This article presents new techniques for parameter identification for nonlinear dynamical discrete-time systems. The methods presented are intended to improve the performance of adaptive control systems such as RTO schemes and adaptive extremum-seeking systems. Using recent results on FT adaptive control, we develop alternative techniques that can be used to guarantee the convergence of parameter estimates to their true values in the presence of model-mismatch and exogenous variables. Three methods are presented. The first two methods rely on system excitation and a regressor matrix, in either case, the true parameters are identified when the regressor matrix is of full rank and can be inverted. The third method is based on a novel set-based adaptive estimation method proposed in Chapter 10 to simultaneously estimate the parameters and the uncertainty associated with the true value. The uncertainty set is updated periodically when sufficient information has been obtained to shrink the uncertainty set around the true parameters. Each method guarantees convergence of the parameter estimation error, provided an appropriate PE condition is met. The effectiveness of each method is demonstrated using a simulation example, displaying convergence of the parameter error estimation error.