Modified Least-squares Algorithm Research Articles

Robust Adaptive Identification of Linear Time-Varying Systems Under Relaxed Excitation Conditions

An on-line modified least-squares identification algorithm is proposed for linear time-varying systems with bounded disturbances under relaxed excitation conditions. An extra term which enhances the tracking ability for time-varying parameters is added to the covariance’s update law. An indicator of the regressor’s excitation level based on the maximum eigenvalue of the covariance matrix is developed. By combining the maximum eigenvalue with its variation trend shown by the sensitivity of the maximum eigenvalue to change in the covariance matrix, a novel identification law, which is switched between a modified least-squares algorithm and a gradient algorithm based on fixed $\sigma $ -modification, is proposed. The boundedness of the estimation error and the covariance matrix are guaranteed via Lyapunov stability theory. The superiority of the proposed method is verified by simulations.

SG parameters estimation based on synchrophasor data

In this study, first, it is shown that the least-squares (LS) algorithm outperforms well known methods such as extended Kalman filter and unscented Kalman filter for synchronous generator (SG) parameters estimation using phasor measurement unit (PMU) data. However, as the LS algorithm may estimate the SG parameters inaccurately if the initial values of SG model state variables are not valid, a modified LS (MLS) algorithm, which estimates the initial values of SG model state variables alongside SG parameters, is proposed. In addition to parameters estimation of an SG classical model, the performance of this algorithm in the estimation of whole electromagnetic parameters and rotor inertia constant of an SG full-order model is evaluated. Note that conventionally, measurements of generators rotor angles were used to estimate SGs full-order model parameters; nevertheless, in the proposed MLS algorithm, online SG parameters estimation is accomplished using PMU data without relying on rotor angle measurement that is difficult to be obtained in practise. Simulation results demonstrate the effectiveness of the proposed algorithm in SG parameters estimation for various disturbances and noisy measurements. Furthermore, the effect of mechanical torque signal unavailability on the proposed algorithm capability is studied, where the efficacy of this algorithm is proven.

Robust adaptive identification of linear time‐varying systems with modified least‐squares algorithm

A modified least-squares algorithm with forgetting factor is proposed and applied to linear time-varying systems. The bound on the Euclidean norm of the estimation error is derived mathematically. When the bounded regressor of the linear time-varying system satisfies persistent excitation condition, this new algorithm can attenuate the influences of bounded disturbances and the change ratio of time-varying parameters effectively through extra term that is added to the covariance's update law. Contrary to the earlier proposed estimation laws, this algorithm does not require any prior knowledge of upper bounds on the parameters and the disturbances. Simulation results demonstrate the effectiveness of the identification law.

Patient-Specific Three-Dimensional Composite Bone Models for Teaching and Operation Planning

Orthopedic trauma care relies on two-dimensional radiograms both before and during the operation. Understanding the three-dimensional nature of complex fractures on plain radiograms is challenging. Modern fluoroscopes can acquire three-dimensional volume datasets even during an operation, but the device limitations constrain the acquired volume to a cube of only 12-cm edge. However, viewing the surrounding intact structures is important to comprehend the fracture in its context. We suggest merging a fluoroscope's volume scan into a generic bone model to form a composite full-length 3D bone model. Materials consisted of one cadaver bone and 20 three-dimensional surface models of human femora. Radiograms and computed tomography scans were taken before and after applying a controlled fracture to the bone. A 3D scan of the fracture was acquired using a mobile fluoroscope (Siemens Siremobil). The fracture was fitted into the generic bone models by rigid registration using a modified least-squares algorithm. Registration precision was determined and a clinical appraisal of the composite models obtained. Twenty composite bone models were generated. Average registration precision was 2.0 mm (range 1.6 to 2.6). Average processing time on a laptop computer was 35 s (range 20 to 55). Comparing synthesized radiograms with the actual radiograms of the fractured bone yielded clinically satisfactory results. A three-dimensional full-length representation of a fractured bone can reliably be synthesized from a short scan of the patient's fracture and a generic bone model. This patient-specific model can subsequently be used for teaching, surgical operation planning, and intraoperative visualization purposes.

Identification of linear time-varying systems using a modified least-squares algorithm

In this paper a modified version of the standard least-squares algorithm is presented. The aim is to use the proposed modified LS algorithm in linear time-varying systems. The proposed modification involves the addition of extra terms to both the parameter estimates’ and the covariance's update laws. We establish a series of properties on the identification error, the parameter estimates and the covariance matrix. These properties are important in an adaptive control context, because LS algorithms provide an easy way of modifying the parameter estimates in order to avoid singular points in the control scheme.

Bias-compensating least squares method for identification of continuous-time systems from sampled data

Abstract Least squares (LS) techniques are applied to the identification problem of continuous-time systems from sampled data of input-output measurements. The linear integral filter, which solves the intial condition problem, is employed for handling time derivatives. The asymptotic bias in the LS estimator is derived, and is compensated in a modified LS algorithm (called a bias-compensating LS method) to obtain consistent estimates of the unknown parameters. When it is unknown, the variance of the noise can be estimated recursively together with the system parameters. The bias-compensating LS method not only has all merits of the LS method but also possesses good consistency properties. It is applicable to both time-invariant and time-varying continuous-time systems. In the time-varying case, an adaptive LS algorithm with a variable forgetting factor is chosen to make the estimates track the changing parameters quickly, and the bias is compensated as is done in the time-invariant case. Representative nu...