Fixed and floating point analysis of linear predictors for physiological hand tremor in microsurgery

This paper presents the fixed and floating point implementations for field-programmable gate arrays (FPGA) of third-order hand tremor predictors using recursive-least square (RLS) and a proposed Kalman adaptation algorithms. The proposed algorithm outperforms RLS in convergence speed and mean square error (MSE). It also shows better numerical convergence than the RLS as the number of bits in fixed-point precision is reduced. Both fixed and floating point realizations are implemented and the hardware tradeoffs are discussed. A modified binary floating point format is proposed that takes advantage of the 18-bit hard macro multiplier within the Xilinx Virtex 5 Architecture in order to gain precision while preserving speed. The increased precision overcomes the prior known issues of explosive divergence and the stalling effect associated with the fixed point implementation of such adaptive algorithms, proving the feasibility of an FPGA based physiological hand tremor predictor.