This paper presents the design of an FPGA-based multiprocessor-system-on-chip (MPSoC) architecture optimized for Multiple Target Tracking (MTT) in automotive applications. An MTT system uses an automotive radar to track the speed and relative position of all the vehicles (targets) within its field of view. As the number of targets increases, the computational needs of the MTT system also increase making it difficult for a single processor to handle it alone. Our implementation distributes the computational load among multiple soft processor cores optimized for executing specific computational tasks. The paper explains how we designed and profiled the MTT application to partition it among different processors. It also explains how we applied different optimizations to customize the individual processor cores to their assigned tasks and to assess their impact on performance and FPGA resource utilization. The result is a complete MTT application running on an optimized MPSoC architecture that fits in a contemporary medium-sized FPGA and that meets the application's real-time constraints.