Abstract
This chapter begins with the application of model-based processing to the towed line array for the case of a narrowband signal. It is the simplest of all of the examples and also clearly manifests the impact of explicitly using the sinusoidal signal configuration and the motion of the array as parts of the relevant model. Some time will be spent on this development so as to familiarize the reader with the details of the development of the UKF solution to the types of problems in this chapter. It will develop the processor as a bearing estimator. The outline of the code for this case will be presented in pseudocode with sufficient detail to allow the reader to develop his or her own MATLAB code.
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Notes
- 1.
A more general form of Eq.â5.3 is Ïâ=â[1 Âħ (vâc)sinθ]Ï 0 where the minus sign allows for array motion in the â x direction.
- 2.
Note that in Table 4.1, there is a term N x +Îş that appears in several places. However, the user has a choice. The term Îş can be replaced with \(\lambda =\alpha ^{2}(N_{x}+\kappa ) - N_{x}\). The relative advantages or disadvantages of this are discussed by Candy [3] on pages 208â209, where the definitions of Îħ and β can be found. The difference between the two manifests itself mainly in the higher order moments of the initial pdf of the problem. In Table 4.1 Îş is used but in the code used here for this problem Îş is replaced with Îğ. The reader is encouraged to try it both ways.
- 3.
Tuning is discussed in detail in Chap.â6
- 4.
Pseudocode is an intermediate step between the common language and programming language, and is useful since it is logically structured, thus allowing the user to configure the actual code based on his or her personal experience while maintaining the proper form of the algorithm.
- 5.
This SNR was picked so as to emulate as closely as possible the experiment carried out in the Baltic sea [15] described below.
- 6.
These estimates are time dependent since the reference used is the first element of the array, and the array is moving. Nevertheless, if the source is also moving, its motion can be found from the resulting range and bearing estimates.
- 7.
This value is that selected for the experimental example which follows in the next section.
- 8.
The five modal functions and their derivatives were each evaluated at 23 points along with the five modal amplitudes.
- 9.
This terminology, although commonplace, is unfortunate, since it is not the ambiguity diagram as originally defined by Woodward [17] which plays an important role in the active sonar problem.
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Sullivan, E.J. (2015). Applications. In: Model-Based Processing for Underwater Acoustic Arrays. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-17557-7_5
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