Birds in the wild are difficult to localize, because their sizes tend to be small, they move swiftly, and they are often visually occluded. However, their location information is crucial for ethological studies on birds' behaviour. Recently, automating the process has been studied as a hot topic, where spatial sensors and sensor networks are commonly used. To avoid the visual occlusion problem, many studies focus on acoustic signal processing by applying microphone arrays and perform 1D azimuth localization through bird songs. In this study, we perform 2D sound source localization in the Cartesian coordinates using azimuths from multiple microphone arrays. To estimate the exact bird's location, we calculate the intersection points of these azimuth lines. Although this approach is simple and easy to be implemented, it has two main issues. One is that even small noise interference in azimuth values results in corrupting the localization data. This leads to a problem, where the intersection points between the azimuth lines do not intersect in one point for a single bird, but in several points. This proves difficulty in estimating the exact location of each bird. Especially in a far-field application, even small noise corruption leads to large localization errors. The other issue is that in the bird's natural habitat, elements such as leaves, grass and rivers are natural noise sources. It is difficult to extract the bird songs in such a noisy environment. We propose an algorithm involving statistic methods, sound feature analysis and machine learning. Based on this approach, a noise robust bird localization system has been established. We have performed numerous simulations to further understand the limitations of the system. Based on the results we have also derived the system's design guidelines, describing how the results change depending on the number of microphone arrays, signal-to-noise ratio, bird's distance from the devices, array's transfer function, type of the singing bird and specific parameter settings used in the algorithms. Such detailed guidelines support interested researchers in creating a similar system, which can contribute to ethological researches.