There has been a recent surge of interest in fuzzy logic and its application to complex systems engineering. While the concept of fuzzy logic has been a subject of research for about 25 years, only recently has this concept gained wider acceptance. Fuzzy logic was developed to allow computers to operate more like humans when dealing with ambiguous concepts. In fuzzy systems, a variable can take on any value between 0 and 1 inclusively, whereas in binary systems these variables can only take on the values of 0 and 1. Therefore using fuzzy logic allows multilevel conditional decisions, and fuzzy algebra to replace binary decisions and boolean algebra in digital systems.

Some specific complex problems in the undersea arena can be made more tractable by use of fuzzy techniques. These problems can be characterized as complex decision problems based on incomplete or uncertain input. This class of problems has frequently been discussed in the fuzzy literature, most particularly by W. J. M. Kickert in Fuzzy Theories on Decision Making: A critical Review. published by Martinus Nijhoff, Leiden, Netherlands, 1978. These problems are also typical of those faced every day by the modem submarine commander.

The essence of the sensor fusion problem is to select a decision from uncertain information from several sensors. The different sensors may consist of sonar arrays, radar arrays, radio frequency arrays, and perhaps vision and thermal sensors. By modeling individual sensors as probabilistic forecasters, and by fusing the probabilities of detection from each of these sources in a central processor, using some fusion rule, it has been shown by R. Krzysztofowicz, in Fusion of Detection Probabilities and Comparison of Multisensor Systems, in the IEEE Transactions on Systems, Man, and Cybernetics, Vol. 20, No.3, of May/June 1990, that a more accurate detection decision can be made. An example of this situation is presented in the following table.

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So there is a contact present to the system. This example shows that although the individual sensors cannot make the detection decision because the probability of detection of each sensor is too low, a decision can be made in a multisensor system with probability fusion, using an appropriate fusion rule. This fusion rule could be contained in the wisdom and experience of a senior decision maker who assesses the reliability of his sensor systems and acts on his feelings, or it can be built into an integrated system as an explicit method of combining multisensor inputs.

The problem or acoustic: modeling is to develop an accurate acoustic model for a given environment. Propagation loss models are typically created from an uncertain knowledge of the acoustic environment in the proximity of the platform and an uncertain knowledge of how the acoustic environment will evolve in time and space. The nearby acoustic environment may be represented in several ways. First, direct measurements of the parameters which affect the acoustic environment (e.g. temperature, salinity, depth) might be made in real-time. Second, historic measurements of these parameters might be used. When conditions and resources allow, real-time measurements are made in the vicinity of the platform and a sound velocity profile (SVP), based on these measurements, is generated. Ocean surface and bottom conditions may be evaluated in real-time, or looked up. If timely measurements are impractical, historic sound velocity profiles as well as historic surface and bottom conditions, are used to generate the propagation loss. In an ideal propagation loss calculation, the temperature, salinity, depth, and surface and bottom conditions in the vicinity of the platform out to the greatest range of interest in all directions must be taken into account to gain an accurate directional representation of the propagation loss. Finally, an estimation of propagation loss based on the platform’s depth is generated from these conditions.

Fuzzy logic has an application to the problem of modeling the acoustic environment. First, by attaching a relative weight to the reliability of real-time and historical measurement, a propagation loss curve generated by a combination of data can be made to favor the measured values. When entirely historic data have been used, a confidence weighting can be associated to create a propagation loss model which more closely reflects reliability of the input. Second, fuzzy logic could be employed to weight the spatial and temporal fluctuations of the SVP. This weighting could have as its basis a correlation with realtime surface conditions and atmospheric data. A number, perhaps the proportional to the variance of the SVP data, could be associated with each SVP data set. When combining data sets, variances could also be combined using some fusion rule to obtain a more realistic propagation loss representation.

The real and historic data could be combined using a fusion rule such that:

1. If a current SVP exists it will be used exclusively.

2. If stale SVPs exist, weigh them with historic values.

3. If only historic values exist, they will be used exclusively, but they will be weighted by reliability.

This idea can be extended to the more complex case of a spatially or temporally varying SVP. In this case, the SVP data sets may have been generated by various sources at different times. Accounting for the reliability of the SVP should yield a more precise propagation loss model. A realistic estimate of the propagation loss could serve as the basis for a determination of the likely ranges of detection.

The contact localizatioo problem is another instance of the sensor fusion problem. The essence of this problem is to optimize the location of a detected contact using a finite number of uncertain or incomplete position measurements. In underwater acoustics this is a particularly important problem. An accurate geographic picture of all contacts and potential contacts is essential. However, in many cases, contacts also have the goal of remaining undetected, which leads to difficulty in localizing contacts once they have been detected. With the intricacies involved in performing contact localization, primarily on acoustic data in a nonisotropic acoustic medium like the ocean, this problem becomes very significant. Here, fuzzy logic could help. By attaching weights to the reliability of sensor outputs, summing the results, and using a reasonable fusion rule, an improved contact localization can be achieved. Again this is something that a senior officer will do instinctively, but this ability can be modelled mathematically and built into an integrated system.

Consider the following example which portrays 3 sonar systems and their accuracy in 3 situations:

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The contact classification problem is another sensor fusion problem. The essence of this problem is to optimize the classification of a detected contact by using uncertain sensor data. One wants to ascertain not only the location of all contacts and potential contacts, but also an indication of what threat, if any, these contacts pose. By classifying a contact and using previously acquired knowledge about that class of contact, one can use this enhanced knowledge to make intelligent operational decisions. By using techniques to fuse the knowl· edge of various sensors, an improved classification decision can be made.

For example, a contact is known to be located with a great degree of certainty 5 miles due east of the platform. Two sensors indicate that the contact is a hostile warship based on partial acoustic signatures, another sensor indicates that the contact is a friendly warship based on a partial acoustic signa· ture, and a fourth sensor suggests that the contact is a neutral merchant ship based on an ambiguous visual contact One can fuse this data to make a structured classification decision.

Consider the following table:

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The result of sensor fusion, based on the fusion of probabilities of several sensors, is that the contact is more likely a Friendly Warship than a Hostile Warship because of the quality of the sensor input that indicated a Friendly Warship classification. This quality is a reflection of the reliability of the sensor. In current systems, this assessment of the sensor quality comes directly from the experience of the commander or his surrogate, who has likely made reliability assessments of his sensor assets for years. In future systems, these assessments may be computer generated.

It is obvious from the previous discussions that the selection of an appropriate fusion rule is very important in the construction of any multisensor system. This fusion rule, whether it is formulated though extensive simulation and explicitly incorporated into a combat system, is the key to accurate decision making. Current systems must rely solely on the experience of the decision maker which may not be flexible enough to incorporate the rapid changes which characterize the modem underwater acoustic environment. A system which is designed to allow real-time creation or modification of the fusion rules would be a powerful system, because it could adapt to deviations in sensor reliability which may result from environmental, hardware, or operator changes. The fusion rule could be constructed to vary with time to allow for known or suspected degradation of hardware or operator reliability. A fuzzy integrated system could present a fused decision result to the senior decision maker. He may still go with his instincts, but he will have at his disposal a more accurate situational assessment upon which to base his decision.