Well the state of the art performance on such tasks is achieved by deep neural networks, and especially, the convolutional ones (CNNs) set you free of extracting hand crafted features. The network learns those features as well as the weights. This way you avoid the hustle or the rots o'ruck. For sequential data input, such as audio signals, recurrent neural nets stand out to be promising.
There are many toolboxes such as TensorFlow, Torch, or CNTK and they would allow you to quickly prototype your ideas.
I have used deep learning successfully in many scenarios, but unfortunately, instrument recognition is not one of them. However, looking into the academia, I already see that there exists some works on instrument recognition and a huge amount of works on understanding of music.
First, a comprehensive list of use in music:
An approach targeting the similar problem published in IEEE/ACM Transactions on Audio, Speech, and Language Processing (TASLP):
Deep convolutional neural networks for predominant instrument
recognition in polyphonic music, Yoonchang Han, Jaehun Kim, and Kyogu
- A youtube demo that uses CNNs: