The allocation of resources to competing entities is a significant problem in various applications areas. There are many examples of situations in which it is necessary to impose a global constraint limiting the total quantities of resources available to individual consumers while there is no global objective to govern the distribution. The problem of limiting peak demand for power among loosely related buildings such as those on a college campus provides an example application. The individual objective performances of some loosely coupled independent buildings can be improved if resources can be exchanged, but such exchange becomes difficult if resource exchanges are required to balance. Since the buildings are independent, the exchange of resources may be required to occur without compromising this independence. A mechanism is presented to support resource exchanges among independent users while assuring that the average resource exchanged remains at zero and the autonomy of the individual users is retained. The presented mechanism uses a simplified form of barter to eliminate the need for gaming in certain cases.

Techniques are considered for processing the outputs of a sensor array that is observingJdistinct signal sources. Three types of wideband signals are discussed: unknown, stochastic, and parameterized. Narrowband signals are a special case. Four types of random errors are discussed: additive sensor noise, sensor gain errors, sensor time-delay errors, and "beam-pointing' errors. It is concluded that the so-called decoupled-beam data processor is a very promising technique, which can be implemented by passing the output ofJindividual "beams" through aJ-input,J-output linear system. When sensor gain-delay and beam-pointing errors are not present, the decoupled-beam data processor provides "infinite sidelobe rejection."

Techniques are discussed for using cloud maps (observations) made on a moving cloud of particles to predict the cloud's future location and shape. The amorphous cloud concept is used to model particle clouds in terms of surfaces moving through state space. Observations are modeled by possibly 'noisy' surfaces obtained by projecting the state space cloud onto the observation space. Deterministic and maximum likelihood 'type' prediction techniques are defined. Explicit algorithms are derived for deterministic prediction in the case of linear dynamics and ellipsoidal cloud maps. These algorithms include a closed-form bound and a non-linear programming technique that was successfully implemented. The analysis is motivated by the problem of a radar observing a cloud of chaff particles in orbit (on a ballistic trajectory) around the earth.

Optimal amplitude modulations for a radar signal are derived and then used to calculate the efficiencies of various sub-optimal modulations. The choice of modulation is constrained by the total energy transmitted and the peak power (amplitude) of the transmitted signal. The peak power constraint is handled by the use of Pontryagin's Maximum Principle, an extension of the calculus of variations recently developed in the U.S.S.R. that is enjoying wide application in optimal control theory. The criterion of optimality is based on the error variances of estimates of the range motion parameters of a reflecting body, where the errors are caused by additive, white, zero mean, Gaussian noise. Explicit results are provided for bodies with constant velocity and bodies with constant acceleration. The analysis covers: 1) incoherent processing of a sequence of many range measurements; 2) coherent processing assuming the RF phase is known, 3) certain aspects of coherent processing assuming the RF phase is unknown. The optimal modulations turn out to be of the "on-off" type, requiring either no transmission or transmission at the maximum allowable power level.

State variable techniques are used to derive new expressions for the likelihood function for Gaussian signals corrupted by additive Gaussian noise. The continuous time case is obtained as a limit of the discrete time case. The likelihood function is expressed in terms of the conditional expectation of the signal given only past and present observations, multipliers, and integrators (adders). Thus, the likelihood function can be generated in real time using a physically realizable system. Time-varying finite-dimensional Markov models are also discussed as they lead to a direct mechanization for the required conditional expectation. A simple example of a multipath communication system is discussed and an explicit mechanization indicated.