Development Of Gyroless Attitude And Angular Rate Estimation For Satellites
Vivek Chandran, K P
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Studies aimed at the development of indigenous low cost star tracker and gyroless attitude and angular rate estimation is presented in the thesis. This study is required for the realization of low cost micro satellites. A target specification of determining the attitude with accuracy (3σ) of 0.05 degrees and attitude rate with accuracy (3σ) in the range of 50rad/sec at a rate of 10 samples/second in all the axes is set as a goal for the study. Different sensor arrays available in the market are evaluated on the basis of their noise characteristics, resolution of the analog-to-digital converter (ADC) present and ability to work in low light conditions, for possible use in the hardware realization of star tracker. STAR1000 APS CMOS array, manufactured by Cypress Semiconductors, qualified these performance criteria, is used for the simulation study. An algorithm is presented for scanning the sensor array, detection of star image and retrieving the information concerning the photoelectron counts corresponding to a star image. The exact designation of the center of the star image becomes crucial as it has direct implications on the accuracy of the estimated attitude. Various algorithms concerning the centroid estimation of a defocused star image on the sensor array to subpixel accuracy are studied and Gaussian Weighed Center of Gravity algorithm is adapted with some modifications and an accuracy of 0.039 pixels is obtained in both horizontal and vertical direction of the array. A one-to-one relationship is established between the stars obtained in the field-of-view (FOV) of the star tracker with the stars present in the star catalog resident in the star tracker through star identification algorithm. A star identification algorithm which relies on the interstar angles and brightness of the stars is developed in this thesis. The interstar angles of the stars visible in the FOV of the star sensor is recorded, compared with the inter-star angles made by the stars selected in the catalog, based on initial brightness match with stars formed on image plane. After identification at the initial epoch, consequent instants can drive information from the previous matches so as to decrease the computational complexity and storage requirement for the subsequent instants. The memory constraints and computational overhead on the processor and the dynamic range of the image detector used in the star tracker are the limiting factors. The stars thus identified with the stars in the catalog are used for the estimation of attitude. A point solution to the attitude estimation problem is computed using a least square based algorithm called ESOQ-2. The algorithm for centroiding of star images and ESOQ-2 for finding the point solution satellite attitude is coded and tested on Da Vinci based emulator. This exercise shows that it is possible to implement above algorithm for real time operations. Estimation of attitude at a given epoch using algorithms like ESOQ-2 does not minimize the noise and error covariance as the attitude estimated at each instant of time depends only on the measurement taken at that particular instant. So a Kalman Filter (KF) based estimation using Integrated Rate Parameter (IRP) formulation called SIAVE algorithm, is adapted, with some modifications, for the estimation of incremental angle and attitude rates from vector observations of stars. From the point solution of attitude estimation problem of the satellite, the incremental angle and angular rate at successive time steps are predicted using a linear KF and refined with the measurements from the stand alone star tracker, taken at discrete time steps, using the SIAVE algorithm. The sensor noise is modeled from the characteristics of STAR1000 sensor array used in the algorithm in order to make the simulations more realistic in nature. The optimality of Kalman filter is based on the assumption that the state and measurement noises are white gaussian random processes and the state dynamics of the plant is completely known. However, for most real systems, modeling uncertainties are present. So a robust state estimator based on H∞ norm minimization is devised. The H∞ filter, based on game theory approach is used to minimize the worst case variance of noise signals with the only assumption on the noise signals that they are energy bounded. The aim is to find the feasibility of using H∞ filter for the estimation of incremental angle and attitude rate of the satellite. The studies shows that H∞ filter with proper tuning can serve as potential estimation scheme for the attitude and angular rate estimation of the satellite. It is found that both Kalman filter and H∞ are able to meet the specified accuracy desired from low cost accurate star sensor.
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