一种改进RLS算法及其在SINS快速对准中的应用

An Improved RLS Algorithm and Its Application in SINS Rapid Initial Alignment

在传统递推最小二乘算法(RLS)中,人为设置的递推初始值将导致状态估计的有偏性,也就丧失了最优性,当量测数据次数较小时尤为严重。摒弃了传统RLS算法"新估计值=旧估计值+修正值"的递推结构,提出了借助中间量进行递推,再由中间量直接作状态估计的改进算法。改进RLS算法状态估计结果与批处理LS算法完全一致,且无需初始状态的任何信息。将改进RLS算法应用于捷联惯导系统(SINS)初始对准。对于一定的初始对准精度要求,理论上改进RLS算法所需的初始对准时间是最短的。最后,SINS初始对准数值仿真结果验证了所提算法的正确性。

The classic recursive least square（RLS） algorithm has a disadvantage,i.e.the artificial setting for state initialization may lead to state estimate bias and then lose optimality,especially under the case of small amount of observations.By rejecting the classic recursive estimate structure of new state value is equal to old state value plus correcting value＇,a new recursive algorithm is proposed.In the improved RLS algorithm,some intermediate variables are introduced,by which the state estimates can be calculated directly.The state estimate results of the improved RLS algorithm is identical to those of the batch least square algorithm,and the initial state statistics are also no more necessary.An example of initial alignment for a strapdown inertial navigation system （SINS） is introduced and the improved RLS algorithm is used to solve the problem.In theory the improved RLS algorithm has the least amount of alignment time under certain alignment accuracy requirement.Finally,some SINS initial alignment simulations are carried out and the results verify the proposed algorithm.