Abstract: This paper extends the idea of minimizing error in the mean fourth power and mean sixth power, etc. to the lattice structure, and develops a family of LMK adaptive gradient lattice algorithms. The convergence behavior of the LMK gradient lattice algorithm is analyzed by deriving the approximate expressions for the mean and covariance functions of the adaptive lattice filter coefficients and the output mean square error of the adaptive lattice filter. A computer simulation has been performed to confirm the theoretical analysis results presented in this paper.