WIDE-BAND MULTIPATH DEPTH ESTIMATION AND PARTIALLY ADAPTIVE SPACE-TIME PROCESSING FOR ACTIVE SONAR
Jeffrey L. Krolik

Department of Electrical and Computer Engineering

DukeUniversity, Box 90291, Durham, NC27708

Ph: (919) 660-5274, Fax: (919) 660-5293, email:

ONR award number: N00014-05-1-0023

OBJECTIVES

The objectives of this project are to develop algorithms for: 1) robust target depth discrimination using multipath time delay differences estimated from wide-band active sonar returns, and 2) improved detection of low velocity targets by model-based partially-adaptive space-time processing of Doppler-sensitive active sonar waveforms received at a towed array. Robust depth discrimination would provide an important classification tool for resolving returns from targets in the water column versus bottom features and/or surface ships. Partially adaptive space-time processing would enhance detection of low-Doppler targets by improved rejection of Doppler-spread reverberation which leaks through conventional beamformer sidelobes.

APPROACH

1.) Multipath Delay and Depth Estimation for Active Sonar in Random Ocean Channels

The most straightforward, but perhaps least robust, method for acoustic source localization is full-field matched-field processing (MFP), which requires the ability to model both the relative phases and amplitudes of multipath arrivals. In our earlier work on depth estimation for active sonar, a narrow-band matched-field processing algorithm, called MFDE, was developed which avoids the requirement to model the complex amplitudes and phases of eachspace-time multipath target return. In more recent work, we have considered depth estimation using wide-band signals, which have the potential to resolve some of the multipath arrivals scattered by the target. In particular, beamformed, match-filtered time series for successive pings often contain multipath returns which are a function of target depth and range. A limitation of ray acoustic models for wideband returns, however, is their inability to handle frequency-dependent spectral distortions that are not explained by the usual linear superposition of scaled and delayed versions of the transmitted signal. These spectral distortions are partially due to the inability to precisely model the frequency-dependent target scattering function and also by temporal multipath fluctuations resulting from scatter off moving platforms.

To achieve better robustness to acoustic model uncertainty, our current work has been aimed at first estimating relative multipath time delays in target returns and then using these to estimate target depth [1]. The following two-step process is an example of such a non-MFP method that is robust to

spectral phase distortions. First, measure some or all of the group delay differences among the multipath components in the data. Second, evaluate a depth-dependent likelihood function with the resulting delay difference data. The simplest approach for measuring group delay differences is to match filter the received signal and then measure the time difference between the strongest two peaks in the output. The theoretical probability distribution of delay differences can be estimated by calculating all possible differences between group delays predicted by a ray-trace algorithm for each hypothesized target depth. Given an observed set of delay differences, this computed probability density function conditioned on depth could be used to generate a likelihood function which can be maximized to estimated target depth. This straightforward approach to maximum likelihood depth estimation has been successfully applied to real 53C data (courtesy of NUWC). An important difficulty in applying the above maximum likelihood depth estimation technique, however, is that it relies upon the measurements of the output of a matched filter which does not account for spectral phase distortions. When the phase distortions are too severe, the matched filter output no longer forms peaks that can be reliably identified as multipath arrivals. Another problem is that the temporal side lobes induced by even moderate phase distortions make it impractical to attempt to extract more than one group delay difference from the data. In work this past year, we have been developing more sophisticated approaches to delay difference estimation which exploits only the shape of the magnitude spectrum of a multipath signal and is thus immune to phase distortion of the signal returns [2].

2)Partially Adaptive Space-Time Processing for Active Sonar

In conventional methods, the notion of space-time processing for active sonar was limited to non-adaptive or single degree-of-freedom post-Doppler spatial null-steering. In our previous research, we developed a more fully adaptive pre-Doppler element-space STAP for active sonar. However, an issue which is key to effective space-time adaptive suppression of Doppler-spread reverberation is the estimation of the reverberation covariance matrix. Specifically, a serious impediment to realizing the promise of STAP for reverberation suppression is the lack of snapshot support. This problem is further exacerbated by the fact that many active sonar settings are bistatic, as is the case for the 53C reverberation received on the MFTA receive array. This effectively increases the dimensionality of the clutter space-time subspace and limits the range extent over which the clutter can be considered stationary. In our work, we have developed a space-time interpolation (STINT) technique [3, 4] which compensates for bistatic effects by interpolating the reverberation to that which would be received by a “virtual” monostatic configuration. This facilitates estimation of the adaptive space-time weights with many fewer snapshots of data than would have been required using the uncompensated bistatic data. Despite this improvement, there remains a need to go further to reduce the number of training snapshots required. In this past year, therefore, we have been developing partially-adaptive model-based active sonar STAP which incorporates additional knowledge about the space-time characteristics of the reverberation. In particular, our recent work concerns development of a model-based covariance matrix regularization method which facilitates improved detection performance [5].

RESULTS

1) Multipath Delay and Depth Estimation for Active Sonar in Random Ocean Channels

This past year we developed several alternative methods for multipath delay estimation in scattering channels for use as the front end to the maximum likelihood depth estimation (MLDE). Two of the proposed methods are based on optimal maximum likelihood (ML) and maximum a posteriori probability (MAP) techniques and the third is a least-squares (LS) approach [2]. These methods were evaluated and compared to our previously derived entropy-based delay estimator (EDE) via simulation and using real microwave laboratory data as described in [2]. Some examples of the resulting estimates obtained with microwave laboratory data are shown in Figure 1 below. The experimental setup consisted of a metal cylindrical target placed in front of a flat reflecting surface. The objective was to estimate the distance of the target from the surface (analogous to depth). A total of four multipaths were predicted between transmitter and receiver. In the example, the model was parameterized in terms of the displacement of the target from the reflecting surface. In order to illustrate that the approaches are robust to spectral phase distortion of the return (as would occur in the sonar delay estimation problem) only the magnitude spectrum of the received data was used. Examples of the resulting ambiguity functions as a function of hypothesized target displacement are shown in Figure 1 for the EDE, ML, MAP, and LS methods. Note that while all these estimators had peaks near the correct displacement of -5 cm, in more extensive testing, the ML and MAP methods outperformed EDE and LS.

The above techniques assume a completely unknown, or equivalently uncorrelated,frequency-dependent phase distortion in the returnand thus use only the magnitude spectrum. Alternatively, it has been suggested that the individual multipaths can be assumed to suffer both phase and amplitude distortions in the frequency domain which are random but correlated across frequency. This hypothesis motivated development of an ML multipath delay estimator based on the following state-space model:

(1)

whereis the observed frequency domain return, is a vector of complex multipath amplitudes at frequency, , encodes the deterministic multipath delays and transmitted waveform, and are complex Gaussian noise terms. Correlation between adjacent frequency bins is controlled by the parameter,. This past year we developed an efficient recursive estimator for multipath delays under this quasi-random signal return model. The method is as an extension of Kalman filtering where ML estimates of the delay parameters, nonlinearly embedded in , are obtained. The procedure involves analytic calculation of the gradient of the likelihood surface with respect to the delay parameters and is thus referred to here as Kalman-gradient ML (KGML) delay estimation. Although simulation testing showed promise, KGML estimates with real IUSW-21 data showed little difference over MLDE methods which assumed uncorrelated phase.

In terms of results with real sonar data this past year, we provided our previous MLDE code (which uses multipath delay estimates obtained directly from sub-banded A-scans of match-filtered 53C outputs) to NUWC for testing on the CRAFT database.

Figure 1: Displacement ambiguity functions obtained using microwave laboratory data (clockwise from top left corresponding to EDE, ML, MAP, and LS estimators)

[Image: Four images which plot ambiguity functions for four methods versus displacement and which have peaks near true displacement. MAP and ML methods appear to give similar performance]

2) Partially Adaptive Space-Time Processing for Active Sonar

During the past year, we have developed a model-based partially-adaptive STAP approach that combines the advantages of using a physical model for the reverberation with adaptive estimation of the power levels in the modeled subspace. Furthermore, the approach is robust to model mismatch, since we allow for adaptivity in the subspace that is not spanned by the modeled reverberation. Limited results using experimental data indicate that improved target discrimination from clutter can be obtained using this model-based partially adaptive approach versus conventional processing. Results with MFTA data indicate that up to a 4 dB improvement in the output signal-to-interference-plus-noise ratio (SINR) can be obtained, as compared with non-adaptive nulling and conventional space-time processing. These results are described in [5] as well as the Ph.D. thesis [4].

To evaluate the performance of partially-adaptive model-based STAP with real data, 1-sec CW-pulse returns from an echo-repeater were injected into real reverberation seen by a mid-frequency MFTA array. The detection performance results obtained for model-based partially adaptive STAP versus several other space-time processing approaches is shown in Figure 2 and 3. Figure 2 compares the receiver operating characteristic (ROC's) of conventional, sample-matrix-inversion with diagonal loading (SMI-DL), deterministic nulling, and our model-based approach. The ROC was computed using 47 real pings injected into reverberation scaled to have the same energy so as to achieve nominally independent identically distributed reverberation realizations. At an input SINR = -35 dB, the ROC of Figure 2 indicates the performance improvement offered by the model-based approach over the other methods. In Figure 3, the probability of detection (PD) plotted versus SINR for fixed probability of false alarm (PFA = 0.1) indicates a performance gain of between 4 and 5 dB for model-based partially adaptive STAP.

Figure 2: ROC's for Sonar STAP Methods Figure 3: PD vs. SINR for Sonar STAP Methods

[Image: Shows ROC of model-based STAP [Image: Shows PD vs. SINR for model based STAP
outperforms conventional, SMI-DL and offers SINR gain of between 4 and 5 dB over
deterministic nulling] conventional methods]

RELATED PROJECTS:
The MFDE effort is related to matched-field altitude estimation (MFAE) for over-the-horizon HF radar which was ONR-sponsored and which has transitioned to joint development by the US and Australia for the ROTHR and JINDALEE radars, respectively.

PUBLICATIONS: The following papers have been published or in press as a result of current FY05 research activities under this grant:

1. G. Hickman and J.L. Krolik, “Wideband target depth estimation in a scattering ocean environment” Proc. of IEEE International Conf. on Acoustics, Speech, and Signal Processing, ICASSP-2005, Philadelphia, March 2005.

2. G. Hickman and J.L. Krolik, "Multipath delay estimation using the magnitude spectrum", Proc. of IEEE Workshop on Statistical Signal Processing, Bordeaux, France, July 2005.]

3. Vijay Varadarajan and Jeffrey L. Krolik, “Joint Space-Time Interpolation for Distorted Linear and Bistatic Array Geometries” IEEE Trans. on Signal Processing, to appear late 2005 (in press).

4. Vijay Varadarajan, Model-based Techniques for Space-Time Adaptive Processing, Ph.D. thesis DukeUniversity, 153 pages, December 2004.

5. Vijay Varadarajan and J.L. Krolik, “Model-based covariance matrix regularization for active sonar”, Proc. of the 38th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA. Nov. 2004.

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