Detection techniques in least squares identification

Parameter estimation schemes based on least squares identification and detection ideas are proposed for ease of computation, reduced numerical difficulties, and bias reduction in the presence of colored noise correlated with the states of the signal generating system. The algorithms are simpler because in the calculations, the state vector is at one point replaced by a quantized version. This technique avoids to some extent numerical difficulties associated with ill-conditioning in least squares schemes and thus obviates the need for square root algorithms and the need for high order precision calculations. In recursive form, the schemes are designed to yield parameter estimates with negligible bias without the additional computational effort or instability risks associated with generalized and extended least squares, recursive maximum likelihood schemes, or the method of instrumental variables. Nonrecursive schemes are designed to minimize computational effort in a batch processing situation while at the same time giving some reduction of bias in the state dependent colored noise situation. The novel algorithms have the limitation that they are suboptimal and there is thus a consequent reduction in the speed of convergence for some applications. The merits of the proposed schemes are assessed via simulation studies in this paper and an adaptive equalization application in a companion paper.