The recursive form for the standard least squares estimation cannot be applied to recursively compute the weighted least squares estimate if the weight matrix is not diagonal. The instrumental variable estimate obtained by the least squares solution of an over-determined system of equations can be viewed as one of the weighted least squares estimates with a non-diagonal weight matrix. In this paper, a recursive form for the weighted least squares estimation with a non-diagonal weight matrix is considered. A new effective and numerically stable recursive algorithm is proposed using QR factorization and J-orthogonal QR factorization for Isermann et al.'s weighted least squares estimate.

This study presents a method for fault diagnosis and fault-tolerant control of a quadcopter. The thrust of each rotor is estimated by solving a least-squares problem that considers the relationship between the acceleration, angular velocity, and thrust of the quadcopter. The ratio of the estimated thrust to the control input is then used for fault diagnosis, which is integrated into nonlinear model predictive control. This approach enables a single controller to handle a wide range of faults regardless of the degree of rotor effectiveness loss or the position and number of failed rotors. Finally, the effectiveness of the proposed method is verified through several simulations that assume an actual quadcopter.

Predicting the condition of machinery and performing maintenance activities in advance is essential for efficient and safe work at construction sites. If the load applied to a machine in operation is known, it is possible to predict failures based on the load conditions. However, the load on construction machinery such as hydraulic excavators changes depending on the work environment and operation, so it is necessary to construct a load estimation model that adapts to these factors. This paper proposes a load estimation modeling method that combines machine learning to determine excavator movements and database-driven modeling. Experiments using a radio-controlled excavator show that the proposed method is effective.