Ocean Dynamics (2012) 62:161–175DOI 10.1007/s10236-011-0483-7

Decision support using the Multistatic TacticalPlanning Aid (MSTPA)

Christopher Strode · Baptiste Mourre · Michel Rixen

Received: 14 January 2011 / Accepted: 26 July 2011 / Published online: 30 August 2011© The Author(s) 2011. This article is published with open access at Springerlink.com

Abstract The Multistatic Tactical Planning Aid(MSTPA) is a tool currently in development at NATOUndersea Research Centre which may be used tomodel the performance of a given multistatic sensornetwork in terms of the probability of detection ofa submarine, the ability to hold a track and whethersuch a track could be correctly classified as such.The tool therefore considers the entire chain ofevents from an initial calculation of signal excess, thegeneration of a contact considering localisation errors,followed by the subsequent tracking and classificationprocess. In its current form, the tool may be usedto plan a particular multistatic scenario throughoperational analysis of many Monte Carlo simulations.The future development of MSTPA will transitiontowards a real-time decision support tool to assistoperators and planners at sea. This study introducesa number of generic decision support techniqueswhich may be wrapped around the MSTPA tool. Theacoustic performance metric that will drive decisionswill of course be subject to uncertainty relating toenvironmental measurements and extrapolations. Theeffect of this uncertainty on acoustic performanceis examined here. Future studies will consider thesensitivity of the eventual decision—in terms of opti-mum sensor positions—to the acoustic uncertainty.

Responsible Editor: John Osler

This article is part of the Topical Collection on Maritime RapidEnvironmental Assessment

C. Strode (B) · B. Mourre · M. RixenNATO Undersea Research Centre,Viale S. Bartolomeo 400, 19126 La Spezia, Italye-mail: strode@nurc.nato.int

Keywords Decision support · MSTPA ·Game theory · Optimisation · Uncertainty

1 Introduction

The Multistatic Tactical Planning Aid (MSTPA) isa tool currently in development at NATO UnderseaResearch Centre (NURC) which may be used to modelthe performance of a given multistatic sensor networkin terms of the probability of detection of a submarine,the ability to hold a track and whether such a trackcould be correctly classified. The tool considers theentire chain of events from an initial calculation ofsignal excess (Harrison 2002), the generation of a con-tact considering localisation errors (Coraluppi 2003),followed by the subsequent tracking and classificationprocesses (Wathelet et al. 2006, 2008b). The premisebehind the MSTPA model is to model each part ofthe chain in relatively simple terms, whilst maintainingsufficient fidelity from signal excess to eventual clas-sification. This methodology drives MSTPA towards itsgoal of becoming a decision support tool as opposed toa purely acoustic model. A more detailed description ofMSTPA and the algorithms it employs may be found inWathelet et al. (2006).

The MSTPA tool is primarily designed to assessthe performance of multistatic scenarios in which, bydefinition, sources and receivers may be spatially dis-tributed on separate platforms. Such a disposition isknown to increase area coverage and decrease theability of a submarine to evade detection since manyacoustic pathways exist between it and the receivers.However, the performance increase comes at the cost

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162 Ocean Dynamics (2012) 62:161–175

of increased operational complexity due to the manypossible sensor geometries and the need for reliableunderwater communication and coordination betweenthe source and receivers. As nations begin to procuresonar systems with a multistatic capability, there is avery real need for a tool such as MSTPA to automatethe planning process and to increase the situationalawareness and understanding of its operators.

The MSTPA tool must consider the optimisation ofboth static and dynamic multistatic networks. The statictype might include a barrier to detect the transit ofa threat submarine through a given area. A dynamicscenario might consider the persistent deployment of anumber of autonomous vehicles with multistatic capa-bility in order to act as a reactive area search network.This scenario is currently receiving much attentionat NURC as part of the cooperative anti-submarinewarfare project in which a distributed and persistentnetwork of autonomous sensors is envisaged (Hugheset al. 2010; Been et al. 2010). This scenario will includethe use of static sources combined with a number ofmobile platforms towing arrays with which to makemultistatic detections. The MSTPA tool may be used asa test bed for AUV behaviours in which realistic falsecontacts are generated in order to test the ability of suchbehaviours to react to the true target whilst discrimi-nating against false contacts and tracks. This report willconsider mostly the static deployment case in order todecrease the number of variables to optimise such thatthe concepts of decision support may be investigated(see Section 3).

In essence, the aim is to investigate generic decisionsupport techniques that may be ‘wrapped around’ theexisting MSTPA model (acting as a central metric cal-culator) in order to aid the decision-making process.This must begin with the automated extraction andanalysis of environmental data—whether measured,modelled or forecast, such that the relevant informationis passed onto the MSTPA model. Already, we seethat the MSTPA acoustic, tracking and classificationengine becomes just one module within a greater chainof decision support techniques. This must be the case,since any optimisation or decision-making process mustat some point determine the effectiveness of given op-tions. It is here that the existing MSTPA modules mustcalculate relevant metrics for the particular scenariobeing considered. The results from the MSTPA modelwill be integrated with techniques to analyse the ex-pected threat decisions, automatically re-examine thescenario and re-plan accordingly to determine a bestsolution. This process will feature elements of bothdecision theory—in order to mathematically describethe options and choices available to both threat and

friendly forces (and to rate their utility)—and gametheory in order to play out the potential combinationsof threat and friendly options until an optimum isdetermined.

Recent advances within the core acoustic elementof the model allow for the ingestion of fully 3-D tem-perature and salinity data as may be measured at sea.The recent REP10 experiment demonstrated rapid en-vironmental assessment in which glider measurements,satellite measurements and advanced oceanographicmodels were combined in a super-ensemble to produceaccurate 3-D maps of temperature and salinity, withforecasts up to 72 h. Initial results are presented inwhich the uncertainty inherent in the oceanographicmeasurements and forecasts are transitioned into thefinal acoustic coverage product. Environmental un-certainty is represented here through the 3-D super-ensemble (3DSE) uncertainty and is sampled in orderto generate a number of candidate temperature andsalinity fields. Each is then used to generate a signalexcess coverage map from which the final operationaluncertainty (the detectability of a submarine) may bedetermined.

The final step in the decision support chain is thepresentation of results to the operator. At this point,a number of human factors come into considerationwhen attempting to present complicated information tooperational personnel. There are two broad approachesto the eventual output of a decision aid. Firstly, thetool may simply output what it has determined to bethe ‘answer’. This may be the optimal positions for allsources and receivers within the scenario and the oper-ator need only implement this plan. Secondly, the toolmight display the performance metrics for a numberof different solutions allowing the operator to makethe final decision. This second option is most likely tobe preferred by the operational community who areintelligent, well-trained professionals that are used tomaking difficult decisions. At this point, the distinctionbetween a decision support tool and a decision makingtool becomes apparent. The tool should assist decisionsby presenting the relevant information together withcandidate solutions such that the operator still has thefinal say. A tool acting as a black box which spits outanswers is unlikely to be trusted.

The following broad topics will be investigated dur-ing the course of this paper, and their application to-wards transitioning MSTPA into a decision supporttool will be discussed:

– Game theory– Optimisation– Oceanographic uncertainty

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Fig. 1 Decision support framework

The above processes will be wrapped around theexisting MSTPA modules as described in Fig. 1. It ishoped that the additional modules will be sufficientlygeneric such that they may be quickly applied to addi-tional scenarios—such as glider path planning—simplyby replacing the core metric calculating module, thatis, replacing a multistatic model with a model of gliderdynamics and data sampling requirements such thatthe same decision theory modules may be applied butwith different calculations of measures of effectiveness.The ability to transform a scientific tool into decisionsupport software is a powerful ideal that will facilitatethe rapid transition of scientific research towards oper-ational relevance.

2 Decision support concepts

Before examining some of the decision support tech-niques in more detail, let us first examine just whatis meant by decision support and what exactly consti-

tutes a good decision. Decision support systems are acore subject area of the information systems disciplineand at the most fundamental level are concerned withrepresenting and processing knowledge for the purposeof improving decision making. An understanding ofdecision support must include that of decisions and de-cision making which in turn requires an understandingof knowledge and knowledge management. A decisionsupport system is a computer-based system that rep-resents and processes knowledge in ways that allowdecision making to be more productive, agile, innova-tive and/or reputable (Burstein and Holsapple 2008). Itis therefore no surprise that the field of data mining(the first module in our proposed decision supportchain) may be considered as the extraction of knowl-edge/information from data. Van Lohuizen identifies aprogression of six states of knowledge beginning withdata, through information, and culminating in a deci-sion as shown in Fig. 2 (Wali Van Lohuizen 1986).

A decision is regarded as a choice between a numberof courses of action, such as the strategies that may beemployed by the decision maker. In the field of deci-sion theory, the decision maker (or rational agent) willchoose the strategy with the greatest expected utility(Von-neumann and Morgenstern 1953)—utility beingthe measure of satisfaction derived from each outcome.A decision support tool mimics this method in that itconsiders all possible choices, assessing each accordingto some metric (the utility) and determining the best.A computer-based system is well suited to assessing alarge number of options in a systematic manner andpresenting this information to the decision maker. Infact, the tool need not return a single best solution buta number of alternatives for the decision maker to com-pare using the system calculated metrics. This highlightsthe nature of the proposed tool as being a decisionsupport tool and not necessarily a decision making tool.

Fig. 2 Knowledge as aprogression of states

164 Ocean Dynamics (2012) 62:161–175

In the military context in which our scenario lies, ablack box spitting out a single decision (instruction)to well-trained intelligent personnel is unlikely to betrusted and will eventually be ignored. Presenting al-ternative solutions along with their respective metrics(time permitting), especially those that could not bedetermined in the operators head, is a far more sensibleapproach.

The presentation of supporting evidence along witha decision may help to alleviate a common problemwith decision support systems. The problem is that ofthe cognitive bias of the operator, whereby he maybe expecting a particular solution and be unwillingto accept any alternative (Davis et al. 2005). Such abias can arise from many factors including habit inwhich familiar results are given more weight based onprevious outcomes. In the military scenarios consideredhere, the decision support tool may have to operate inthe face of ingrained doctrine and training. If a resultis presented which appears to contradict this, perhapsbecause complicated environmental factors were previ-ously unaccounted for, the operator may question theresult. As soon as a result is questioned, the trust inthe tool is compromised and it may soon be ignoredall together. This problem may be countered by supple-menting results with evidence in the form of a metriccalculation and possible alternative courses of actionwith lower metrics. In effect, the operator is broughtinto the decision process and is allowed to make up hisown mind with help from the tool.

There is then a balance which must be found be-tween the level of information presented by the tooland the level of understanding required by the opera-tor. As already discussed, a single answer determinedby the tool requiring no thought on the part of theoperator is not an ideal situation—nor is displaying alloutcomes with some metric that is not understood bythe operator. This suggests a two-pronged approach toimproving automated decision support tools:

1. The tools must be made more user-friendly.2. The user should be trained to understand the un-

derlying assumptions/metrics of the tool.

In effect, the goal is to optimise the fit betweenthe decision tool and its user by developing the tooland training the operator. Current decision sciencerecommends a number of ways to increase the usageand trustworthiness of these tools through the followingdesign features (Davis et al. 2005):

1. Allow personalisation—decision makers rate a toolas more usable when they can customize certainfeatures.

2. Use graphical interfaces—decision makers rategraphical tools as more trustworthy than text-basedmodules.

3. Maintain interactivity—decision makers prefer in-teractive tools to non-interactive tools.

4. Limit pre-processing of data—decision makers pre-fer decision support calculations (such as rankingalternatives) that can be easily linked to conceptsin the ‘hard data’. They should have access to all ofthe underlying data used by the tool.

We will leave the precise definition of our perfor-mance metric until the next section where we considerthe scenario in more detail. However, regardless of themetric, we may elaborate on what is a good decision—or at least what exactly the proposed decision supportsystem should achieve. To this end, two desirable out-comes are considered:

1. The performance metric is better than an otherwisemanual solution.

2. The solution is derived faster than a manualsolution.

Generally, the tool should decrease the effort re-quired to plan a mission whilst at the same time result inbetter operational performance. We might expect, forexample, a reduction in the level of resources required(platforms, fuel, staffing etc.) to fulfil a given mission.This leads towards two forms of optimum result: one inwhich the mission outcome is the same but required lessresources and another in which the mission outcome isitself improved.

The second point above is an important one in thatit considers the time taken to generate a decision. Mil-itary forces seek to win an engagement by making de-cisions quicker than the enemy using a concept knownas the OODA loop, standing for observe, orient, decideand act (developed by military strategist and USAFColonel John Boyd). Friendly forces seek to ‘get inside’the enemies OODA loop by making their decisionsfaster to gain the advantage (Rosenberg 2010). In fact,making a less optimum decision faster than the ene-mies optimum decisions can allow for friendly forcesto out manoeuvre the enemy and gain the upper hand.This particular way of thinking applies mostly to moredynamic scenarios and threats than will be consideredin the context of this study. However, since we seekto produce generic modules that may be applied toany scenario, the speed at which decisions are madeshould be considered. One possible scenario that is notfar removed from that considered here is the optimumdeployment and behaviour of a fleet of autonomousunderwater vehicles. If the decision aid can react to

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changes in the environment and platform positionsfaster than the threat submarine, then the system havethe advantage.

An important note should be made regarding theproblem of uncertainty within decision support sys-tems, in particular, the effect of environmental uncer-tainty on sonar performance—crucial for the scenariosconsidered here. For example, the translation of un-certainty in sound velocity profile (as determined byinterpolation from glider tracks) to uncertainty in signalexcess is examined here. However, this relates to asingle step within the decision support process, and fur-ther studies will examine the flow of uncertainty frominput data to eventual optimum decision. The problemof uncertainty in both input data and output decisionsmight require a search for a strategy that is most robust.In this case, an optimum solution is one that is leastsusceptible to the inevitable uncertainties within thedecision process. As an example, consider the problemof mine clearance. A mine hunter might plan a missionand, on completion, report that the area clearance isbetween 65% and 70%. This accurate result will allowthe planners of the operation to conduct further minehunting operations and allow for the eventual passageof follow-on traffic through the area. However, a clear-ance result of between 50% and 90%—although onaverage higher—reduces the confidence of the missionplanners and does not allow for accurate follow onplanning.

3 The scenario

The baseline scenario considered in this study is that ofthe deployment of a fixed network of multistatic sonarsensors attempting to detect the transit of a submarinethrough an area of interest. This scenario type is re-ferred to as a barrier and is common in anti-submarinewarfare (ASW) operations whereby a submarine issuspected to transit through a well-defined area. Con-stricted transit through a specified area may occur dueto geographical narrowing of the water space—a chokepoint, or perhaps at the exit of a port or harbourfacility. Such a scenario serves to decrease a numberof variables and results in a more manageable scenariowith which to begin the transition of MSTPA towardsdecision support software.

A barrier scenario allows for a well-defined scenarioarea through which a target must transit. This leadsto a better understanding of target behaviour/missionsince it must in general enter one side of the scenarioarea and exit at the opposite end. This is in contrast toan area search problem in which no such assumption

may be made as to the general motion of the targetwhich might even chose to remain stationary in orderto remain undetected for as long as possible.

A further assumption is that the receiving nodes arecovert—the submarine cannot detect them. This is animportant assumption and one that is often quoted asbeing an inherent advantage of multistatic systems—the inability of a target to determine where the re-ceivers are located will limit his ability to counter themand thus raise the performance of the network. Insuch a scenario, the target will of course be awareof the presence of the sound source, by counter de-tecting its transmission, but will have no way of de-termining any information about the number (if any)and position of the distributed network of multistaticreceivers.

Having settled upon a particular scenario (problem),a suitable performance metric must be defined. Weconsider the number of detections, track initiations orsuccessful classifications of a submarine for a givenmultistatic sensor configuration. Such a metric alsoleads to the corresponding measure of success for thethreat, this being the negative of the network successmetric. These metrics lead nicely into the domain ofgame theory as will be seen in Section 4.

4 Game theory

Game theory is an extension of decision theory in whichthe utility (measure of success) of a player’s strategy isa function of the strategy chosen by the other player.The sensor placement scenario is a two-player game inwhich one—the target—seeks to minimise the numberof times he is detected—whilst the other player—thenetwork planner—seeks to maximise the number ofdetections. Since the metrics of the two players arecompletely opposed, the game is non-cooperative. Insuch a game, each player must have at least an eye onminimising the payoff to the other player whilst stillseeking to maximise his own. The following discussionpresents initial analysis combining the use of the A*path planning algorithm within a game theoretic setting(Strode 2009).

The A* algorithm may be described as follows:Given a weighted directional graph G with a distin-guished start node s and a set of goal nodes τ , theoptimal path problem is to find a least-cost path from sto any member of τ , where the cost of the path may, ingeneral, be an arbitrary function of the weights assignedto the nodes and branches along that path (Dechter1985). The algorithm applies an additive evaluationfunction f (n) = g(n) + h(n), where g(n) is the cost of

166 Ocean Dynamics (2012) 62:161–175

the currently evaluated path from s to n and h(n) isa heuristic estimate of the cost of the path remainingbetween n and any member of τ .

Let us assume that both the multistatic networkplanner and submarine commander are aware of theexistence of a barrier consisting of a source and threereceivers—though not their actual location. This is anecessary assumption of equal knowledge and is es-sential to solving the game. We begin the analysis byconsidering a total of eight possible sensor geometriesusing an ad hoc design—the process may be appliedto any number of geometries within the constraints ofprocessing time (the current analysis is completed in7 min). Note that in some cases a receiver is placed atthe same position as the source resulting in a combinedmonostatic and multistatic network. The submarine isassumed to enter the scenario area, detect and localisethe source and thereafter choose a strategy—or path—with which to transit the barrier. The submarine usesthe A* path planning algorithm to determine his opti-mal track against each possible sensor geometry (G1–G8) using the technique described in Strode (2009).The resulting optimum tracks—those with the leastdetections—are shown in Fig. 3 for all eight potentialnetwork geometries.

Of course, the submarine commander cannot knowwhich geometry has been deployed, nor can the multi-static network planner know which track the submarinewill adopt. Consequently, both players must determinethe number of detections for each optimised trackagainst all network geometries. In other words, whathappens if the submarine chooses to optimise againstG3 but the planner chose G6? The game theoreticelement comes into play when we consider the follow-ing thought process—the target can optimise perfectlyagainst a particular geometry but the planner knowsthis and so will not lay it. In effect, we consider amore realistic level of threat intelligence in which thesubmarine does not have complete knowledge of thenetwork—and therefore cannot simply generate a sin-gle optimum track through it.

A game theoretic solution is only as complete asthe consideration of the various strategies that mightbe employed by each player. For instance, might weconsider a further random path or straight path whichthe target could employ as a strategy against the net-work? This is a common problem when setting up agame theoretic solution—not considering all possiblechoices. However, in this case, we are giving the targetthe ability to generate an optimum track in all cases. Weknow from Strode (2009) that the resulting A* pathsare optimum and always better than a straight (or anyother) path.

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Fig. 3 Optimised path for target transiting from top to bottomthrough barrier

Suppose we add an additional column to the decisionmatrix for a straight line transit through the network.Since the A* track is optimal, the payoff to the targetfor the straight track must be worse. In fact, even if thestraight track was optimal, the A* would have returnedthat same track. Therefore, all payoffs for the straightline tactic will be worse or the same as that of the A*

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equivalent. The straight line tactic is then dominatedby the A* tactic and can be removed from the matrixwithout affecting the outcome of the game. This is thecase for any other potential tactic that can be envisaged.Consequently, we need not consider any other targettactics. The only room for improvement is to considermore and more potential geometries—planner strate-gies. A further study will examine the robustness of themixed strategy to additional geometries—in effect, theoptimum spatial resolution of potential sensor positionsmust be determined. The combination of optimum pathgeneration with a game theoretic approach is a pow-erful one employing intelligent path planning whilsttaking into account the target’s incomplete knowledgeof the network geometry.

The number of target detections for all combina-tions of planner and target strategy are given in matrixformat in Table 1. The score within each element ofthe array gives the payoff to the planner—the payoffto the target is the negative of the displayed value. Inthis way, the planer seeks to maximise the number inthe array whilst, at the same time, the target seeks tominimise. This game may be described as two player,non-cooperative, zero sum. The matrix given in Table 1is said to be the normal form of the game in which thepayoff to the row player (the planner) is given. Thematrix is later referred to as aij with subscripts i and jrelating to rows (planner strategy) and columns (targetstrategy), respectively.

What information can be derived from Table 1?The aim is of course to determine the optimal sensorgeometry to deploy—in a game theoretic sense, thiswill be a compromise between the conflicting aims ofboth planner and target. A quick analysis reveals that,as expected, if the target optimises against the correctgeometry (values along the diagonal), the number ofdetections is reduced, usually to zero. Geometries 5and 6 would appear to be the best option from theplanner’s point of view since, even if the target correctlyoptimises against them, he is still detected. However,if a particular geometry was an obvious choice for the

planner, the target would simply optimise correctly andthe result of the game would be (at best) a singledetection. In keeping with the premise of MSTPA,a single detection is unlikely to allow the planner toreact against the threat and generate a suitable firecontrol solution—requiring the generation of a trackand subsequent classification as a threat. Game theorymay be used to solve the decision matrix in such a wayas to find the optimal solution for the planner—and byextension the target.

It can also be seen that, on occasion, a target opti-mising against the wrong geometry still remains unde-tected. For example, had the target chosen to optimiseagainst G4 but the network was in fact G2 he is stillundetected. This analysis might suggest that geome-try G2 should not be adopted by the planner sincethere are two possible outcomes resulting in zero targetdetections.

Inspection of Table 1 reveals that no strategies foreither planner or target are dominated—that is alwaysequal or worse than any other. The solution of thisgame is expected to be a mix of strategies for bothplanner and target. Since if a single geometry was theplanners best strategy, the target could counter it andguarantee a worst case of a single detection. Manygames of this type result in a mixed solution by whicheach strategy is given a probability that it should beemployed. In this way, the target cannot know exactlywhich geometry will be deployed and must in turnimplement his own mixture of strategies. This is aninteresting result since it hints towards the value of thecovert receivers. We know that if the target could de-termine the location of the receivers, he could optimiseagainst the geometry and greatly reduce the number ofdetections. The game theoretic solution acknowledgesthis fact and therefore returns a mixture of strategiesfor the planner in order to maintain an ‘element ofsurprise’ over the target.

The result of the game theoretic solution, assuming itis greater than 1, provides a convenient measure of thevalue of covertness. A normal form matrix, as given in

Table 1 Matrix game for abarrier scenario (showingpayoff to planner)

Planner strategy Target strategy (geometry to optimise against)

(geometry to lay) G1 G2 G3 G4 G5 G6 G7 G8

G1 0 14 0 10 16 14 16 9G2 9 0 5 0 13 9 13 9G3 11 21 0 15 15 16 15 9G4 15 11 8 0 13 14 13 11G5 19 29 22 42 1 20 9 11G6 10 12 7 7 10 1 10 1G7 23 20 14 19 10 16 0 0G8 20 17 17 17 14 14 9 0

168 Ocean Dynamics (2012) 62:161–175

Table 1, may be solved using linear programming tech-niques (Owen 1995), whereby a mixed strategy over theset of pure strategies can be found that optimises theexpected payoff to both players. A mixed strategy isa vector defining the probability with which each purestrategy should be played. If the planner uses the mixedstrategy xi = (x1, ..., xm), he can assure himself of anexpectation at least equal to λ, where λ is any numbersuch that

∑aijxi ≥ λ for j = 1, . . . , n where aij is the

matrix given in Table 1, represented mathematicallybelow.

ai, j =

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a2,1 a2,2 · · · a2, j...

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...

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⎟⎟⎟⎠

Thus, the problem of obtaining an optimal strategyfor the planner reduces to the linear program

Maximise λ subject to

−m∑

i=1

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m∑

i=1

xi = 1

xi ≥ 0 i = 1, . . . , m

Similarly, the solution for the target reduces to thelinear program

Minimise μ subject to

−n∑

j=1

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n∑

j=1

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yi ≥ 0 j = 1, . . . , n

Solving the linear program using the Matlab toolboxresults in the following mixed strategy for the planner:

x = (0.1, 0.0, 0.0, 0.7, 0.2, 0.0, 0.0, 0.0)

whilst the target will employ the mixed strategy

y = (0.0, 0.0, 0.2, 0.1, 0.4, 0.0, 0.0, 0.3)

The value of the game derived from the above so-lution is 10.6, this being the average number of targetdetections made by the network. Note that, had the tar-get known the position of the receivers, he would have

been detected no more than once. This then measuresthe value of the covertness of the network.

A question arises, however, as to the meaning of thisaverage result and indeed the probability distributionover geometries, for a network that will be laid onlyonce. Whilst a number of threat submarines may indeedattempt to penetrate the barrier over time—applyingan appropriate strategy mix—the network itself is de-ployed only once and is thereafter fixed. Consequently,a strategy mix for the planner might seem rathermeaningless—except that it suggests he should lay oneof several geometries—thereby depriving the threat ofcomplete knowledge. The decision support tool can ofcourse roll a dice to determine which of the geometriesthe planner should lay according to the mixed strategysolution. The important point is that the target cannotknow which geometry was laid, even if he used thesame decision support tool whilst pretending to be theplanner. This concept is known as a ‘chance device’(Wagner et al. 1999) and ensures that the opponentcannot predict the outcome.

Williams (1954) states:

Consider a non-repeatable game which isterribly important to you, and in which youropponent has excellent human intelligence ofall kinds. Also assume that it will be murder-ous if your opponent knows which strategyyou will adopt. Your only hope is to select astrategy by a chance device which the enemiesintelligence cannot master—he may be luckyof course and anticipate your choice anywaybut you have to accept some risk. Game theorysimply tells you the characteristics your chancedevice should have.

It is possible that the game theoretic approach beapplied to the more dynamic scenario in which thebehaviour of mobile sensors is considered. In this case,a normal form matrix could be envisaged in whichsensor strategies are no longer a fixed position buta complete description of a particular behaviour. Forexample, a behaviour may be a simple close rangeapproach or the maximise signal-to-noise ratio (SNR)behaviour described in LePage (2010). Similarly, targetbehaviours could range from simple random coursealterations (assuming he has not detected the mobilesensor) or maximise range (assuming he has detectedthe sensor). A normal form payoff matrix, containingall combinations of sensor and target behaviour, couldbe determined from simulations and solved using thetechnique described above.

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5 Optimisation

Work has been conducted on the addition of op-timisation routines to the MSTPA tool. In particu-lar, the use of genetic algorithms (GA) to optimisestatic sensor placement and dynamic platform way-points has previously been reported in Wathelet et al.(2008a).

The approach taken in MSTPA to determine theoptimum placement of selected ASW assets against athreat submarine is to maximise a number of mea-sures of effectiveness (MOE). Current MOEs includethe detection area coverage and the probability that asubmarine will be detected or tracked before crossinga barrier. Optimisation algorithms are used in MSTPAto determine the best placement of the ASW assets bymaximising these MOEs.

MSTPAs optimiser uses a set of heuristic optimisa-tion algorithms. These are used to maximise the MOEsthat describe the ASW mission of interest. The missionscurrently in MSTPA include static area surveillance,barrier operation and force protection. The MOEs thatrelate to these missions are, respectively, area cover-

age, barrier coverage and area coverage around a highvalue unit.

MSTPA maximises the MOEs, namely the detectionarea coverage and the probability that a submarine willbe detected or tracked before crossing a barrier, usinga set of optimisation algorithms from the JavaEvA(a Java implementation of Evolutionary Algorithms)open source library (Streichert and Ulmer 2005). Al-though many algorithms are included as part of thislibrary, such as simulated annealing, hill climbers andMonte Carlo search, the main technique used and re-ported in Wathelet et al. (2008a) is a GA.

The basic concept of a genetic algorithm is to looselymodel the principle of evolution through natural selec-tion. The algorithm represents a typical solution to theproblem as a vector of source and receiver positions.A population of these individuals is created, and opera-tors such as mutation and recombination are applied onthe population of individuals to arrive at an individualthat maximises the fitness function. For example, in thearea coverage scenario, the GA will determine the xand y position of each asset that maximises the areacoverage function.

Fig. 4 Sequential outputfrom MSTPA geneticalgorithm

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The example shown in Fig. 4 shows intermediatesensor positions generated by the genetic algorithm(labelled 1–3) on its way towards finding the optimalsolution (4). The performance metric in this case is thearea of the scenario with a signal excess value greaterthan 0 (shaded blue). The scenario includes a mono-static sensor (Tx+Rx) with an additional multistaticreceiver (Rx) which may be placed anywhere in thescenario area. The environment is characterised by aniso-velocity sound speed profile over a continental shelfbathymetry shown in the figure.

The GA solution shown in Fig. 4 generated 1,000candidate geometries on its way towards the optimalsolution. The area coverage metric for each geometryrequired 75 × 75 signal excess calculations. The solu-tion therefore required over 5.5 million signal excesscalculations, each taking into account range-dependentbathymetry. The iso-velocity sound speed assumption,combined with the fast closed-form algorithms de-scribed in Harrison (2002), allowed for the solution tobe obtained in only 7.5 min. Signal excess is determinedto be the difference between the actual SNR and thatrequired for the sonar system to register a detection.The acoustic propagation and reverberation is mod-elled using a mode stripping approach with Lambert’slaw scattering (Harrison 2002).

When modelling individual targets transitingthrough a network, there are a number of options asto what their precise behaviour may be. The simplestapproach is to model a large number of targetson different (but unchanging) headings. For each

geometry, the percentage that were detected maybe determined and used as a cost measure withinan optimisation routine. When considering a barrierscenario in which targets transit through a networkfrom ‘top’ to ‘bottom’, perhaps on headings between160◦ and 200◦, it was often the case that a largeproportion of targets would have been tracked atsome point during their transit. This can give a falseimpression of the effectiveness of the network due tothe assumption that all targets are completely unawareof its presence and continue ‘blindly’ on. This type ofthreat behaviour is unlikely considering the ability tocounter detect the source.

There is then a scale of threat intelligence that maybe applied to the problem of optimising network per-formance. The simplest and least intelligent threat isthe straight running one already discussed. We mightthen imagine targets that are aware of the transmissionof the source and attempt to evade in some reactiveway. Lastly, as a worst-case (most intelligent) target,we might consider one with complete knowledge of thenetwork and an ability to generate an optimum (e.g.least detectable) path through it. A network that isoptimised against such a worst-case target is likely tobe the most robust.

The worst-case, most intelligent threat has previ-ously been modelled using the A* algorithm with whichit determines an optimal path through the networkaccording to a number of metrics (Wathelet et al. 2008a;Strode 2009). The combination of the A* algorithmwith the game theoretic approach detailed in Section 4

Fig. 5 Typical glider trackshowing temperaturemeasurements

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Fig. 6 3-D sound speedvolume from super-ensembleoutput with bathymetry

of this paper considers the fact that the target cannotknow the location of covert receivers and must makea ‘best guess’ as to how to penetrate the barrier. Thisthen relates to an intermediate level of intelligencebetween simple straight running and that of completeknowledge.

6 Accounting for environmental uncertainty

Recent advances within the core acoustic element ofthe MSTPA model account for fully 3-D temperatureand salinity data. The advanced acoustic module isan extension of the original mode theory framework

developed for the iso-velocity case and maintains asignificant speed advantage over other tools. The abilityto generate a fast acoustic performance map over ascenario area which includes realistic bathymetry andfully range-dependent temperature and salinity (and byextension sound speed) allows for more accurate calcu-lations of operational performance metrics. However,the ability of the model to account for environmen-tal information at ever-increasing resolutions leads toquestions of the ability of surface platforms to ade-quately measure the environment.

An ASW surface platform will typically deploy anexpendable bathythermograph (XBT) probe in orderto determine the variation of water temperature with

Fig. 7 Ten sound speed(metres per second) profilesamples at 25 locationsuniformly distributed overscenario area (north to top)(sound speed profiles showtop 200 m of water columnonly)

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depth at a particular location within the scenario area.The temperature profile is converted to a sound speedprofile and is assumed to apply to the whole scenarioarea which could be well in excess of 100 km2. Acousticcalculations are performed to determine the perfor-mance of a given sonar sensor against a target of aparticular target strength—in which the propagation ofsound is strongly affected by the gradient of the mea-sured sound speed profile. It is common knowledge,amongst oceanographers and acousticians alike, thatthe undersea environment is complex and dynamic andthat a sound speed profile measured at a particularpoint cannot be applied to the scenario area as a whole.

A tool such as MSTPA can account for as manydiscrete sound speed profiles as can be measured overa scenario area, perhaps by a number of distributedXBTs. Additionally, the tool can infer such profiles

from 3-D measurements of temperature and salinityusing the Chen–Millero formula (Chen and Millero1977). Of course, no measurement device can coveran entire scenario area in both position and depthto obtain a true picture of the complex underwaterenvironment. To address this shortfall, NURC is cur-rently employing underwater gliders to make persis-tent measurements of temperature and salinity overlarge areas at various depths due to the continuousdiving and surfacing movement method they employ.However, even these data do not cover all points inposition and depth within a scenario area—a typicalglider measurement profile is shown in Fig. 5, colourcoded according to the measured temperature value.Intelligent extrapolation of the glider measurements isrequired to provide oceanographic information at allpoints within the water volume. However, any such

Fig. 8 Signal excess(decibels) samples

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extrapolation process introduces uncertainty as therange from measured values increases.

Initial results are presented here to investigate theimpact of uncertainty in sound speed—due to the nec-essary extrapolation of measured values of temperatureand salinity—on the eventual operational performancemetric. The performance metric considered here isthat of the predicted signal excess in decibels for asubmarine of constant 10-dB target strength operatingat a depth of 20 m. Such an acoustic calculation isstrongly dependent on variations in sound speed in bothrange and depth as sound is propagated from the sonarsensor.

The sound speed profiles used in this study werededuced from 3DSE temperature and salinity predic-tions. The 3DSE method (Lenartz et al. 2010) combinesseveral ocean model predictions using optimal weightscomputed during a recent past learning period whenobservations are available. In the present implemen-tation, three high-resolution ( 1-km) models are used:Regional Ocean Modelling System run at NURC, 3-D Model for Applications at Regional Scale providedby PREVIMER (www.previmer.fr) and Navy CoastalOcean Model run at the Naval Research Laboratory.The 3DSE forecast is associated with an uncertainty es-

timate based on the assimilation of observations duringthe learning period.

The approach to be followed here is that of per-turbing the input temperature data according to theestimated uncertainty at each point. Each tempera-ture perturbation is fed into MSTPA, along with themean salinity profile, in order to determine the full3-D sound speed profile. This results in a number ofpossible signal excess maps from which the mean andstandard deviation may be extracted. A convenient sin-gle output—capturing both the mean and uncertaintyof all perturbations—is the probability of detection.This calculation considers all perturbed signal excessvalues in a cell and determines the fraction with positivevalues. A positive value of signal excess, by definition,will result in a detection of the target submarine.

Figure 6 shows an example of the 3-D sound speedvolume resulting from the super-ensemble temperatureand salinity output. The data shown in Fig. 6 maybe perturbed, according to the estimated uncertainty,to generate a number of probable outcomes. For thispreliminary analysis, the data were sampled 100 timesover 2 standard deviations—each point within the full3-D sound speed volume is perturbed assuming a nor-mal distribution. Figure 7 shows the first 250 m of ten

Fig. 9 Signal excess statistics

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(c) Probability of detection

(b) Standard deviation of signal excess (dB)showing bathymetry contours

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perturbed sound speed profiles at 25 locations uni-formly distributed around the scenario area. Note thatin some locations the bathymetry is less than 250 mresulting in shortened profiles.

All 100 sound speed profiles were then used togenerate 100 signal excess coverage maps, of whichsix are shown in Fig. 8. In each case, a generic LFAStype monostatic sonar was placed at 9.47◦ longitude,43.5◦ latitude at a depth of 20m. The resulting standarddeviation in signal excess and probability of detectionare shown in Fig. 9.

Due to the complicated nature of underwater soundpropagation, a small change in sound speed profilegradient in one location may result in a large changein signal excess at another location. It can be seen inFig. 8 that the region to the east of the sensor positionremains fairly constant—note that the samples shownin the figure were those with greatest deviation fromthe mean. Also the region at the extreme west ofthe scenario appears fairly constant—corresponding todeep water and more stable sound speed profile. Aninitial inspection shows that the uncertainty in signalexcess appears to increase with sea bed slope. This maybe seen in Fig. 9b in which standard deviation is plottedtogether with bathymetry contours.

7 Discussion and conclusion

This study has detailed a number of generic decisionsupport techniques that may be applied to the problemof multistatic sonar network design. It is envisaged thatsuch techniques will be wrapped around the existingMSTPA to provide a decision support functionality.The acoustic tool becomes the central metric calculatorwithin a greater scheme of decision support concepts.Such a scheme will close the loop between rapid en-vironmental assessment and the eventual operationalperformance of deployed assets. Such a tool may beused on board a platform in order to assist the tacticaldecisions of the operator. The tool therefore transitionsfrom a planning aid which may be used prior to thedeployment of assets (employing Monte Carlo simu-lations of potential scenarios), to a more operationaltool on board the assets themselves providing real-timedecision support.

The generic nature of the decision support tech-niques will allow for integration into different scenar-ios. This is the aim of the Environmental Knowledgeand Operational Effectiveness program in which anumber of scenarios, the performance of each being afunction of environmental measurements, will be con-

sidered for inclusion in decision support tools. Theseinclude:

– Multistatic network deployment (considered here)– Optimal deployment of gliders for environmental

sampling– Planning naval interdiction against piracy

The transition of an otherwise scientific tool, usedas a central metric calculator, into a more operationaldecision support system is a powerful ideal. This will fa-cilitate the timely transition of scientific research toolsinto more operational scenarios.

The initial investigation of the effect of uncertaintywithin oceanographic predictions will form the basisfor more detailed studies conducted during 2011. Thisstudy has demonstrated the resulting uncertainty inacoustic coverage as a function of uncertainty in ex-trapolated temperature and salinity predictions. Animportant result will be the sensitivity of the eventualoptimum sensor locations to this uncertainty.

Open Access This article is distributed under the terms of theCreative Commons Attribution Noncommercial License whichpermits any noncommercial use, distribution, and reproductionin any medium, provided the original author(s) and source arecredited.

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