Wideband Cross-ambiguity Function Research Articles

Bat biosonar echo analysis using spatial audio and wideband matched-filter techniques

Bats and dolphins show tremendous aptitude in hunting prey in difficult conditions. These conditions include large amounts of clutter, perhaps reverberation, and interfering signals/noisy backgrounds. Bats have been extensively studied to learn more about how they detect, track, and intercept prey. One important aspect of many of these studies is to understand the acoustics around the bat’s head. In this work, a new reproduction methodology using spatial audio and matched-filter techniques will be presented. A custom-built tetrahedral 1st order soundfield microphone that captures high-frequency sound up to 80 kHz from all directions was developed to measure bat echoes in B-format. The three-dimensional echoes that the bat received, now in Ambisonic B-format were further processed using a wideband matched-filter. The matched-filter produces a wideband cross-ambiguity function (WAF) of received data and the transmitted signal for every 1 deg in azimuth and elevation. The thresholded matched-filter output provides precise estimates of bearing, elevation, range, and normal velocity. This poster will present details of the hardware and software development along with experimental results that illustrate the capabilities of this new approach.

Time delay estimation in the presence of source or receiver motion

Generalized cross-correlation of the outputs of two spatially-separated sensors provides an estimate of the time delay (or differential time of arrival) of a broadband acoustic signal at the pair of sensors. The time lag at which the cross-correlation function attains its maximum value corresponds to the time delay. However, if relative motion between the source and the sensors leads to the time scales of the received signals being mismatched, then the time delay will be in error. This mismatch in the time scales is also referred to as the differential Doppler effect. Two practical examples are presented that demonstrate this effect, which is observed when a jet aircraft transits over and along the axis of two widely-spaced microphones or a scuba diver travels past two spatially separated hydrophones. It is shown that the correct time delay and relative time scale can be obtained by implementing wideband cross-correlation with differential Doppler compensation using the continuous wavelet transform. The continuous wavelet transform has the same functional form as the more familiar wideband cross-ambiguity function.

Efficient Wideband Parameter Estimation Using Arbitrary Enveloped LFM Signals via Hermite Decompositions

Signals with finite time support are frequently used in active sonar and radar processing. In these applications, for efficient computations, it is necessary to have a compact description of the signals' shape and time evolution. For this purpose, the Hermite series expansions are used in this paper to approximate an arbitrary enveloped linear frequency modulated signal. The Hermite basis functions are based on the product of Hermite polynomials and a Gaussian function. The analytical expressions for the Fourier transform of linear frequency modulated (LFM) Hermite functions are presented. It is proposed to use the Fourier transform of LFM Hermite functions for efficient computation of the wideband cross-ambiguity function (WCAF) for target parameter estimation in active sonar processing. Efficient 2-D search methods are also proposed to obtain parameters from the WCAF.

Efficient wideband signal parameter estimation using a radon-ambiguity transform slice

A novel efficient technique based on a single slice Radon-ambiguity transform (RAT) for time-delay and time-scale estimation is proposed. The proposed approach combines the narrowband cross-ambiguity function (NBCAF), the wideband cross-ambiguity function (WBCAF), and a single slice RAT to estimate multiple target parameters in noisy environments. The square modulus of Gaussian-enveloped linear frequency modulated (GLFM) signals has high-energy centrality in the ambiguity plane. Its peaks in the NBCAF fall along nearly straight lines whose slopes depend on the Doppler rates of the moving targets. These lines could be effectively detected by computing the entire Radon transform of the NBCAF for all possible angles; however, it is a computationally intensive procedure. It is shown that without calculating the entire RAT, it is possible to estimate target parameters using only a single slice of the RAT, i.e., using an appropriate projection of the NBCAF. It is demonstrated that the proposed method can successfully separate overlapping targets efficiently. The efficiency is achieved due to fast Fourier transform (FFT)-bascd processing, use of a single slice of RAT, and the use of only one-dimensional (1-D) searches.

Passive wideband cross correlation with differential Doppler compensation using the continuous wavelet transform

An estimate of the time difference for the signal emitted by a stationary source to arrive at two spatially separated sensors is given by the time displacement that maximizes the cross-correlation function. For a fast moving source, however, this estimate is found to be in error because the time scales of the received signals are different for the two sensors. The correct time delay can be extracted by evaluating the continuous wavelet transform, which has the same functional form as the wideband cross-ambiguity function. When the signal-to-noise ratio is high, the coordinates of the ambiguity surface’s global maximum provide reliable estimates of both the differential time of arrival (or time delay) and the ratio of the time scales of the signals received by the two sensors. The continuous wavelet transform is computed using the one-step chirp z-transform method, the cross-wavelet transform method, and the two-step methods where multirate sampled replicas of the sensor waveforms are cross correlated, or else the sensor waveforms are interpolated using the discrete Fourier transform prior to cross correlation. The latter method is applied to real acoustic data recorded from an orthogonal configuration of three microphones during the low-altitude transit of a jet aircraft. The resulting time delay estimates are used to calculate the variation with time of the azimuth and elevation angles of the aircraft during the transit.

Wavelet based approach for joint time delay and Doppler stretch measurements

A new wavelet-based algorithm for joint time delay and Doppler stretch estimation in passive radar, sonar, and GPS applications is described. By taking the cross wavelet transform of the noisy outputs from two spatially separated sensors, the wideband cross ambiguity function (WBCAF) can be computed. This in turn provides a direct measurement of the time difference and Doppler stretch between the two signals. The Cramer-Rao lower bound (CRLB) is derived and the performance of the proposed algorithm is analyzed. It is found that the theoretical variances of the estimates are unbiased and approach the CRLB at high signal-to-noise ratio (SNR). In order to improve the accuracy of the estimation under noisy environment, a simple denoising method is introduced. Simulation results are given to corroborate the analysis.

Wide-band, proportional-bandwidth Wigner-Ville analysis

The Wigner-Ville (W-V) distribution is a time-frequency representation that yields a highly accurate estimate of instantaneous frequency. It is related to the narrow-band ambiguity function by an internal transform, and it can be used in a variety of detection and estimation problems. A spectrogram constructed with constant bandwidth filters can be obtained by convolving two W-V distributions or by forming a magnitude-squared narrow-band cross-ambiguity function. The wide-band ambiguity function represents the Doppler effect with dilation or compression rather than with frequency shift as in the narrow-band approximation. The Q distributions, a modified W-V representation that is related to the wide-band ambiguity function by an integral transform, is defined. A spectrogram constructed with proportional-bandwidth or constant-Q filters can be obtained by a convolution-like operation involving two Q distributions or by forming a magnitude-squared wide-band cross-ambiguity function. The Q distribution is thus a wide-band version of the W-V distribution. Properties of the Q distribution indicate that it may prove useful for detection and parameter estimation as well as for tomographic measurement of wideband scattering functions with relatively few transmitted waveforms. >