In order to overcome the various disadvantages of standalone INS and GPS, these systems are integrated using nonlinear estimation techniques and benefits of the two complementary systems are obtained at the same time. The standard and most widely used estimation algorithm in the INS/GPS integrated systems is Extended Kalman Filter (EKF). Linearization step involved in the EKF algorithm can lead to second order errors in the mean and covariance of the state estimate. Another nonlinear estimator, Unscented Kalman Filter (UKF) approaches this problem by carefully selecting deterministic sigma points from the Gaussian distribution and propagating these points through the nonlinear function itself leading third order errors for any nonlinearity. Scaled Unscented Transformation (SUT) is one of the sigma point selection methods which gives the opportunity to adjust the spread of sigma points and control the higher order errors by some design parameters. Determination of these parameters is problem specific. In this thesis, effects of the SUT parameters on integrated navigation solution are investigated and an &ldquo / Adaptive UKF&rdquo / is designed for a tightly-coupled INS/GPS integrated system. Besides adapting process and v measurement noises, SUT parameters are adaptively tuned. A realistic fighter flight trajectory is used to simulate IMU and GPS data within Monte Carlo analysis. Results of the proposed method are compared with standard EKF and UKF integration. It is observed that the adaptive scheme used in the sigma point selection improves the performance of the integrated navigation system especially at the end of GPS outage periods.

The enhancement of the reliability, security, and resiliency of electric power systems depends on the availability of fast, accurate, and robust dynamic state estimators. These estimators should be robust to gross errors on the measurements and the model parameter values while providing good state estimates even in the presence of large dynamical system model uncertainties and non-Gaussian thick-tailed process and observation noises. It turns out that the current Kalman filter-based dynamic state estimators given in the literature suffer from several important shortcomings, precluding them from being adopted by power utilities for practical applications. To be specific, they cannot handle (i) dynamic model uncertainty and parameter errors; (ii) non-Gaussian process and observation noise of the system nonlinear dynamic models; (iii) three types of outliers; and (iv) all types of cyber attacks. The three types of outliers, including observation, innovation, and structural outliers are caused by either an unreliable dynamical model or real-time synchrophasor measurements with data quality issues, which are commonly seen in the power system. To address these challenges, we have pioneered a general theoretical framework that advances both robust statistics and robust control theory for robust dynamic state and parameter estimation of a cyber-physical system. Specifically, the generalized maximum-likelihood-type (GM)-estimator, the unscented Kalman filter (UKF), and the H-infinity filter are integrated into a unified framework to yield various centralized and decentralized robust dynamic state estimators. These new estimators include the GM-iterated extended Kalman filter (GM-IEKF), the GM-UKF, the H-infinity UKF and the robust H-infinity UKF. The GM-IEKF is able to handle observation and innovation outliers but its statistical efficiency is low in the presence of non-Gaussian system process and measurement noise. The GM-UKF addresses this issue and achieves a high statistical efficiency under a broad range of non-Gaussian process and observation noise while maintaining the robustness to observation and innovation outliers. A reformulation of the GM-UKF with multiple hypothesis testing further enables it to handle structural outliers. However, the GM-UKF may yield biased state estimates in presence of large system uncertainties. To this end, the H-infinity UKF that relies on robust control theory is proposed. It is shown that H-infinity is able to bound the system uncertainties but lacks of robustness to outliers and non-Gaussian noise. Finally, the robust H-infinity filter framework is proposed that leverages the H-infinity criterion to bound system uncertainties while relying on the robustness of GM-estimator to filter out non-Gaussian noise and suppress outliers. Furthermore, these new robust estimators are applied for system bus frequency monitoring and control and synchronous generator model parameter calibration. Case studies of several different IEEE standard systems show the efficiency and robustness of the proposed estimators. / Ph. D. / The enhancement of the reliability, security, and resiliency of electric power systems depends on the availability of fast, accurate, and robust dynamic state estimators. These estimators should be robust to gross errors on the measurements and the model parameter values while providing good state estimates even in the presence of large dynamical system model uncertainties and non-Gaussian thick-tailed process and observation noises. There are three types of gross errors or outliers, namely, observation, innovation, and structural outliers. They can be caused by either an unreliable dynamical model or real-time synchrophasor measurements with data quality issues, which are commonly seen in the power system. The system uncertainties can be induced in several ways, including i) unknowable system inputs, such as noise, parameter variations and actuator failures, to name a few; ii) unavailable inputs, such as unmeasured mechanical power, field voltage of the exciter, unknown fault location; and iii) inaccuracies of the model parameter values of the synchronous generators, the loads, the lines, and the transformers, to name a few. It turns out that the current Kalman filter-based dynamic state estimators suffer from several important shortcomings, precluding them from being adopted by power utilities for practical applications. To address these challenges, this dissertation has proposed a general theoretical framework that advances both robust statistics and robust control theory for robust dynamic state and parameter estimation. Specifically, the robust generalized maximum-likelihood-type (GM)- estimator, the nonlinear filter, i.e., unscented Kalman filter (UKF), and the H-infinity filter are integrated into a unified framework to produce various robust dynamic state estimators. These new estimators include the robust GM-IEKF, the robust GM-UKF, the H-infinity UKF and the robust H-infinity UKF. Specifically, the GM-IEKF deals with the observation and innovation outliers but achieving relatively low statistical efficiency in the presence of non-Gaussian system process and measurement noise. To address that, the robust GM-UKF is proposed that is able to achieve a high statistical efficiency under a broad range of non-Gaussian noise while maintaining the robustness to observation and innovation outliers. A reformulation of the GM-UKF with multiple hypothesis testing further enables it to handle three types of outliers. However, the GM-UKF may yield biased state estimates in presence of large system uncertainties. To this end, the H-infinity UKF that depends on robust control theory is proposed. It is able to bound the system uncertainties but lacks of robustness to outliers and non-Gaussian noise. Finally, the robust H-infinity filter framework is proposed that relies on the H-infinity criterion to bound system uncertainties while leveraging the robustness of GM-UKF to filter out non-Gaussian noise and suppress outliers. These new robust estimators are applied for system bus frequency monitoring and control and synchronous generator model parameter calibration. Case studies of several different IEEE standard systems show the efficiency and robustness of the proposed estimators.