[71

Ausherman, D. A, Kozma, A., Walker, J. L., Jones, H. M., and Poggio, E. C. (1984)

Developments in radar imaging. IEEE Transacfions on Aerospace and Electronic Systems, AES-20, 4 (Jdy 1984), 363-400.

Jain, A., and Palel, I. (1992) SAWSAR imaging of a nonuniformly rotating target. IEEE Transactions on Aerospace and Electronic Systems, 28, 1 (Jan. 1992), 317-321.

Subaperture autofocus for synthetic aperture radar. IEEE Transactions on Aerospace and Electronic Systems, 30, 2 (Apr. 1!294), 617-621.

Motion compensation for ISAR via centroid tracking. IEEE Transactions on Aerospace and Electronic Systems,

Calloway, T. M., and Donohoe, G. W. (1994)

Itoh, T., Sueda, H., and Watanabe, Y. (1996)

32, 3 (July 1996), 1191-1197. Wahl, D. E., Eichel, P. H., Ghiglla, D. C., and Jakowatz, C. V., Jr. (1994:

Phase gradient autofocus-A robust tool for high resolution SAR phase correction. IEEE Transactions on Aerospace and Electronic Systems, 30, 3 (July 1’394), 827-835.

Chen, V. C. (1995) Reconstruction of inverse synthetic aperture images using adaptive time-frequency wavelet transforms. SPIE Proceedings on Wavelet Application, 2491 (1995), 373-386.

Qian, S., and Chen, D. (1994) Decompositi(3n of the Wigner-Ville distribution and time-frequency distribution series. IEEE Transactions on Signal Processing, 42, 10 (Oct. 1994), 2836--2842.

Signal representation using adaptive normalized Gaussian functions. Signal Processing, 36 (Mar. 1994), 1-1 1.

Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41 (Dec. 1993),

Qian, S . , and Chen, D. (1994)

Mallat, S. G., and Zhang, Z. (1993)

3397-3415. Trintinalia, L. C., and Ling, H. (1997)

Joint time-frequency ISAR using adaptive processing. IEEE Transactions on Antennas and Propagation, 45, 2 (Feb. 1997), 221-227.

Ling, H., Wang;, Y., and Chen, V. C. (1997) ISAR image formation and feature extraction using adaptive joint time-frequency processing. SPIE Proceedings on Wavelet Application, 3078 (1997).

Werness, S . , Cirrara, W., Joyce, L., and Franczak, D. (1990) Moving target imaging algorithm for SAR data. IEEE Transoctions on Aerospace and Electronic Systems, 26, 1 (Jan. 1990), 57-67.

Carrara, W. G., Goodman, R. S., and Majewski, R. M. (1995)

Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Boston: Artcch House, 1995.

Radon transformation of time-frequency distributions for analysis of inulticomponent signals. IEEE Tranwctions on Signal Processing, 42, 11 (Nov.

Wood, J. C., and Barry, D. T. (1994)

1994), 31668-3177.

Comments on “Low Observable Target Motion Analysis Using Amplitude Information”

It is felt that practical considerations are as important as the appropriateness of the mathematics that was availed in developing a scientific paper. The authors assumed that underwater targets maintain constant speed and course for considerably long durations [ 11. Accordingly, they tested the algorithm against a scenario where the target does not maneuver for a duration as long as 900 s. In practice, it is rare. If a vessel has to move from point P, to destination point P,, then it does so as shown in Fig. 1. It moves in small segments and in each, its course and speed can be considered as constant. The angle made with mean line of path is so chosen that the distance between P, and P, is minimum. Simultaneously, movement in straight line is discouraged to avoid easy detection. Modern targets rarely move in a straight line beyond 4 to 6 min. In underwater, target motion analysis (TMA) considers tracking of only nonmaneuvering targets. While estimating the target motion parameters, it is customary to use a normalized square innovation process to find out whether the target is maneuvering or not. Once maneuvering is confirmed, the entire process is reinitialized. It is thus not feasible to find out acceleration components using bearing-only measurements.

Fig. 1 .

The contention of the authors on the target motion and measurement models being realistic is debatable. In my opinion, the observer dynamics that are assumed is generally not observed. Moreover, according to the simulation and the contents shown in [I , Fig. 31, the observer has an infinite turning rate, while an observer in underwater can turn at utmost 1 degls.

It took 15 min. to generate the solution with 30 samples in batch processing. A good solution with 486 processor, 33 MHz exclusively for this is realized in 2-3 s. The authors adopted a rough grid

Manuscript received August 15. 1997

IEEE Log NO. T-AES/34/2/03212.

0018-9251/98/$10.00 @ 1998 IEEE

CORRESPONDENCEL 677

search to find global maximum and this resulting point is availed for the initial guess for k = 2. This is continued until k = K , until global maximum is found. Maximum likelihood estimator (MLE) in batch processing does not appear to be suitable for real time applications, as it uses iteration and search methods to find out the solution. For real time applications, sequential processing is preferable. However MLE can be used after converting into sequential process. In practice, one measurement every 0.5 s from the sonar detection processor is required and the solution is improved with every new measurement. Hence the computation time is to be completed within 0.5 s so that the processor gets ready to receive the new measurement.

without amplitude information for both the sonar types meeting the Cramer-Rao lower bound (CRLB) even under low signal-to-noise ratio (SNR) conditions. The authors seem to feel that even without using amplitude information under low SNR conditions, the solution is useful. But according to Table 111, when the first and second components of X,,, are 5000 and 35000, its estimated values are 6370 (error is 20%) and 41370 (error is 30%), respectively. The difference between the true and estimated values is large. The amplitude information is therefore always required to obtain good solution at low SNR.

The authors validated the efficiency of the estimator with normalized estimation squared error process. Here only one estimate is made and so only one sample is available for this error process making the size of the window equal to one. The only available error sample is considered as a Gaussian sample. In the highly noise corrupted scenario with bearing measurement error with 0.866 deg rms, this verification is not adequate.

There is no scope to extend this algorithm to find out whether the target is maneuvering or not, as the same normalized squared error process with window of size one alone has to be used. Samples are insufficient to test target maneuver using statistical methods for efficient decisions.

this paper.

The authors have claimed an efficient estimation

I suggest the following for better appreciation of

1. Think of a processing of measurements that is completed within 0.5 s .

2. The algorithm of TMA should be such that it reduces the computation and also the processor has to be capable of accepting one new measurement every half second.

3. In the context of observability problems in passive target tracking for obtaining target acceleration, the algorithms provide for testing normalized squared error process with every new measurement. This enables to conclude whether the target is maneuvering or not.

4. The algorithm has to provide sufficient accurate solution within 4-5 min, ensuring a weapon homing zone more than the error ellipse zone of estimated values. The present targets rarely move in constant course and speed for periods exceeding 5 to 6 min.

needs consideration. Problems in maintaining auto tracking, false alarms, etc., during observer maneuver need attention.

Also there is an unfortunate error in [ 1, Fig. 21. The bearing is considered with respect to True North in (4), but in Fig. 2 it is shown with Engineering convention.

5. Minimum observer dynamics like turning rate

S. KOTESWARA RAO Scientist ‘E’ Naval Science and Technological Laboratory Ministry of Defense Visakhapatnam-530027, A.P. India

REFERENCE

[l ] Kirubaran, T., and Bar-Shalom, Y. (1996) Low observable target motion analysis using amplitude information. IEEE Transactions on Aerospace and Electronic Systems, 32,4 (Oct. 1996), 1367-1384.

Authors’ Reply

While appreciating the comments made by S. Koteswara Rao, the authors feel that most of the comments are due to incomplete reading or misconceptions on the commentator’s part.

velocity (CV) model used in the paper is rather restrictive. Careful inspection will yield that this is already acknowledged in the paper in the Introduction as well as the Conclusions.

As the commentator illustrates in his Fig. 1, it is obvious that the target may not travel from the initial point to the end point on a straight line with a fixed velocity. However, its path can consist of a series of CV legs, again as illustrated by the commentator. The methodology proposed in the paper is applicable to these CV legs. This is precisely what the authors mean in the Introduction by “it is common for an underwater target to maintain constant speed and course for considerably long durations.” Maneuver detection (detecting changes from one CV leg to another) is not handled in the paper because that would require a recursive or a sliding window-based technique. A sliding window maneuver detection

The commentator points out that the constant

Manuscript received December 18, 1997.

IEEE Log No. T-AES13412103213.

0018-9251/98/$10.00 @ 1998 IEEE

678 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 34, NO. 2 APRIL 1998