Yi-Te Chiang

Maximum-likelihood-based filtering for attitude determination via GPS carrier phase

A maximum-likelihood-based (ML-based) filter is proposed for attitude determination via the GPS carrier phase observables. The quaternion representation is adopted here to describe the attitude. Hence, the norm constraint on the quaternion should be considered. The ML estimation with Lagrange multipliers can be used to consider simultaneously the evolution equation and the constraint, and to minimize the error covariance matrix. The attitude determination via GPS carrier phase observables is fulfilled in two steps. The first step is the GPS carrier phase ambiguity resolution. After the integer ambiguities being fixed, the ML-based filter is used to determine the optimal attitude. The advantage of adopting the quaternion as the state vector to describe the kinematic behavior is that no singular problems arise. To verify our algorithm, the simulation has been conducted. In the simulation, the white noises are added on the carrier phase observables to assess the performance of the proposed method. The body frame is formed by three non-colinear GPS antennae which are mounted on a platform with two aluminum bars representing the baseline vectors. According to the simulation, our method is sound and effective.

Data fusion of three attitude sensors

A reliable Spacecraft attitude determination system, which integrate the measurements coming from the star tracker (STR), Global Positioning System (GPS) and gyros, is presented. The linearized state propagation and state update are two key algorithms in the data fusion. For state propagation, the primary information is provided by the high rate (16 Hz) sensors (gyros), whose measurement offsets are calibrated by the integrated filter. For state update, the primary information is provide by the low rate (1 Hz) sensors (STR and GPS). To minimize the update errors, the covariance matrices associated to different sensors are selected as the weightings. From the simulation results, our ideas are verified to be sound and effective.

Estimation of relative orientation using dual quaternion

In this thesis, we use dual quaternion to solve relative orientation, which replaces the traditional way of coplanarity condition and least square solution. Through proposing Linearized Iteration Method, we use only one camera to deal with this problem. Through use of dual quaternion, we find the relative orientation by comparing the projection of lines respect to 2-D Camera systems.

ESTIMATION of 3-D TRANSFORMATION FROM 2-D OBSERVING IMAGE USING DUAL QUATERNION

Abstract In this thesis, we use dual quaternion to replace rotation matrix R and translation vector which expressed objects transformation in usual. The best benefit of dual-quaternion is that it is able to handle rotation and translation simultaneously and apply continuous product of dual quaternion operating with a kind of special vector–dual vector to express a serious of rotation and translation. We find that dual quaternion has special relationship in 3-D transformation and 2-D image plane, and use this relationship to estimate objects transformation from 2-D observing image. Because of the benefit of dual quaternion–easily to handle and express a serious of transformation, we make above estimation more practically and reality using dual-quaternion. At last, we design a simulation to prove our method has better practicality and is more convenient to estimate 3-D transformation.

Half-Duplex Ranging System by Dual Frequency and Code Correlation

In this paper, we propose an integrated ranging methodology utilizing code correlation and carrier phase detection. The phase detection possesses high precision while it suffers the problem of ambiguous integer cycles. We employ code correlation to aid the search of the integer, so the system is capable of ranging with high precision and long distance. Besides, the signal is transmitted with half-duplex mechanism to eliminate the code and phase offset between two transceivers. In our simulation, the measurable distance is up to 2 km, with ranging root mean square error RMSE approximately 10 cm under signal to noise ratio 13 dB.

A closed-form algorithm for eliminating user position biases caused by satellite constellation changes

In GPS positioning, the user position is derived by the pseudo-range measurements and the user-satellite geometric matrix. When the satellite constellation changed, either gaining or losing satellites, it may cause the user position biases. The instantaneous biases in position solution are not desirable in some applications. An algorithm called position bias filter has been proposed to solve the problem. Also, a modified algorithm is designed to reduce the computation burden of original algorithm by a recursive method. In this paper, we propose a closed-form algorithm for eliminating the user position biases. The algorithm remains the low computation in a few satellites change (less than four) of satellite constellation without recursive calculation.

Filter design for attitude determination using GPS and gyro: frequency domain approach

A constant gain estimator is proposed to integrate the GPS and gyro measurements for aircraft attitude determination. Through frequency domain approach, a pair of high pass and low pass filters are employed. Concerning GPS and gyros errors, we apply power spectral density (PSD) properties to select the cut-off frequencies. Once these values are determined, we can derive the associated Kalman gains. Since the PSD specifications of gyros are provided by equipment manufactory, the Kalman gains can be designed in advance. The reduction of the burdens of online computations, which are unavoidable in the traditional Kalman, make our algorithms suitable for real systems. From the assessment of software simulations, the proposed filter is sound and effective.