In this paper, the problem of weighted block recursive least squares (RL-4S) adaptive filtering is formulated in the context of block fast transversal filter (FTF) algorithm. This "modified block FTP algorithm" is derived by modifying the constrained block-LS cost function to guarantee global optimality. This new soft-constrained algorithm provides an efficient way of transferring weight information between blocks of data. The tracking ability of the algorithm can be controlled by varying the block length and/or a soft constrained parameter. This algorithm is computationally more efficient compared with other LS-based schemes. The effectiveness of this algorithm is tested on a reallife problem dealing with underwater target identification from acoustic backscatter. The process involves the identification of the presence of resonance in the acoustic backscatter from a target of unknown shape submerged in water.