a multi-objective genetic algorithm method for active...

A Multi-Objective Genetic Algorithm Method for Active Sonar Clutter Reduction

Mark A. Gammon DRDC – Atlantic Research Centre

Defence Research and Development Canada Scientific Report DRDC-RDDC-2015-R197 September 2015

© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2015

© Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 2015

DRDC-RDDC-2015-R197 i

Abstract

Target-like echoes from the use of active sonar, commonly known as 'clutter', is a particularly difficult problem when trying to separate real from false contacts. A method for reducing the amount of clutter in tracking underwater targets and providing a likely target area is accomplished by using an iterative Multi-Objective Genetic Algorithm (MOGA). The MOGA developed requires the automatic selection of a Pareto optimal result of the likely target position. The optimization minimizes the position of the genetic population with the last given contact positions, as one objective, while using an average position based on a history of optimal solutions as a second objective. In order to concentrate on a particular area, the algorithm is applied iteratively, taking into account the size of the area being examined and other constraints. In each subsequent iteration, a smaller area is used to limit the amount of clutter being examined. After a nominal number of iterations, the area of the probable target location and the optimal target result from the algorithm are examined to determine whether the MOGA has determined a good position estimate. A simulation of the performance of the algorithm in a clutter environment is used to investigate the robustness of this particular method. The application of this approach may be of significant benefit in future configurations of acoustic processing systems developed from the DRDC Atlantic Research Centre's System Test Bed (STB).

Significance to Defence and Security

The methodology may be of significant use in the development of multistatic systems such as future configurations of acoustic processing systems developed from the DRDC Atlantic Research Centre's System Test Bed (STB).

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Résumé

Les échos semblables à une cible causés par l'utilisation de sonars actifs et communément appelés « fouillis » constituent un problème particulièrement difficile lorsqu’on tente de séparer les vrais des faux contacts. Il existe une méthode permettant de réduire le volume du fouillis lors de la poursuite de cibles sous-marines et offrant une zone-cible probable au moyen d’un algorithme génétique multi-objectif (MOGA) itératif. Le MOGA qu’on a mis au point requiert la sélection automatique d'un optimum de Pareto de la position probable de la cible. L'optimisation minimise la position de la population génétique, ainsi que les dernières positions données, comme premier objectif, tout en utilisant une position moyenne basée sur un historique de solutions optimales, comme deuxième objectif. Afin de se concentrer sur un domaine particulier, on applique l'algorithme de manière itérative tout en tenant compte de la taille de la zone examinée et d'autres contraintes. Dans chaque itération ultérieure, une zone plus petite est utilisée pour limiter le volume de fouillis examiné. Après un nombre nominal d'itérations, on examine la zone où se trouve l'emplacement probable de la cible et l’optimum de la cible calculé à partir de l'algorithme pour déterminer si le MOGA a permis d’obtenir une bonne estimation de la position. On utilisera une simulation de la performance de l'algorithme dans un environnement de fouillis pour étudier la robustesse de cette méthode particulière. L'application de cette approche peut s’avérer très avantageuse pour les configurations futures des systèmes de traitement acoustique mis au point au banc d’essai de système (STB) du Centre de recherches de RDDC Atlantique.

Importance pour la défense et la sécurité

L’utilisation de cette méthodologie peut s’avérer importante dans l’élaboration de systèmes multistatiques tels que les configurations futures des systèmes de traitement acoustique mis au point au banc d’essai de système du Centre de recherches de RDDC Atlantique.

DRDC-RDDC-2015-R197 iii

Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Significance to Defence and Security . . . . . . . . . . . . . . . . . . . . . . i Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Importance pour la défense et la sécurité . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . v 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Multi-Objective Genetic Algorithm (MOGA) . . . . . . . . . . . . . . . . 3 2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 General Multi-Objective Problem Definition . . . . . . . . . . . . . . 6 2.4 Genetic Algorithm Approach . . . . . . . . . . . . . . . . . . . . 8

2.4.1 Sequential Objective Genetic Algorithm (SOGA) . . . . . . . . . . 9 2.4.2 Area Search Reduction Algorithm . . . . . . . . . . . . . . . . 10

3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1 One Ship Scenario . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Two Ship Scenario . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Three Ship Scenario . . . . . . . . . . . . . . . . . . . . . . . 25

4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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List of Figures

Figure 1: A Concept for Multistatic Sonar Employment. . . . . . . . . . . . . . 4

Figure 2: Example Area used for MATLAB Simulation with Own-ship (Green), Target (Black) and Clutter (Red). . . . . . . . . . . . . . . . . . . . . . 5

Figure 3: Example of a Two Objective Non-Dominated (Pareto) Solution with a Pareto Front. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 4: Sequential Objective Genetic Algorithm. . . . . . . . . . . . . . . . 10

Figure 5: One Ship (Green) versus One Target (Black) within Field of Clutter (Red). . . 13

Figure 6: Optimal Solutions at Each Time Step (Cyan) after 1st Iteration and Final Solution (Red Hexagon). . . . . . . . . . . . . . . . . . . . . . . 14

Figure 7: Optimal Solutions at Each Time Step (Cyan) after 2nd Iteration and Final Solution (Red Hexagon). . . . . . . . . . . . . . . . . . . . . . . 15

Figure 8: Optimal Solutions at Each Time Step (Cyan) after 3rd Iteration and Final Solution (Red Hexagon). . . . . . . . . . . . . . . . . . . . . . . 16

Figure 9: Optimal Solutions at Each Time Step (Cyan) after 4th Iteration and Final Solution (Red Hexagon). . . . . . . . . . . . . . . . . . . . . . . 17

Figure 10: Range of Final Optimal Solution to Target for One Ship versus One Target for 100 Runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Figure 11: Two Ship (in Green) Scenario within a Field of Clutter. . . . . . . . . . . 19

Figure 12: Two Ship Scenario—1st Iteration. . . . . . . . . . . . . . . . . . . 20

Figure 13: Two Ship Scenario—2nd Iteration. . . . . . . . . . . . . . . . . . . 21

Figure 14: Two Ship Scenario—3rd Iteration. . . . . . . . . . . . . . . . . . . 22

Figure 15: Two Ship Scenario—4th Iteration. . . . . . . . . . . . . . . . . . . 23

Figure 16: Absolute Range from Optimal Average Solution for Two Ships versus One Target for 100 Runs. . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 17: Absolute Range from Last Optimal Solution for Two Ship Scenario for 100 Runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 18: Three Ship Scenario—Start. . . . . . . . . . . . . . . . . . . . . . 26

Figure 19: Three Ship Scenario—1st Iteration. . . . . . . . . . . . . . . . . . . 27

Figure 20: Three Ship Scenario—2nd Iteration. . . . . . . . . . . . . . . . . . 28

Figure 21: Three Ship Scenario—3rd Iteration. . . . . . . . . . . . . . . . . . 29

Figure 22: Three Ship Scenario—4th Iteration. . . . . . . . . . . . . . . . . . . 30

Figure 23: Absolute Range from Optimal Solution for Three Ship Scenario for 100 Runs. 31

DRDC-RDDC-2015-R197 v

Acknowledgements

The author would like to personally thank Mr. William Campbell, Defence Scientist (ret.), for his support, assistance and encouragement during this study.

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DRDC-RDDC-2015-R197 1

1 Introduction

1.1 Background

The use of legacy passive and active sonar systems to detect submarines and conduct Anti-Submarine Warfare (ASW) missions is being transformed, by some navies at least, by the use of multiple platforms equipped with, for example, low frequency active sonar systems [1]. This has also meant that the requirements for generation of a recognized maritime picture below the surface become more complex. One of the problems when using multiple sonar systems, both active and passive, on multiple platforms has been the integration and fusion of disparate types of data. This problem was investigated using a Genetic Algorithm (GA) in which both active and passive data were used to generate estimated contact positions for localization of the target [2][3].

The focus of this study is to develop an algorithm that can localize a target given an environment cluttered with false contacts. Clutter, the common terminology for false target-like echoes, is generated by ensonifying the underwater environment and receiving numerous returns, as one example, from irregularities in the sea bottom. The physical causes of clutter are due to the fact that unlike passive sonar in which detections are made against a background of ambient noise, contacts are made against a background of reverberation [4]. The difficulty in perceiving the actual contact from numerous false contacts for the case of multistatic active sonar has been investigated by various means such as fusion algorithms [5] and examination of the occurrence of 'specular' detections [6]. The current investigation examines the potential for reducing the amount of false contacts that have to be considered by other conventional means, such as the use of Kalman filters and data association methods for track generation [7].

Evolutionary Algorithms (EA) and Artificial Neural Networks (ANN or NN) offer effective methods for conducting optimization and for data analysis. EA techniques may be separated into GAs, Evolution Strategies (ESs) and Evolutionary Programming (EP). In this study, the term GA is predominantly used to reflect the encoding and characteristics of the algorithm, unless reference is made to a specific technique.

Using a GA for this type of tracking problem has been undertaken by several other researchers. After working on the active/passive fusion problem at DRDC Atlantic, a GA was used for a passive sonar Target Motion Analysis (TMA) problem [8]. Other researchers have used a GA to solve an n-dimensional assignment problem for data association in multiple target tracking problems [9][10].

1.2 Aim

The aim of this report was to document the Multi-Objective GA (MOGA) developed and provide simulation results to investigate the possibility of further development and testing using realistic data and under realistic operational conditions. However, at this stage no further work in this area is envisaged and no further development is planned.

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1.3 Motivation

The motivation of this work is to investigate the use of the MOGA developed previously from hull form optimisation to determine its suitability for tracking type problems and as a filter for the sonar operator’s aid in reduction of clutter. Clutter is predominant in multistatic active sonar in particular and in many cases passive contacts are not easily resolved as well. The current use of Multi-hypothesis Kalman filters works well when the environment is amiable and when multiple tracks can be resolved into a probabilistic target using m-of-n types of filters that can initiate and start tracks as well as drop tracks that are no longer sustained. The use of a MOGA may be able to provide another means or toll for the operator to resolve tracks in highly clutter and difficult environments. There may also be advantages in using a MOGA, for example, over a simple averaging technique. Constraints can easily be built into a MOGA. These could be factors such as platform speeds for both sensors and targets, and possibly restrictions on target locations or probable areas for defining the search. The flexibility of a MOGA could easily allow such external search factors to be incorporated.

1.4 Outline

The outline of this report is as follows; the basics of a genetic algorithm and the multiple-objective algorithm used in this report are presented in Section 2; Section 3 looks at the application of the algorithm to three test cases, a single ship versus one target, two ships versus one target, and three ships versus one target. Each ship uses active sonar data with the MOGA for tracking purposes. Section 4 presents a summary and conclusions.


2 Multi-Objective Genetic Algorithm (MOGA)

2.1 Background

Multi-objective genetic algorithms have been used for various types of optimization problems including the fusion of active and passive sonar. The ability of GAs to provide robust solutions for global optimization is well documented and GAs have been used for numerous types of engineering optimization problems [11]. Genetic algorithms have been used in different ways for data-fusion problems including the optimization of parameters for tracking algorithms and optimization of the bandwidth for selection of a priori observations. However, in general, algorithms for tracking algorithms have focused more on using Kalman filters and associated methods for conducting Target Motion Analysis (TMA) [12].

Definitions for passive and active sensors are reiterated here. The passive sensor records information already present in its surroundings or environment while the active sensor initiates an action whose response results in information recorded by the sensor. In other words, the active sensor introduces a disturbance, energy or new factor into the environment as a stimulus and checks the response, while the passive sensor measures the environment without changing it. For the case of multistatic active sonar, one sensor sends out an active sonar ping, while another (or multiple) sonars passively receive and process the sonar returns for subsequent target detection and tracking.

Figure 1 shows a concept for a possible deployment of a multistatic sonar system comprised of ships, aircraft, and a helicopter, while a blue force submarine could also be employed as a receiver (not shown in the diagram). The concept for operation of multistatic sonars can improve the overall probability of detection of a target submarine for ASW missions. As shown in the diagram, an active source, which could be the helicopter equipped with, for example, the Helicopter Long-Range Active Sonar (HELRAS), or using a Vertical Projector (VP) low frequency sonar which is towed behind a maritime coastal defence vessel, can provide the transmitter sources. The latter was the case in the Networked Underwater Warfare (NUW) technology demonstration project [13]. Other sources depicted include active sonobuoys such as the AN/SQS 565 active source sonobuoy.

A monostatic sonar is the case when only one ship or sensor is both transmitting and receiving acoustic signals. Bistatic sonar is the situation in which one active sonar provides an active transmission or "ping" while passive sonar receives the target echoes associated with the transmission. For the multistatic sonar case, more than one passive sonar receives the pings reflected from the target, and indeed, more than one active sonar source could be actively transmitting. This leads to a great deal of information from the numerous returns on multiple sensors, requiring data fusion techniques to sort out the picture. It should be noted that without inter-platform communications, sonar transmitters would fill the acoustic environment with noise, thus, overwhelming the sensors. It is therefore an essential requirement that the activity of the platforms be coordinated in real-time.


Figure 1: A Concept for Multistatic Sonar Employment.

Along with reflections from the target, as mentioned there will be numerous contacts generated which are termed false contacts, and/or clutter. In some cases, the clutter can be acoustically filtered by several means to reduce the number of actual false contacts; hence for the purpose of this discussion, clutter is unfiltered contacts; while contacts refer to a cluster of threshold crossings associated with detections which are defined as a processed signal excess. A track is a list of contacts that have been associated by a tracking filter [14]. The term tracklets is also used to refer to a discontinuous series of small tracks [15].

2.2 Problem Description

For the purpose of this study, a square search area is defined with 40 km sides and the origin in the centre, as shown in Figure 2. Two platforms, one the sensor ship and one target, are randomly placed in the area. The own-ship sensor is marked by a green circle. The target is marked by a black square. In this area, red asterisks indicate randomly generated clutter contacts.

A simulated event serial is defined with duration of three hours and a time resolution of initially three minute intervals which was reduced to one minute intervals. At each interval, a recorded position is made that corresponds to either clutter contacts (or false contacts), or for a certain percentage of the time, a contact corresponding to the actual target position. For the simulation,


the target position is assumed to be revealed approximately one third or 30% of the time, hence for example, for 60 time steps of three minute intervals, 20 of the intervals positions correspond to the actual target location.

Figure 2: Example Area used for MATLAB Simulation with Own-ship (Green),

Target (Black) and Clutter (Red).

The problem can be stated as follows;

Problem: Given a series of target-like echoes, determine an estimated contact area close to the actual target if the false contacts are assumed as randomly generated points, and assuming the target displays a definite non-random position that evolves over time.

This problem statement assumes a number of qualities distinguishing the false contacts from the actual target positions, which is that the target positions will be a distinct number of contacts derived from a definitive track, assumed for both target and sonar sensor own-ship position to be traveling in straight lines. The clutter, on the other hand, is assumed to be randomly generated anomalies reflected from bottom irregularities and for other reasons, which appear for the sake of this study as randomly generated points in the area. In actual fact, clutter may not be randomly generated, but closely associated with the bottom topography, or generated from other false contacts, such as ship wrecks [4]. Other simulations have adopted different approaches.


2.3 General Multi-Objective Problem Definition

In order to use a MOGA for this problem, the problem must be formulated into a minimization problem. The problem is formulated as a requirement to determine a vector of decision variables as follows [16];

* * * * *1 2 3, , ,....

T

nx x x x x*x *x x

(1)

where , 1,2,...jx j n are the decision variables. For this study, the decision variables include the X and Y position of the possible target solution i.e.,

1 2;x X x Y (2)

where (X,Y) represents the solution co-ordinates at each time interval of interest.

If constraints are added to the problem, then they should take the form in which the solution must satisfy m inequality constraints,

( ) 0, 1,...i ig x i m (3)

and p equality constraints of the form,

( ) 0, 1,...i ih x i p (4)

where gi and hi are functions of xi and p should be less than the number of decision variables n in order to avoid being over-constrained [16]. The only constraints at this time are the limits of the solution domain, which can be captured by the size of the chromosome. A chromosome is a solution to the problem at hand; it is usually a binary bit string and represents an individual in a population of solutions [17]. The solutions must optimize the vector function,

1 2, ,...T

kf f x f x f xT

f f f f (5)

where k = number of objectives.

In shortened form,

*

xf opt f x

*f f , : kff 0, 0nx g x h x 0n hn h0n (6)


The multi-objective definition of optimality, known as Pareto optimality, is defined as a point in n-dimensional space represented by

*x * (7)

such that for every x , and 1,2,...I k either *

i I i if x f x*

f or there is at least

one i I such that *

i if x f x*

f (for minimization problems) or *

i if x f x*

f (for

maximization problems).

In other words, in multiple objective optimization, there is not necessarily a single solution that is best, as in the case of single optimization, due to the fact that a minimization in one objective might result in an increase in other objectives. However, there is usually a set of solutions which are non-dominated or Pareto optimal, in which no improvement in any objective function is possible without sacrificing at least one of the other objectives [11]. Definitions for Pareto optimality, dominated and non-dominated solutions can be found in literature. A cursory definition is that a dominated solution is one in which another better solution can be found in at least one objective without sacrificing the performance in a other objectives; whereas a non-dominated solution is one where no improvements can be found in the objective without a reduction in performance in at least one of the other objectives. This creates a solution space delineating a Pareto front or frontier, as depicted in Figure 3 for two objectives. The Pareto front or Pareto set represents the set of parameterizations that are all Pareto optimal, also known as Pareto efficient.

Figure 3: Example of a Two Objective Non-Dominated (Pareto) Solution with a Pareto Front.

As shown in Figure 3 above, an improvement in Objective 2 degrades Objective 1, and vice versa. In this study, the term near-optimal is used to describe a choice that achieves some compromise in the performance objectives while satisfying any constraints for the problem. This compromise would tend towards to centre of the front and away from the endpoints. For example,

00.5

11.5

22.5

33.5

44.5

0 1 2 3 4 5

Objective 2

Objective 1

Pareto Front


a value of (2,2) might be considered a good compromise in Figure 3. Since it is desired to use a single optimal solution instead of searching the entire Pareto front, the algorithm should be able to allow selection of a Pareto Optimal value from the Pareto front, or a limited number of such values.

In this study, the number of objective values, k, is limited to 2. The objective functions and represent the distance to the contact position and the distance to the average of the last

known optimal position, respectively. The objective functions for this problem reflect the need to direct the genetic population towards the latest known contact position; hence the first objective is simply the range between the genetic population member's position (xsolution, ysolution) and that of the contact (xcontact,ycontact), i.e.;

(8)

However, this objective function alone does not result in a very good solution. As the simulation uses the MOGA at each timestep, a running average can be kept of the optimal solutions generated from each of the previous timesteps. Hence a second objective is used that compares the range from each of the genetic member's solution (xsolution,ysolution) to that of the running average (xaverage,yaverage) of the Pareto Optimal solutions generated by the MOGA each timestep;

(9)

where (xaverage,yaverage) is the average position based on a running average of the optimally generated positions. Using the second objective, a better solution is generated for the target position.

2.4 Genetic Algorithm Approach

Multi-objective genetic algorithms or evolutionary algorithms have in general taken three paths [18]. The first is the aggregate methodology that necessitates the estimation of weighting factors and introduces a fuzzy aspect to the overall result. This has been applied to multi-criteria decision making problems and weighted matching problems. The second is the use of non-Pareto methods that treat different objectives in turn, but generally suffers from the problem of averaging as in the Vector Evaluated Genetic Algorithm (VEGA) approach presented by Schaffer (1985) [19]. That approach has been offset by the use of Pareto methods that explore the Pareto non-dominated front. The Pareto approach uses the ranks applied by different levels of dominated and non-dominated solutions to assign fitness in a population and guide the search. Pareto methods represent the focus of most current research. The latter approach is extensively researched and numerous methods to increase the efficiency of the optimization in determining the Pareto front have been proposed. These techniques offer the benefit of being able to provide a designer with multiple solutions that are each satisfactory in the optimal definition sense of being non-dominated. The problem is that excellent performance in one objective may result in poor performance in another objective. Thus a compromise solution is often the better choice. In the

)(1 xf)(2 xf


terms of multi-objective optimization, this translates into choosing candidates in the Pareto front that provide optimal or near-optimal performance in all objectives.

Typically, in most MOGA, the number of solutions in the Pareto front after several iterations is often close to the original population sample size. As a result, especially when considering more than two objectives, most of the population would be the candidates on the Pareto front. Again, this would result in too many non-dominated candidates for practical consideration. Using more than three objectives in the optimization would prove difficult to conceptualize as well. For this reason, the following Sequential Objective Genetic algorithm was developed to deal with this issue.

2.4.1 Sequential Objective Genetic Algorithm (SOGA)

The MOGA used in this study was originally designed for an engineering optimization problem involving hull form design [20][21]. The optimization problem involved the use of the objectives which required a compromise solution in order to offer a single near-optimal solution instead of a search of the complete Pareto front. A GA is a stochastic search and optimization technique that has the following five basic components [11];

1. A genetic representation of solutions to the problem;

2. A way to create an initial population of solutions;

3. An evaluation function rating solutions in terms of their fitness;

4. Genetic operators that alter genetic compositions of offspring during reproduction; and

5. Values for the parameters of GAs i.e., a means of translating the genetic solution into an actual solution for the problem.

For this particular problem, the solution is represented as a chromosome consisting of two parts, the X and Y values of the target's position. The initial population (typically a population of 100 is used) is generated as a random (X,Y) value. The evaluation functions are simply the two objective functions given previously. Genetic operations of cross-over and mutation are used with typical values set to 0.8 for probability of crossover and 0.1 for probability of mutation. The crossover and mutation functions are more fully described in textbooks on the subject [11][17].

For this investigation, a particular MOGA was used to address the multi-objective issues by automatically determining a compromise solution. The purpose of generating the MOGA solver was alluded to earlier, that is, the problem is not, conversely, the search for all solutions from the entire Pareto front, which is usually the only optimal strategy available in multi-objective problems. While aggregation or other preferential and interactive techniques are used, the goal in this study was to achieve some level of automation, i.e., to be able to come up with a few or a single compromise solution.

The following was developed in order to address some of these specific issues. The canonical Genetic Algorithm by Goldberg (1989) [22] is modified as shown in Figure 4 by treating each objective sequentially. For each objective the population is evaluated separately, and the genetic


operations are applied after each evaluation to generate the next population. The current optimum, if there is one, is returned at each evaluation. In some ways this approach is similar to the VEGA approach where different subpopulations are kept separate for a number of generations, then allowed to mix. That method allowed the population to approach a compromise solution that would perform well for more than one objective.

Figure 4: Sequential Objective Genetic Algorithm.

Unlike VEGA, the proposed methodology selects parents that are based on only one objective. The next objective in the sequence is evaluated with the population generated from parents that performed well from the previous objective. The treatment of the multi-objective problem is reduced to single objectives in sequence, similar to a gradient method in which each function’s evaluation leads to a determination of the direction of search. The relative importance of which objective is used was found to be immaterial, as long as the requisite number of iterations, of a minimum of approximately 10 generations, is used [20]. However, this could vary with the design problem and only the specific design problem here is discussed. Further research in the generic application of this method would be required. It should be noted that the requirement to have a sufficient population size, as well as a minimum number of generations, means that the efficiency of the genetic algorithm is subject to the degree of processing required to evaluate each objective. Furthermore, the accuracy of the results is also subject to the individual solutions provided by the functional evaluations of each objective as well.

2.4.2 Area Search Reduction Algorithm

The initial problem as previously mentioned start with an arbitrary 40 km by 40 km box. Once the MOGA is applied to this area, the final positional solution is used as a centre point in which to reduce the search area and provide a focus to re-apply the algorithm. The algorithm is then run


again for the reduced area, which notionally is reduced by halving side length. This means that the next area would use a 20 km by 20 km box. The concept is to eliminate many of the outlying clutter points, assuming that the real target solution is within the reduced are defined by the final solution. In this manner, subsequent iterations can halve the area until a final search area and final solution is obtained. For the purpose of this study, these re-applications of the MOGA are referred to as iterations in the following text. The first iteration refers to the first application of the MOGA, followed by a 2nd, 3rd and final 4th iteration of reapplication of the MOGA. This means that the final area would be reduced to a 2.5 km by 2.5 km search area.

Instead of halving the length of each side, a factor was introduced which was called, for lack of a better term, the range-on-speed factor. The calculation of the range is based on a range-on-speed factor, multiplied by the run time duration; originally, this is range-on-speed factor used 200 metres/minute multiplied by 60 time-steps by the original time interval of three minutes/time-step for a distance of 36000 metres. For each iteration, the range-on-speed factor is then reduced by half. This could have been simplified by taking a quarter of the area, or half of each side, at each iteration. Using the first approach, the 1st iteration uses the 40 km by 40 km box. A range-on-speed factor of 200 was used. In the second iteration, a 100 range-on-speed factor means the area was reduced to 18 km by 18 km area. For the 3rd iteration, the rang-on-speed factor of 50 is used, giving an area of 9 km by 9 km. The final search area of 400 metres by 4500 metres was used for the 4th iteration, given the range-on-speed factor of 25.


3 Results

In order to test the use of this particular approach, a MATLAB simulation was developed that allowed some test cases to be examined, with some variation of the algorithm parameters. In all cases, the number of population samples was 100 members, and at each time step the MOGA was run for 1000 generations. The results presented here are for three different test cases; when there is only one ship versus one target, two ships versus one target, and for three ships versus one target. Originally, more than one target was considered; however, the simpler cases are presented here. The time span of the simulation is three hours, using a three minute time step reflecting a ping schedule of every three minutes.

3.1 One Ship Scenario

Figure 5 shows a single run of the single ship (and single target) case, noting that the ship and target are held within a box between (-) 10 km to (+) 10 km in both x and y axes, with the origin at the centre of the box. The clutter is allowed to generate between (-) 20 km to (+) 20 km. For each run, a start position for both the ship and target within the box was randomly chosen along with a random heading. The constant speed of both target and ship was selected randomly between 0 and 5 knots for each run.

It should be noted that there are certain artificialities in this model. The own-ship position is not required, as no evaluation is made utilizing the range between the ship and target; hence, no ship position is required. The target is also constrained to be inside -10 km to 10 km box centred at the origin in order to simulate the detection of a target in that area. Other than detection within that area, no assumptions or other physical models are assumed for the probability of detection within that area. However outside that area, while a detection of false contacts can be made out to -20 km to 20 km, no target detection is assumed. In other words, the model is somewhat akin to a 'cookie-cutter' model except that a cookie-cutter model would use a radial distance extending out from the own-ship position.

The previous assumptions are enabled at the start of the simulation. When a target is generated it also assumes a random course and speed. If the target "escapes" outside the initial box it continues to be reported. The clutter contacts also continue to be reported.

Another very large assumption made with the model is that only a single contact, whether real or false, occurs at each time step. While Figure 5 shows a diagram that looks like a (randomly generated) clutter map, in fact this is the result after the complete three hour period or 180 time steps for one minute intervals. The reality is that the clutter map at each time step would look similar to the figure and that the problem is enormously simplified by presenting only one false or real contact at each time step. As previously mentioned, one could assume post-processing and/or operator input has been used to select contacts of interest. In this case, the problem devolves into how to differentiate the real contacts from false ones derived from clutter.


Figure 5: One Ship (Green) versus One Target (Black) within Field of Clutter (Red).

The result in Figure 6 shows how the MOGA assessed the final optimal solution after the first iteration. The progress of each solution is shown by cyan square symbols; the last optimal solution is shown as a red hexagon larger in font than the clutter point, shown approximately 1000 metres to the left of the target. Note that the entire area from (-) 20 km to (+) 20 km is being used with all of the false feature information as well as the target information.

To generate the simulated data, either a false contact or a real contact is generated at each time step. For the data above 30% of the time a real contact is generated at the target position, while 70% of the contacts are false and randomly positioned within the area.

For the next iteration, the side of the area is divided in half, using only contacts that are within quarter of the original area of the final average optimal solution. The calculation of the range is based on a range on speed, multiplied by the run time duration; originally, this is set at 200 (units) multiplied by 60 by a time step of three (minutes) for a distance of 36000 metres; this could be simplified by taking a quarter of the area, or half of each side, at each iteration.


Figure 6: Optimal Solutions at Each Time Step (Cyan) after 1st Iteration

and Final Solution (Red Hexagon).


For the second iteration, as shown in Figure 7, the area is reduced and the number of contacts is decreased to those within a range of 100(m/s)*3min*60s/min=18000 metres from the average optimal position determined in the first iteration. The solution has moved away from the target somewhat, to approximately 4000 metres, but the target is still within the smaller area.

Figure 7: Optimal Solutions at Each Time Step (Cyan) after 2nd Iteration and

Final Solution (Red Hexagon).


The 3rd iteration is shown in Figure 8 with a large reduction in the amount of false contacts, a smaller area within a side length of 9000 metres, and an optimal solution that is within several hundred metres of the target.

Figure 8: Optimal Solutions at Each Time Step (Cyan) after 3rd Iteration



The final 4th iteration is shown in Figure 9 is probably unnecessary, as the solution is still within several hundred metres of the target. The false contacts are reduced even further to just a few that are within 4500 metres from the 3rd iteration’s average optimal solution.

Figure 9: Optimal Solutions at Each Time Step (Cyan) after 4th Iteration


Figure 10 shows the Monte Carlo results for the absolute values of the average optimal solutions from the target for 100 individual runs where the target and the ship are randomly placed in the area of interest. The minimum average optimal distance is 82 metres, while the maximum is 23565 metres. However, the average distance to target is 4762 metres, with a standard deviation of 4849 metres. This result is less than the final optimal solution in this case. Nevertheless, the final optimal solution is the one that is used to indicate the proximity to the target in the following two cases.


It should be noted that in two distinct one ship scenario Monte Carlo runs using two distinct sets of 100 runs each, substantially different average results (as well as final results) were obtained. This implies that for statistical purposes, a greater number of samples would lead to more definitive statistics from which to draw conclusions. However, the 100 run case is used for illustration purposes for these three test cases.

Figure 10: Range of Final Optimal Solution to Target for One Ship versus

One Target for 100 Runs.

As previously mentioned, the average of the optimal solutions is used as input to one of the objectives in the MOGA approach. Although it is useful to know the absolute values of final solution with respect to the target, it is also apparent from the last two test cases that the average optimal solution is in some cases closer to the target than the last optimal position. The average of the optimal positions is the position that is used to dictate where the algorithm centres the new search area, as expressed by the 2nd objective. The final result may not be actually as good as this average solution.

3.2 Two Ship Scenario

Figure 11 shows an example start positions for two ships (in green) and the clutter generated after three hours (in red) versus a single target (in black), with contacts generated from each ship having both false and true target positions. This doubles the number of false contacts but also


doubles the number of true target positions. Again, 30 percent of the contacts are the true target positions as in the previous case. As well the same assumptions and parameters were maintained as in the previous one ship scenario.

Figure 11: Two Ship (in Green) Scenario within a Field of Clutter.


Figure 12 shows the result after one iteration, with the average of the optimal solutions (in cyan) and the final optimal solution (in magenta) centering somewhere between the target and the two ships, at approximately 9500 metres from the target.

Figure 12: Two Ship Scenario—1st Iteration.


Figure 13 shows the result after a second iteration, with a result that is approximately the same as in the first iteration. Note however, that fewer clutter contacts are being used even though the search area is still the same. This is due to the application of the range-on-speed factor.

Figure 13: Two Ship Scenario—2nd Iteration.


In Figure 14, the results are presented after a third iteration, in which the area is significantly reduced, using fewer clutter contacts. The final position is substantially closer to the target being approximately 2000 metres from the target. Figure 15 shows the result after the 4th iteration, with a final position now being about 1500 metres from the target, and very few clutter points.

Figure 14: Two Ship Scenario—3rd Iteration.


Figure 15: Two Ship Scenario—4th Iteration.


Average results for two ships versus one target, for 100 Monte Carlo runs, are shown in Figure 16. The minimum range was 78 metres, while the maximum was 18000 metres. The average was 3900 metres with a standard deviation of 4500 metres. The average result is less than the one ship test case, which is intuitively expected.

Figure 16: Absolute Range from Optimal Average Solution for Two Ships

versus One Target for 100 Runs.


Figure 17 shows the range of the last optimal solution for each of 100 Monte Carlo runs for the same 2 ship / 1 target test case. The results for four iterations of the algorithm show a minimum result of 10 metres, and a maximum result of 16,000 metres. The average solution of 5300 metres with a standard deviation of 4600 metres indicates the performance of the algorithm in absolute terms.

Figure 17: Absolute Range from Last Optimal Solution for Two Ship Scenario for 100 Runs.

3.3 Three Ship Scenario

Figure 18 shows a three ship scenario. All the same assumptions as in the previous two cases are maintained. Note the additional clutter generated from contacts reported from the third ship.


Figure 18: Three Ship Scenario—Start.

Figure 19 shows the results after one iteration, with the final position generated being somewhere between the three ships, at approximately 10,000 metres from the target (as the red octagon). Figure 20 through to Figure 22 show the results after two, three, and four iterations, respectively. The final positions are also respectively, 6 km, 1 km, and 1.5 km from the target.


Figure 19: Three Ship Scenario—1st Iteration.


Figure 20: Three Ship Scenario—2nd Iteration.


Figure 21: Three Ship Scenario—3rd Iteration.


Figure 22: Three Ship Scenario—4th Iteration.

Figure 23 shows the case for three ships, giving the absolute values of the final optimal solution from the target for 100 individual runs where the target and the ship are randomly placed in the area of interest. The results for four iterations of the algorithm show a minimum result of 7 metres, and a maximum result of 13,000 metres. The average solution of 3400 metres with a standard deviation of 4000 metres indicates the relative performance of the algorithm in absolute terms.


Figure 23: Absolute Range from Optimal Solution for Three Ship Scenario for 100 Runs.


4 Summary and Conclusions

The problem of filtering through false contacts or clutter to find a real target is not trivial, and a great deal of effort and research into methods of using data association principles and numerous acoustic approaches have been developed to try and solve this problem. Multistatic active sonar presents both opportunities and new challenges, particularly in trying to present a cohesive underwater picture to the operator. The approach presented in this study is based on the use of a robust optimization methodology using genetic algorithms, and in a multi-objective approach, such that the resulting Multi-Objective Genetic Algorithm (MOGA) can be used in an iterative fashion to reduce the search area to something more manageable.

The results show that on average, the MOGA approach could reduce the final range to the target to 6400 metres, for the one ship scenario. The result for two ships was 5200 metres and for three ships an average range to the target of 3400 metres was observed. However, a small sample size of only 100 individual runs was conducted for each test case. While no further work is being expended on this project, it should be noted that the conclusions could be modified if a larger sample size was used, in the order of 500 to 100 samples for each case.

Future research would have concentrated on the use of actual contact and clutter data, and extend the method to multiple targets. Further ways to revise the algorithm to use objectives that are more refined based on acoustic system information rather than just using contact positions was also an area of possible research.

The motivation of this work was to investigate the use of the MOGA developed previously from hull form optimisation to determine its suitability for tracking type problems and as a filter for the sonar operator’s aid in reduction of clutter. Clutter is predominant in multistatic active sonar in particular and in many cases passive contacts are not easily resolved as well. The current use of Multi hypothesis Kalman Filters works well when the environment is amiable and when multiple tracks can be resolved into a probabilistic target using m-of-n types of filters that can initiate and start tracks as well as drop tracks that are no longer sustained. The use of a MOGA may be able to provide another means or toll for the operator to resolve tracks in highly clutter and difficult environments.

However, by itself it is not a panacea and reliance of the traditional or classical methods of resolving bearing ambiguities, as well as relying on the sonar operator’s experience and familiarity with the environment are still required. Nevertheless this study showed that some promise can be seen in the results.


References

[1] http://www.navy.mil/navydata/policy/asw/asw-conops.pdf.

[2] Ince, L., Gammon, M.A., Hazen, M., "Genetic Algorithm for Target Motion Analysis", Presentation, Canadian Operational Research Society, May 2005.

[3] Gammon, M.A., "An Evolutionary Approach for Fusion of Active and Passive Sonar Contact Information", The 9th International Conference on Information Fusion, Florence, Italy, 10–13 July 2006.

[4] Prior, Mark K. and Baldacci, Alberto, "The physical causes of clutter and its suppression via sub-band processing", IEEE Oceans Conference 2006. Published in OCEANS 2006, Date of Conference:18–21 Sept. 2006, Conference Location : Boston, MA.

[5] Ehlers, Frank, "NURC's Multistatic Sonar Project", Technical Report, NURC-FR-2009-003, February 2009.

[6] Grimmet, D. et al, "Modeling Specular Occurrence in Distributed Multistatic Fields", IEEE Oceans 2008 Conference, 8–11April 2008, Kobe, Japan.

[7] Alireza Toloei and Saeid Niazi,” State Estimation for Target Tracking Problems with Nonlinear Kalman Filter Algorithms”, International Journal of Computer Applications (0975 – 8887), Volume 98–No.17, July 2014.

[8] Ince, L. et al., "An Evolutionary Computing Approach for the Target Motion Analysis (TMA) Problem for Underwater Tracks", Expert Systems with Applications, Vol. 36, No. 2P2, March 2009.

[9] Turkmen, I. et al, "Genetic Tracker with Neural Network for single and multiple target tracking", Neurocomputing, 69 (16–18), pp. 2309–2319, October, 2006.

[10] Turkmen, I. and Guney,K. "Genetic Tracker with adaptive neuro-fuzzy inference system for multiple target tracking", Expert Systems with Applications, 35 (4) pp. 1657–1667, November 2008.

[11] M. Gen and R. Cheng, Genetic Algorithms & Engineering Optimization, John Wiley and Sons, 2000.

[12] Peters, D.J., "A Practical Guide to Level One Data Fusion Algorithms", DRDC Atlantic, Technical Memorandum DREA TM 2001-201, December, 2001.

[13] W.A.Roger, M.E.Lefrançois, G.R.Mellema, and R.B.MacLennan, Networked Underwater Warfare TDP - A Concept Demonstrator for Multi-Platform Operations, Proceedings of the 7th ICCRTS Conference, Quebec City, September 2002.


[14] Marcel Lefrançois, Information Exchange Requirements for Networked Underwater Warfare, DRDC Atlantic Technical Memorandum TM2004-168, October 2004.

[15] Prokaj, J. et al, "Inferring Tracklets for Multi-object Tracking", 2011 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), Colorado Springs, CO, 20–25 June 2011.

[16] Coello Coello, C.A., An empirical study of evolutionary techniques for multiobjective optimization in engineering design. PhD thesis, Tulane University, New Orleans, Louisiana, 1996.

[17] M. Gen and R. Cheng, Genetic Algorithms & Engineering Design, John Wiley and Sons, 1997.

[18] Coello Coello, C. et al, "Evolutionary Algorithms for Solving Multi-Objective Problems", Springer Science, 2007.

[19] Schaffer, J., "Multiple Objective Optimization with Vector Evaluated Genetic Algorithms", in Proceeding of the First International Conference on Genetic Algorithms, pp. 93–100, edited by J.J. Grefenstette, Lawrence Erlbaum Associates, Hillsdale, N.J., 1985.

[20] M.A. Gammon, Ship Hull Form Optimization by Evolutionary Algorithm, Doctoral Thesis, Yildiz Technical University, Istanbul, Turkey, 2004.

[21] Gammon, M.A., "Optimization of Fishing Vessels Using a Multi-Objective Genetic Algorithm", Journal of Ocean Engineering, July, 2011.

[22] Goldberg, D., "Genetic Algorithms in Search, Optimization and Machine Learning", Addison-Wesley, Reading, MA, 1989.

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1. ORIGINATOR (The name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g., Centre sponsoring a contractor's report, or tasking agency, are entered in Section 8.) DRDC – Atlantic Research Centre Defence Research and Development Canada 9 Grove Street P.O. Box 1012 Dartmouth, Nova Scotia B2Y 3Z7 Canada

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parentheses after the title.) A Multi-Objective Genetic Algorithm Method for Active Sonar Clutter Reduction

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Target-like echoes from the use of active sonar, commonly known as 'clutter', is a particularly difficult problem when trying to separate real from false contacts. A method for reducing the amount of clutter in tracking underwater targets and providing a likely target area is accomplished by using an iterative Multi-Objective Genetic Algorithm (MOGA). The MOGA developed requires the automatic selection of a Pareto optimal result of the likely target position. The optimization minimizes the position of the genetic population with the last given contact positions, as one objective, while using an average position based on a history of optimal solutions as a second objective. In order to concentrate on a particular area, the algorithm is applied iteratively, taking into account the size of the area being examined and other constraints. In each subsequent iteration, a smaller area is used to limit the amount ofclutter being examined. After a nominal number of iterations, the area of the probable target location and the optimal target result from the algorithm are examined to determine whether the MOGA has determined a good position estimate. A simulation of the performance of the algorithm in a clutter environment is used to investigate the robustness of this particular method. The application of this approach may be of significant benefit in future configurations of acoustic processing systems developed from the DRDC Atlantic Research Centre's System Test Bed (STB).

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Les échos semblables à une cible causés par l'utilisation de sonars actifs et communémentappelés « fouillis » constituent un problème particulièrement difficile lorsqu’on tente de séparer les vrais des faux contacts. Il existe une méthode permettant de réduire le volume du fouillis lors de la poursuite de cibles sous-marines et offrant une zone-cible probable au moyen d’un algorithme génétique multi-objectif (MOGA) itératif. Le MOGA qu’on a mis au point requiert la sélection automatique d'un optimum de Pareto de la position probable de la cible. L'optimisation minimise la position de la population génétique, ainsi que les dernières positions données, comme premier objectif, tout en utilisant une position moyenne basée sur un historique de solutions optimales, comme deuxième objectif. Afin de se concentrer sur un domaine particulier, on applique l'algorithme de manière itérative tout en tenant compte de la taille de la zone examinée et d'autres contraintes. Dans chaque itération ultérieure, une zone plus petite est utilisée pour limiter le volume de fouillis examiné. Après un nombre nominal d'itérations, onexamine la zone où se trouve l'emplacement probable de la cible et l’optimum de la cible calculé à partir de l'algorithme pour déterminer si le MOGA a permis d’obtenir une bonne estimation de la position. On utilisera une simulation de la performance de l'algorithme dans un environnement de fouillis pour étudier la robustesse de cette méthode particulière. L'application de cette approche peut s’avérer très avantageuse pour les configurations futures des systèmes de traitement acoustique mis au point au banc d’essai de système (STB) du Centre de recherches de RDDC Atlantique.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and could be helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus, e.g., Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified. If it is not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title.) Multistatic Active Sonar; Clutter; Multiobjective Genetic Algorithm

a multi-objective genetic algorithm method for active...

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