Generalized Nonlinear Complementary Attitude Filter

This work describes a family of attitude estimators that are based on a generalization of Mahony's nonlinear complementary filter. This generalization reveals the close mathematical relationship between the nonlinear complementary filter and the more traditional multiplicative extended Kalman filter. In fact, the bias-free and constant gain multiplicative continuous-time extended Kalman filters may be interpreted as special cases of the generalized attitude estimator. The correspondence provides a rational means of choosing the gains for the nonlinear complementary filter and a proof of the near global asymptotic stability of special cases of the multiplicative extended Kalman filter

Extended-Kalman-filter-based dynamic mode decomposition for simultaneous system identification and denoising

A new dynamic mode decomposition (DMD) method is introduced for simultaneous online system identification and denoising in conjunction with the adoption of an extended Kalman filter algorithm\color{black}. The present paper explains the extended-Kalman-filter-based DMD (EKFDMD) algorithm and illustrates that EKFDMD requires significant numerical resources for many-degree-of-freedom (many-DoF) problems and that the combination with truncated proper orthogonal decomposition (trPOD) helps us to apply the EKFDMD algorithm to many-DoF problems. The numerical experiments of the present study illustrate that EKFDMD can estimate eigenvalues from a noisy dataset with a few DoFs better than or as well as the existing algorithms, whereas EKFDMD can also denoise the original dataset online. In particular, EKFDMD performs better than existing algorithms for the case in which system noise is present. The EKFDMD with trPOD can be successfully applied to many-DoF problems, including a fluid-problem example, and the results reveal the superior performance of system identification and denoising. Note that these superior results are obtained despite being an online procedure

Comparisons of nonlinear estimators for wastewater treatment plants

This paper deals with five existing nonlinear estimators (filters), which include Extended Kalman Filter (EKF), Extended H-infinity Filter (EHF), State Dependent Filter (SDF), State Dependent H-Infinity Filter (SDHF) and Unscented Kalman Filter (UKF) that are formulated and implemented to estimate unmeasured states of a typical biological wastewater system. The performance of these five estimators of different complexities, behaviour and advantages are demonstrated and compared via nonlinear simulations. This study shows promising application of UKF for monitoring and control of the process variables, which are not directly measurable

Target Tracking in Non-Gaussian Environment

Masreliez filter which is a Kalman type of recursive filter is implemented and validated. The main computation in Masreliez filter is to evaluate the score function which directly influences the estimates of the target states. Scalar approximation for score function evaluation is extended to vector observations, implemented and validated. The simulation studies have shown that the performance of the Masreliez filter is relatively better than that of the conventional Kalman filter in the presence of significant glint noise in the observation