Traditional target tracking using monostatic radar systems typically relies on centralized or decentralized architectures, where all data is transmitted to a fusion center for processing the position and velocity of mobile targets. This approach not only introduces a single point of failure and can lead to increased data transmission times, particularly when the fusion center is distant from individual radar nodes, but it also faces scalability issues and potential bottlenecks when data accumulates at the fusion center. To address these challenges, we introduce a Distributed Alternating Direction Method of Multipliers (DADMM) for target localization within a radar network, wherein each radar node shares its observed data only with immediate neighboring nodes, achieving consensus on the estimated target locations and velocities. Our simulations, which incorporate critical parameters such as the number of radar nodes, radar geometry, and Signal-to-Noise Ratio (SNR), assess their impact on estimation accuracy and convergence speed. The results demonstrate that the proposed DADMM not only effectively eliminates the single point of failure, but also enhances system efficiency and robustness. We also incorporate two distinct stopping criteria for position and velocity estimations, enabling us to promptly fix the first accurately estimated parameter and reallocate computational resources to more effectively refine the remaining parameters, which streamlines computational efforts by focusing on unresolved parameters. We highlight the additional benefits of our proposed framework, and present directions for future work.