Fixed and Floating-Point Implementations of Linear Adaptive Techniques for Predicting Physiological Hand Tremor in Microsurgery

This paper presents the fixed and floating-point implementations for field-programmable gate arrays (FPGAs) of third-order hand tremor predictors using recursive-least square (RLS) and a proposed Kalman adaptation algorithm. 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 Virtex 5 Architecture in order to gain precision while preserving clock 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. In order to demonstrate the tradeoff between the performance and the hardware complexity, we quantify the penalty paid by the system in terms of MSE due to the use of lower precision arithmetic.