency can be extracted (see Huang, Y., et al., On-Line Flicker Measurement of Gaseous Flames by Image Processing and Spectral Analysis, Measurement Science and Technology, v. 10, pp. 726-733, 1999). Similarly, if intrusion detection is required in a given application of alarm system 14, position and movement-related information can be extracted.

[0026] In some embodiments, verification sensor 20 of FIG. 1, (i.e., video sensor 30 in FIG. 2) may be a non-video verification sensor that is heterogeneous relative to sensors 18. In some of these embodiments, verification sensor 20 uses a different sensing technology to measure the same type of parameter as one or more of sensors 18. For example, sensors 18 may be PIR motion sensors while verification sensor 20 is a microwave-based motion sensor. Such sensor heterogeneity can reduce false alarms and enhance the detection of genuine alarm events.

[0027] In one embodiment of the present invention, opinions O₁-O₃, O_v, and O_F are each expressed in terms of belief, disbelief, and uncertainty in the truth of an alarm event x. As used herein, a “true” alarm event is defined to be a genuine alarm event that is not a nuisance alarm event. The relationship between these variables can be expressed as follows:
b_x+d_x+u_x=1,  (Equation 1)
where b_x represents the belief in the truth of event x, d_x represents the disbelief in the truth of event x, and u_x represents the uncertainty in the truth of event x.

[0028] Fusion architecture 31 can assign values for b_x, d_x, and u_x based upon, for example, empirical testing involving sensors 18, verification sensor 20, environment 16, or combinations of these. In addition, predetermined values for b_x, d_x, and u_x for a given sensor 18 can be assigned based upon prior knowledge of that particular sensor's performance in environment 16 or based upon manufacturer's information relating to that particular type of sensor. For example, if a first type of sensor is known to be more susceptible to generating false alarms than a second type of sensor, the first type of sensor can be assigned a higher uncertainty u_x, a higher disbelief d_x, a lower belief b_x, or combinations of these.

[0029] FIG. 3 shows a graphical representation of a mathematical model for use with sensor fusion architecture of FIG. 2. FIG. 3 shows reference triangle 50 defined by Equation 1 and having a Barycentric coordinate framework. For further discussion of the Barycentric coordinate framework see Audun Josang, A LOGIC FOR UNCERTAIN PROBABILITIES, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 9, No. 3, June 2001. Reference triangle 50 includes vertex 52, vertex 54, vertex 56, belief axis 58, disbelief axis 60, uncertainty axis 62, probability axis 64, director 66, and projector 68. Different coordinate points (b_x, d_x, u_x) within reference triangle 50 represent different opinions ω_x about the truth of sensor state x (either 0 or 1). An example opinion point ω_x with coordinates of (0.4, 0.1, 0.5) is shown in FIG. 3. These coordinates are the orthogonal projections of point ω_x onto belief axis 58, disbelief axis 60, and uncertainty axis 62

[0030] Vertices 52-56 correspond, respectively, to states of 100% belief, 100% disbelief, and 100% uncertainty about sensor state x. As shown in FIG. 3, vertices 52-56 correspond to opinions ω_x of (1,0,0), (0,1,0), and (0,0,1), respectively. Opinions ω_x situated at either vertices 52 or 54 (i.e., when belief b_x equals 1 or 0) are called absolute opinions and correspond to a ‘TRUE’ or ‘FALSE’ proposition in binary logic.

[0031] The mathematical model of FIG. 3 can be used to project opinions ω_x onto a traditional 1-dimensional probability space (i.e., probability axis 64). In doing so, the mathematical model of FIG. 3 reduces subjective opinion measures to traditional probabilities. The projection yields a probability expectation value E(ω_x), which is defined by the equation:
E(ω_x)=a_x+u_xb_x,  (Equation 2)
where a_x is a user-defined decision bias, u_x is the uncertainty, and b_x is the belief. Probability expectation value E(ω_x) and decision bias a_x are both graphically represented as points on probability axis 64. Director 66 joins vertex 56 and decision bias a_x, which is inputted by a user of alarm filter 22 to bias opinions towards either belief or disbelief of alarms. As shown in FIG. 3, decision bias a_x for exemplary point ω_x is set to equal 0.6. Projector 68 runs parallel to director 66 and passes through opinion ω_x. The intersection of projector 68 and probability axis 64 defines the probability expectation value E(ω_x) for a given decision bias a_x.

[0032] Thus, as described above, Equation 2 provides a means for converting a subjective logic opinion including belief, disbelief, and uncertainty into a classical probability which can be used by threshold comparator 42 of FIG. 2 to assess whether an alarm should be filtered out as a nuisance alarm.

[0033] FIGS. 4A and 4B each show a different method for aggregating multiple opinions to produce an aggregate (or fused) opinion. These methods can be used within fusion architecture 31 of FIG. 2. For example, the aggregation methods of FIGS. 4A and 4B may be used by opinion operator 38 in FIG. 2 to aggregate opinions O₁-O₃ and O_v, or a subset thereof.

[0034] FIG. 4A shows a multiplication (also referred to as an “and-multiplication”) of two opinion measures (O₁ and O₂) plotted pursuant to the mathematical model of FIG. 3 and FIG. 4B shows a co-multiplication (also referred to as an “or-multiplication”) of the same two opinion measures plotted pursuant to the mathematical model of FIG. 3. The multiplication method of FIG. 4A functions as an “and” operator while the co-multiplication method of FIG. 4B function as an “or” operator. As shown in FIG. 4A, the multiplication of O₁ (0.8,0.1,0.1) and O₂ (0.1,0.8,0.1) yields aggregate opinion O_A (0.08,0.82,0.10), whereas, as shown, in FIG. 4B, the co-multiplication of O₁ (0.8,0.1,0.1) and O₂ (0.1,0.8,0.1) yields aggregate opinion O_A (0.82,0.08,0.10).

[0035] The mathematical procedures for carrying out the above multiplication and co-multiplication methods are given below.

[0036] Opinion Q_1^2 (b_1^2,d_1^2,a_1^2) resulting from the multiplication of two opinions O₁ (b₁,d₁,a₁) and O₂ (b₂,d₂,u₂,a₂) corresponding to two different sensors is calculated as follows:

[0037] $b_{1^2}=b_1{b}_2$ $d_{1^2}=d_1+d_2-d_1{d}_2$ $u_{1^2}=b_1{u}_2+b_2{u}_1+u_1{u}_2$ $a_{1^2}=\frac{u_1{a}_2{b}_1+b_2{u}_2{a}_1+a_1{a}_2{u}_1{u}_2}{u_{1^2}}$

[0038] Opinion Q_1v2 (b_1v2,d_1v2,u_1v2,a_1v2) resulting from the co-multiplication of two opinions O₁ (b₁,d₁,a₁) and O₂ (b₂,d₂,u₂,a₂) corresponding to two different sensors is calculated as follows:

[0039] $b_{1\bigvee 2}=b_1+b_2-b_1{b}_2$ $d_{1\bigvee 2}=d_1{d}_2$ $u_{1\bigvee 2}=d_1{u}_2+d_2{u}_1+u_1{u}_2$ $a_{1\bigvee 2}=\frac{u_1{a}_1+u_2{a}_2-a_2{b}_1{u}_2-a_1{b}_2{u}_1-a_1{a}_2{u}_1{u}_2}{u_1+u_2-b_1{u}_2-b_2{u}_1-u_1{u}_2}$

[0040] Other methods for aggregating opinion measures may be used to aggregate opinion measures of the present invention. Examples of these other methods include fusion operators such as counting, discounting, recommendation, consensus, and negation. Detailed mathematical procedures for these methods can be found in Audun Josang, A LOGIC FOR UNCERTAIN PROBABILITIES, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 9, No. 3, June 2001.

[0041] Tables 1-3 below provide an illustration of one embodiment of fusion architecture 31 of FIG. 2. The data in Tables 1-3 is generated by an embodiment of alarm system 14 of FIG. 1 monitoring environment 16, which includes an automated teller machine (ATM). Security system 14 includes video sensor 30 having onboard motion detection and three seismic sensors 18 for cooperative detection of attacks against the ATM. Seismic sensors 18 are located on three sides of the ATM. Video sensor 30 is located at a location of environment 16 with line of sight view of the ATM and surrounding portions of environment 16.

[0042] Opinion operator 38 of sensor fusion architecture 31 of FIG. 2 produces final opinion O_F as a function of seismic opinions O₁-O₃ and verification opinion O_v (based on video sensor 30) using a two step process. First, opinion operator 38 produces fused seismic opinion O_1-3 as a function of seismic opinions O₁-O₃ using the co-multiplication method of FIG. 4B. Then, opinion operator 38 produces final opinion O_F as a function of fused seismic opinion O₁-O₃ and verification opinion O_v using the multiplication method of FIG. 4A. In the example of Tables 1-3, for an alarm signal to be sent to alarm panel 24 by alarm filter 22, threshold comparator 42 of sensor fusion architecture 31 requires that final opinion O_F include a belief b_x greater than 0.5 and an uncertainty u_x less than 0.3. Each of opinions O₁-O₃, O_v, and O_F of Tables 1-3 were computed using a decision bias a_x of 0.5.

[0043]

TABLE 1
	O1	O2	O3	O1-3	OV	OF
bx	0.0	0.0	0.0	0.0	0.0	0.0
dx	0.8	0.8	0.8	0.512	0.8	0.9
ux	0.2	0.2	0.2	0.488	0.2	0.1

[0044] Table 1 illustrates a situation in which none of the seismic sensors have been triggered, which yields a final opinion O_F of (0.0,0.9,0.1) and a probability expectation of attack of 0.0271. Since final opinion O_F has a belief b_x value of 0.0, which does not exceed the threshold belief b_x value of 0.5, alarm filter 22 does not send an alarm to alarm panel 24.

[0045]

TABLE 2
	O1	O2	O3	O1-3	OV	OF
bx	0.05	0.8	0.05	0.8195	0.85	0.70
dx	0.85	0.1	0.85	0.0722	0.05	0.12
ux	0.1	0.1	0.1	0.10825	0.1	0.18

[0046] Table 2 illustrates a situation in which the ATM is attacked, causing video sensor 30 and one of seismic sensors 18 to detect the attack. As a result, opinion operator 38 produces a final opinion O_F of (0.70,0.12,0.18), which corresponds to a probability expectation of attack of 0.8. Since final opinion O_F has a belief b_x value of 0.70 (which exceeds the threshold belief b_x value of 0.5) and an uncertainty u_x value of 0.18 opinion O_F (which falls below the threshold uncertainty u_x value of 0.3), alarm filter 22 sends a positive alarm to alarm panel 24.

[0047]

TABLE 3
	O1	O2	O3	O1-3	OV	OF
bx	0.8	0.8	0.8	0.992	0.85	0.84
dx	0.1	0.1	0.1	0.001	0.05	0.05
ux	0.1	0.1	0.1	0.007	0.1	0.11

[0048] Table 3 illustrates a situation in which the ATM is again attacked, causing video sensor 30 and all of seismic sensors 18 to detect the attack. As a result, opinion operator 38 produces a final opinion O_F of (0.84,0.05,0.11), which corresponds to a probability expectation of attack of 0.9. Since final opinion O_F has a belief b_x value of 0.84 (which exceeds the threshold belief b_x, value of 0.5) and an uncertainty u_x value of 0.11 opinion O_F (which falls below the threshold uncertainty u_x value of 0.3), alarm filter 22 sends a positive alarm to alarm panel 24.

[0049] FIG. 5 illustrates one method for producing verification opinion O_v of FIG. 2 as a function of verification information I_v. FIG. 5 shows video sensor 30 of FIG. 2 monitoring environment 16, which, as shown in FIG. 5, includes safe 60. In this embodiment, video sensor 30 is used to provide verification opinion O_v relating to detection of intrusion object 62 in proximity to safe 60. Verification opinion O_v includes belief b_x, disbelief d_x, and uncertainty u_x of attack, which are defined as a function of the distance between intrusion object 62 and safe 60 using pixel positions of intrusion object 62 in the image plane of the scene. Depending on the distance between intrusion object 62 and safe 60, uncertainty u_x and belief b_x of attack vary between 0 and 1. If video sensor 30 is connected to a video content analyzer 34 capable of object classification, then the object classification may be used to reduce uncertainty u_x and increase belief b_x.

[0050] As shown in FIG. 5, the portion of environment 16 visible to visual sensor 30 is divided into five different zones Z₁-Z₅, which are each assigned a different predetermined verification opinion O_v. For example, in one embodiment, the different verification opinions O_v for zones Z₁-Z₅ are (0.4, 0.5, 0.1), (0.5, 0.4, 0.1), (0.6, 0.3, 0.1), (0.7, 0.2, 0.1), and (0.8, 0.1, 0.1), respectively. As intrusion object 62 moves from zone Z₁ into a zone closer to safe 60, belief b_x in an attack increases and disbelief d_x in the attack decreases.

[0051] Some embodiments of alarm filter 22 of the present invention can verify an alarm as being true, even when video sensor 30 of FIG. 2 fails to detect the alarm event. In addition, other embodiments of alarm filter 22 can verify an alarm event as being true even when alarm system 14 does not include any verification sensor 20.

[0052] For example, FIG. 6 shows one embodiment of alarm system 14 of FIG. 1 that includes three motion sensors MS₁, MS₂, and MS₃ and video sensor 30 for detecting human intruder 70 in environment 16. As shown in FIG. 6, motion sensors MS₁-MS₃ are installed in a non-overlapping spatial order and each sense a different zone Z₁-Z₃. When human intruder 70 enters zone Z₁ through access 72, intruder 70 triggers motion sensor MS₁ which produces a detection signal. In one embodiment, upon alarm filter 22 receiving the detection signal from MS₁, video sensor 30 is directed to detect and track intruder 70. Verification opinion O_v (relating to video sensor 30) and opinions O₁-O₃ (relating to motion sensors MS₁-MS₃) are then compared to assess the nature of the intrusion alarm event. If video sensor 30 and motion sensor MS₁ both result in positive opinions that the intrusion is a genuine human intrusion, then an alarm message is sent from alarm filter 22 to alarm panel 24.

[0053] If video sensor 30 fails to detect and track intruder 70, (meaning that opinion O_v indicates a negative opinion about the intrusion), opinions O₁-O₃ corresponding to motion sensors MS₁-MS₃ are fused to verify the intrusion. Since human intruder 70 cannot trigger all of the non-overlapping motions sensors simultaneously, a delay may be inserted in sensor fusion architecture 31 of FIG. 2 so that, for example, opinion O₁ of motion sensor MS₁ taken at a first time can be compared with opinion O₂ of motion sensor MS₂ taken after passage of a delay time. The delay time can be set according to the physical distance within environment 16 between motion sensors MS₁ and MS₂. After passage of the delay time, opinion O₂ can be compared to opinion O₁ using, for example, the multiplication operator of FIG. 4A. If both of opinions O₁ and O₂ indicate a positive opinion about intrusion, a corresponding alarm is sent to alarm panel 24. In some embodiments, if an alarm is not received from motion sensor MS₃ within an additional delay time, the alarms from motion sensors MS₁ and MS₂ are filtered out by alarm filter 22. Also, in some embodiments, if two or more non-overlapping sensors are fired almost at the same time, then these alarms are deemed to be false and filtered out.

[0054] The above procedure also applies to situations where alarm system 14 does not include an optional verification sensor 20. In these situations, alarm filter 22 only considers data from sensors 18 (e.g., motion sensors MS₁-MS₃ in FIG. 6).

[0055] In addition, to provide additional detection and verification capabilities, alarm system 14 of FIG. 6 can be equipped with additional motion sensors that have overlapping zones of coverage with motion sensors MS₁-MS₃. In such situations, multiple motion sensors for the same zone should fire simultaneously in response to an intruder. The resulting opinions from the multiple sensors, taken at the same time, can then be compared using the multiplication operator of FIG. 4A.

[0056] In some embodiments of the present invention, opinion operator 38 of sensor fusion architecture 31 uses a voting scheme to produce final opinion O_F in the form of a voted opinion. The voted opinion is the consensus of two or more opinions and reflects all opinions from the different sensors 18 and optional verification sensor(s) 20, if included. For example, if two motion sensors have detected movement of intruding objects, opinion processors 32 form two independent opinions about the likelihood of one particular event, such as a break-in. Depending upon the degree of overlap between the coverage of the various sensors, a delay time(s) may be inserted into sensor fusion architecture 31 so that opinions based on sensor signals generated at different time intervals are used to generate the voted opinion.

[0057] For a two-sensor scenario, voting is accomplished according to the following procedure. The opinion given to the first sensor is expressed as opinion O₁ having coordinates (b₁, d₁, u₁, a₁), and the opinion given to the second sensor is expressed as opinion O₂ having coordinates (b₂, d₂, u₂, a₂), where b₁ and b₂ are belief, d₁ and d₂ are disbelief, u₁ and u₂ are uncertainty, and a₁ and a₂ are decision bias. Opinions O₁ and O₂ are assigned according to the individual threat detection capabilities of the corresponding sensor, which can be obtained, for example, via lab testing or historic data. Opinion operator 38 produces voted opinion O_{1{circle around (x)}2} having coordinates (b_{1{circle around (x)}2}, d_{1{circle around (x)}2}, u_{1{circle around (x)}2}, a_{1{circle around (x)}2}) as a function of opinion O₁ and opinion O₂. Voted opinion O_{1{circle around (x)}2} is produced using the following voting operator (assuming overlap between the coverage of the first and second sensors):

[0058] When k=u₁+u₂−u₁u₂≠0

[0059] $b_{1\otimes 2}=\frac{b_1{u}_2+b_2{u}_1}{k}$ $d_{1\otimes 2}=\frac{d_1{u}_2+d_2{u}_1}{k}$ $u_{1\otimes 2}=\frac{u_1{u}_2}{k}$ $a_{1\otimes 2}=\frac{u_1{a}_2+u_2{a}_1+\left(a_1+a_2\right)u_1{u}_2}{u_1+u_2-2u_1{u}_2}$

[0060] When k=u₁+u₂−u₁u₂=0

[0061] $b_{1\otimes 2}=\frac{b_1+b_2}{2}$ $d_{1\otimes 2}=\frac{d_1+d_2}{2}$ $u_{1\otimes 2}=0$ $a_{1\otimes 2}=\frac{a_2+a_1}{2}$

[0062] The voting operator ({circle around (x)}) can accept multiple opinions corresponding to sensors of same type and/or multiple opinions corresponding to different types of sensors. The number of sensors installed in a given zone of a protected area in a security facility is determined by the vulnerability of the physical site. Regardless of the number of sensors installed, the voting scheme remains the same.

[0063] For a multiple-sensor scenario with redundant sensor coverage, the voting is carried out according to the following procedure:
O_{1{circle around (x)}2, . . . , {circle around (x)}n}=O₁{circle around (x)}O₂{circle around (x)} . . . {circle around (x)}O_i{circle around (x)} . . . {circle around (x)}O_n
where O_{1{circle around (x)}2, . . . , {circle around (x)}n} is the voted opinion, O_i is the opinion of the i^th sensor, n is the total number of sensors installed in a zone of protection, and {circle around (x)} represents the mathematical consensus (voting) procedure.

[0064] In some embodiments, if the sensors are arranged to cover multiple zones with minimal or no sensor coverage overlap, then time delays are be incorporated into the voting scheme. Each time delay can be determined, for example, by the typical speed an intruding object should exhibit in the protected area and the spatial distances between sensors. In this case, the voted opinion O_{1{circle around (x)}2}, . . . , {circle around (x)}n is expressed as:
O_{1{circle around (x)}2, . . . , {circle around (x)}n}=O₁(T₁){circle around (x)}O₂(T₂){circle around (x)} . . . {circle around (x)}O_i(T_i){circle around (x)} . . . {circle around (x)}O_n(T_n)
where T₁, . . . , T_n are the time windows specified within which the opinions of the sensors are evaluated. The sequence number 1, 2 . . . n in this case does not correspond to the actual number of the physical sensors, but rather the logic sequence number of the sensors fired within a specific time period. If a sensor fires outside the time window, then its opinion is not counted in the opinion operator.

[0065] In some embodiments of the voting operator, opinions corresponding to a plurality of non-video sensors 18 can be combined using, for example, the multiplication operator of FIG. 4A and then voted against the opinion of one or more video sensors (or other verification sensor(s) 20) using the voting operator described above.

[0066] As described above with respect to exemplary embodiments, the present invention provides a means for verifying sensor signals from an alarm system to filter out nuisance alarms. In one embodiment, an alarm filter applies subjective logic to form and compare opinions based on data received from each sensor. Based on this comparison, the alarm filter verifies whether sensor data indicating occurrence of an alarm event is sufficiently believable. If the sensor data is not determined to be sufficiently believable, the alarm filter selectively modifies the sensor data to filter out the alarm. If the sensor data is determined to be sufficiently believable, then the alarm filter communicates the sensor data to a local alarm panel.

[0067] Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention.