Greedy Sensor Selection for Weighted Linear Least Squares Estimation Under Correlated Noise

Density Weighted Linear Least Squares

for an unknown vector of parameters β0 and an unknown univariate function τ(·). This model is implied by many important limited dependent variable and regression models, as discussed in Ruud (1986) and Stoker (1986). Consistent estimators for β0, up to an unknown scale factor, have been developed by Ruud (1986), Stoker (1986), Powell, Stock, and Stoker (1989), Ichimura (1993), and others. In th...

Weighted Least Squares Estimation with Missing Data

Power System State Estimation Using Weighted Least Squares (WLS) and Regularized Weighted Least Squares(RWLS) Method

In this paper, a new formulation for power system state estimation is proposed. The formulation is based on regularized least squares method which uses the principle of Thikonov’s regularization to overcome the limitations of conventional state estimation methods. In this approach, the mathematical unfeasibility which results from the lack of measurements in case of ill-posed problems is elimin...

Combined l1 and greedy l0 penalized least squares for linear model selection

We introduce a computationally effective algorithm for a linear model selection consisting of three steps: screening–ordering–selection (SOS). Screening of predictors is based on the thresholded Lasso that is `1 penalized least squares. The screened predictors are then fitted using least squares (LS) and ordered with respect to their |t| statistics. Finally, a model is selected using greedy gen...

Linear least squares localization in sensor networks

Localization in sensor networks is critical for search and rescue. Linear least squares (LLS) estimation is a sub-optimum but low-complexity localization algorithm based on measurements of location-related parameters. Commonly, there are two types of LLS localization algorithms using range measurements; one is based on introducing a dummy variable (called LLS-I), and the other is based on the s...