In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random variables.The p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild conditions.In addition,a numerical simulation is carried out to study the finite sample performance of the theoretical results.Finally,a real data analysis is provided to further verify the effect of the model.
With the increasing application of UAVs,UAV positioning technology for indoor complex environment has become a hot research issue in the industry.The traditional UWB positioning technology is affected by problems such as multipath effect and non-line-of-sight propagation,and its application in complex indoor environments has problemssuch as poor positioning accuracy and strong noise interference.We propose an improved LSE-EKF optimisation algorithm for UWB positioning in indoor complex environments,which optimises the initial measurement data through a BP neural network correction model,then optimises the coordinate error using least squares estimation to find the best pre-located coordinates,finally eliminates the interference noise in the pre-located coordinate signal through an EKF algorithm.It has been verified by experiments that the evaluation index can be improved by more than 9%compared with EKF algorithm data,especially under non-line-of-sight(NLOS)conditions,which enhances the possibility of industrial application of indoor UAV.
