In collaborative estimation a network of nodes, each indirectly observing an underlying source, communicate with each other to form improved estimates of the underlying source. This paper derives an efficient collaborative estimation algorithm achieving high performance estimates with low communication and complexity utilizing tools from multiterminal source coding theory and modern practical coding theory. Relevant theoretical limits based on achievability from multiterminal source coding are first presented in order to characterize efficient tradeoffs between communication and estimation performance and inspire the architecture of the collaborative estimation code. Next low complexity tools from modern practical coding theory are utilized to get a practical collaborative estimation algorithm approaching these performance limits. The developed algorithm utilizes successively refined trellis coded quantization (SR-TCQ) to provide necessary diverse descriptions of the source, and low-density parity-check (LDPC) codes to provide an efficient means of compressing these descriptions for low complexity belief propagation decoding with side information. Comparing the communication versus estimate quality tradeoff performance attained by the developed low complexity scheme with that obtainable with an inner bound, an average distortion gap of only 1.0 and 1.6 dB at average rates of 3.32 and 2.33 b/s, respectively, is observed.