Maryam Kiani

State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization

Abstract New heuristic filters are proposed for state estimation of nonlinear dynamic systems based on particle swarm optimization (PSO) and differential evolution (DE). The methodology converts state estimation problem into dynamic optimization to find the best estimate recursively. In the proposed strategy the particle number is adaptively set based on the weighted variance of the particles. To have a filter with minimal parameter settings, PSO with exponential distribution (PSO-E) is selected in conjunction with jDE to self-adapt the other control parameters. The performance of the proposed adaptive evolutionary algorithms i.e. adaptive PSO-E, adaptive DE and adaptive jDE is studied through a comparative study on a suite of well-known uni- and multi-modal benchmark functions. The results indicate an improved performance of the adaptive algorithms relative to original simple versions. Further, the performance of the proposed heuristic filters generally called adaptive particle swarm filters (APSF) or adaptive differential evolution filters (ADEF) are evaluated using different linear (nonlinear)/Gaussian (non-Gaussian) test systems. Comparison of the results to those of the extended Kalman filter, unscented Kalman filter, and particle filter indicate that the adopted strategy fulfills the essential requirements of accuracy for nonlinear state estimation.

Concurrent orbit and attitude estimation using minimum sigma point unscented Kalman filter

Concurrent orbit and attitude determination (COAD) plays a key role in reducing the cost of navigation and control subsystem for small satellites. This article is devoted to the problem of the COAD of satellites. A measurement package consisting of three axis magnetometer (TAM) and a sun sensor is shown to be sufficient to estimate the attitude and orbit information. To this end, an autonomous gyro-less COAD algorithm is proposed and implemented through the centralized data fusion of the TAM and the sun sensor. The set of nonlinear-coupled roto-translation dynamics of the satellite is used with a modified unscented Kalman filter (MUKF) to estimate the full satellite states. The MUKF is specially proposed to substantially cut the run time by minimizing the number of required sigma points. The results indicate that the adopted strategy fulfills the essential requirements of accuracy and the speed of state estimation. Local observability is demonstrated and an extensive Monte Carlo simulation has shown desirable stability characteristics for the proposed algorithm. Additionally, a sensitivity analysis on the orbital elements and sensor characteristics is performed to verify the feasibility and utility of the MUKF over a wider acceptable range of sensory and operating environments.

Spacecraft Attitude and System Identification Using Marginal Reduced UKF Utilizing the Sun and Calibrated TAM Sensors

This paper deals with attitude determination, parameter identification and reference sensor calibration simultaneously. A LEO satellite’s attitude, inertia tensor as well as calibration of Three-Axis-Magnetometer (TAM) are estimated during a maneuver designed to satisfy persistency of excitation condition. For this purpose, kinematic and kinetic state equations of spacecraft motion are augmented for the determination of inertia tensor and TAM calibration parameters including scale factors, misalignments and biases along three body axes. Attitude determination is a nonlinear estimation problem. Unscented Kalman Filter (UKF) as an advanced nonlinear estimation algorithm with good performance can be used to estimate satellite attitude but its computational cost is considerably larger than the widespread, low accuracy, Extended Kalman Filter (EKF). Reduced Sigma Points Filters provide good solutions and also decrease run time of UKF. However, in contrast to nonlinear problem of attitude determination, parameter identification and sensor calibration have linear dynamics. Therefore, a new Marginal UKF (MUKF) is proposed that combines the utility of Kalman Filter with Modified UKF (MMUKF). The proposed MMUKF utilizes only 14 sigma points to achieve the complete 25-dimensional state vector estimation. Additionally, a Monte Carlo simulation has demonstrated a good accuracy for concurrent estimation of attitude, inertia tensor as well as TAM calibration parameters in significantly less time with respect to sole utilization of the UKF.