Sources of numerical errors in both the square-root normalized and unnormalized least squares lattice algorithms

The problem of qualifying the sources of numerical error in both the square-root normalized and unnormalized least squares lattice algorithms is addressed with emphasis on fixed-point hardware implementations. Types of errors are grouped into those caused by numerical overflow, roundoff errors from fixed-point multiplications, and errors inherent in the recursive least squares lattice algorithm itself. Since roundoff error increases with the number of required multiplications and as the mangitudes of the multiplied fixed-point numbers decrease, a slightly modified least squares lattice algorithm is presented which should control overflow errors while minimizing the number of multiplications on the input data and avoiding normalization constants which can become quite small. Numerical errors inherent to recursive least squares lattice algorithms are also presented.