A Bayes Risk-Based Cost Function to Allocate Scan Time for Object Detection

Abstract

Advancements in radar technology such as phased array antennas, digital beamforming, and adaptable waveform generation have led to the flexibility in controlling radar resources such as scan time, beamwidth and bandwidth during a radar mission. This new flexibility has led to a new research topic, radar resource management. Radar resource management involves the allocation of radar resources in order to achieve the highest performance in a radar mission. This thesis focuses on a specific scenario where a radar is tasked with deciding multiple object presence decisions located at multiple scan directions. The resource considered is the scan time allocated to each scan direction. To optimally allocate the scan time over the scan directions, a cost function is formulated, where the expected performance of an individual decision of an object being present or absent is formulated as the expected Bayes risk. The expected performance of all individual decisions in the same scan direction, are summed to obtain an expected task performance. The global performance at the system level is formulated using two approaches. The Sum approach formulates a cost function at the system level as the sum of the expected cost of each task. The Max approach formulates a cost function that minimizes the maximum of all expected task costs. Simulations have been performed to demonstrate the flexibility of the Sum and Max approach to adapt the scan time allocation based on different scenarios, including multiple object presence decisions per scan direction, sequential measurements, and a birth-death process regarding the presence of an object over time. Simulations demonstrate that using the Sum and Max approaches for the allocation of scan time results in an improved performance compared to the uniform distribution of the scan time resource over all scan directions.