An improved method for estimating Lyapunov exponents of chaotic time series, Phys. On time-scales shorter than several seconds, sea clutter can be described as the sum of complex exponentials. Finally, it is necessary to explicitly adjust the scaling12 of SˆC f. This is transformed in the bottom graph, with wraparound and grating lobes included, and gives the theoretical spectrum dashed line that should be observed at the receiver. Henceforth, we will refer to such an algorithm as a direct tracking algorithm. In the latter case, the contribution of noise to the radar return is strong.
A dark color indicates a strong return, which is associated with wave crests. In this case, in fact, as explained in reference 21, the low-resolution radar performs a spatial averaging over many waves and the radar cannot see the different features of the waves passing through the resolution cell during the recording process. Clearly, the Bayesian receiver has a more robust performance than the correlation anomaly receiver. In implementing the above idea, a somewhat better resolution is achieved than by using 2. Other studies have tried to provide some theoretical basis for the selection of the clutter behavior in order to make the problem mathematically tractable. A key point to note here is that since all the variables of the system are geometrically related to each other in a nonlinear manner, as shown in 4. The darker the pixel, the higher the probability of target detection.
The frame size was 128, the forward-backward window size was 53, and the target inertia parameter was 6. This leads to the correspondence between physical angle θ and wavenumber φ seen in Fig. A target detection was declared when the correlation fell below the detection threshold of 0. But from an information-theoretic point of view, the intermediate detection step based on hard decisions wastes important information; we say so because a real number lying between 0 and 1 is rounded off to an integer. The variations of the local power, due to the amplitude modulation of the speckle introduced by the tilting of the small-scale structure, are modeled as a random slow-varying process referred as texture. Multitaper spectral analysis of high-frequency seismographs, J. .
It is interesting to also try to link the variability of φ to φ itself. Is there chaos in plankton dynamics? By virtue of the discrete sampling of all measured dimensions, the search space is partitioned into a set of resolution cells. In particular, we measure the effect of long waves on the seaclutter amplitude and spectrum, and we propose a statistical model that takes into account the physical phenomena mentioned above. It contains the probabilities that event q preceded event r. Wiley also publishes its books in a variety of electronic formats.
Formulation of the process state-evolution and measurement equations including the respective dynamic and measurement noise processes , which are most appropriate for the physical realities of sea clutter. He is a Fellow of the Royal Society of Canada, and a Fellow of the Institute of Electrical and Electronics Engineers. Time—Frequency Analysis of Sea Clutter 91 David J. Therefore, to see clearly the effect of the long waves on the radar returns, we should analyze datasets2 where the Bragg scattering is dominant. In the frequency domain, the presence of periodicity in the power, and then of an amplitude-modulating effect of the swells, is evidenced by the time-varying spectrogram.
Then the correlation anomaly receiver operated on a simulated target plus clutter, on a range cell by range cell basis. Referring back to the nonlinear state-space model of 4. Algorithm 178: Direct search, Collected algorithms from Commun. The signal-to-noise ratio was found to be 17 dB for dataset L2 and 31 dB for dataset H, the difference being caused by the difference in range and the reduced overall power of lower sea-state clutter. In Chapter 2, following the original article on which the chapter material is based, the references are listed in alphabetical order.
Dataset: Starea4 of November 7, range cell 3. Third, the independent sampling condition i. Uncovering nonlinear dynamics: The case study of sea clutter, Proc. The correlation properties of gamma and other nonGaussian processes generated by memoryless nonlinear transformation, J. The emphasis is on point statistics, with no attention given to the temporal dimension. The a priori information is incorporated as follows.
It does, however, have useful approximate solution. The color axis shows log x˜ , where x˜ is the complex envelope of the received signal. The bias observed in this case seems to have a periodic behavior. The absolute minimum of the functional in 5. But as a coarse approximation, 4. The results for the correlation anomaly receiver are shown in Fig. When the mean velocity of the scatterers is high at a given instant, then the spread around that mean is also high.