Aircraft Flight Parameter Estimation Using Acoustic Multipath Delays

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1 I. INTRODUCTION Aircraft Flight Parameter Estimation Using Acoustic Multipath Delays KAM W. LO, Senior Member, IEEE BRIAN G. FERGUSON, Member, IEEE Defence Science and Technology Organisation Australia YUJIN GAO ALAIN MAGUER Thales Underwater Systems Australia In a multipath propagation environment, two or more attenuated and delayed replicas of the same radiated signal are received at a sensor. Although multipath propagation is often regarded as an undesired physical phenomenon, it can be utilized for certain applications. For example, in ocean acoustics, the difference in the times of arrival between the various multipaths can provide information about the location of the source if an acoustic propagation model is available [1 2]. For broadband acoustic sources in motion, multipath propagation results in a pattern of interference fringes, known as the Lloyd s mirror effect [3], in the time-frequency distribution of the sensor output. A model has been recently developed for the acoustical Lloyd s mirror effect observed when a jet aircraft (or other airborne source of broadband sound) travels with uniform linear motion over an acoustic sensor located above a hard ground [4 5]. Fig. 1 shows the observed Thesignalemittedbyanairborneacousticsourcearrivesat a stationary sensor located above a flat ground via a direct path and a ground-reflected path. The difference in the times of arrival of the direct path and ground-reflected path signal components, referred to as the multipath delay, provides an instantaneous estimate of the elevation angle of the source. A model is developed to predict the variation with time of the multipath delay for a jet aircraft or other broadband acoustic source in level flight with constant velocity over a hard ground. Based on this model, two methods are formulated to estimate the speed and altitude of the aircraft. Both methods require the estimation of the multipath delay as a function of time. The methods differ only in the way the multipath delay is estimated; the first method uses the autocorrelation function, and the second uses the cepstrum, of thesensoroutputoverashorttimeinterval.theperformances of both methods are evaluated and compared using real acoustic data. The second method provides the most precise aircraft speed and altitude estimates as compared with the first and two other existing methods. Fig. 1. Observed interference fringe pattern for typical jet aircraft transit. Manuscript received January 4, 2002; revised August 1, 2002; released for publication October 28, IEEE Log No. T-AES/39/1/ Refereeing of this contribution was handled by P. K. Willett. Authors current addresses: K. W. Lo and B. G. Ferguson, Defence Science and Technology Organisation, PO Box 44, Pyrmont, NSW 2009, Australia; Y. Gao, Thales Underwater Systems, 274 Victoria Road, Rydalmere, NSW 2116, Australia; A. Maguer, Technical Directorate, Thales Underwater Systems, Sophia Antipolis, France /03/$17.00 c 2003 IEEE interference fringe pattern for a typical jet aircraft transit. Based on the model of the Lloyd s mirror effect, two methods have been formulated to estimate the flight parameters of the source [5 6]. In both methods, the time-frequency distribution of the sensor output is treated as an image. This image is preprocessed to enhance the fringe pattern and then the flight parameters are extracted from the resultant image by optimizing a cost function. Described here are two alternative methods for flight parameter estimation using a single sensor, which donot require any time-frequency signal analysis and image preprocessing. Both methods measure the temporal variation of the multipath delay (time difference between the arrival of the ground-reflected IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 39, NO. 1 JANUARY

2 Fig. 2. Geometrical configuration of airborne source and sensor. path signal and the direct path signal), and then minimize the sum of the squared deviations of the noisy multipath delay estimates from their predicted values over a sufficiently long period of time. The two methods differ in the way the multipath delay is estimated. In the first method, the multipath delay is estimated by autocorrelating the sensor output over a short time interval. In the second method, the multipath delay is estimated using short time cepstrum analysis. The performances of the proposed flight parameter estimation methods are evaluated using real data recorded from the individual sensors of a large microphone array for 10 jet aircraft transits, and the results are compared with those obtained using the previous methods [5]. II. MULTIPATH TIME-DELAY MODEL Consider an airborne acoustic source (aircraft) moving in a straight line at constant subsonic speed v and constant altitude h t over a hard ground as depicted in Fig. 2. An acoustic sensor is located at a height h r above the ground. The source is at the closest point of approach (CPA) to the sensor at time c,withthe ground range at the CPA being d c. The source emits a broadband random acoustic signal, which arrives at the sensor via a direct path and a ground-reflected path. A model for the temporal variation of the multipath delay is derived below using a quasistationary approach. To calculate the multipath delay at a given time t, the source is assumed to be fixed at the position at an earlier time (<t)which accounts for the sound propagation delay from the source to the sensor. The source-sensor geometry used for the calculation is depicted in Fig. 3. The multipath delay at time t is given by D(t)=[R r ( ) R d ( )]=c (1) where c is the speed of sound propagation in air, and R d ( ) andr r ( ) are the respective lengths of the direct Fig. 3. Source-sensor geometry for calculation of multipath delay at time t, where = t R( )=c. and ground-reflected paths at time : q R d ( )= v 2 ( c ) 2 + dc 2 +(h t h r )2 (2) R r ( )= q v 2 ( c ) 2 + dc 2 +(h t + h r )2 : (3) Assuming h t À h r and using a first order approximation, it can be shown that D(t)» = 2h t h r =cr( ) (4) where R( ) is the slant range (measured from point O) of the source at time : q R( )= v 2 ( c ) 2 + dc 2 + h2 t : (5) Equation (4) can be written as D(t)» = 2(h r =c)siná( ) (6) where Á( ) is the elevation angle (measured at point O) of the source at time. It follows from (6) that the source elevation angle can be estimated from the multipath delay as Á( )=sin [cd(t)=2h r ]and 0 <D(t) 2h r =c. The relationship between and t needs to be defined. Here is chosen as the emission time of the signal that arrives at point O at (later) time t, thatis, = t R( )=c (7) where R( )=c is the time required for sound to propagate from the source to point O. Substituting (5) into (7) and solving the resulting quadratic equation for gives = c + c2 (t c ) Ã(h t ) c 2 v 2 (8) where q Ã(h t )= (ht 2 + d2 c )(c2 v 2 )+v 2 c 2 (t c ) 2 : (9) 260 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 39, NO. 1 JANUARY 2003

3 Equating (7) and (8), it can be shown that c R( )= c 2 v 2 [Ã(h t ) v2 (t c )]: (10) Substituting (10) into (4) yields the desired model: where D(t)» = 2(cr 2 v2 r )=c2 r p 2 (cr 2 v2 r )+c2 r v2 t (t c )2 v r v t (t c ) (11a) v r = v=h r v t = v=h t q = 1+(d c =h t ) 2 c r = c=h r : Note that D(t) is a function of fv r,v t, c, g, or equivalently, the flight parameters fv,h t, c,d c g. Equation (11) can also be derived from the destructive-interference frequency model described in [4 5], using the fact that the direct path and ground-reflected path signal components interfere destructively at frequency f n (t) when their phase difference is an odd integer multiple of ¼, thatis, 2¼f n (t)d(t)=(2n 1)¼, wheren =1,2,:::: III. FLIGHT PARAMETER ESTIMATION (11b) (11c) (11d) (11e) A nonlinear least-squares (NLS) approach is adopted to estimate the flight parameters using the time sequence of multipath delay estimates from the acoustic sensor. Define the parameter vector z =[v r,v t, c, ] T, where the superscript T denotes matrix transpose. The estimate of z, denoted as ẑ =[ˆv r, ˆv t, ˆ c, ˆ ] T, is obtained by minimizing the cost function KX P(z)= [ ˆD(t k ) D(t k,z)] 2 (12) k=1 where ˆD(t k ) is the estimated value of the multipath delay at time t k and D(t k,z) is the corresponding predicted value using (11), for 1 k K. Giventhe sensor height h r, the speed, altitude, and CPA ground range of the source are then estimated as ˆv = h r ˆv r (13a) ĥ t = ˆv=ˆv t (13b) ˆd c = ĥtpˆ 2 1 : (13c) The multipath delay at time t k is estimated using 1) the autocorrelation function [7] and 2) the cepstrum [8] of the sensor output over a short time interval centered at time t k. (Appendix A briefly describes multipath delay estimation based on these methods.) The resulting flight parameter estimation methods are referred to as the autocorrelation NLS method and cepstrum NLS method, respectively. There are different definitions for the cepstrum of a signal [8 11]. It is defined here as the inverse Fourier transform of the logarithm of the signal s power spectrum [11]. The word cepstrum was derived from the word spectrum, and the terminology used in cepstrum analysis was derived from the terminology used in spectrum analysis, for example, quefrency from frequency and rahmonics from harmonics. The positive time lag ( 2h r =c) atwhich the autocorrelation function is a maximum gives the estimate of D(t k ). Similarly, the quefrency ( 2h r =c) at which the cepstrum is a maximum gives the estimate of D(t k ). The minimization of the cost function in (12) is performed numerically using the Levenberg-Marquardt method [12], which has proven to be more robust than the Gauss Newton method. Define the error vector e(z)=[ˆd(t 1 ) D(t 1,z),:::, ˆD(t K ) D(t K,z)] T (14) and the Jacobian matrix J(z)=[r z e T (z)] T (15) where r z =[@=@v r,@=@v v,@=@ c,@=@ ] T is the gradient operator. The n +1th estimate of z is given by ẑ n+1 = ẑ n [J T (ẑ n )J(ẑ n )+¹I] J T (ẑ n )e(ẑ n ), n 1 (16) where ¹ is a convergence factor [12]. The initial estimate ẑ 1 =[ˆv r o, ˆv t o, ˆ c o, ˆ o ] T is obtained using the following procedure (based on the properties of D (t) as described in Appendix B). 1) Find the time ˆt o o at which ˆD (t) 1= ˆD(t) isthe minimum. 2) Compute ˆ o =2ˆD (ˆt o o )=c r. 3) Calculate ˆv o r = c r ˆ_D + + ˆ_ D ˆ_D + ˆ_ D µ 4 and ˆv t o = c r ˆ_D + ˆ_D ˆ_D + ˆ_ D where ˆ_ D and ˆ_ D + are the respective gradients of the two straight lines that provide best fit to the first few (typically ten) and last few data points of ˆD (t). 4) Calculate IV. ˆ o c = ˆt o o ˆ oˆv o r c r ˆv o t EXPERIMENTAL RESULTS The performance of the proposed flight parameter estimation method is evaluated using real data recorded from a large microphone array as depicted in Fig. 4. The array consists of 21 microphones located at a height of 0.55 m above a level ground composed :, LO ET AL.: AIRCRAFT FLIGHT PARAMETER ESTIMATION USING ACOUSTIC MULTIPATH DELAYS 261

4 Fig. 4. Sensor configuration of microphone array used in field experiment. of compact soil. The positions of sensors 1 to 19 and sensors 19 to 21 are collinear along the EW and NS directions, respectively. While sensors 1 to 15 are uniformly spaced at 0.9 m, the intersensor spacings for sensors 15 to 19 are not uniform but increase by factors of 2 from 12.6 to m. Sensors 19 to 21 are uniformly spaced at m. A jet aircraft flies over the planar array 10 times with a constant speed of 300 knots at various altitudes: 1000 ft, 1250 ft, 1500 ft, 1750 ft, and 2000 ft. There are two aircraft transits at each altitude. The flight path of the aircraft during each transit is level with the ground and approximately parallel to the EW direction. The speed of sound propagation in air is 340 m/s. The output of each microphone is sampled at a frequency of 7111 Hz. The data recorded from the outputs of the 21 microphones for the 10 aircraft transits (that is, a total of 210 real data sets) are used after the trial to test the proposed methods. A. Autocorrelation NLS Method The data from each microphone are processed in overlapping blocks, each containing 1024 samples, with 75% overlap between two consecutive data blocks. The autocorrelation of each data block is implemented in the frequency domain using the fast Fourier transform (FFT). The location of the peak of the autocorrelation function in the positive time lag axis gives the multipath delay estimate, which is refined using 3-point quadratic interpolation. As a typical example, Fig. 5 shows the normalized autocorrelogram (an intensity plot showing the variation with time of the normalized autocorrelation function, with the horizontal axis corresponding to time and the vertical axis corresponding to the time lag variable of the normalized autocorrelation function) for a particular aircraft transit. Fig. 6 Fig. 5. Normalized autocorrelogram (intensity plot showing temporal variation of normalized autocorrelation function, with horizontal axis corresponding to time and vertical axis corresponding to time lag variable of normalized autocorrelation function) for a particular jet aircraft transit. Fig. 6. Multipath delay versus time for same aircraft transit considered in Fig. 5. Estimated values from autocorrelogram (dots). LS fit (solid line). shows, as dots, the time sequence of multipath delay estimates extracted (automatically) from Fig. 5 by locating the peak of each time slice of the autocorrelogram in the positive time lag axis. With the proposed method, the estimates of the flight parameters correspond to the parameter values that provide a least-squares (LS) fit of the multipath time-delay model (11) to the time sequence of multipath delay estimates. The LS fit is shown as a solid curve in Fig. 6, and the actual and estimated values of the flight parameters are shown at the top of Fig. 6. The multipath delay estimate at a given sensor time t is used in (6) to calculate the elevation angle of the aircraft at an earlier source time (which is related to t via (8)). Fig. 7 shows, as dots, the 262 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 39, NO. 1 JANUARY 2003

5 Fig. 7. Elevation angle of aircraft versus time for same aircraft transit considered in Fig. 5. Estimated values (dots). Predicted values (solid line). estimated elevation angle of the aircraft versus sensor time t. The solid curve in Fig. 7 is the elevation angle trajectory predicted by the estimated flight parameters. There are 21 data sets for each aircraft transit (one data set per sensor). Figs. 8(a) and 8(b) show, respectively, the mean values (denoted as black-filled circles) of the speed estimates and altitude estimates for each of the 10 aircraft transits. Each error bar represents 1 standard deviation in the estimates and each white-filled circle indicates the actual value. The cumulative probability distributions (CPDs) of therelativeerrorsintheestimatesoftheaircraft speed and altitude are calculated using the estimated parameter values for all 210 data sets, and the results are shown in Fig. 8(c). Here, the CPD of a relative error at " is the probability that the magnitude of the relative error is less than or equal to ". The (empirical) CPD is calculated as follows. First the relative error data are sorted in ascending order of magnitude: "(1) <"(2) < <"(n) < "(N), where N(= 210) is the number of data points. Then the CPD at "(n) is given by n=n. Fig. 8(b) also shows, as rectangles, the altitude estimates from [13], which were obtained using the wavefront curvature (passive ranging) technique. With this technique [13], the data from the linear subarray consisting of sensors 19, 20, and 21 are processed in blocks. Each data block from the middle sensor of the subarray (sensor 20) is cross-correlated with the corresponding data blocks from the other two sensors, and the resulting time delay estimates are then used to calculate the source range relative to the middle sensor of the subarray. The minimum of the source range track (range estimate versus time) gives an estimate of the source altitude h t, provided h t is much larger than the CPA ground range relative to the middle sensor. The altitude estimate obtained using the wavefront curvature technique for each aircraft transit is consistent with (or within 1.5 standard deviations from the mean value of) those obtained using the autocorrelation NLS method. Fig. 8. Results obtained using the autocorrelation NLS method. (a) Mean value of speed estimates for each aircraft transit (black-filled circles), where error bars represent 1 standard deviation and white-filled circles indicate actual values. (b) Similar to (a) but for aircraft altitude. Rectangles denote estimates obtained using wavefront curvature technique [13]. (c) CPDs of relative errors in speed (solid line) and altitude (dashed line) estimates. B. Cepstrum NLS Method The data from each microphone are processed in overlapping blocks, each containing 1536 samples, with 75% overlap between two consecutive data LO ET AL.: AIRCRAFT FLIGHT PARAMETER ESTIMATION USING ACOUSTIC MULTIPATH DELAYS 263

6 Fig. 9. Cepstrogram (intensity plot showing temporal variation of cepstrum, with horizontal axis corresponding to time and vertical axis corresponding to quefrency variable of cepstrum) for the same aircraft transit considered in Fig. 5. blocks. Each data block is divided into three 75% overlapping sections and their periodograms are calculated using a 1024-point FFT. The three periodograms are then averaged to give the power spectrum of the data block. The cepstrum of the data block is obtained by applying a 2048-point FFT to the logarithm of its power spectrum. Each peak in the cepstrum corresponds to a rahmonic and the position of the first rahmonic (peak) along the quefrency axis gives the multipath delay estimate. As a typical example, Fig. 9 shows the cepstrogram (an intensity plot showing the variation with time of the cepstrum, with the horizontal axis corresponding to time and the vertical axis corresponding to the quefrency variable of the cepstrum) for the same aircraft transit considered in Fig. 5. Fig. 10 shows, as dots, the time sequence of multipath delay estimates extracted (automatically) from Fig. 9 by locating the peak of each time slice of the cepstrogram in the quefrency axis. The LS fit of the multipath time-delay model to the time sequence of multipath delay estimates is shown as a solid curve in Fig. 10, and the actual and estimated values of the flight parameters are shown at the top of Fig. 10. Figs. 11(a) and 11(b) show, respectively, the mean values (denoted as black-filled circles) of the speed estimates and altitude estimates for each of the 10 aircraft transits. Each error bar represents 1 standard deviation in the estimates and each white-filled circle indicates the actual value. Fig. 11(c) shows the CPDs of the relative errors in the estimates of the aircraft speed and altitude. Fig. 11(b) also shows, as rectangles, the altitude estimates obtained using the wavefront curvature technique [13]; each of these estimates is consistent with (or within 2 standard Fig. 10. Multipath delay versus time for same aircraft transit considered in Fig. 5. Estimated values from cepstrogram (dots). LS fit (solid line). deviations from the mean value of) those obtained using the cepstrum NLS method. C. Comparison with Previous Methods The proposed methods estimate the flight parameters by measuring the temporal variation of the multipath delay. The previous methods, namely the NLS and GHT (generalized Hough transform) methods [5], utilize the acoustical Lloyd s mirror effect observed in the time-frequency distribution of the sensor output for flight parameter estimation. In these methods, the spectrogram is preprocessed to enhance the interference fringe pattern, and then the flight parameters are extracted from the destructive-interference curves of the fringe pattern by optimizing a cost function. The NLS method requires the estimation of the destructive-interference frequencies while the GHT does not. The performances of these methods were evaluated in [5] using the same sets of real data considered here. The spectrogram of each microphone output was computed using a 2048-point FFT for each data block consisting of 607 samples (tapered with a Hanning window and padded with 1441 zeros) with two consecutive data blocks being overlapped by 75% (455 samples). Only the first and second destructive-interference curves were used to estimate the flight parameters. The mean values and standard deviations of the speed and altitude estimates for each of the 10 aircraft transits, together with the CPDs of the relative errors in the estimates of these two parameters, can be found in [5]. BasedontheCPDresults,itseemsthatthe autocorrelation NLS method provides more accurate aircraft speed and altitude estimates than the other 264 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 39, NO. 1 JANUARY 2003

7 TABLE I Comparison of Variability in Aircraft Speed and Altitude Estimates for Proposed Methods and Previous Methods [5] Method Speed (knots) Altitude (feet) Cepstrum NLS Auto-correlation NLS NLS [5] GHT [5] Method Speed (%) Altitude (%) Cepstrum NLS Auto-correlation NLS NLS [5] GHT [5] Note: Top: Average standard deviation. Bottom: Average relative standard deviation. Fig. 11. Results obtained using cepstrum NLS method. (a) Mean value of speed estimates for each aircraft transit (black-filled circles), where error bars represent 1 standard deviation and white-filled circles indicate actual values. (b) Similar to (a) but for aircraft altitude. Rectangles denote estimates obtained using wavefront curvature technique [13]. (c) CPDs of relative errors in speed (solid line) and altitude (dashed line) estimates. three methods (cepstrum NLS, NLS, GHT). However, any measurement uncertainty in the actual flight parameter values could alter the CPD results, which would mean that the performance comparison based on the CPD results would not be reliable. A definite conclusion that can be drawn from the present field experiment is that the variability in the aircraft speed and altitude estimates is least (that is, the precision is best) when using the cepstrum NLS method as compared with the other three methods. (Here the distinction between the terms accuracy and precision should be noted [14]. Accuracy refers to the closeness of the measurements to the actual value of the physical quantity, whereas the term precision is used to indicate the closeness with which the measurements agree with one another independently of any systematic error involved.) The variability is measured here using the average standard deviation and the average relative standard deviation. The average standard deviation is simply the standard deviations averaged over the 10 aircraft transits. The average relative standard deviation is calculated by first dividing the standard deviation by the mean value for each aircraft transit and then averaging the results over the 10 aircraft transits. These two variability measures of the aircraft speed and altitude estimates are shown in Table I for all four methods. Both variability measures are in favor of the cepstrum NLS method. The result of a smaller variability (higher precision) in the parameter estimates when using the cepstrum NLS method as compared with the autocorrelation NLS method is consistent with Figs. 5 and 9, that is, the time-delay track in the cepstrogram is less noisy than that in the autocorrelogram. V. CONCLUSIONS Jet aircraft emit high intensity broadband sound. The experimental results demonstrate that both autocorrelation NLS method and cepstrum NLS method are able to provide satisfactory estimates of the speed and altitude of a low-flying jet aircraft. These two methods are more computational efficient than the NLS and GHT methods [5] as they do not require time-frequency image preprocessing that is time consuming. Based on the results of the LO ET AL.: AIRCRAFT FLIGHT PARAMETER ESTIMATION USING ACOUSTIC MULTIPATH DELAYS 265

8 present experiment, the cepstrum NLS method has the smallest variability (highest precision) in the aircraft speed and altitude estimates, followed by the autocorrelation NLS method, then the NLS method, and finally the GHT method. With the cepstrum NLS method, the average standard deviations (over the 10 aircraft transits) for the aircraft speed and altitude estimates are 22.6 knots and ft, respectively, and the corresponding average relative standard deviations are 7.4% and 9.1%, respectively. The cepstrum NLS method has been implemented in a land-based acoustic aircraft detection and classification system [15]. APPENDIX A. MULTIPATH DELAY ESTIMATION Using the quasi-stationary assumption for the moving source, the signal received at the sensor over a short time interval centered at time t can be modeled as (ignoring the noise): x(t 0 )=s(t 0 )+ s[t 0 D(t)] for jt 0 tj <± (17) where s(t 0 ) is the direct path arrival of the source signal, is a relative attenuation factor for the ground-reflected path, and D(t) is the multipath delay givenby(1). Autocorrelation Method: The autocorrelation function of x(t 0 )isgivenby R x ( 0 )=(1+ 2 )R s ( 0 )+ R s [ 0 D(t)] + R s [ 0 + D(t)] (18) where R s ( 0 ) is the autocorrelation function of s(t 0 ) and 0 is the time lag variable. Equation (18) shows that R x ( 0 ) has three peaks located at 0 =0, D(t) respectively. Since D(t) > 0, the positive time lag at which R x ( 0 ) is a maximum provides an estimate of D(t). Cepstrum Method: The multipath delay can also be estimated using cepstrum analysis. This method is based on the principle that the logarithm of the power spectrum of a signal containing an echo (ground-reflected component) has an additive periodic component due to that echo. Therefore, the inverse Fourier transform of the log-power spectrum exhibits a peak (rahmonic) at the echo delay (multipath delay). Higher order rahmonics may also appear at integer multiples of the multipath delay. Mathematically, the power cepstrum of the signal x(t 0 ) is defined as x( 0 )=F flogjx(f)j 2 g (19) where X(f) is the Fourier transform of x(t 0 ), F denotes the inverse Fourier transform operator, and 0 is the quefrency variable of the cepstrum. The location of the first peak of x( 0 ) provides an estimate of D(t). APPENDIX B. PROPERTIES OF D (T) As t! 1, D (t) varies linearly with t and the gradients of the two asymptotes are given by _D = 1 µ c 2 r v t : (20) 2 c r v r The minimum value of D (t) isd o»= c r =2 which occurs at t» o = c +( v r =c r v t ). ACKNOWLEDGMENTS The authors gratefully acknowledge Mr. Lionel Criswick, Defence Science and Technology Organisation, for his contributions to this paper, and Prof. R. B. Randall, the University of New South Wales, for his early work on flight parameter estimation using cepstrum analysis. REFERENCES [1] Friedlander, B. (1988) Accuracy of source localization using multipath delays. IEEE Transactions on Aerospace and Electonic Systems, 24 (July 1988), [2] Rosenberger, J. C. (1989) Passive localization. In Y. T. Chan (Ed.), Underwater Acoustic Data Processing, Boston: Kluwer Academic Publishers, 1989, [3] Stacey, P. J. (1998) Localisation from Lloyd s mirror features. In Proceedings of the Undersea Defence Technology Europe 98 Conference, London, UK, 1998, [4] Lo, K. W., and Ferguson, B. G. (1999) Passive estimation of aircraft motion parameters using destructive interference between direct and ground-reflected sound waves. In Proceedings of 1999 Information, Decision and Control, Adelaide, Australia, Feb. 1999, [5] Lo, K. W., Perry, S. W., and Ferguson, B. G. (2002) Aircraft flight parameter estimation using acoustical Lloyd s mirror effect. IEEE Transactions on Aerospace and Electonic Systems, 38 (Jan. 2002), [6] Lo, K. W., Perry, S. W., and Ferguson, B. G. (1999) An image processing approach for aircraft flight parameter estimation using the acoustical Lloyd s mirror effect. In Proceedings of the Fifth International Symposium on Signal Processing and its Applications, Brisbane, Australia, Aug. 1999, [7] Ianniello, J. P. (1983) The variance of multipath time delay estimation using autocorrelation. Technical memo TM , Naval Underwater Systems Center, New London CT, [8] Bogert, B. P., et al. (1963) The quefrency analysis of time series for echoes: cepstrum, pseudo-autocovariance, cross cepstrum and saphe cracking. In M. Rosenblatt (Ed.), Proceedings of the Symposium on Time Series Analysis, New York: Wiley, 1963, IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 39, NO. 1 JANUARY 2003

9 [9] Oppenheim, A. V., and Schafer, R. W. (1989) Discrete Time Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, [10] Polydoros, A., et al. (1981) The differential cepstrum: definition and properties. In Proceedings of the IEEE International Symposium on Circuits and Systems, 1981, [11] Randall, R. B. (1987) Frequency Analysis (3rd ed.). Naerum, Denmark: Bruel & Kjaer, [12] Dennis, J. E., and Schnabel, R. B. (1983) Numerical Methods for Unconstrained Optimisation and Nonlinear Equations. Englewood Cliffs, NJ: Prentice-Hall, [13] Ferguson, B. G. (2000) Variability in the passive ranging of acoustic sources in air using a wavefront curvature technique. Journal of the Acoustical Society of America, 108 (2000), [14] Topping, J. (1962) Errors of Observation and Their Treatment (3rd ed.). London: Chapman and Hall, 1962, [15] Sendt, J., Pulford, G., Gao, Y., and Maguer, A. (2002) A system for automatic classification of aircraft flyovers using acoustic data. In Proceedings of 2002 Information, Decision and Control, Adelaide, Australia, Feb. 2002, Kam W. Lo (S 84 M 89 SM 00) received the B.Sc. degree in applied mathematics in 1983, and the B.E. (Honors Class I) and Ph.D. degrees in electrical engineering in 1985 and 1989, respectively, all from the University of New South Wales, Sydney, Australia. During the period of 1985 to 1994, he held various positions, including teaching assistant the research associate at the University of New South Wales, lecturer at the Hong Kong Polytechnic University, research scientist at the Defence Science and Technology Organisation in Adelaide, and microwave engineer at the Commonwealth Scientific and Industrial Research Organisation in Sydney. Since 1995 he has been working with the Defence Science and Technology Organisation in Sydney, where he is now a senior research scientist. He has conducted research in various areas, including antenna adaptive beamforming, microwave circuit design, radar system modeling and performance evaluation, antenna analysis, and signal processing. His current research interest is development of advanced signal processing algorithms for multifunction land-based acoustic surveillance systems, and advanced mine hunting sonar systems. Brian Ferguson (M 93) received, between 1972 and 1983, the B.Sc. (Honors), Dip.Ed., M.Sc. (by research) and Ph.D. degrees from the Universities of Sydney and New South Wales, Australia. From 1974 to 1984, he was a physicist with the Australian Department of Science and Technology, where his research activities were in the fields of solar radio astronomy and ionospheric physics. In 1984, he joined the Submarine Sonar Group of he Royal Australian Navy Research Laboratory, which was incorporated into Australia s Defence Science and Technology Organisation in He is currently employed at a principal research scientist, where he leads a group involved in the research development of advanced mine hunting sonar systems and multi-function land-based acoustic surveillance systems. His work has been published widely in international scientific and engineering journals. Dr. Ferguson is a Fellow of the Acoustical Society of America, a Senior Member of the Australian Institution for Radio and Electronics Engineers, and a Member of the Australian Institution of Engineers. LO ET AL.: AIRCRAFT FLIGHT PARAMETER ESTIMATION USING ACOUSTIC MULTIPATH DELAYS 267

10 Yujin Gao received the B.E, M.E., and Ph.D. degrees and is currently a senior sonar study engineer at Thales Underwater Systems (TUS) Pty Ltd. Prior to joining TUS Pty Ltd in 2000 he was a senior research fellow of the DSTO Centre of Expertise in Vibration Analysis at the University of New South Wales, Sydney, Australia, carrying out research into diagnostics of helicopter gearboxes. His current research interests include sonar function studies, signal processing applications to sonar, and vibration analysis. Alain Maguer received the Ph.D. degree in acoustics and signal processing from the University of Lyon, France, in Between 1986 and 1991 he worked for Thomson Marconi sonars in Sophia Antipolis, France. In 1991, he joined SACLANTCEN, the NATO Undersea Research Centre, where he worked for eight years on transient detection and classification, and on buried mine detection and classification. I 1999, he joined Thales Underwater Systems in Sydney, Australia, to lead the General Sonar Studies Group. In August 2002, he returned to France to join the Technical Directorate of Thales Underwater Systems in Sophia Antipolis. His research interests are sonar, statistical signal and array processing, synthetic aperture processing, and automatic detection and tracking. 268 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 39, NO. 1 JANUARY 2003