MIMO system identification is a fundamental concern in a variety of applications. Various iterative and recursive MIMO system identification algorithms exist in the literature. The iterative algorithms suffer from high computational cost due to large matrix computations and recursive algorithms suffer from slow convergence speed. This paper proposes a fast recursive exact least squares algorithm for MIMO system identification with fast convergence speed and low computational cost. The recursions of the algorithm give rise to a lattice structure. The lattice structure is less sensitive to round-off errors, coefficients variations and can also be used for model order reduction. Although in this work we estimate an FIR (finite impulse response) model of the MIMO system, the framework can also be used for IIR (infinite impulse response) models, and for estimating linear periodically time varying (LPTV) and multivariable systems. The theory proposed is validated using simulation results.

MIMO系统识别是各种应用中的基本问题。文献中存在各种迭代的和递归的MIMO系统识别算法。由于矩阵计算量大，因此迭代算法的计算成本较高，而递归算法的收敛速度较慢。提出了一种快速递归的精确最小二乘算法，用于MIMO系统的识别，具有收敛速度快，计算成本低等优点。该算法的递归产生了晶格结构。晶格结构对舍入误差，系数变化较不敏感，也可用于模型阶数减少。尽管在这项工作中我们估算了MIMO系统的FIR（有限冲激响应）模型，但该框架也可以用于IIR（无限冲激响应）模型，用于估计线性周期性时变（LPTV）和多变量系统。仿真结果验证了所提出的理论。