Real-Time Wideband Active Sonar EcholocationSimulator with MATLAB/GUI

Jason Chien-Hsun TsengDepartment of Information Engineering, Kun Shan University, Taiwan

Abstract

This paper gives a description of an active sonar simulator with MATLAB-GUI platform developedfor the numerical simulation of the wideband active sonar echolocation system in order to provide thedata needed for testing sonar signal processing schemes. Instead of testing the data on more expensivemachine, the simulator runs on a PC, which is of attractive low cost, for fast performance evaluationof an adaptive noise cancelling (ANC) based target detection algorithm on a set of real test data. Thebuilt-in algorithm proposed for multi-target detection is hybrid, a combination of an adaptive ANCneuro-fuzzy scheme in the first instance and followed by an iterative optimum target motion estimation(TME) scheme. The neuro-fuzzy scheme is based on the ANC concept with the core processor of ANFIS(adaptive neuro-fuzzy inference system) to provide an effective fine tuned signal. The resultant outputis then sent as an input to the optimum TME scheme composed of two-gauge trimmed-mean (TM)levelization, discrete wavelet denoising (WDeN), and optimal continuous wavelet transform (CWT) forfurther denosing and targets identification. Its aim is to recover the contact signals in an effective andefficient manner and then determine the Doppler motion (radial range, velocity and acceleration) at verylow signal-to-noise ratio (SNR). Quantitative results obtained by the PC-based simulator are robust inpredicting targets’ Doppler motion within various scenarios with the maximum false detection of 1.5%,which is applicable in the real world.

Keywords: Wideband Active Sonar Echolocation, ANC Neuro-Fuzzy, Wavelet Denoise, CWT.

即時的寬頻活躍聲納回音定位模擬器使用MATLAB/GUI

曾建勳崑山科技大學資訊工程系

摘要

本文描述一臺專為多種頻率的活躍聲波探側器回音定位系統数值所設計的活躍聲波探側模擬器使用MATLAB-GUI 平臺, 其目的是為了模擬測試處理聲纳信號所需要提供的數據。有別於使用昂贵的机器來測試聲纳信號數據，這個模擬器使用個人電腦去快速模擬一組時實際資料, 使用一個適應性雜訊消除技術的目標偵測演算法，如此具有相對吸引力的低成本。此提出之內建演算法於多重目標偵測為一種混合演算法，亦即是使用適應性 ANC 類神經模糊伴随疊戴最佳目標行為估計 (TME) 計劃。類神經模糊的計劃是根据據的 ANC 概念之核心處理器 ANFIS (能適應的神經模糊的推理系统) 去提供一個有效的優化的信號。其輸出信號然後被送到一個最佳化 TME 計劃, 由下列所組成為了要進一步處理雜訊與目標辨識: 二階段測量 (TM) levelization，除雜訊分離小波 (WDeN) 和最佳化連續小波變換 (CWT)。這個聲波探側模擬器的目標是要在非常低信號噪音比 (SNR) 的環境下, 以最有效和高效率的方法去恢復所傳送出的信號, 然後決定目標物之多譜勒儀行動 (輻形範圍，速度和加速度))。以個人電腦模擬器所得到的定量結果顯示出所預估多目標多譜勒儀行為的堅實性, 其各種方案所得之最大錯誤偵查率為1.5%，亦即是可適用於實際聲纳信號的偵測。

關鍵字: 寬頻活躍聲納回音定位, ANC 類神經模糊, 除雜訊小波, 連續小波變換.

1 IntroductionRecovering active acoustic sonar returns in mul-

tipath media is a core problem of underwater signalprocessing to detect and classify underwater targets.Because the system is concerned with estimation oftargets’ motion parameters, it is well known that theimplementation of such system exploits the time-scalejoint representation of target echoes [1]. The tech-nique used to measure time and scale of objects iscommonly known as the cross correlation or matchedfilter processing [2]. As in the wideband environ-ment, this technique estimates the time-delay andscale-change by cross correlation of overlapping seg-ments of the received complex signal with a set of ba-sis functions matched to the transmitted signal. Thismethod is then referred to as wideband replica corre-lation (WRC). The standard WRC processing workswell for the most problems and has optimum perfor-mance with the noise-free signal or the maximum out-put signal-to-noise ratio (SNR) condition [3]. In thepresence of severe interference or in highly distortingmedia such as spread or multipath channels [4], theWRC processing, however, degrades the underlyingback scattering returns. Together with the systemcharacteristics such as beam patterns and transmit-ted signal, the severe interference has made the detec-tion even more difficult. This is because sharp peaksare more sensitive to a sidelobe correlation interfer-ence mainly arising from unwanted harmonics of thetransmission, which correlate with the replica. Thisassertion is even more justified for harmonic ghostsbeing generated by overlapping these unwanted har-monics after reflection from the first break (the inter-face between the surface of the earth formation andthe covering water) with the weak reflections fromdeep reflecting interfaces [4].

A fast hybrid denoising algorithm [5, 6, 7] basedon an ANC neuro-fuzzy processor and optimal wavelettransforms has been developed for multi-target wide-band active sonar echolocation system for which oneor more underwater target returns are masked by in-terference. The aim of the hybrid algorithm is pro-posed to recover the contact signals in an effectiveand efficient manner and then determine the Dopplermotion parameters (radial range, velocity and ac-celeration) at various target strength of SNR. To-gether with the real data set supported by the DERAUK, the sonar simulator driven by the hybrid algo-rithm is used to evaluate performances of the hy-brid algorithm in terms of targets’ motion detectionbased on Doppler time-scale and time-delay of thereceived echo via matched optimal filtering mecha-nisms (i.e. training sets). The detection process ofthe sonar simulator is illustrated in Fig. 1. The simu-lator models targets, reverberation, propagation andthe receiver chain, which is composed of two distinc-tive schemes: adaptive ANC neuro-fuzzy scheme anditerative optimum target motion estimation (TME)

TM-a TM-a1 2

Levelization

OptimalCWT

Figure 1: The detetion process of an active sonar sim-ulator. (a) adaptive ANC neuro-fuzzy scheme. (b)Iterative TME scheme.

scheme. The adaptive ANC neuro-fuzzy scheme de-picted in Fig. 1(a) is based on the adaptive noise can-celling concept [8] with the core processor of ANFIS(adaptive neuro-fuzzy inference systems [9]), whilethe iterative optimum TME scheme depicted in Fig. 1(b)is based on the optimal wavelet transforms with mul-tilevel threshold denoising. Using the adaptive learn-ing intelligent systems, unwanted parts of the targetreturns including harmonic ghosts and those interfer-ence/noise contained in the higher frequency rangesare removed, and hence to effectively improve the tar-get strength. We note that a priori the echo signals ofinterest are in the lower frequency ranges. The stageof noise cancelling exploits capabilities of ANFIS intracking both linearity and nonlinearity in multidi-mensional input space and thus alleviating the side-lobe correlation interference.

The resultant signal is then proceeded by the it-erative optimum TME scheme for further localizingpotentials and then recovering the contact signal viamatched filtering mechanisms. Process steps include:two-gauge trimmed-mean (TM) levelization, discretewavelet denoising (WDeN) [10], and optimal CWToperation via FIR filtering structure. More specif-ically, the TM-levelization step is a dynamic level-based process controlled by two gauges not only tokeep updating the TME scheme but also to removepower of most excessive sharp detail in the sense oftrimmed mean estimation. Following from the TMstep, the WDeN step associated with an octave sub-band decomposition is applied. Its functionality is tofurther suppress the remaining noise part of the train-ing data and thus produce fine tuned test cells for thefinal step of target mapping, the optimal CWT opera-tion via FIR matched filtering mechanisms (i.e. train-ing sets). Here the similarity measurement in terms

Figure 2: The active sonar simulator with MATLAB-GUI platform.

of CWT signal mapping is optimized in the scale do-main by the combination of golden section searchand successive parabolic interpolation method [11].By combining the adaptive ANC neuro-fuzzy schemein the first place with the iterative optimum TMEscheme, the active ANC-TME hybrid sonar simula-tor is developed for real-time applications in DSP-FPGA hardware implementation. It’s task is to sim-ulate rapidly and accurately when processing targets’echoes in the presence of severe interference, a com-bination of backscattered reverberation and ambientnoise. Different options with respect to choosing aparticular simulator exist. For this case, we have cho-sen Matlab-GUI platform as illustrated in Fig. 2 dueto its relative simplicity and fast learning curve. Thevarious features incorporated in the simulators allowdifferent scenarios to be studied in real-time with aninteractive user interface. Without using more ex-pensive machine to test the real sonar data, excellentperformance of the built-in algorithm indicated byoutputs of the simulator with scenarios chosen hasbeen shown to be suitable for the detection of un-derwater targets’ Doppler motion at very low targetstrength. Quantitative analyses of the performanceevaluation obtained by the PC-based simulator foreach returns of ping have even shown that the hy-brid algorithm not only meets the development re-quirements but also provides a higher degree of sig-nal detection capability with an increased robustnessagainst false signal detections.

2 Review of Techniques2.1 WRC processing and optimum de-

tection algorithmLet us consider wideband signals in a multiple

nondirectional sonar channels for which the receivedwaveform g(t) can be described mathematically as [2]

g(t) =∑Ii=1 αigi(t) + η(t). (2.1)

This model accounts for superposition of contact sig-nal known as target signatures gi(t) as in Eq. (2.2),which are received Doppler distorted pulses in theL2(Ω) Hilbert Space of finite energy at time t ∈ Ω ⊂ℜ. Furthermore, the background interference η(t) asin Eq. (2.3) involves reverberation waveform r(t) andadditive ambient noise n(t):

gi(t) =√Siψ(Si(t−Di)) (2.2)

η(t) = ~(t) ∗ r(t) + n(t) (2.3)

Here parameters are defined by ψ the transmitted sig-nal (pulse), αi amplitude (attenuation value) for theith echo, Si true Doppler scale for the ith echo, Di

true round-trip time-shift for the ith echo, ~, an un-known channels of arbitrary noise path filter. Rever-berations due to multiple reflection from the mediumboundaries including the surface, volume and bottomusually contribute in varying proportions. The com-mon scenario is chosen for which the sonar devices areassumed to be mounted either on a surface ship or un-derwater submarine [12]. As a result, the scatteringprocess and the dependence of the received reverber-ation on range can be modelled in terms of having anintensity with exponential statistics or an envelope, asquare root of the intensity, with the Rayleigh statis-tic. The probability density function of the rever-beration model is then given by ρ(γ|σ) = γ

σ2 e−γ2/2σ2

where γ is the amplitude of the envelope and σ is thestandard deviation representing the expected levelof intensity. The aim of the model in Eq. (2.1) isto isolate specular returns from the background in-terference by using the wideband replica correlation.Hence, a pair of scale-time joint motion parameters(Si, Di) associated with the ith return can then be es-timated by solving the maximization problem of thewideband ambiguity function WCψg(s, τ) over bothparameters simultaneously:

maxs.t.(s>0,τ∈ℜ)

||WCψg(s, τ)||2 = ||WCψg(s∗, τ∗)||2.(2.4)

Here WCψg(si, τ) associated with the ith specular re-turn having the Doppler scale si is defined as

WCψg(si, τ) =

∫ ∞

−∞g(t)ψsi(t− τ)dt (2.5)

= ⟨g, ψsi(t− τ)⟩ (2.6)

which utilizes ψsi(t) ≡ √siψ(sit) as a template to

form the hypothetical signal. As a result, the ith ele-ment of optimum can be found by s∗i = Si ≈ εS, ε > 0

and τ∗i = Di ≈ D. Due to computational expensiveas two decision variables involved and encounteringdifficulties in dealing with severe interference [4], itsuggests to consider basis functions ψs,τ (t) alreadyappeared as wavelets. Provided the variable changes 7→ 1

s , the inner product of WRC used as a similaritymeasurement is then a CWT of g(t) with respect toψ(t) [10]. Consequently, the aim of echolocation de-tection may be solved by seeking the local maximumof CWT coefficients:

maxs>0,τ∈ℜ

||CWTψ g(s, τ)||2. (2.7)

Given time support t ∈ [0, T ] for g(t), a discrete-time version of the CWT consists of dividing the timeinterval into N sub-intervals, and approximating theinput signal as g ≡ [g(t0), . . . , g(tN−1)] where tk =(k + 1) TN . The discrete CWT coefficients obtainedfor the sampled input signal g at the scale s can berepresented by a bank of FIR filter output responsewith filter coefficients h(s, ℓ) [5], i.e.,

CWTψ g[s, k] = y[s, k] = h(s, k) ∗ g(k)=

∑mink,n−1ℓ=max0,k−L h(s, ℓ)g(k − ℓ),

(2.8)

for k = 0, . . . , n+L−2. Here the filter tap range, dueto the symmmetric structure of the mother wavelet,is setting as

[−sTψ, sTψ]sTψ

(2Tψfψ − 1) ≡ [0, L− 1] (2.9)

with sampling rate fψ and effective support [−Tψ, Tψ]of the mother wavelet ψ. Due to the discrete settingby the FIR filtering occurred in the abscissa time-domain, a pair of optimizers (s∗, τ∗) can be evalu-ated using the following optimal target training andmapping algorithm [5]:

Algorithm 2.1 Set i = 1. Let us denote∑[ 2N+L2 ]

k=[L2 ]|y[s, k]|2 ≡ f(s) (2.10)

where y[s, k] = h(s, k)∗g(k) and g is a denoised signalof g. Denote fn(s), n = 1, 2, . . . by the n-th derivativeof f(s). Define ϵ > 0 and parameters s0, smin, smaxas CWT reference scales corresponding to the Dopplerscales s0, smin, smax which represent the stationary,minimum and maximum target motions, respectively.Let k0, kmin, kmax be time indices corresponding tothe Doppler scales s0, smin, smax, respectively.

1. Given parameters s0, smin, smax, find an opti-mizer s∗i that maximizes f(s), i.e.,

s∗i = argmaxs>0

f(s). (2.11)

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Figure 3: (a)Fuzzy inference system. (b)An equiva-lent ANFIS architecture

2. Knowing the scale s∗i , the corresponding time-delays τ∗ni,j = τ∗i (k

nj ), j = 1, 2 . . . can be obtained

for which indices knj are given by

knj = argmax(n,k)

|fnk (s∗i )− fk(s∗i )| (2.12)

where functions fnk and fk are denoted by thekth sample of the functions.

3. Let var(f) be the variance of the values in f .If the stopping criteria

max(var(fnk (s∗i ))) ≥ max(var(η(ti)) (2.13)|knj − k0|

max|kmin − k0|, |kmax − k0|< 1 (2.14)

are satisfied, then stop and set (s∗, τ∗) = (s∗i , τ∗i (k

nj ));

otherwise return to Step 1) with index i replacedby i+ 1.

2.2 ANFIS learning, TM-levelizationand Wavelet Denoising operations

• ANFIS: The adaptive network represented bythe ANFIS architecture [9] is based on the Sugeno’sfuzzy if-then rule [13] for which the fuzzy rea-soning mechanism is derived for an output ηfrom a given input training data set n(t) as de-picted in Fig. 3(a). In theory, the network iscombined with the gradient descent and least-squares methods. The gradient descent methodis in the forward path to upgrade the premiseparameters, while the least-squares method isin the backward path to identify the consequentparameters. As a result, the nonlinear relation-ship between η(n(t)) and n(t) is identified andthus producing an estimate η in the output.

Schematic description of the adaptive networkrepresented by the ANFIS architecture can beviewed in Fig. 3(b)[5, 6, 7]. Instead of sup-pressing the interference η(t) from the primarychannel, the ANFIS operation takes g as a con-taminated version of η(t) in the primary chan-nel for training. Further inside into the ANFISoperation and its process layers can be foundin [9].

• TM-levelization: Its functionality is to gener-ate a dynamic level-based process controlled bytwo gauges as depicted in Fig. 1(b): TMα1 , theexternal gauge and TMα2 , the internal gauge.As the TM-levelization process slides throughthe ANC output, the TMα1 is set iterativelyup. Its task is to generate loops that keepupdating the optimum TME scheme, removingpower of most of the sharp detail informationin the sense of trimmed mean estimation, andto achieve fast convergence towards an optimaltarget mapping in the CWT operation. WithTMα1 being set, the internal gauge TMα2 isoperated iteratively down to preserve the po-tentials arisen from the previous mapping, i.e.the data trimmed percentage rate goes down.When the level of TMα1 increases, more peaksof similar level to the contact signal become re-vealed. At the same time, decreasing the levelof TMα2 results in less and less power of po-tentials being removed in order to preserve thecontact signal. Note that when the proceededsignal has a strong target strength, the TM stepcan be skipped to increase the process speed ofthe TME scheme. This setting can be alwaysdone at the first iteration of the TME scheme.

• WDeN: The wavelet denoising operation is de-signed to further suppress the noise part of thetraining data followed by the TM step or re-sulted from the ANC scheme by applying thethresholding rule to the detail coefficients. Thisoperation is proven to be efficient and can beviewed as a nonparametric estimation of the de-sired noise-free signal [14]. The de-noising pro-cedure proceeds in three steps:

1. Decomposition: Choose a wavelet, and spec-ify a level N. Compute the wavelet decom-position of the signal at the level N.

2. Detail coefficients thresholding: For eachlevel from 1 to N, select a threshold andapply thresholding rule to the detail coef-ficients.

3. Reconstruction: Compute wavelet recon-struction based on the original approxi-mation coefficients of the level N and themodified detail coefficients of levels from 1to N.

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Figure 4: The 2ms long Morlet wavelet as a contactsignal in the echolocation system.

3 Simulation results3.1 Input data description for ANC neuro-

fuzzy schemeIn the ANC neuro-fuzzy scheme illustrated in Fig.

1(a), four channels of interference signal correspond-ing to the returns from 16 pings of 1s duration, de-livered in complex format, together with the samenumber of contact signal, are used to form the pri-mary and reference inputs to the ANC scheme. Morespecifically, as depicted in synthetic echo setting ofTable 1, the contact signal is the mother wavelet inthe CWT mapping and is adopted as Morlet wavelet [2]

ψ(t) = exp(−αt2) exp(j2πfct). (3.1)

The waveform consists of a window function gov-erned by α = 9.5657MHz and a modulation func-tion adjusted by fc = 20kHz, a central frequency ofthe waveform. Fig. 4 illustrates the 2ms long Morletwavelet as a contact signal employed in the echolo-cation system. In the following evaluations, the 16pings of returns are based on the various levels ofthe target strength in the range SNR = [−30, 0]db.In addition, four channels of interference signal in-clude the first two channels with reverberation r andwhite Gaussian noise n mixed together in each chan-nel. This constitutes the major source of interferencesignal for the input of unknown corrupting channelof noise path filter I (~1) and yields the output ηr+n.The remaining two channels contain solely the whiteGaussian noise with zero mean and variance 0.04 tofeed into the corrupting channel of noise path filter II(~2) and also yields the output ηn. The channels ofnoise path filters are to simulate the worse detectablesituation in highly distorting media. For simplicitybut still representing an extreme case of the classi-cal tests, channels of noise path filter are chosen as

follows:

~1(x1, x2) = 50(x1 + x2) + 100~2(x1, x2) = 50(x2 − x21)

2 + (1− x1)2.

(3.2)

Input data of ANFIS de-noise operation as given inthe ANFIS setting of Table 1 includes four Gaussianmemory functions (MFs) on each of the two input-output training pairs. Due to the sampling frequencyof the returns, there are totally 100k input-outputdata pair. Among them 50% of the data set is takenfor the training modes, while the remaining 50% isfor the checking modes to validate the identified fuzzymodel.

3.2 Input data description for the TMEscheme

The input data for the optimum TME scheme islisted in Table 1. In the step of TM-levelization,it contains 5 basic level set up empirically withinthe range [0.15, 0.75]× 10−3 and being updated withan increase of 60%. In the step of wavelet decom-position, different levels of target strength can beviewed by using a unique mother wavelet. In all ex-amples presented here, the largest scale level is setto be 16 and the orthogonal mother wavelet is em-pirically chosen as the Daubechies extremal phasewavelet [10] of order 10. Soft threshold is adoptedfor the mother wavelet to yield minimax performancefor mean square error against an ideal procedure.The CWT mother wavelet is adopted by the Morletwavelet as described in Eq. (3.1) with the duration of2ms illustrated in Fig. 4. The waveform is sampledat 32Hz with effective support [−5, 5] for the low-est level of similarity measurement within the scalerange [25, 36]. The resultant signal is then split intoFIR filter banks with the tap range [250, 360].

3.3 ResultsTogether with the real data set supported by DERA

UK as part of the torpedo homing research programme,the sonar simulator with MATALB-GUI platform inFig. 2 is ready to evaluate the performance of theANC-TME hybrid algorithm for two scenarios of themultiple targets’ motion estimation. As illustratedin Table 1 for the sonar environment, there were 16data sets received for various target strength. Fur-thermore, the strength of signal to reverberation ismeasured by the target’s echo to reverberation wave-form.

3.3.1 Scenario I

This scenario is to estimate target’s Doppler mo-tion (radial range, velocity and acceleration) at thesignal strength of SNR=-30db for two targets’ pingnoted by T1 and T2. More specifically, the ping T1is from a sonar guided modern torpedo (such as the

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spearfish torpedo) launched below the surface by asubmarine. The torpedo’s mission is to search forand home in its target with the ping T2. The tor-pedo is thus assumed moving away from the signalreceiver with initial speed based on its parent vehi-cle, and its radial acceleration is calculated at themoment when it is firing. The pinged target T2 isassumed almost stationary with slow motion towardsthe signal receiver. Detail of both targets are listedin the table 2. Combined with the four input chan-nels received together with the noise path filters alldepicted in Figs. 5(a)-(f), the complex signal is ob-tained and depicted in Fig. 6(c), while Fig. 6(a)-(b)are given for reference. As can be viewed clearly,pings T1 and T2 are completely buried in the back-ground interference. By the setting of initial param-eters given in Table 1, Figs. 7(a) and 8(a) show theoutput of ANC neuro-fuzzy scheme with 5 epochs ofANFIS operation employed for training and validat-ing the complex signals. Performing the first WDeNof the optimum TME scheme yields outputs givenin Fig. 7(b) for echo T1 and Fig. 8(b) for echo T2.Followed by the optimal CWT similarity measure-ment, the estimated location of ping T1e as depictedin Fig. 7(c) is accurately matched to the ideal pingT1 with 3 sampling points difference. While, a falsealarm occurred in Fig. 8(c) for T2 is due to its weakreturned signal as can be viewed by Fig. 6(a). As a re-sult, the first level of TM-levelization with the gaugelevel TMα1 = TMα2 = 7.5 × 10−4 is performed toget rid of excessive noise and yields the 2nd WDeNoutput shown in Fig. 8(d). Performing the optimalCWT measurement, the location of T2 is successfullypinged at T2e with 4 sampling points difference asillustrated in Fig. 8(e).

3.3.2 Scenario II

This scenario is to consider various levels of thetarget strength in the range SNR = [−30, 0]dB with2db element evenly spaced for the estimation of to-tal 16 echo returns. Here each return contains twopings of target signal, T1 and T2. Statistical resultsin the sense of the normalized absolute error (NAE)and the relative absolute error (RAE) will be used toexamine the performance of the hybrid algorithm. Toefficiently implement the hybrid algorithm, the rangeof ANFIS epoch in the simulator is set based on 6different ranges of SNR. That is, for the ranges ofSNR level [−5(k+ 1),−5k− 1]dB, k = 0, . . . , 5, theircorresponding iterations are set at 2 ≤ [1.5k/2], k =1, . . . , 6 epoches. Figs. 9(a)-(e) and 10(a)-(e) showprediction errors of target motion parameters in termsof NAE of the T1 and T2 targets, respectively. Inall 16 trials, clearly each estimate of parameter hasaccurately matched their corresponding correct oneswith the maximum false detection of 1.5%. In addi-tion, the overall error measurements of RAE as canbe seen in Fig. 9(f) and 10(f) of each target parame-ters are also about 1.5% false detection rate. Fig. 11demonstrates the computational efficiency of the hy-brid algorithm in dealing with both targets in varioustarget strength with average cost of 31.476 sec pertrial.

4 ConclusionIn this contribution, an active sonar simulator

with built-in algorithm, ANC-TME hybrid algorithmdeveloped previously for real-time applications in FPGAhardware implementation, was described and employedto evaluate the performance and tracking of the hy-brid algorithm by real data set. The various featuresincorporated in the simulators allow different scenar-ios to be studied in real-time with an interactive userinterface. Without using more expensive machine totest the real sonar data, excellent performance of thealgorithm indicated by outputs of the simulator withscenarios chosen has been shown to be suitable forthe detection of underwater targets’ Doppler motionat very low target strength. Quantitative analysesof the performance evaluation obtained by the PC-based simulator for each returns of ping have evenshown that the hybrid algorithm not only meets thedevelopment requirements but also provides a higherdegree of signal detection capability with an increasedrobustness against false signal detections.

AcknowledgmentThis work acknowledges the technical support by

DERA (UK) and the financial support by NSC (Tai-wan) under grant no.: NSC 98-2221-E-168-028.

References[1] R. Young, Wavelet Theory and Its Applications,

Kluwer Academic Publisher, Bosten, 1993.

[2] L. G. Weiss, “Wavelets and wideband correlationprocessing,” IEEE Signal Processing Magazine,pp. 13-32, 1994.

[3] H. Naparst, “Dense target signal processing,”IEEE Trans. Inform. Theory, vol. 37, pp. 317-327, 1991.

[4] P. Delaney and D. Walsh, “Performance analysisof the incoherent and skewness matched filter de-tectors in multioath environments,” IEEE Jour-nal of Oceanic Engineering, vol. 20, no. 1, pp.80-84, 1995.

[5] C. H. Tseng and M. Cole, “Towards smart-pixel-based implementation of wideband active sonarecholocation system for multi-target detection,”ICSPCS2008, Gold Coast, Australia, 2008.

[6] C. H. Tseng, and M. Cole,“Optimum multi-targetdetection using an ANC neuro-fuzzy scheme andwideband replica correlator,” IEEE ICASSP2009,pp. 1369-1372, Taipei, Taiwan.

[7] C. H. Tseng, “Effective wideband acoustic sonarsignal detection based on adaptive neuro-fuzzyprocessor and optimal wavelet transform,” The17th National Conference on Fuzzy Theory andIts Application, pp. 817-822, Kaohsiung, 2009.

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Table 1: Critical Parameters Setting.Sea Depth (m) 100Sonar Depth (m) 50

Sonar Wind Speed 6 m/s(≈ sea state 3)Environment Seabed Type Medium Sand

Setting Number of Beams 1Beamwidth 3dB (≈ 40 degrees)Maxi. Target Range (m) 500Pulse Morlet Wavelet

Synthetic Pulse Length (ms) 2Echo Echo Duration (s) 1

Environment Sampling Frequency (Hz) 100kSetting Amplitude (αi) 0.1

SNR range (dB) [-30,0]Data Set per Source 2

ANFIS MFs per Input 4Environment MF Type Gaussian

Setting Input-Output Data Load 100kTraining/Checking Rate [50%, 50%]

TM Basic Step Range [0.15, 0.75]× 10−3

Level Setting Increment Percentage 60%DWT Wavelet Type Daubechies 10

Denoise Decomposition Level 16Setting Threshold Type Soft

Wavelet Type Morlet WaveletCWT Support Range [−5, 5]

Mother Wavelet Scale Range [25, 36]Setting Sampling Frequency (Hz) 32

Filter Tap Range [250, 360]

Table 2: Comparison between Ideal outputs and the TME outputs.Synthetic echo T1 T2Algorithm Output Ideal TME Ideal TMETOA (s) .25 .254813 .60 .5995Location(pts) 25585 25582 60060 60056Acceleration (m/s2) 35 34.4706 −.05 −.1256Initial velocity (kn) 20.0 −1.0Final Velocity (kn) 37.7037 37.7032 −1.05067 −1.05066

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−5

0

5(a)

Am

plitu

de

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1000

0

1000

2000

Am

plitu

de

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−1000

0

1000

2000

(c)

Am

plitu

de

Time (sec)

T1 T

2

Figure 6: Time-domain received signal echoes.(a)Noise-free synthetic echoes: T1 and T2.(b)Additive Interference consisting of reverbera-tion of Morlet and WGN(0,0.04) sampled at 100kHz. (c)Composite returned signal with the targetstrength SNR=−30dB.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

5

10

AN

FIS

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

20

40

60

80

WD

eN

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

2000

4000

6000

(c)

CW

T

Time (sec)

T1

T1

T1 T

1e

Figure 7: (a)ANC neuro-fuzzy output of the 1st tar-get ping T1 with 5 ANFIS epochs. (b)Output of the1st WDeN without TM-levelization. (c) Output ofthe 1st optimal CWT mapping: |f3(s∗1)− f0(s∗1)|.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

05

10

AN

FIS

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

20406080

WD

eN

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

200040006000

(c)

CW

T

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−10

0

10

WD

eN

(d)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

200040006000

(e)

CW

T

Time (sec)

T2

T2

T2

T2e

T2e

T2

Figure 8: (a)ANC neuro-fuzzy output of the 2nd tar-get ping T2 with 5 ANFIS epochs. (b)Output of the1st WDeN without TM-levelization. (c) Output ofthe 1st optimal CWT mapping: |f3(s∗1) − f0(s∗1)|.(d) Output of the 2nd WDeN with TMα1

= TMα2=

7.5×10−4. (e) Output of the 2nd optimal CWT map-ping: |f3(s∗2)− f0(s∗2)|.

−30 −25 −20 −15 −10 −5 0024

x 10−3 (a)

NA

ER

(%)

−30 −25 −20 −15 −10 −5 0024

x 10−3 (b)

NA

Eτ(%

)

−30 −25 −20 −15 −10 −5 0011.5

(c)

NE

a(%)

−30 −25 −20 −15 −10 −5 00

5x 10

−4 (d)

NE

v(%)

−30 −25 −20 −15 −10 −5 0024

x 10−3

dB

(e)

NA

Es(%

)

Range(R) Time−Delay(t) Acc.(a) Scale(s)011.5

(f)

RA

E(%

)

Figure 9: Performance evaluation using NAE (%) andRAE (%) for T1 at the SNR range of [−30, 0]dB:(a)NAE range. (b)NAE round-trip time-delay (τ).(c)NAE radial acceleration (a). (d)NAE Dopplerscale (s). (e)RAE motion parameters

−30 −25 −20 −15 −10 −5 002

x 10−3 (a)

NA

ER

(%)

−30 −25 −20 −15 −10 −5 002

x 10−3 (b)

NA

Eτ(%

)

−30 −25 −20 −15 −10 −5 00 0.50.8

(c)

NE

a(%)

−30 −25 −20 −15 −10 −5 00

0.51

x 10−3 (d)

NE

v(%)

−30 −25 −20 −15 −10 −5 002

x 10−3

dB

(e)

NA

Es(%

)

Range(R) Time−Delay(t) Acc.(a) Scale(s)0 0.51 1.5

(f)

RA

E(%

)

Figure 10: Performance evaluation using NAE (%)and RAE (%) for T2 at the SNR range of [−30, 0]dB:(a)NAE range. (b)NAE round-trip time-delay (τ).(c)NAE radial acceleration (a). (d)NAE Dopplerscale (s). (e)RAE motion parameters

−30 −25 −20 −15 −10 −5 00

5

10

15

20

25

30

35

40

45

dB

Tim

e (

se

c)

ANCTME T

1

TME T2

Figure 11: Computational time consumption for thedetection of T1 and T2 at the SNR range of [−30, 0]dBwith average cost of 31.476 sec/trial.