FPGA Curved Track Fitters and a Multiplierless Fitter Scheme

The standard least-squares curved track fitting process is tailored for FPGA implementation so that only integer multiplications and additions are needed. To further eliminate multiplication, coefficients in the fitting matrices are carefully chosen so that only shift and accumulation operations are used in the process. Comparison in an example application shows that the fitting errors of the multiplierless implementation are less than 4% bigger than the fitting errors of the exact least-squares algorithm. The implementation is suitable for low-cost, low-power applications in high energy physics detector trigger systems.