Sun Sensor Research Articles

Deterministic and Recursive Approach in Attitude Determination for InnoSAT

Attitude determination system (ADS) was indispensable in attitude control of satellite. Especially for InnoSAT due to the limitation of budget, weight, and power, the attitude was determined using onboard position sensors. Previous research has successfully implemented the attitude determination using only Earth's magnetic field sensors for small attitude angle, but the approach produced quite big error for large attitude angle. This paper presents attitude determination for InnoSAT using combination of sun sensors and earth's magnetic field for large attitude angle. The attitude was determined using a deterministic (QUEST) and recursive (EKF) approach. A problem arises when using the sun sensors while the satellite experiencing eclipse. Consequently, the accuracy of both approaches was analyzed at eclipse and no eclipse conditions. The result shows that deterministic approach produced better accuracy at no eclipse but recursive approach produced better accuracy at eclipse. The strategy to apply the both approaches and eclipse conditions also discussed in this paper.

A Position Control Review for a Photovoltaic System:Dual Axis Sun Tracker

The Sun Tracker is an automated solar panel that actually follows the sun position to increase the power production. After some measurements, the Sun Tracker increases the power production by more than 40% by keeping the panels parallel to the sun that makes the sun rays fall perpendicularly on the solar panel. In this paper, we present a sun tracker without using sun sensors. The sun tracking is performed by changing the solar panel orientation in horizontal andvertical directions by two motors. The control of these motors is ensured by a microcontroller. The proposed system has the capability to track using the location data of the sun.

Spin-Axis Attitude Determination and Covariances in Local Sun-Earth Frame

This paper presents practical analytical models for spin-axis attitude determination using measurements generated by sun and Earth sensors. In particular, explicit expressions for the least-squares estimates and their associated covariance matrices are established. The adoption of the local reference frame defined by the instantaneous sun and Earth vectors leads to compact analytical results. These results provide a more immediate understanding of the attitude error covariance matrix in terms of its dependence on the sun–Earth geometry. The application of the covariance results is illustrated by using the actual geometrical in-orbit conditions of two satellites.

The Research of Micro-Satellite Attitude Determination Based on Predictive Filter

— An extended predictive filter is presented for attitude determination of Micro-satellite based on the basic theory of predictive filter. This algorithm enhances the precision of kinematics equation, accurately estimates satellite attitude angle and angular velocity using measurement vectors from magnetometer and sun sensors by predicting model errors and angular velocity errors one step ahead. In addition, a new measurement model is derived about angular velocity, which improved the efficiency of the use of measurement vectors. Simulation results show both the high reliability and precision of this method.

Design and Manufacturing of Sun Motion Simulator Applied to Satellites Attitude Determination

Environmental simulation has an essential contribution in attitude determination and control verification tests of satellites. Specifically, real-time modeling of space environment can provide more precise and adapted simulation of real world in order to enable satellite attitude determination system by online outputs of sensors. Design and manufacturing of a moving mechanism which simulates the motion of real Sun relative to the satellite is proposed in this paper. Indeed, an artificial Sun carried by the mechanism will sensitize Sun Sensors mounted on a 3DOF model of satellite and finally the outputs of sensors are used to determine the attitude of the model satellite. The procedure of designing and manufacturing such a mechanism is described as follows. Firstly, the motion of Sun relative to the satellite on a specific orbit was ascertained. Next, considering the constraints such as laboratory space and its equipments, an appropriate mechanism was designed conceptually to satisfy the requirements. Then, the detailed characteristics of the mechanism were determined in the preliminary design phase and approved in the detailed design phase of the project. Finally, in order to verify the designed mechanism, a scaled down prototype was fabricated. Developmental tests on the prototype proved the ability of the model to simulate the Sun motion relative to the satellite properly.

Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask

Nowadays sun sensors are being more widely used in satellites to determine the sunray orientation, thus development of a new version of sun sensor with lighter mass, lower power consumption and smaller size it of considerable interest. This paper introduces such a novel digital sun sensor, which is composed of a micro-electro-mechanical system (MEMS) mask with an N-shaped slit as well as a single linear array charge-coupled device (CCD). The sun sensor can achieve the measurement of two-axis sunray angles according to the three sun spot images on the CCD formed by sun light illumination through the mask. Given the CCD glass layer, an iterative algorithm is established to correct the refraction error. Thus, system resolution, update rate and other characteristics are improved based on the model simulation and system design. The test of sun sensor prototype is carried out on a three-axis rotating platform with a sun simulator. The test results show that the field of view (FOV) is ±60° × ±60° and the accuracy is 0.08 degrees of arc (3σ) in the whole FOV. Since the power consumption of the prototype is only 300 mW and the update rate is 14 Hz, the novel digital sun sensor can be applied broadly in micro/nano-satellites, even pico-satellites.

Unscented Kalman filter for spacecraft attitude estimation using Quaternions and Euler angles

A spacecraft attitude estimation approach based on the Unscented Kalman Filter is derived. For nonlinear systems the Unscented Kalman Filter uses a carefully selected set of sample points to map more accurately the probability distribution than the linearization of the standard Extended Kalman Filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. The filter formulation is based on standard attitude- vector measurements using a gyro-based model for attitude propagation. This paper compares the performance of a new technique, the Unscented Kalman Filter, when two different mathematical constructs are used to represent the attitude: the Euler angles and quaternions. In this study, the attitude of satellite is estimated with real time algorithms using real data supplied by gyros, Earth sensors and Sun sensors that are on board of the CBERS-2 (China Brazil Earth Resources Satellite).

Simultaneous celestial positioning and orientation for the lunar rover

In order to obtain absolute heading angle and position, lunar rover needs the support of autonomous celestial navigation system (CNS). This paper proposes a sun observation based simultaneous celestial positioning and orientation (SCPO) algorithm for the lunar rover under stationary position. Firstly we measure the sun orientation by a sun sensor and the gravity orientation by an inclinometer; secondly combine them with sun ephemeris; finally solve this problem with quaternion estimation (QUEST). By analyzing affects of the sensor's system error (such as the installation errors, bias, etc.) and random noise under stationary conditions, these two types of errors can be eliminated using joint calibration. Executing the SCPO on the moon is demonstrated through simulation. The algorithm is carried out with an experiment on the earth surface, and results demonstrate the high consistency of our simulation.

Sun Sensor Navigation for Planetary Rovers: Theory and Field Testing

In this paper, we present an experimental study of sun sensing as a rover navigational aid. Algorithms are outlined to determine rover heading in an absolute reference frame. The sensor suite consists of a sun sensor, inclinometer, and clock (as well as ephemeris data). We describe a technique to determine ground-truth orientation in the field (without using a compass) and present a large number of experimental results (both in Toronto and on Devon Island) showing our ability to determine absolute rover heading to within a few degrees.

Modelling of spacecraft spin period during eclipse

Abstract. The majority of scientific satellites investigating the Earth magnetosphere are spin stabilized. The attitude information comes usually from a sun sensor and is missing in the umbra; hence, the accurate experimental determination of vector quantities is not possible during eclipses. The spin period of the spacecraft is generally not constant during these times because the moment of inertia changes due to heat dissipation. The temperature dependence of the moment of inertia for each spacecraft has a specific signature determined by its design and distribution of mass. We developed an "eclipse-spin" model for the spacecraft spin period behaviour using magnetic field vector measurements close to the Earth, where the magnetic field is dominated by the dipole field, and in the magnetospheric lobes, where the magnetic field direction is mostly constant. The modelled spin periods give us extraordinarily good results with accumulated phase deviations over one hour of less than 10 degrees. Using the eclipse spin model satellite experiments depending on correct spin phase information can deliver science data even during eclipses. Two applications for THEMIS B, one in the lobe and the other in the lunar wake, are presented.

A novel multi-aperture based sun sensor based on a fast multi-point MEANSHIFT (FMMS) algorithm.

With the current increased widespread interest in the development and applications of micro/nanosatellites, it was found that we needed to design a small high accuracy satellite attitude determination system, because the star trackers widely used in large satellites are large and heavy, and therefore not suitable for installation on micro/nanosatellites. A Sun sensor + magnetometer is proven to be a better alternative, but the conventional sun sensor has low accuracy, and cannot meet the requirements of the attitude determination systems of micro/nanosatellites, so the development of a small high accuracy sun sensor with high reliability is very significant. This paper presents a multi-aperture based sun sensor, which is composed of a micro-electro-mechanical system (MEMS) mask with 36 apertures and an active pixels sensor (APS) CMOS placed below the mask at a certain distance. A novel fast multi-point MEANSHIFT (FMMS) algorithm is proposed to improve the accuracy and reliability, the two key performance features, of an APS sun sensor. When the sunlight illuminates the sensor, a sun spot array image is formed on the APS detector. Then the sun angles can be derived by analyzing the aperture image location on the detector via the FMMS algorithm. With this system, the centroid accuracy of the sun image can reach 0.01 pixels, without increasing the weight and power consumption, even when some missing apertures and bad pixels appear on the detector due to aging of the devices and operation in a harsh space environment, while the pointing accuracy of the single-aperture sun sensor using the conventional correlation algorithm is only 0.05 pixels.

Pico-satellite Autonomous Navigation with Magnetometer and Sun Sensor Data

This article presents a near-Earth satellite orbit estimation method for pico-satellite applications with light-weight and low-power requirements. The method provides orbit information autonomously from magnetometer and sun sensor, with an extended Kalman filter (EKF). Real-time position/velocity parameters are estimated with attitude independently from two quantities: the measured magnitude of the Earth's magnetic field, and the measured dot product of the magnetic field vector and the sun vector. To guarantee the filter's effectiveness, it is recommended that the sun sensor should at least have the same level of accuracy as magnetometer. Furthermore, to reduce filter's computation expense, simplification methods in EKF's Jacobian calculations are introduced and testified, and a polynomial model for fast magnetic field calculation is developed. With these methods, 50% of the computation expense in dynamic model propagation and 80% of the computation burden in measurement model calculation can be reduced. Tested with simulation data and compared with original magnetometer-only methods, filter achieves faster convergence and higher accuracy by 75% and 30% respectively, and the suggested simplification methods are proved to be harmless to filter's estimation performance.

Attitude Determination of Nano Satellite Based on Gyroscope, Sun Sensor and Magnetometer

With the fast development of nano-satellite applications, higher requirements on the method and accuracy for determining attitude of Nano-satellite are presented. Aiming at the accuracy requirements of attitude determination of sun-oriented mode of the nano-satellite, an integrated attitude sensor is built with combining of gyroscope, magnetometer and sun sensor. Furthermore, the extended Kalman filter is used to fuse measurement data from gyroscope, magnetometer and sun sensor. A simulation model of attitude determination is built, and a few simulations are performed. The simulation results show that the accuracy of the integrated attitude determination sensor proposed in this paper can meet the accuracy requirement (0.05. Deg.) of nano-satellite attitude determination.

Design and Fabrication of an Albedo Insensitive Analog Sun Sensor

A sun sensor is usually included in a satellite for optically measuring the position relative to the sun. The accuracy of a conventional sun sensor is affected by reflected sunlight at the nearby earth atmosphere: the albedo radiation. The part of the spectrum at near IR (1.5μm) is not included in the albedo radiation, due to the high water absorption in the earth atmosphere. The feasibility of such a near infrared (IR) analog albedo insensitive sun sensor in terms of the design constraints and fabrication is presented. The proposed sensor system comprises a spectral selective coating layer, a black absorbing coating layer, an anti-reflection layer, an InGaAs quadrant detector and is built on a sapphire substrate. The black absorbing ensures that the position measurement is not affected by back-reflected light from the detector surface. A lift-off process is used for patterning of the coating layer.

A quantum search algorithm for future spacecraft attitude determination

In this paper we study the potential application of a quantum search algorithm to spacecraft navigation with a focus on attitude determination. Traditionally, attitude determination is achieved by recognizing the relative position/attitude with respect to the background stars using sun sensors, earth limb sensors, or star trackers. However, due to the massive celestial database, star pattern recognition is a complicated and power consuming job. We propose a new method of attitude determination by applying the quantum search algorithm to the search for a specific star or star pattern. The quantum search algorithm, proposed by Grover in 1996, could search the specific data out of an unstructured database containing a number N of data in only O(N) steps, compared to an average of N/2 steps in conventional computers. As a result, by taking advantage of matching a particular star in a vast celestial database in very few steps, we derive a new algorithm for attitude determination, collaborated with Grover's search algorithm and star catalogues of apparent magnitude and absorption spectra. Numerical simulations and examples are also provided to demonstrate the feasibility and robustness of our new algorithm.

Nonlinear observers for spacecraft attitude estimation in case of yaw angle measurement absence

This paper provides a brief presentation and a useful comparison between two nonlinear observers Extended Kalman Filter (EKF) and sliding mode observer (SMO). Both can be used for moderate-accuracy attitude determination systems for Low Earth Orbit (LEO) Earth-pointing spacecraft (s/c), which is typically achieved using Gyroscopes, Earth, and Sun sensors for attitude sensing. The use of these observers provides a substitute for the yaw data in case of the s/c eclipse periods or limited field of views. The nonlinear observability for this system is analytically investigated via the calculation of Lie derivatives to check the possibility of the system states estimation. The performances of both observers are presented, the SMO stability is proved and the SMO enhanced estimates are shown by simulation.

A Miniaturized Two Axis Sun Sensor for Attitude Control of Nano-Satellites

This paper describes the design, fabrication, characterization, and satellite integration of a miniaturized two axis sun sensor which has been used in the attitude control system of the Spanish nano-satellite NANOSAT-1B. This device is made of four silicon photodiodes monolithically integrated in a crystalline silicon substrate, protected by a transparent cover glass assembled on the same silicon die against space radiation damage. The sensor fabrication combines standard silicon processing technology with a high performance solar cell fabrication process. The sensor, including electronics and mechanical and electrical interfacing with the satellite, has a small size (3 cm × 3 cm) and low weight (24 gr.), with a sun field-of-view greater than ±60° with an angle accuracy better than 0.15°. Three of these sensors have already been integrated in the NANOSAT-1B platform that has been successfully launched in July 2009.

Cubesat solar sail 3-axis stabilization using panel translation and magnetic torquing

A Cubesat mission with a deployable solar sail of 5 meter by 5 meter in a sun-synchronous low earth orbit is analyzed to demonstrate solar sailing using active attitude stabilization of the sail panel. The sail panel is kept parallel to the orbital plane to minimize aerodynamic drag and optimize the orbit inclination change caused by the solar pressure force normal to the sail surface. A practical control system is proposed, using a combination of small 2-dimensional translation of the sail panel and 3-axis magnetic torquing which is proved to have sufficient control authority over the gravity gradient and aerodynamic disturbance torques. Miniaturized CMOS cameras are used as sun and nadir vector attitude sensors and a robust Kalman filter is used to accurately estimate the inertially referenced body rates from only the sun vector measurements. It is shown through realistic simulation tests that the proposed control system, although inactive during eclipse, will be able to stabilize the sail panel to within ± 2 ° in all attitude angles during the sunlit part of the orbit, when solar sailing is possible.

Pose estimation using linearized rotations and quaternion algebra

In this paper we revisit the topic of how to formulate error terms for estimation problems that involve rotational state variables. We present a first-principles linearization approach that yields multiplicative error terms for unit-length quaternion representations of rotations, as well as for canonical rotation matrices. Quaternion algebra is employed throughout our derivations. We show the utility of our approach through two examples: (i) linearizing a sun sensor measurement error term, and (ii) weighted-least-squares point-cloud alignment.

A simple suboptimal Kalman filter implementation for a gyro-corrected satellite attitude determination system

This article presents a simple Kalman filter implementation for correcting gyro-determined satellite attitude estimates with attitude measurements made using external sensors such as sun sensors, magnetometers, star trackers, and so on. This article first generalizes a recently developed non-linear observer for the gyro-corrected attitude determination problem. By implementing the steady-state Kalman filter in the framework of this non-linear observer, a computationally simple filter is obtained with suboptimal steady-state performance. This is important for applications where computational power is limited, such as in micro-/nano-satellite applications. Additionally, in the absence of process and measurement noise, this implementation of the Kalman filter is globally stable. The resulting filter uses constant steady-state Kalman filter gains. It is demonstrated that close-to-optimal steady-state performance is obtained.