Multisensor Decision And Estimation Fusion

In practice, one is very often faced with a decision-making problem, i.e., selecting a course of action among several possibilities. For instance, in a digital communication system, one of several possible symbols is transmitted over a channel, we need to determine the symbol that was transmitted based on the received noisy observations. In a radar detection system, a decision based on the radar return is to be made regarding the presence or absence of a target. In a medical diagnosis problem, based on an electrocardiogram, one needs to determine if the patient has a heart attack. In a target recognition problem, one needs to identify the type of aircraft being detected based on some observed aircraft features. In all of the above practical applications, the common issue is to make a decision from several possibilities based on available noisy observations, where the truly present phenomenon cannot be observed directly. The branch of statistics dealing with these type of problems is known as statistical decision or hypothesis testing.

From this chapter through Chapter 4, in order to use the global optimization strategy, we suppose that the fusion rule is fixed. We concentrate on investigating optimal sensor rules under this fusion rule. For notational simplicity, we start with the simplest multisensor decentralized decision system, namely, the two sensor binary decision system. We focus on Bayes decision problem. However, the basic idea and methods which we derive for this simplest case can be extended to the general multisensor m-ary distributed decision system as well as to the Neyman-Pearson decision and the sequential decision problem

In this chapter, we will not limit the number of sensors to two and not limit sensors transmission to a single binary number as done in the last chapter. In fact, to improve the decision accuracy, if additional communication bandwidth is available, from each sensor more than one binary number could be transmitted out. In the first six sections of this chapter, we will suggest a discretized iterative algorithm to approximate the optimal local (sensor) compression rules under a fixed fusion rule for the distributed multisensor Bayes binary decision problem. First, we will show that any general fusion rule can be formulated as a bi-valued polynomial function of the local compression rules. Then, under a given fusion rule, we will present a fixed point type necessary condition for the optimal local compression rules and propose an efficient discretized iterative algorithm and prove its finite convergence. After this, we will consider the optimal fusion rule problem for a class of the systems with a specific communication pattern. For such a system, namely an /-sensor system, suppose that the total number of bits transmitted by l —1 sensors are fixed, we can change the number of bits transmitted by the l sensor to a certain number, which is determined completely by the total number of bits transmitted by other l —1 sensors. For those systems with the modified communication pattern, we will present an optimal fusion rule, and prove that this fusion rule is not only superior to all possible fusion rules under the original communication pattern, but also an optimal fusion rule for the modified communication pattern. Furthermore, we will prove that even if the lth sensor now can transmit uncompressed observational data to the fusion center, the performance cannot be better than that achieved by the aforementioned optimal fusion rule. Moreover, this optimal fusion rule does not depend on the statistical properties of the observational data, or even on the decision criteria. It only depend on the total number of bits transmitted by other l — 1 sensors. Numerical examples support the above results and give

In this chapter, we consider more general multisensor multi-hypothesis decision systems.

In chapter 4, we have derived a number of results on the optimal sensor rules with a fixed fusion rule for general multisensor m-ary network decision systems. To achieve globally optimal performance, the previous results are obviously not enough because the number of all possible fusion rules are very large and exhaustive searching for the optimal fusion rule is computationally intractable. Therefore, in Sections 5.3-5.7, we are going to extend the results on the optimal fusion rule and some related interesting properties derived in Section 3.5 to more general network decision systems discussed in Chapter 4. On the other hand, in terms of the two-level optimization strategy in the distributed decision system, a local sensor may first need a locally optimal sensor rule based on its own information for its own local goal, and then send its decision result to the fusion center. Finally, the fusion center fuses all received local decision results to get an optimal final decision. When all sensor rules (not only sensor outputs) are well known, the optimal final fusion can reduce to the conventional decision problem at the second level. We will formulate and solve it thoroughly in Section 5.1. If only the sensor outputs can be known, some results on reducing the number of valuable fusion rules are presented in Section 5.2 in both two-level optimization and global optimization senses. Here, by valuable fusion rules we mean that they must contain an optimal fusion rule.

In this chapter, we consider the multisensor interval estimation fusion which is different from the point estimation fusion. In the point estimation problems, a popular criterion is to minimize the distance between the estimate and the true value under a proper metric, such as the minimum variance estimation. In spite of the true value unknown, the error distance is still able to be minimized via given the second moments of model noises, such as the parameter estimation for a linear model, or Kalman filtering. In the interval estimation problems, although there still exist some metrics to measure error distance between intervals and true value, such as Hausdorff metric (for example, see [36]), minimizing the error distance has no much practical value. Therefore, from practical point of view, the interval estimation problem of true value is much more in favor of the interval coverage probability (confidence degree) and the length of the covering interval. On the other hand, there may be some connections between the two types of estimations. When one derives a minimum error variance point estimation, the neighborhood of an estimate should usually have greater coverage probability of the true value. This leads us to simplify interval estimation fusion in some cases (see Subsection 7.1.4).