Abstract
A discretized version of a continuous optimization problem is considered for the case where data is obtained from a set of dispersed sensor nodes and the overall metric is a sum of individual metrics computed at each sensor. An example of such a problem is maximum-likelihood estimation based on statistically independent sensor observations. By ordering transmissions from the sensor nodes, a method for achieving a saving in the average number of sensor transmissions is described. While the average number of sensor transmissions is reduced, the approach always yields the same solution as the optimum approach where all sensor transmissions occur. The approach is described first for a general optimization problem. A maximum-likelihood target location and velocity estimation example for a multiple node noncoherent multiple-input multiple-output (MIMO) radar system is later described. In particular, for cases with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> good quality sensors with ideal signals and sufficiently large signal-to-interference-plus-noise ratio (SINR), the average percentage of transmissions saved approaches 100% as the number of discrete grid points in the optimization problem <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> becomes significantly large. In these same cases, the average percentage of transmissions saved approaches ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -1)/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> × 100 % as the number of sensors <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> in the network becomes significantly large. Similar savings are illustrated for general optimization (or estimation) problems with some sufficiently well-designed sensors. Savings can be even larger in some cases for systems with some poor quality sensors.
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