Sonar performance models

10.1 Background

The ultimate purpose of sonar performance modeling is two-fold. First, advanced sonar concepts can be optimally designed to exploit the ocean environment of interest. Second, existing sonars can be optimized for operation in any given ocean environment.

In the case of naval sonars, performance prediction products can be tailored to individual sonar systems by providing the sonar operators with on-scene equipment mode selection guidance. When combined with current tactical doctrine, this information product is commonly referred to as a tactical decision aid (TDA). These decision aids are used by the force commanders to optimize the employment of naval assets in any particular tactical environment at sea. Performance prediction products help both the force commanders and sonar operators to better understand and thus exploit the ocean environment from a tactical standpoint. Sonar performance models also support various naval underwater acoustic surveillance activities.

Tactical decision aids are in the realm of engagement modeling, which will be discussed more fully in Chapter 12. In essence, engagement models use sonar detection performance data (either measured or predicted by sonar performance models) to simulate integrated system performance. These simulations are usually conducted in the context of a naval force that is set in opposition to a hypothetical threat force. The output data typically include exchange ratios, which are useful in determining force level requirements and in developing new tactics.

Sonar performance models use active and passive sonar equations to generate performance predictions. Mathematical models of propagation, noise and reverberation generate the input variables required for solution of these equations. This hierarchy of models was previously illustrated in Figure 1.1. Sonar performance models can logically be separated into active sonar models and passive sonar models, as would be suggested by the distinction between active and passive sonar equations.

The complexity of the sonar performance-modeling problem is a natural consequence of the naval operations that these models support. In modern naval battle group operations, for example, TL must be calculated along a multiplicity of paths connecting widely separated sources and receivers. Noise interference from nearby consort vessels must be factored into sonar performance calculations together with distant merchant shipping and local weather noises. Furthermore, scattering and reverberation from bathymet-ric features and volumetric false targets must be efficiently and realistically modeled. The demands placed on computational efficiency and database management are enormous. Underwater acoustic modelers face challenges that severely tax existing mathematical methods. Moreover, with the advent of multistatic scenarios involving multiple sets of separated sources and receivers, true 3D modeling is no longer a theoretical luxury but rather a practical necessity.

This situation has become even more complex with the heightened interest in shallow-water sonar operations. Acoustic interactions with highly variable sea floor topographies and compositions further compound already intensive scattering and reverberation calculations. In addition, the sound-speed field in shallow-water areas is often characterized by high spatial and temporal variability. As a result, statistical approaches have been explored in order to obtain meaningful predictions of active sonar performance in shallow-water environments. In the MOCASSIN model, for example, Schneider (1990) provided the option to specify a stochastic sound speed field in order to approximate the horizontal variability typical of coastal regions.

10.2 Sonar equations

The sonar equations are simple algebraic expressions used to quantify various aspects of sonar performance. These equations vary according to active or passive sonars, and within active sonars they further differentiate according to noise or reverberation limited conditions. The various system and environmental parameters that make up the sonar equations are listed in Table 10.1 together with reference locations and brief descriptions. A condensed statement of the equations is presented below (Urick, 1983: chapter 2):

Active sonars (monostatic)

Noise background

Reverberation background

Passive sonars

Table 10.1 Sonar parameter definitions and reference locations


Symbol Reference


Source level

Transmission loss

Receiving directivity index

Reverberation level

Recognition differential

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