Sensor Resource Management driven by threat projection and priorities

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Information Sciences 178 (2008) 2007–2021 www.elsevier.com/locate/ins

Sensor Resource Management driven by threat projection and priorities Joseph Anderson, Lang Hong * Department of Electrical Engineering, Wright State University, Dayton, OH 45435, USA Received 30 August 2005; received in revised form 18 January 2007; accepted 29 November 2007

Abstract This paper extends previous Sensor Resource Management (SRM) work by addressing information flow from sensor inputs to SRM, through four levels of the US DoD’s Joint Directors of Laboratories (JDL) sensor fusion model. The method flexibly adapts to several domains/problems. Human situation awareness information needs are linked to sensor control in a manner similar to perception management. The key to effective integration of JDL levels is the timely determination of the highest priorities via threat projection accomplished via Probabilistic Accumulative Situation Calculus (PASC), which quantifies threat intent using an appropriate level of automated context-based reasoning. The accuracy of the threat projection is improved over time using self-learning techniques. The multiple sensor system levels are unified primarily using the structure of quantified priorities. Algorithms are presented for a radar sensor resource allocation and adjustment method in which the dwell time per track parameter is the key radar sensor resource to be managed. A developed application of the method to an Integrated Air Defense System (IADS) sensor system problem is detailed, with simulation results shown to demonstrate the effectiveness of the method. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Sensor Resource Management; Situation Calculus; Threat projection; Prioritization; Radar

1. Introduction This paper presents a Sensor Resource Management (SRM) system that strives to make the best possible use of the available sensors to achieve a sensor system goal. The specific application chosen for demonstration of the SRM system is a military application called an Integrated Air Defense System (IADS). An Integrated Air Defense System (IADS) sensor system attempts to prevent threat aircraft from passing through its airspace and attacking targets on the ground. An IADS consists of a network of air defense radars with associated sensors and surface-to-air missiles, under the direction of a Command and Control center. The operational goal for a SRM associated with an IADS is to help provide good Situation Awareness for IADS operators by maintaining tracks a high percentage (>90%) of the time that the objects are within the IADS *

Corresponding author. Tel.: +1 937 775 5053; fax: +1 937 775 3936. E-mail addresses: [email protected], [email protected] (L. Hong).

0020-0255/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2007.11.029

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area. Track maintenance is especially important for high priority tracks, even in stressing conditions such as jamming and/or a large number of tracks. Typically, IADS must meet objectives such as achieving minimal tracking error and even distribution of tracking assignments amongst sensors. IADS have a mixture of sensor types with varying characteristics that must be accommodated. Representative scenarios can be very active with many objects/tracks which must be simultaneously tracked, identified, and classified. Specifically, the SRM must find the best actions/sequence of actions with sensors to accomplish the above goal, including sensor allocation and sensor mode changes. For this effort it was desired that the sensor system be able to automatically focus sensor resources on tracks of greatest interest to IADS operators, and alert the operators to projected threat actions, while continuing to meet typical IADS objectives. This automated threat projection system must be reliable and accurate, and should be able to learn threat behaviors over time. The US DoD’s Joint Directors of Laboratories (JDL) model describes four levels of sensor fusion spanning sensor measurements through Sensor Resource Management commands [10]. Progress has been made in improving the sensor data processing at all four levels of the JDL model; however, there remain some weak areas where improvements are very helpful [7,15]. This paper enhances previous work by explicitly addressing information flow from sensor inputs at Level 1 to SRM at Level 4. In this method human information needs are linked to sensor control in a manner similar to perception management [12]. A useful structure for unifying Levels 1–4 is quantified priorities; the method described in this paper incorporates an extension of the priority structures of [14] and the ‘‘utilities” of [5]. Timely determination of the highest priorities via threat projection is an important issue. A key element of this method is Probabilistic Accumulative Situation Calculus (PASC), which performs the threat projection needed to take early sensor management action. PASC is an extension of Situation Calculus [6,13,16] that quantifies threat intent using an appropriate level of automated context-based reasoning similar to that described in [19] and [21]. PASC also learns how to better predict threat behavior based on experience over time. Algorithms were developed for a radar sensor resource allocation and adjustment method in which the dwell time per track parameter is the key radar sensor resource to be allocated based on [17,18]. This straightforward allocation and adjustment method ties in well with the prioritization scheme identified above. This paper gives simulation results to demonstrate the effectiveness of this method for an IADS. 2. Problem formulation Fig. 1 shows the proposed general methodology at a basic conceptual level, mapped against the classic JDL model. At Level 4, the SRM makes sensor allocation/assignment and mode adjustment decisions, sends the commands to the sensors, and interfaces with human operators regarding the commands. A key for the preferential allocation and adjustment logic is the Prioritization system that ranks tracks highest to lowest. Since Prioritization is a type of threat assessment it falls into Level 3, as does the threat projection function that determines the highest priority threats. The logical computations needed for Prioritization and Projection are best done with Symbols that reflect the current situation. The process of aggregating track position and ID information into Symbolic representations of the situation fits well into Level 2. Sensor inputs are tied to threat concern level via symbolic states; for the IADS application the symbolic states are based on wellknown fire control ‘‘rules of thumb” or doctrine. The symbols must be domain-specific to be meaningful and useful. Optimal tracking as well as track ID and type classification based on multiple sensors are tasks that fit into Level 1. As described in more detail below, using this methodology is an effective and general way to address a variety of SRM problems. The greatest human perceptual concern in this case is asserted to be preventing bad things from happening, such as bombs destroying our High Value Assets (HVAs). To prevent these ‘‘bad things” from happening in a combat situation, the SRM and operator must know in advance when a threat is about to do a serious negative action, so that the appropriate resources can be applied to prevent the action. For instance, more sensor resources may be assigned to better track and destroy incoming aircraft. Projection of threat actions and intents is very challenging. In this paper a relatively well-developed part of Artificial Intelligence called Situation Calculus was adapted to deduce threat intention, and heavily modified with probabilistic considerations. The resulting method is called ‘‘Probabilistic Accumulative Situation Calculus,” described in detail later. The Symbolic computations mentioned in Fig. 1 allow us to take advantage of

J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021

Human Interface

Level 4 Sensor Management

2009

Human Interface Projections Warnings Actions

Sensor Allocation & Adjustment

Sensor Commands

Priorities

Level 3 Threat Assessment

Threat Projection (PASC)

Track Prioritization Symbolic States

Compute Symbolic States

Level 2 Situation Assessment ID, Type & Mode

Level 1 Sensor Integration

JDL Model

Positions & Rates

Track ID, Classification & Track Filter Mode SRM Model

Sensor Pointing

Sensor Measures

Fig. 1. Sensor Resource Manager spans several JDL levels.

Situation Calculus’ semantic logic. The tracks with the most threatening actions get highest priority, the most sensor resources, and the most immediate reactions. Discrete sensor allocation/adjustment logic is built around these prioritization considerations, which help to tie the parts of system together. Also, object tracking and ID/Type/Mode information must continuously flow into the information pipeline at the first level for the SRM to operate effectively. Warning the human operator is crucial for key sensed events such as threat aircraft in the process of destroying our HVAs. 3. Sensor Resource Manager Fig. 2 shows the mechanization details of the SRM system functions for an IADS. The sensor relative position measurements (Range, Azimuth angle and elevation angle) are input to the Tracking Filter to generate _ The IADS command chain communications sysfiltered Cartesian positions and rates (X, Y, Z, and X_ ; Y_ ; Z). tem provides the overall alert level (high or normal) to the SRM system. The symbolic state computations (in blue1) generate the symbols in red. Fly_Toward_X, Cross_Border and Formation_Fly are computed via relatively simple relative geometry calculations. Threat status (Threat/Foe, Friendly, Neutral, or Unknown), type classification and mode identification measurements are provided by Electronic Support Measures (ESM) and Identification Friend, Foe or Neutral (IFFN) sensors and associated/correlated with the source position tracks generated by the tracking filter. Symbolic states for each track are the inputs for both the Prioritizer and Probabilistic Accumulative Situation Calculus functions. The details and the seven levels of the Prioritizer are shown in Table 1. Prioritization of tracks plays a large part in the SRM system. The development of this particular Prioritizer was driven by fire control logic domain knowledge. Determination of priority is determined by discrete logic for priority levels 1–4 as shown in Table 1. For computational efficiency, Probabilistic Accumulative Situation Calculus (PASC) is utilized only for tracks that have already achieved a priority level of 4 based on discrete logic; this efficient structure is similar to one described in [8]. The goals that are of significant interest to sensor system users are application specific and are limited to three in number; they include the following:

1

For interpretation of color in Figs. 2, 8 and 10, the reader is referred to the web version of this article.

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J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021 Sensor Commands

Allocator / Adjuster Prioritizer Levels 5&6

Postulated Goals:

HVA_Attack

Prioritizer

Symbolic States:

MVA_Attack

Probabilistic Accumulative Situation Calculus

Levels 1-4

Probability Factors:

ARM_Attack

Operator Warning Direct Action

Prob. Fact Is True

High_Alert_Level

Pfact

State

Pcorr

Prob. Fact is Correlated to Goal

Database

Attack_Aircraft

Support_Jam

Fly_Toward_X Attack_Mode Cross_Border Formation_Fly Threat_Status Launch_ARM

Correlation To Source

Compute Symbolic State:

Range < Border R< Msl Rng

|Aspect Angle| < 15 deg For 3 sec

ψ1 ~ ψ 2 V1 ~ V2 Dist12 < 5 k For 3 sec

Track Filter Sensor Command Measurements: Chain

ESM, IFFN

Range, Azimuth, Elevation

Fig. 2. SRM system details.

Table 1 Priority levels Priority

Track states

6 5 4 3 2 1 0 1

Threat projection = Attacking_High_Value_Asset OR ARM_Attack Threat projection = Attacking_Medium_Value_Asset Fast Closing AND Threat AND Attack_Aircraft AND (Jam OR Attack_Mode OR Cross_Border) Fast Closing AND Threat AND Attack_Aircraft (Fast Closing OR Cross_Border) AND Threat Threat OR ((Fast Closing OR Close) AND Neutral) Unknown OR (Far Away AND Neutral) Friendly

(1) Attack of a blue (friendly) High Value Asset (HVA). (2) Anti-Radiation Missile (ARM) attack of a blue (friendly) radar. (3) Attack of a blue (friendly) Medium Value Asset (MVA). While other goals may be of some interest, they do not require special attention by the Sensor Resource Manager. The Probabilistic Accumulative Situation Calculus function will project the goal (if any apply) of the given track when it is called with the current Symbolic facts, their Probabilities of fact (Pfact), and their Probabilities of being correlated to the goals (Pcorr). If a significant projection is made the priority level will be set to 5 or 6, the operator will be warned and, for the ARM attack, direct action will be taken (radar shutdown or counter-measures). The priorities in turn drive the sensor Allocator and Adjuster functions, which issue commands to the sensors to allocate/assign tracks and adjust sensor thresholds via mode changes. Consistent with fire control logic domain knowledge, the most threatening tracks reflected in Table 1 get higher priority (and more attention). Refs. [14,3] provided some of the input regarding fire control logic.

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Priority level is typically defined as threat tracks higher than friendly tracks, while neutral and unknown tracks fall in between. Tracks that are at shorter ranges and closing faster (with the radars, HVA or MVA) get higher priority. Threat attack aircraft are of greater concern than other types such as cargo aircraft, especially when the presence of support jamming and radar emissions in attack mode indicates an attack of some sort is about to begin. These rules of thumb drive the discrete logic implementation for priority levels 1–4. To incorporate human operator intuition and judgment, optional dynamic human input will increase the computed priority level for a given track, which will cue the SRM to maintain a good track on the selected object. In computing the symbolic states as addressed in Fig. 2, three main relative geometry computations are performed. (1) The symbolic state Cross_Border is set to true if the range along the track’s bearing to the ESA is less than the range to the border. (2) Formation_Fly (or Formation_Flight) is declared true when two or more tracks have the same heading angle and velocity within a pre-set tolerance for duration of more than 3 s. (3) Fly_Toward_X is a kinematic projection which measures the likelihood the track is flying toward the object, which in turn drives the logical threat projection for the PASC. If the track is headed straight toward the radars, HVA, or MVA the corresponding Aspect Angle will be close to zero in magnitude. The logic used here is to declare Fly_Toward_X (where X is radars, HVA, or MVA) to be true if the Aspect Angle k magnitude stays below 15° for more than 3 s (see Fig. 3). The 3 s criterion is intended to avoid declaring Fly_Toward_X when the Aspect Angle passes quickly through zero. The probability of fact for Fly_Toward_X is dependent on the tracking position uncertainty for the track, as indicated in Fig. 3. A rule for zig-zagging tracks has been developed, but for brevity’s sake is not presented here. Computations of most Pfact values are based directly on sensor specifications. Pfact values for Support_Jam, Attack_Aircraft, Threat_Status, and Attack_Mode are based on IFFN and ESM specifications. A tracking filter was used for the multi-sensor integration of track position information. The function of the tracking filter loop is to minimize track error. The Interacting Multiple Model/Joint Probabilistic Data Association Filter (IMM/JPDAF) was used for excellent tracking performance in the presence of false alarms and multiple tracks with trajectories that intersect. In the simulation scenario described later the two primary threat tracks provide a challenge by flying in formation and crossing tracks more than once. Refs. [2,11] describe the theory behind the IMM/JPDAF, and [9] describes the utility of incorporating target identification into the tracking algorithm. [4] provided a detailed MATLAB Electronically Scanned Array (ESA) radar model which was a major part of the simulation used for this research. The MATLAB model calls the Prolog PASC threat projection function via a unique interface. Note that the general method described in Fig. 1 applies well to many other applications including Naval air defense, military tracking of ground force movements, tactical aircraft on-board sensor fusion, robotic sensing, automotive ‘‘smart highway” sensing, and Air Traffic Control (ATC). For example, this method applied to ATC would predict when the probability of tracks colliding is high, then assign additional sensor resources

Position Uncertainty λ t

HVA

P fact

1.0

t + Δt λ= Aspect Angle

Track Trajectory

Kinematics

-15 0 15 Relative Angle (deg)

Probability

Fig. 3. Kinematic projection of track toward High Value Asset (HVA).

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to the high priority problem tracks, and alert the ATC operators. Symbolic states relevant to ATC might include ‘‘Tracks Closing On Each Other at a High Rate,” ‘‘Tracks Deviating From Assigned Vectors,” etc. 4. Probabilistic Accumulative Situation Calculus (PASC) for threat projection The theoretical development of PASC begins with Situation Calculus (also referred to as Action Theory), which is a relatively mature part of Artificial Intelligence that has been applied extensively in the cognitive robotics field. Situation Calculus provides a consistent, rigorous, general methodology for defining automated reasoning. In applying Situation Calculus, a logical methodology is applied starting with events of some human operator interest, and ‘‘working backwards” to facts that would likely exist if this event were about to occur. Situation Calculus implementations use Prolog’s symbolic pattern-matching and logical chaining capability to determine the sequence of steps (also called sub-goals or actions) which could occur that would lead from the symbolic facts to the final goal or event. References for the development of PASC were the detailed explanations of [13,6] (a ConGolog paper), and [16]. These papers describe the theory, mathematics and practical use of Situation Calculus for several applications in considerable detail using Prolog-like syntax. Below is a pre-condition equation in Situation Calculus form for the IADS application: PossðAttack Approachðx; r1; sÞÞ  Attack AircraftðrÞ ^ Fly Towardðx; sÞ

ð1Þ

‘‘Poss” can be interpreted as Attack_Approach ‘‘is possible if” the symbols on the right are true. The precondition is combined with an Effect Axiom or Fluent to yield the goal HVA_Attack: PossðAttack Approachðx; r1; sÞÞ ^ Support Jamðr1; sÞ ^ Cross Borderðr1; sÞ ^ Attack Modeðx; r1; sÞ ^ Formation Flyðr1; r2; sÞ  HVA Attackðx; doðAttack Approachðx; r1; sÞ; sÞÞ;

ð2Þ

where x = HVA, r1 and r2 = tracks 1 and 2, and s = the current situation. In execution, symbols and sub-goals are logically ‘‘chained together” to move from the initial state s to the hypothesized goal HVA_Attack. The logical behavior of a threat can modeled in some detail by using the rich features in Situation Calculus. To give Situation Calculus the probabilistic yet reliable qualities needed for threat projection applications, some modifications were made to create Probabilistic Accumulative Situation Calculus. In many previous Situation Calculus works, non-deterministic branching is used to generate multiple possible action sequence options. The implementation used here is a modification of existing Situation Calculus algorithms such as those described in [6,13], in particular to add accumulative probability considerations without the non-deterministic branching. A similar approach is taken in [16]; however, accumulative probability is not addressed in that paper. Hence, the name is Probabilistic Accumulative Situation Calculus. With these modifications the Symbolic Projections are efficient and reliable and take into account the following probability categories: (1) Pcorr, which is the a priori probability (Belief Factors) that certain actions/goals (such as an attack of a High Value Asset) will occur given certain facts. This is also defined as the probability that a symbol/fact is correlated to a goal. (2) Pfact is the probability that a certain fact is true given both sensor uncertainty and kinematic projection uncertainty. The cumulative evidential probability for two probabilities that supply evidence is derived using Bayesian probability theory. Eq. (3) below gives the Bayes theorem starting point for the probability that the hypothesis H is true given the interpretation of the information, I P ðH jIÞ ¼

P ðIjH Þ  P ðH Þ ; P ðIÞ

ð3Þ

where P(IjH) is the probability that the interpretation of the information is correct upon assuming that H is true, the asterisk denotes multiplication, P(H) is the prior probability that H is true – the probability that

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would be assigned if no explicit information about H is available at all, and P(I) is the probability that would be assigned to the correctness of the interpretation of the information if there were no assumptions made about any hypothesis. As detailed in [20], the application of a priori probabilities, complimentary (negative) hypothesis, and odds that include N pieces of information I result in a useful equation for accumulation of evidence. Eq. (4) below shows the derived relation for the accumulation of individual probabilities 1–N into an overall probability that the hypothesized goal H is true. It is assumed that the probabilities for I1, I2, . . ., IN are independent QN i¼1 P ðI i jH Þ : ð4Þ P ðH jI 1 I 2    I N Þ ¼ QN QN P ðI jH Þ þ i¼1 ð1  P ðI i jH ÞÞ i i¼1 For the purposes of threat projection using Situation Calculus the pair-wise form of Eq. (4) is shown in Eq. (5) below; the equation function is called Accum (short for accumulate). This function can be used iteratively to accumulate the probability the hypothesis H is true in a way that fits well with logical chaining P ðH jI 1 I 2 Þ ¼ AccumðI 1 ; I 2 Þ ¼

P ðI 1 jH Þ  P ðI 2 jH Þ P ðI 1 jH Þ  P ðI 2 jH Þ þ ð1  P ðI 1 jH ÞÞ  ð1  P ðI 2 jH ÞÞ

ð5Þ

Eq. (6) below is used to give the probability for the ith piece of evidence P(IijH). Eq. (6) is developed from Eq. (3) by realizing that P(I) is defined the same way as Pfact, was defined previously, and P(HjI) is defined the same way as Pcorr was defined previously. The a priori P(H) term is assumed to be unity for our purposes P ðI i jH Þ ¼ P ðI i Þ  P ðH jI i Þ ¼ P facti  P corri

ð6Þ

Fig. 4 shows the algorithm for the pair-wise accumulation of individual probabilities shown in terms of Pfact, Pcorr, and Symbols for N = 3 individual probabilities. The mathematical result is the same as would be expected using Eq. (4) with N = 3 pieces of information. For large numbers of individual probabilities additional multiplications and pair-wise accumulations can be added in ‘‘daisy-chain” fashion. The pair-wise Accum numerical function was programmed into Prolog such that accumulative evidential probability is computed ‘‘on-the-fly” simultaneously with symbolic pattern matching and logical chaining. Fig. 5 shows the completion of the threat projection process for an attack on an HVA (HVA_Attack), based upon four symbols of Eq. (2) (Formation_Flight, Cross_Border, Attack_Mode, and Support_Jam) and their associated Pfact, Pcorr probabilities. Probabilistic Accumulative Situation Calculus performs logical chaining of the four symbols, computes the probability that HVA_Attack is true, compares this probability to a threshold, and determines the threat projection state for HVA_Attack (true or false). The computations of Fig. 5 are only performed if HVA_Attack is ‘‘possible,” that is when Fly_Toward_HVA and Attack_Aircraft are true. Note the Pcorr values are those that are used when the High_Alert_Level symbol is true. Fig. 6 shows probabilities for representative symbolic states along with one of three postulated goals (HVA_Attack) at one point in a scenario. In this case, the HVA_Attack probability is slightly above the threshold of 87% at which a High Value Asset attack is declared. A similar process is used for goals MVA_Attack and ARM_Attack. This methodology is flexible and easily extensible using semantic declarations for more symbols and for other applications. The PASC system P

Symbol 1:

Symbol 2:

fact 1

Pcorr 1 P fact 2 Pcorr 2

X

P( I | H ) 1

Pair-wise Accumulation X

P( I | H ) 2 P

Symbol 3:

fact 3

Pcorr 3

X

P( I | H ) 3

Pair-wise Accumulation

Fig. 4. Pair-wise accumulation shown for N = 3.

P( H | I I I ) 123

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J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021 P

Pcorr Cross _ Border

factCross _ Border P

P

Logical Chaining

Pcorr Attack _ Mode

fact Attack _ Mode factFormation_ Flight

Pcorr Formation _ Flight

Threat Projection P

factSupport _ Jam

Pcorr Support _ Jam

P( H | I I I I ) 12 3 4

HVA_Attack (True or False) Threshold Fig. 5. Logical chaining and probability accumulation for the goal HVA_Attack.

_A tta ck HV A

in g Fo rm at io n_ Fl y Cr os s_ Bo rd er

Su pp o

At ta ck _M

od e

Threshold

rt_ Ja m m

Probability

60 sec into Scenario 100 90 80 70 60 50 40 30 20 10 0

Fig. 6. Percentage probabilities for track states and postulated goals.

‘‘connects the dots” if it is possible to go from the present situation to the postulated goal (or actually, backwards from the future goal to the present situation). If the probability of goal (or sub-goal) drops below a preset threshold along the way, the back-tracking terminates. In the Prolog language used to implement PASC, Backward-chaining vs. Forward chaining are logically equivalent ways to get from facts to goals, but there are differences in terms of computational efficiency. Also, within Prolog a skilled operator can ask the program how it arrived at a conclusion, and get a comprehendible symbolic answer as a built-in Prolog feature. The accuracy of the threat projection logic will be improved over time by updating the Probabilistic Accumulative Situation Calculus logic and correlation probabilities via a self-learning strategy. Also, these updates reduce the Projection false alarm rate. In particular, the values within the Pcorr database of shown in Fig. 2 will be updated using a neural network as described in [1]. The system must be stable and reliable for the operator, therefore the Prolog ‘‘logic-base” must not be changed too fast. 5. Allocation and adjustment Priority-driven sensor allocation and adjustment is used continually during sensor system operation. This task is especially stressing during conditions of large number of tracks, radar jamming, and/or large ranges. More specifically, stressing conditions occur when the total dwell time required for the sensor system radars to continue to detect all tracks exceeds the maximum allowable ‘‘frame time” for all track dwells. The radars will lose tracks due to either missed detections (dwell times too short) or tracks exiting the range gate or radar beam width (frame time too long). During these stressing periods Eq. (7) is violated:

J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021

   N X M X   T DWELLj  T FRAMEi  6 0;    i¼1 j¼1

2015

ð7Þ

where T DWELLj , estimated dwell time needed to maintain track j; T FRAMEi , Radar i frame time; N, number of radar sensors; M, number of tracks. TFRAME is the time allowed to keep tracks from exiting range and angle gates. It is a function of acceleration capability, position, velocity, and error covariance for each track. The allocation and adjustment algorithm operates at every processing frame on a continuous basis: Step 1. The algorithm finds the combination which minimizes resources spent and stays within sensor frame time ‘‘budgets” (more later). Step 2. If step 1 fails to bring the total dwell times below sensor budgets, adjust/reduce Signal-to-Noise Ratio Threshold (SNRT) from 18 dB to 6 dB for sensors with total dwell time for allocated tracks > frame time. With this reduction comes a greater risk of passing false alarms through to the tracking filter. (Note that for a broad population of sensors reduction of SNRT is only available at an ‘‘all or nothing” level for each sensor, not at a per-track level.) Step 3. If step 2 fails to bring the total dwell times below sensor budgets, the last resort is to drop tracks as follows: (a) Lowest priority tracks first; (b) When several tracks are at same priority level, tracks will be dropped for the highest estimated dwell time tracks first.

Step 1 is the finding of the combination which minimizes resources spent and stays within sensor ‘‘budgets”. Dwell time is computed using the TDWELL Eq. (8). For the ESA Radar maximum frame time TFRAME equations are described in [1] and were taken from [18] with minor modifications. The maximum frame time is computed for each track, and the minimum value for all the tracks is used for TFRAME. For the other standard (non-ESA) radar sensors the frame time is a fixed scan time, although the scans can be interrupted to acquire a new assigned target. The sequence of algorithm computations is as follows: 1. For each track, initially assign the sensor having minimum estimated dwell time. 2. If the sensor sum is over the limit, the algorithm redistributes by iteratively swapping track assignments between the most overloaded sensor and the most under-loaded sensor until the condition of Eq. (7) is met. The track is chosen for which the swap comes closest to bringing the total allocated dwell time to just below the allowed frame time. For tracks with priority of 5 or 6, at least two sensors will be assigned to the track. Typically an IR sensor will be assigned to provide tracking robustness in the presence of radar jamming. Dwell times TDWELL are determined by extension of the simplified detection functions of [17]. Eq. (8) gives TDWELL in seconds for a single track   loge ð1  P d Þloge P1fa R4 ð4pÞ3 Ltot ðN þ J Þ T DWELL ¼ ð8Þ 0:4805rk2 Gt Gr P t Table 2 Equation 11 parameter definitions Pd R N r Gt Pt

Probability of detection Range Thermal noise energy Track Radar cross section Transmit gain Transmitter power

Pfa Ltot J k Gr

Probability of false alarm Total losses for Radar system Jamming energy Transmit wavelength Receive gain

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Table 2 defines the parameters of Eq. (8). Note that TDWELL rises dramatically with range R, and jamming J. Also, the summation of TDWELL values for a large number of tracks may result in substantial total TDWELL values, especially for tracks with low radar cross sections. 6. Simulations and discussions Simulations were performed for a variety of scenarios with different numbers of tracks and other track trajectories. The scenario described here is the HVA Attack scenario with ten tracks. This scenario includes an IADS sensor system (see Fig. 7) with:  1 ESA Radar w/240 km range.  Also at the ESA Radar site are an infrared sensor with 40 km range, a Precision ESM with 100 km range, a Missile Warning System (MWS) with 30 km range, and one IFFN, good to 240 km range for Threat/ Friendly/Neutral and good to 120 km for aircraft type. This IFFN is right 95% of time.  2 Additional Radars w/120 km range, and 1 HVA.  No simulated missiles or guns – sensor system only.  10 aerial ‘‘tracks”, two of which attack the HVA. Fig. 8 shows the filtered track performance results of two simulation runs, one with the SRM described in the previous sections (henceforth called ‘‘SRM”) and one with a more traditional sensor management method (assigned sectors without SNRT reduction). Stand-off jamming is turned on just before targets 1 and 2 turn toward the HVA to cover their aggressive change of course. On the left side of Fig. 8 it can be seen that with SRM the sensor system maintains track on six tracks throughout the 150 s run, while the results on the right side show the system without SRM can only keep track on one track. Most importantly, with SRM the two most critical tracks that attack the HVA (tracks 1 and 2) are maintained. The intent of the simulation runs is to show the following:

N W

TRACK 10

E

Political Border

RADAR 2

S

TRACK 8 & 9

TRACK 4 & 5

ESA RADAR 1 IR MWS

AIRFIELD HVA

TRACK 6 & 7

IFFN ESM TRACK 1 & 2

ISR AIRCRAFT TRACK 3 RADAR 3 Fig. 7. Ten track scenario with HVA.

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2017

Fig. 8. Tracking performance with and without SRM.

(1) The threat projection logic can determine that two threat aircraft were setting up an attack on a High Value Asset (HVA). (2) Based on the HVA attack warning, the Sensor Resource Manager maintains track on the two threat aircraft with a combination of re-assignment, SNRT adjustment and an additional sensor to reduce the chance that the two tracks would be lost at a critical time. (3) Due to low tracking errors, friendly weapon systems could engage and destroy the two threat aircraft before the HVA was damaged. (4) Without the threat projection logic and related prioritized SRM actions, the Sensor System loses the two tracks at exactly the wrong time. (5) In this case, the HVA would be destroyed without the threat projection logic. The HVA would have survived with the threat projection logic. Without SRM the two main red and green tracks (targets 1 and 2 of Fig. 8) disappear from the screen as they approach the light blue cross that represents the High Value Target (HVA). The high level of jamming causes the loss of track. When radar track is maintained and a second IR sensor was used to keep the ESA pointed at the two tracks, the tracking performance greatly improves, and the IADS can now shoot down the ingressing tracks if the command is given. Fig. 9 shows additional data relative to the scenario shown in Fig. 8. The sequence from sensor inputs to sensor commands is illustrated in Fig. 9 for track 1 only. Note that between 80 and 110 s, Aspect Angles to the HVA drop to about zero. The probability value for the FlyTowardHVA symbol rises to over 90% between 80 and 110 s based on this Aspect Angle. Also, heading angles and velocities of tracks 1 and 2 (not shown) are close enough to each other to declare a high probability of FormationFly for both tracks. Track 1 trajectory passed ‘‘CrossBorder” approximately 50 s into the run. Due to the status change for symbols CrossBorder, FlyTowardHVA, and FormationFly, the Probabilistic Accumulative Situation Calculus declares HVA_Attack, which drives the priority level to a value of 6 prior to the onset of jamming. The detected Jamming leads to a larger value of PHVA, meaning greater certainty that an HVA attack is imminent. A priority of 6 means the track gets preferential treatment in assigning radar resources and a second, IR, sensor is assigned. The large spike in required total Dwell Time at 87 s of time is due to a large increase in jamming intended to blind the sensors to the impending attack. The reduction in SNRT commanded by the SRM at 87 s helps bring the total dwell time back below the maximum frame time, while Signal to Noise Ratio (SNR) levels stay above the reduced threshold to maintain track. The bottom of Fig. 9 shows the SRM-determined priorities for all tracks/targets, as well as the sensor assignments to radars 1, 2, or 3 (a sensor assignment of zero means the track was dropped). As can be seen, the higher priority tracks avoid being dropped, particularly for tracks 1 and 2.

2018

J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021

Fig. 9. Sequence from sensor inputs to sensor commands.

The SRM was compared to three other sensor management methods for the ten track scenario shown in Fig. 8. These methods are commonly practiced ‘‘assigned sector” methods. Method one is a very effective Range Priority method with two features in response to strong jamming – first, the SNRT is reduced to 6 dB (same as for the SRM), second, the tracks that are most distant from the sensor are dropped preferentially. Method two is also a Range Priority method, however SNRT is fixed and not reduced (Fig. 8 shows example results for method 2 on the right side). Method three represents a non-prioritized system and has two features: first, the SNRT is reduced to 6 dB, second, tracks are dropped in Random Priority order. Three output performance statistics selected are (1) Composite Track Percentage, (2) Number of Targets Lost by the end of the run, and (3) a discrete value for maintenance of track on the two highest priority targets (Two Primary Targets Held). Composite Track Percentage measures the fraction of total simulation time that targets are being tracked by the sensor management system for all ten targets, weighted by track priority consistent with Table 1 priorities. ‘‘Two Primary Targets Held” is an important output because track information for both targets is significant input to determining the threat intent of the two tracks. Fig. 10a, c, and e were generated for the conditions of Fig. 8 (jam time of 87 s) and show generally better performance for the SRM versus the other methods, although at low jamming levels the Number of Targets Lost is lower for method 1 than for the SRM. The lower number of lost targets is due to method 1’s preference

J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021

2019

Fig. 10. Comparison of performance parameters for four Sensor Management Systems.

for close targets, even if they are lower priority. For Composite Track Percentage and Two Primary Targets Held, the SRM shows a significant advantage over the other three methods at the higher jamming levels. In fact the SRM is the only method that maintains track on both primary targets at jamming levels above

2020

J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021

Table 3 Averaged results of Monte Carlo runs SRM

Method 1

Method 2

Method 3

Mean number targets lost

Low High

4.8 7.0

3.2 6.4

8.2 8.9

6.9 8.1

Mean Composite Track Percentage

Low High

93 83

93 81

77 75

90 78

Two primary targets held (Mean)

Low High

0.80 0.52

0.71 0.00

0.00 0.00

0.11 0.01

1.7  1015 J. Based on this jamming level performance trend, jamming level was categorized into two ranges (High and Low) for the Monte Carlo runs shown in Fig. 10b, d, and f. Low jamming level is varied via random uniform distribution between 0.2 and 1.7  1015 J, and High jamming level is varied between 1.7 and 4.6  1015 J. Monte Carlo simulation runs were performed 20 times for each jamming level range to filter out the random effects of simulated radar noise and false targets on tracking performance. Also, an effort was made to minimize ‘‘scenario-dependency” to the extent practical by varying two key characteristics of the scenario: (1) the initiation time of the jamming, and (2) the positions of the tracks. Jamming initiation time at 87 s is the ideal tactic for the threat tracks 1 and 2 because the turn toward the HVA is covered up. Jam times of 65 and 110 s are also evaluated for purposes of scenario variability, however the lower jam times give the radar operators significantly more warning that something is afoot, and the late jam time occurs after the turn, at a time when track 1 and 2 intent may have already been discerned by operators. Three positions were evaluated for tracks 6 and 7 – (1) in Radar 1’s sector, at a shorter range than tracks 1 and 2, (2) in Radar 1’s sector, at a greater range than tracks 1 and 2 (shown in Fig. 8), and (3) in Radar 3’s sector. More tracks in the sector for Radar 1 put greater pressure on Radar 1 at jamming time. Fig. 10b, d, and f show mean comparative performance statistics for High and Low jamming levels (indicated along the top) for three jamming times (indicated along the bottom) and three track 6 and 7 positions (three symbols above each jamming time for each method compared). Over 1440 simulation runs were performed to generate the statistics. The trends previously observed in Fig. 10a, c, and e still hold; that is, the SRM performs better than methods 1, 2, and 3 at higher jamming levels. This trend is even more pronounced for Two Primary Targets Held, where the SRM is effective as much as 95% of the time, while the other methods are effective 5% of the time or less. Incidentally, the scenarios run for jamming times of 65 s are very challenging for all the methods. Table 3 shows comparative performance statistics in which data is averaged for all jam times and tracks 6 and 7 positions. Again, the previously discussed trends with jamming level and method still hold. Shown in blue are the Two Primary Targets Held data for high jamming level, where the SRM is effective 52% of the time while only the random method 3 has any effectiveness (1%). 7. Conclusions This paper showed information flow from sensor inputs at Level 1 to SRM commands at Level 4 addressed in a comprehensive and consistent manner, and successfully applied an SRM to an Integrated Air Defense System (IADS) sensor system problem to show performance improvements relative to other methods. The combination of (1) quantified priorities and (2) timely determination of the highest priorities via threat projection using Probabilistic Accumulative Situation Calculus (PASC) was key to tying together the four levels of sensor fusion in a practical and effective manner. Prioritization was used systematically to tie together human information needs and sensor resource control. Necessarily, a self-learning method for continually improving the PASC threat projections was developed and implemented via a supervised Neural Network, then demonstrated. Future work is expected to include application of the SRM to more scenarios and to mobile sensor platforms.

J. Anderson, L. Hong / Information Sciences 178 (2008) 2007–2021

2021

References [1] Joseph Anderson, Comprehensive Sensor Resource Management Driven by Priorities and Threat Projection (Dissertation), Wright State University, 2005. [2] Yaakov Bar-Shalom, Xiao-Rong Li, Multitarget-Multisensor Tracking: Principles and Techniques, 1995. [3] A. Berrached, M. Beheshti, A. de Korvin, R. Alo´, Applying fuzzy relation equations to threat analysis, in: Proceedings of the 35th Annual Hawaii International Conference on System Sciences (HICSS-35.02), September 2002, pp. 684–688. [4] W.D. Blair, G.A. Watson, T. Kirubarajan, Y. Bar-Shalom, Benchmark for radar resource allocation and tracking maneuvering targets in the presence of ECM, IEEE Transactions on Aerospace and Electronic Systems (1998) 1097–1114. [5] Hugh Durrant-Whyte, James Manyika, Data Fusion and Sensor Management: An Information-Theoretic Approach, Prentice Hall, 1995. [6] Giuseppe De Giacomo, Yves Lespe´rance, Hector J. Levesque, ConGolog, A concurrent programming language based on the situation calculus, Artificial Intelligence 121 (2000) 109–169. [7] David L. Hall, Alan Steinberg, Dirty secrets in multisensor data fusion, CECOM RDEC Night Vision and Electronic Sensors Directorate Report, 2001, pp. 1–16. [8] Matthias Hans, Winfried Baum, Concept of a hybrid architecture for Care-O-bot, in: Proceedings of the 10th IEEE International Workshop on Robot and Human Interactive Communication, 2001, pp. 407–411. [9] Lang Hong, Ningzhou Cui, Mark T. Pronobis, Stephen Scott, Simultaneous ground moving target tracking and identification using wavelets features from HRR data, Information Sciences 162 (3–4) (2004) 249–274. [10] Lang Hong, Sensor your world better: multisensor/information fusion, IEEE CSS Newsletter 10 (3) (1999) 7–8, 12–13, 28. [11] Lang Hong, Ningzhou Cui, An interacting multipattern probabilistic data association algorithm for target tracking, IEEE Transactions on Automatic Control 46 (8) (2001) 1223–1236. [12] L. Ronnie, M. Johansson, Xiong Ning, Perception management: an emerging concept for information fusion, Information Fusion 4 (2003) 231–234. [13] Hector J. Levesque, Raymond Reiter, Yves Lespe´rance, Fangzhen Lin, Richard B. Scherl, GOLOG: a logic programming language for dynamic domains, The Journal of Logic Programming (1997) 59–83. [14] J.M. Molina Lopez, Jesus Garcia Herrero, F.J. Jimenez Rodriguez, J.R. Casar Corredera, Cooperative management of a net of intelligent surveillance agent sensors, International Journal of Intelligent Systems 18 (2003) 279–307. [15] Stan Musick, Keith Kastella, Comparison of sensor management strategies for detection and classification, in: Ninth National Symposium on Sensor Fusion, 11–13 March, 1996, pp. 1–23. [16] David Poole, Probabilistic horn abduction and Bayesian networks, Artificial Intelligence 64 (1) (1993) 81–129. [17] Marie de Vilmorin, Emmanuel Duflos, Philippe Vanheeghe, Michel Prenat, Optimal Sensors Management Strategies based on the Modeling of Detection Functions, IEEE, 2000, pp. 2327–2332. [18] Gregory A. Watson, Multisensor ESA resource management, in: Proceedings of the IEEE Aerospace Conference, Snowmass, CO, vol. 5, 1998, pp. 13–27. [19] Ewa Straszecka, Combining uncertainty and imprecision in models of medical diagnosis, Information Sciences 176 (20) (2006) 3026– 3059. [20] Peter Sturrock, Applied scientific inference, Journal of Scientific Exploration 8 (4) (1994) 491–508. [21] Yongchuan Tang, Jiacheng Zheng, Generalized Jeffrey’s rule of conditioning and evidence combining rule for a priori probabilistic knowledge in conditional evidence theory, Information Sciences 176 (11) (2006) 1590–1606.