Meiping Wu

A Numerical-Integration Perspective on Gaussian Filters

This paper proposes a numerical-integration perspective on the Gaussian filters. A Gaussian filter is approximation of the Bayesian inference with the Gaussian posterior probability density assumption being valid. There exists a variation of Gaussian filters in the literature that derived themselves from very different backgrounds. From the numerical-integration viewpoint, various versions of Gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations. A common base is provided for the first time to analyze and compare Gaussian filters with respect to accuracy, efficiency and stability factor. This study is expected to facilitate the selection of appropriate Gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

Unscented Kalman filtering for additive noise case: augmented versus nonaugmented

This paper concerns the unscented Kalman filtering (UKF) for the nonlinear dynamic systems with additive process and measurement noises. It is widely accepted for such a case that the system state needs not to be augmented with noise vectors and the resultant nonaugmented UKF yields similar, if not the same, results to the augmented UKF. In this letter, we find that under the condition of n+/spl kappa/=const, the basic difference between them is that the augmented UKF draws a sigma set only once within a filtering recursion, while the nonaugmented UKF has to redraw a new set of sigma points to incorporate the effect of additive process noise. This difference generally favors the augmented UKF in that the odd-order moment information is partly captured by the nonlinearly transformed sigma points and propagated throughout the recursion. The simulation results agree well with the analyses.

Improved multi-position calibration for inertial measurement units

Calibration of inertial measurement units (IMU) is carried out to estimate the coefficients which transform the raw outputs of inertial sensors to meaningful quantities of interest. Based on the fact that the norms of the measured outputs of the accelerometer and gyroscope cluster are equal to the magnitudes of specific force and rotational velocity inputs, respectively, an improved multi-position calibration approach is proposed. Specifically, two open but important issues are addressed for the multi-position calibration: (1) calibration of inter-triad misalignment between the gyroscope and accelerometer triads and (2) the optimal calibration scheme design. A new approach to calibrate the inter-triad misalignment is devised using the rotational axis direction measurements separately derived from the gyroscope and accelerometer triads. By maximizing the sensitivity of the norm of the IMU measurement with respect to the calibration parameters, we propose an approximately optimal calibration scheme. Simulations and real tests show that the improved multi-position approach outperforms the traditional laboratory calibration method, meanwhile relaxing the requirement of precise orientation control.

INS/GPS Integration: Global Observability Analysis

Observability is an important aspect of the state-estimation problem in the integration of the inertial navigation system (INS) and the Global Positioning System (GPS) as it determines the existence and nature of solutions. In most previous research, conservative observability concepts, e.g., local observability and linear observability, have extensively been used to locally characterize the estimability properties. In this paper, a novel approach that directly starts from the basic observability definition is used to investigate the global observability of the nonlinear INS/GPS system with consideration of the lever arm uncertainty. A sufficient condition for the global observability of the system is presented. Covariance simulations with an extended Kalman filter (EKF) and a field test are performed to confirm the theoretical results. The global observability analysis approach is not only straightforward and comprehensive but also provides us with new insights that were unreachable by conventional methods.

Observability of Strapdown INS Alignment: A Global Perspective

Alignment of the strapdown inertial navigation system (INS) has strong nonlinearity, even worse when maneuvers, e.g., tumbling techniques, are employed to improve the alignment. There is no general rule to attack the observability of a nonlinear system, so most previous works addressed the observability of the corresponding linearized system by implicitly assuming that the original nonlinear system and the linearized one have identical observability characteristics. Strapdown INS alignment is a nonlinear system that has its own characteristics. Using the inherent properties of strapdown INS, e.g., the attitude evolution on the SO(3) manifold, we start from the basic definition and develop a global and constructive approach to investigate the observability of strapdown INS static and tumbling alignment, highlighting the effects of the attitude maneuver on observability. We prove that strapdown INS alignment, considering the unknown constant sensor biases, will be completely observable if the strapdown INS is rotated successively about two different axes and will be nearly observable for finite known unobservable states (no more than two) if it is rotated about a single axis. Observability from a global perspective provides us with insights into and a clearer picture of the problem, shedding light on previous theoretical results on strapdown INS alignment that were not comprehensive or consistent. The reporting of inconsistencies calls for a review of all linearization-based observability studies in the vast literature. Extensive simulations with constructed ideal observers and an extended Kalman filter are carried out, and the numerical results accord with the analysis. The conclusions can also assist in designing the optimal tumbling strategy and the appropriate state observer in practice to maximize the alignment performance.

Calibration of Three-Axis Magnetometer Using Stretching Particle Swarm Optimization Algorithm

In this paper, a stochastic optimization algorithm is proposed to calibrate the three-axis magnetometer onboard. The sensor errors, namely, hard iron, soft iron, nonorthogonality, scale factors, and bias, are taken into account. Particle swarm optimization (PSO) strategy is used to do the calibration, enhanced by the stretching technique to improve the accuracy and robustness. The performance of this algorithm is evaluated with a series of laboratory experiments and a field experiment of autonomous underwater vehicle. Comparisons with other analytical calibration methods are made. The results demonstrate that both the PSO and the stretched PSO algorithm can significantly compensate the magnetometer readings, and the latter algorithm has higher accuracy and more robustness.

Nonlinear Tracking-Differentiator for Velocity Determination Using Carrier Phase Measurements

Differential computation is necessary in velocity determination using carrier phase measurements from the global navigation satellite system (GNSS). A method of nonlinear tracking-differentiator is proposed to suppress both noise amplification and time delay introduced by differentiation. The carrier phase rate can be derived more precisely using the nonlinear tracking-differentiator and the time delay is compensated by second-order derivative estimation from the outputs of the differentiator. Simulation and experiments for the Gobal Positioning System (GPS) and Chinese Beidou system show that this approach can effectively improve the accuracy of velocity determination, especially under noisy or bad geometry situations.

A Multi-Position Calibration Algorithm for Inertial Measurement Units

∗As an inertial sensors assembly, the inertial measurement unit (IMU) must be calibrated before being used. This paper proposes a new IMU multi-position calibration algorithm that takes the Earth’s rotation rate and gravity as inputs, and calculates calibration parameters based on the two facts that: 1) norm of the accelerometer measurement vector is equal to the magnitude of gravity; 2) the dot product of gyro measurement vector and accelerometer measurement vector is equal to minus dot product of the Earth’s rotation rate and gravity. Two theorems about the rank of the involved matrix are given to prove the feasibility of estimation. The algorithm features that no high-precise instruments such as a turntable are in principle necessary. Simulations show feasibility of the proposed calibration algorithm.

Strapdown inertial navigation using dual quaternion algebra: error analysis

In a strapdown inertial navigation system (INS), the general displacement of a rigid body is traditionally separately modeled and analyzed, i.e., direction cosine matrix or quaternion for rotation analysis and vector for translation analysis. As a subsequent work of a companion paper (Wu et al., 2005), this paper adopts dual quaternion algebra, a most concise and unified mathematical tool for representing the general displacement of a rigid body, to analyze error characteristics of the strapdown INS. Two new error models in terms of quaternion algebra are developed: the additive dual quaternion error (ADQE) model and multiplicative dual quaternion error (MDQE) model. Both are expected to facilitate the future inertial navigation-based integrated navigation filter.

Constrained total least-squares calibration of three-axis magnetometer for vehicular applications

Strapdown three-axis magnetometer is widely used to determine the heading angle of a vehicle to which it is attached. Unfortunately, the outputs of three-axis magnetometer are often distorted by various magnetic field sources. Therefore, a calibration procedure must be performed before it is used. This paper presents a new calibration algorithm to determine calibration parameters based on a constrained total least-squares (CTLS) technique. A Newton iteration method is utilized to determine the CTLS solution. Unlike existing calibration algorithms, the proposed algorithm yields efficient estimates without assuming a priori knowledge of the noise distribution. Thus, it is easily implemented and suitable for practical applications. The results of simulations and experiments reveal the superiority of the proposed algorithm to the compared algorithms.