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MP98W0000177
MITRE PAPER
Modeling and Prediction Software forAdvanced Processor Builds
September 1998
Joseph W. Creekmore
Sponsor: ASTO Contract No.: DAAB07-97-C-E601Dept. No.: W097 Project No.: 07988771AA
The views, opinions and/or findings contained in this reportare those of the MITRE Corporation and should not beconstrued as an official Government position, policy, ordecision, unless designated by other documentation.
© 1998 The MITRE Corporation
Corporate HeadquartersMcLean, Virginia
Abstract
This report describes a software suite which was developed for modeling and performanceprediction of advanced processor builds for the submarine acoustic superiority initiative. Thesoftware implements mathematically-based models and analysis techniques that facilitate a morethorough understanding of signal processing algorithm functionality, commonality, and perfor-mance relative to anticipated threat and noise environments. The entire software suite has beenimplemented in the MATLAB programming language and includes several graphical user in-terfaces for selection of signal processing functions and parameter entry. A description of eachprogram is provided, emphasizing user requirements while deferring algorithm details to otherassociated MITRE reports.
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Acknowledgement
The author would like to acknowledge the contributions of Dr. Garry Jacyna and Dr. DavidColella in the preparation of this report.
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1. Introduction
The modeling and prediction software described in this report provides realistic performanceprediction for Advanced Processor Builds (APB) at the algorithm level. The goal is to identifystrengths and weaknesses of individual system components and indicate how component ca-pability impacts overall system performance. The software implements mathematically-basedmodels and analysis techniques that facilitate a more thorough understanding of signal process-ing algorithm functionality, commonality, and performance relative to anticipated threat andnoise environments.
The modeling and prediction algorithms described herein are currently being integrated intothe the Naval Undersea Warfare Center (NUWC) Submarine Systems Effectiveness Assessment(SUBSEA) performance prediction model in support of the Navy’s Modeling and Predictionprogram. Although these algorithms comprise the first Advanced Processor Build (APB-1),it is anticipated that new signal processing algorithms in future builds will be modeled andincorporated in upgraded versions of the software.
The emphasis in this report is on user requirements for execution of the beamformer, tracking,detection, and acoustic contact correlation programs, as well as to describe the variety of optionsavailable in each program and the resulting myriad of signal processing paths. The goal is topresent the reader with an appreciation of the flexibility of the system in evaluating individualsystem components as well as the impact of these components on downstream processing.
The entire software suite has been implemented in the MATLAB programming languageand includes several graphical user interfaces for selection of signal processing functions andparameter entry. A description of each program is provided, emphasizing user requirementswhile deferring algorithm details to other associated MITRE reports.
2. Model-Based Performance Prediction
System performance prediction methodologies typically fall into two categories, MonteCarlo-based and model-based. The primary advantage of model-based performance predictionis that it provides a deeper insight into system performance. Critical issues such as identificationof conditions which lead to poor performance are more readily addressed using model-basedperformance prediction.
To illustrate, suppose we are examining a simple mechanical system consisting of a massattached to a spring and damper mechanism as shown in Figure 1. A driving functionF(t)
serves as the input to the system, whereF(t) is composed of a deterministic components(t)
and a noise processn(t) whose statistics are known a-priori. With the Monte Carlo approach,the system is treated as a “black box,” and a set of noise process exemplars is used as input tothe system. Output results are then recorded and a histogram is computed as anestimateof thesystem probability density function.
In contrast, each component of the system is modeled analytically with the model-basedapproach. A mathematical description of the deterministic components(t) as well as a statisticaldescription of the noise processn(t) are then used tocalculatethe system probability densityfunction. Figure 2 illustrates the two methods of density function estimation; for comparative
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Figure 1: Monte Carlo-Based Performance Prediction vs. Model-Based Performance Prediction
purposes, a histogram has been formed by discretizing the analytical probability density function.As shown in this example, the output results of the two methods are nearly identical.
3. Modeling and Prediction Software Suite
In this section, we describe each component of the modeling and prediction software suite.User specification of the sonar processing functions and associated parameter entries are accom-plished through graphical user interfaces (GUIs). Performance analysis results are also displayedthrough a GUI which allows the user to examine the output of each processing function.
Each of the following subsections is devoted to one of the primary components of the mod-eling and prediction software. The software suite is modular in that there is a one-to-onecorrespondence between processing blocks displayed in the main GUI and MATLAB programswhich execute each processing function.
3.1. Main Graphical User Interface
The user begins by executing the main program “apb1gui” at the MATLAB prompt. Thisopens the main graphical user interface (GUI) as shown in Figure 3. Note that initially the GUIincludes only menus for the the signal type and array type. The signal type includes passivenarrowband (PNB), Type-1, and passive broadband (PBB), as well as pairs derived from thesethree types. Consequently, the nine choices for signal type are as follows:
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Figure 2: Density Function Estimation via Monte Carlo-Based vs. Model-Based Prediction
• PNB
• Type-1
• PBB
• PNB / PNB
• PNB / Type-1
• PNB / PBB
• Type-1 / Type-1
• Type-1 / PBB
• PBB / PBB
The array type reflects operational towed arrays of interest to the Navy and includes twoapertures of the the TB-23 towed array:
• TB-23 conventional aperture
• TB-23 Z-aperture
as well as the TB-16 and TB-29 towed arrays.After selection of the signal type and array type, the GUI is updated to indicate user selections
as well as the signal processing functions to be performed. Figure 4 shows the updated GUI forthe PNB signal type and TB-23(Z) array type. Note that the signal processing functions includethe beamformer, tracker, and detector. In case the user selects a signal pair, the GUI includes aprocessing path for both signals as well as a block for acoustic contact correlation as shown inFigure 5 for the PNB/PBB signal pair. Note that five additional menus appear in the GUI for the
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Figure 3: Initial Graphical User Interface Window
two beamformers, the two detectors, and acoustic contact correlation. These menus include thefollowing options which are described in subsequent sections:
Beamformer Detector Acoustic Contact Correlation
Conventional Energy Detector Cluster FusionMVSC Beam Cross-Correlator Cluster Detection
MVSC Element BINSMVDR Element Completeness and Correctness
Table 1: Graphical User Interface Menus
After menu options have been selected, the user clicks on the “Enter Parameters” button tobring up the target, signal, and noise parameter menu as shown in Figure 6. Target parametersrefer to the kinematics of the target submarine and include:
• Initial range (yds)
• Initial bearing (deg)
• Course (deg)
• Speed (kts)
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Figure 4: Updated Graphical User Interface Window for PNB Signal Type
where the initial bearing and course are specified in degrees clockwise with respect to North.Signal parameters depend on signal type and are listed below in Table 2.
PNB Type-1 PBB
Initial Frequency (Hz) Initial Frequency (Hz) Lower Band Edge (Hz)Time Average per Scan (sec)Time Average per Scan (sec) Upper Band Edge (Hz)
Bandwidth (Hz) Time Average per Scan (sec)
Table 2: Signal Parameters
Note that all three signal types include time average per scan as a parameter, but only PNBand Type-1 include initial frequency. Moreover, Type-1 and PBB include parameters for signalbandwidth unlike the PNB signal type.
Finally, noise parameters include temporal and spatial noise types. Thetemporalnoise typespecifies the shape of the noise frequency spectrum and applies to the PBB signal type only,while thespatialnoise type specifies the shape of the noise spatial spectrum and applies to allsignal types as shown below in Table 3.
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Figure 5: Updated Graphical User Interface Window for PNB/PBB Signal Type
Spatial Noise Type PBB Temporal Noise Type
Use Isotropic Noise WhiteEnter Noise File Colored Shallow
Colored Deep
Table 3: Noise Parameters
Note that the spatial noise type includes an option to enter a noise file with the desireddirectional noise characteristics. A description of the noise file format is presented in Section 3.7.
The final parameter included in the target, signal, and noise parameter menu is theProcessing Mode. The selections are as follows:
• Use Ideal Covariance
• Enter Propagation Filename
Selection of “Use Ideal Covariance” results in computation of a signal covariance matrixwhich reflects a direct path only. Alternatively, the user may specify an existing propagation filerepresenting a season and site of interest which contains parameters for direct path and multipatharrivals at the array. Details of the propagation file contents are presented in Section 3.7.
After completion of the parameter menu entries, the user clicks on the button “Execute” asshown at the bottom of Figure 6. This begins the execution of a series of MATLAB programsincluding those corresponding to the beamformer, tracker, and detector. For the case of a signal
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Figure 6: Parameter Menu for Target, Signal, and Noise Parameters
pair, the beamformer, tracker, and detector are executed forbothsignals, followed by the specifiedacoustic contact correlation program.
At completion of the processing programs, a GUI appears to allow the user to examine theoutput of each processing function as shown in Figure 7. (For the case of a single signal, onlythe top row of Figure 7 appears in the GUI). Results are displayed by clicking any of the buttonslabeled:
• Array Gain
• Power Degradation
• Track Errors
• Min Detect Level
• Track Maintenance
as well as the button corresponding to the acoustic contact correlation function. Each of thebuttons in Figure 7 corresponds to the output of one of the processing programs. The “ArrayGain” button corresponds to the output of the beamformer program, the “Track Errors” buttoncorresponds to the output of the tracking program, and the “Min Detect Level” button correspondsto the output of the detector program.
Additionally, although they are not shown in Figure 5, the “Power Degradation” button corre-sponds to the output of a program which computes the signal power loss due to target dynamics,
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Figure 7: Graphical User Interface for Displaying Output of Processing Programs
and the “Track Maintenance” button corresponds to an additional output of the detector programwhich is described below. The following sections present details for each of the processingfunctions, including a description of both input parameter choices and output plot results.
3.2. Beamformer
The purpose of the beamformer program is to compute array gain as a function of the targetfrequency, bearing, and signal-to-noise ratio (SNR). The beamformer options listed in Table 1include:
• Conventional
• MVSC Beam
• MVSC Element
• MVDR Element
The first option refers to conventional delay-and-sum-beamforming, while the remainingthree options refer to adaptive beamformers. The two options “MVSC Beam” and “MVSCElement” refer to two versions of the Minimum Variance Soft Constraint (MVSC) adaptivebeamformer. Thebeam-basedMVSC adaptive beamformer uses conventional beam time seriesas input while theelement-basedMVSC adaptive beamformer uses element-level time series
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Scan Index
CB
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ain
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Figure 8: Array Gain for PNB Signal using Conventional Beamformer
as input. The last option “MVDR Element” refers to the element-level Minimum VarianceDistortionless Response (MVDR) adaptive beamformer. Details may be found in [2].
In conventional delay-and-sum processing, array gain is independent of SNR since the con-struction of beams is not conditioned on inputs to the array. However, this property is not sharedby the class of MVSC adaptive beamformers, where array gain is a function of SNR. This arisesfrom the white noise gain constraint which is added to improve the stability of the filter weights.A description of the properties of the beam-based MVSC adaptive beamformer is given in [1].
The output of the selected beamformer may be examined by clicking on the “Array Gain”button on the results GUI. For all choices of beamformer, array gain plots appear as as functionof scan index or SNR. To illustrate, Figure 8 shows the array gain for a 50 Hz PNB signal usingthe conventional beamformer. Note that array gain is plotted as a function of scan index andvaries less than 0.03 dB. The periodic nature of the array gain is due to the target traversingseveral beams.
For the PBB signal, array gain is plotted as a function of scan index for the low, middle, andhigh frequencies in the specified band as shown in Figure 9 [85 Hz - 135 Hz]. Note that thearray gain varies by nearly 2 dB over the specified PBB band.
For the adaptive beamformers, array gain is plotted as a function of both scan index as wellas SNR. In addition, the Array Gain Improvement (AGI) ratio, which measures the gain (or loss)relative to the conventional beamformer, is also plotted as a function of both scan index andSNR. Figure 10 illustrates the MVSC array gain for the 50 Hz PNB signal. Note that the AGIis approximately 0.39 dB at SNRs below -10 dB; however, at SNRs above -10 dB the AGI ratio
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14
14.5
15
15.5Conventional Beamformer
Scan Index
CB
F G
ain
(dB
)
Figure 9: Array Gain for PBB Signal using Conventional Beamformer
becomes negative which indicates that the conventional beamformer outperforms the MVSCadaptive beamformer.
The same effects are illustrated in Figure 11 for the PBB signal, where the array gain andAGI ratio are plotted as a function of both scan index and SNR for the low, middle, and highfrequencies of the specified band.
3.3. Power Degradation
The power degradation programs compute the signal power loss as a function of the targetfrequency and bearing. For PBB signals, the signal power loss is computed as a function ofbearing only. The power programs use array parameters along with known target frequency andbearing vectors and coherent integration time to compute a power loss matrix which is outputand stored for use by other programs in the simulation chain.
Figure 12 illustrates the output of one the power programs for a PNB signal emanating froma target with a speed of 15 kts. Note that even at this relatively high speed, the signal power lossis less than 1 dB over frequency and bearing.
3.4. Jarvis Tracker
The purpose of the Jarvis tracker programs is to compute the RMS errors associated withtracking a target in frequency and bearing. Two varieties of tracking algorithms were modeled
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2Array Gain Improvement Ratio
SNR (dB)
AG
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Figure 10: Array Gain for PNB Signal using MVSC Beam-Based Beamformer
depending on the subsequent detector program as shown in Table 4. Note that the Type-1 andPBB signal types include both the energy detector and cross-correlator, but that the PNB signaltype includes only the energy detector. User specification of the tracker program is implicitthrough selection of the detector type in the main GUI window as shown in Figure 5. The detailsof the analytical procedures used to bound performance of the track functions are given in [3].
PNB Type-1 PBB
Energy Detector Energy Detector Energy DetectorCross-Correlator Cross-Correlator
Table 4: Tracking Algorithms Employed For Each Signal Type
The output of the tracker may be examined by clicking on the “Track Errors” button on theresults GUI. A figure appears which plots RMS tracking errors as a function of SNR. Figure 13illustrates the plots which are created for the PNB signal type using energy detection. Notethat RMS tracking errors are plotted for frequency, bearing, frequency rate, and bearing rate.For frequency and bearing RMS tracking errors, two curves are plotted as a function of SNR.The upper curves represent the raw RMS tracking error at the output of frequency and bearinginterpolators, while the bottom curves represent the smoothed RMS tracking errors at the output
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−2
−1
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1Array Gain Improvement Ratio
SNR (dB)
AG
I Rat
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Figure 11: Array Gain for PBB Signal using MVSC Beam-Based Beamformer
of the Jarvis frequency and bearing trackers.For the PBB and Type-1 signal types, RMS tracking errors are plotted for bearing and bearing
rate as shown in Figure 14 for the PBB signal type using energy detection. As in the PNB signalcase, note that two curves are plotted as a function of SNR and represent raw RMS trackingerrors at the output of the bearing interpolator as well as the smoothed RMS tracking errors atthe output of the Jarvis bearing tracker.
3.5. Detector
The detector programs compute the minimum detectable level (MDL) as a function of pro-cessing time (or scan index) assuming a 50% detection probability and a false alarm probabilityof 10−7. Both the energy detector and cross-correlator were modeled, although the PNB signaltype includes only the energy detector as indicated in Table 4.
For all three signal types, two curves are plotted corresponding to optimal and track-before-detect detection results. The lower curve represents the Automatic Line Integration (ALIT)receiver; this detector is optimal when the target track is known and is a lower bound on MDLin the presence of tracking errors. The upper curve includes tracking errors derived from thetracking program. The performance bounds on these detectors are derived in [4].
The output of the detector program may be examined by clicking on the “Min Detect Level”button on the results GUI. A figure appears which plots the minimum detectable level in decibelsas a function of the scan index. Figure 15 illustrates the plot which is created for the PNB signal
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Bearing (deg)
Rel
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egra
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Pow
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dB)
Figure 12: Power Degradation for a 15 kt Target PNB Signal
type using energy detection. (For the PNB signal type, the MDL is computed relative to a 1 Hzbandwidth). Note that MDLs for the optimal and suboptimal detectors differ by approximately2 dB after processing 25 scans.
One additional figure of merit is output by the detector program, i.e.,track maintenanceprobability. This is the probability of maintaining target track over a specified time interval(number of scans) as a function of SNR. Figure 16 illustrates the track maintenance probabilityfor the PNB signal type. The three curves are referenced to the first, middle, and last scan. Notethe sharp rise in probability near a SNR of -20 dB for all three curves.
3.6. Acoustic Contact Correlation
The acoustic contact correlation (ACC) programs perform data fusion on contact data fromany pair of signals to arrive at a target similarity assessment. As indicated in Table 1, theseprograms include:
• Cluster Fusion
• Cluster Detection
• Bayesian Inference Network (BIN)
• Completeness and Correctness
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Signal−to−Noise Ratio (dB)
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Signal−to−Noise Ratio (dB)
RM
S E
rror
(de
g/se
c)
Figure 13: RMS Tracking Error for PNB Signal Type
In all cases, the beamformer, Jarvis tracker, and detector programs are executed sequentiallyfor the first signal and then the second signal prior to execution of the ACC program. The outputof the selected ACC program may be examined by clicking on the corresponding button on theresults GUI.
The cluster fusion program computes the RMS bearing and bearing-rate errors derived froma fusion of individual Jarvis track errors as a function of SNR. (For the PNB/PNB signal pair,the fused RMS frequency-rate error is also computed). All track errors are referenced to thefinal scan.
Figure 17 illustrates the fused track errors for the PNB/PBB signal pair. In both plots, Thetop two curves represent the RMS bearing and bearing-rate Jarvis track errors for the PNB andPBB signals. The bottom curves represent the fused RMS bearing and bearing-rate track errors.
The cluster detection program computes the minimum detectable level (MDL) based on fusedlikelihood ratio statistics derived from a pair of signals as a function of scan index. Figure 18illustrates the fused MDL for a pair of PBB signals each with a 50 Hz bandwidth. The top twocurves represent the MDLs for the two PBB signals, while the bottom curve represents the fusedMDL. Note that a gain of approximately 1 dB is achieved at the 25th scan.
The cluster detection program also computes fused track maintenance probabilities derivedfrom a pair of signals as a function of SNR. Figure 19 illustrates the fused track maintenanceprobability for the same PBB/PBB signal pair. The leftmost curve represents the fused trackmaintenance probability as a function of SNR at the 25th scan.
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Signal−to−Noise Ratio (dB)
RM
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0.04
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0.065PBB Energy Detect Bearing−Rate Track Error
Signal−to−Noise Ratio (dB)
RM
S E
rror
(de
g/se
c)
Figure 14: RMS Tracking Error for PBB Signal Type
The Bayesian Inference Network (BIN) program computes the probability of correct cluster(target) association for a pair of signals based on geometric evidence which includes bearingand bearing-rate track error variances. The BIN receiver operator characteristic is displayedby plotting the probability of correct cluster association as a function of the probability of falsecluster association for fixed SNRs in increments of 10 dB. Details of the structure of the BayesianInference Network are given in [5].
Figures 20 through 22 illustrates the output of the BIN program for the PNB/PBB signalpair at SNRs of -10 dB, 0 dB, and 10 dB for 1, 2, and 3 iterations of the network. Note thatperformance improves with SNR and that the probability of correct cluster association is nearunity at a SNR of 10 dB.
The final ACC option is the completeness and correctness metric devised by the AppliedPhysics Laboratory at Johns Hopkins University (APL/JHU). Figure 23 illustrates the output ofthe completeness and correctness program for the PNB/PBB signal pair. The top curve representscompleteness, while the bottom curve represents correctness.
3.7. Propagation and Noise Files
The APB modeling and prediction software suite includes options to input propagationand/or noise files. The user may specify an existing propagation file representing a season andsite of interest which contains parameters for direct path and multipath arrivals at the array.
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Scan Number
Min
imum
Det
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Leve
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1 H
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B)
Figure 15: Minimum Detectable Level for PNB Signal Type
These propagation files were generated by the Naval Undersea Warfare Center (NUWC) incollaboration with MITRE and present the opportunity to examine various scenarios and theireffect on sonar system performance prediction.
After selecting the option “Enter Propagation Filename” on the parameter menu shown inFigure 6 and starting execution, a menu appears with existing propagation files from which toselect. Each of these propagation files is a MATLAB file containing a four-column matrix whichis packed as follows. Each submatrix is indexed to frequency, where the first column is rangein yards, the second column is travel time in seconds, the third column is propagation loss indecibels, and the fourth column is number of surface reflections. Additionally, each submatrixbegins with a header row of the form[0, 0, 0, fi], wherefi is the corresponding frequency forthat submatrix.
Programs which use these propagation files compute a signal covariance matrix based on theinput target parameters and propagation file parameters. A separateN × N covariance matrixis computed for each discrete frequency, whereN is the number of array elements.
The noise files quantify thevertical noise and contain levels in decibels as a function ofelevation angle (−90◦ to 90◦) for a fixed azimuth angle. After selecting the option “Enter NoiseFilename” on the parameter menu shown in Figure 6 and starting execution, a menu appears withexisting noise files from which to select. Each of these noise files is a MATLAB file containinga 361-column matrix which is packed as follows. Each two-row submatrix is referenced tofrequency and azimuth angle, where the second row contains the vertical noise distribution as a
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Signal−to−Noise Ratio (dB re. 1 Hz)
Tra
ck M
aint
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ce P
roba
bilit
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Figure 16: Track Maintenance Probability for PNB Signal Type
function of elevation angle in 0.5 degree increments. The first row in each two-row submatrixis of the form[fi, φj , −1, 0, 0, 0, ..., 0], wherefi is the corresponding frequency andφj is thecorresponding azimuth angle for that submatrix.
Programs which use the vertical noise distribution file compute a noise covariance matrixbased on sound speed, array parameters, and the noise vertical distribution. As for the signalcovariance matrix, a separateN ×N covariance matrix is computed for each discrete frequency,whereN is the number of array elements.
3.8. Anticipated Enhancements
Since future advanced processor builds are scheduled on an annual basis, corresponding en-hancements to the APB modeling and prediction software suite are also anticipated. For example,APB-2 is expected to include processing for passive ranging, with several candidate algorithmsunder consideration. Additionally, improvements to the existing beamforming, tracking, anddetection algorithms are continally being evaluated.
We anticipate modeling these new and modified processing functions and incorporatingsoftware into the system to reflect these enhancements. As the modeling and prediction softwaresuite evolves, older versions reflect the Acoustic Rapid COTS Insertion (ARCI) system at thatphase of development. This permits comparison of current and legacy systems, and complementssea trials for evaluation.
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Signal−to−Noise Ratio (dB)
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Signal−to−Noise Ratio (dB)
RM
S (
deg/
s)
Figure 17: Fused Track Errors
3.9. APB Modeling and Prediction MATLAB Programs
Table 5 below lists the name of each of the MATLAB programs which comprise the APBmodeling and prediction software suite. The second column is a brief description of the functionof each of the programs. All of the graphical user interface functions are accomplished by theprogramsapb1gui.m, processgui.m, andresultsgui.m.
The current version of the software suite is available to interested parties upon request.Requirements include MATLAB version 5.0 or higher. The software suite is portable acrossplatforms with minor variations in the appearance of the graphical interface displays.
4. Summary and Conclusions
This report has described a software suite developed at MITRE for modeling and performanceprediction of advanced processor builds for the submarine superiority initiative. The softwareincorporates mathematically-based models that permit evaluation of signal processing algorithmfunctionality relative to anticipated threat and noise environments. The entire software suite hasbeen implemented in the MATLAB programming language and includes several graphical userinterfaces for selection of signal processing functions and parameter entry.
A description of the programs which model the beamformer, tracker, detection, and acousticcontact correlation functions was provided, emphasizing user requirements for execution of the
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Scan Number
Figure 18: Fused Detection Minimum Detectable Level
programs while deferring algorithm details to other associated MITRE reports. The variety ofprocessing options was described, and sample outputs of each of the processing programs wereillustrated. It is anticipated that new processing options planned for future advanced processorbuilds will be modeled and incorporated into the modeling and prediction suite.
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Figure 19: Fused Track Maintenance Probability
References
[1] Colella, D., “Array Gain as a Function of SNR for the Beam-Based MVSC AdaptiveBeamformer,” MITRE Paper 98W0000064, February, 1998.
[2] Cox, H., Zeskind, R., and Owen, M., “Robust Adaptive Beamforming,” IEEE Trans. ASSP,Vol. 35, No. 10, 1987, pp. 1365-1376.
[3] Jacyna, G., “ARCI Track Performance Bounds,” MITRE Paper 98W0000050, February,1998.
[4] Jacyna, G., “ARCI Detection Performance Bounds,” MITRE Paper 98W00000164, Septem-ber, 1998.
[5] Jacyna, G. and Christou, C., “Incorporation of Range and Range Rate Evidence into Acous-tic Contact Data Fusion,” MITRE Paper 98W0000089, February, 1998.
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Miss Association Probability
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Bayesian Inference Network ROC Curves (1,2, and 3 iterations)
SNR (dB) = −10
Figure 20: Bayesian Inference Network Receiver Operator Characteristic for SNR = -10 dB
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Figure 21: Bayesian Inference Network Receiver Operator Characteristic for SNR = 0 dB
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Figure 22: Bayesian Inference Network Receiver Operator Characteristic for SNR = 10 dB
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Figure 23: Completeness and Correctness
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again.m Array gainapb1gui.m Master GUI programarrow.m Draws arrows for GUI displaysbinacc.m Calculates cluster association at output of BINcovsig.m Signal covariance based on propagation lossfix_visibility.m Patch for plotting resultsinit_acc.m Initialization for acoustic contact correlationinit_array.m Initialization for array definitionsinit_pbb.m Initialization for PBB signalinit_pnb.m Initialization for PNB signalinit_type1.m Initialization for Type-1 signaljarvisaccd.m Jarvis ACC detectionjarvisaccest.m Jarvis ACC frequency/bearing errorsjarviscomp.m Cluster completeness and correctness metricsjarviscor.m Jarvis tracker errors for Type-1 cross-correlationjarviscord.m Jarvis detection for Type-1 cross-correlationjarvisded.m Jarvis detection for Type-1 energy detectionjarvised.m Jarvis tracker errors for Type-1 energy detectionjarvispcor.m Jarvis tracker errors for PBB cross-correlationjarvispcord.m Jarvis detection for PBB cross-correlationjarvispded.m Jarvis detection for PBB energy detectionjarvisped.m Jarvis tracker errors for PBB energy detectionjarvispnb.m Jarvis tracker errors for PNB energy detectionjarvispnbd.m Jarvis detection for PNB energy detectionkinematics.m Calculates target dynamicsncov.m Ideal isotropic noise covariance matrixnoisecov.m Noise covariance matrix from noise filepbbpower.m PBB power loss as function of bearing ratepnbpower.m PNB power loss as function of freq/bearing ratesprocessgui.m Identifies processing chain and executes programsresultsgui.m Provides options for plotting, printingscov.m Ideal signal covariance matrixtaylor.m Taylor shading coefficientstype1power.m Type-1 power loss as function of freq/bearing rates
Table 5: MATLAB Programs
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