Nonlinear observer design for integration of DGPS and INS

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided di¤erence filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMSbased IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WNbased processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

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“…The true linear acceleration a b and the true angular velocity o b ib in the body frame can be written approximately as (Vik et al 1999):…”

Section: Ins/gps Integrationmentioning

confidence: 99%

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

El-Diasty¹,

El-Rabbany²,

Pagiatakis³

2007

Journal of Applied Geodesy

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“…Vik et al 12 proposed a new method that directly utilizes nonlinear quaternion kinematics but assumes biases that exponentially decay. Boskovic et al 8,9 proposed a nonlinear bias observer based upon quaternion kinematics; however, the convergence proof assumes the vehicle attitude never passes through ±180…”

Section: -5mentioning

confidence: 99%

A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation

Galante

Sanner

2012

AIAA Guidance, Navigation, and Control Conference

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Deterministic errors in angular rate gyros, such as thermal biases, can have a significant impact on spacecraft attitude knowledge. In particular, thermal biases are often the dominant error source in MEMS gyros after calibration. Filters, such as MEKFs, are commonly used to mitigate the impact of gyro errors and gyro noise on spacecraft closed loop pointing accuracy, but often have difficulty in rapidly changing thermal environments and can be computationally expensive. In this report an existing nonlinear adaptive filter is used as the basis for a new nonlinear adaptive filter designed to estimate and cancel thermal bias effects. A description of the filter is presented along with an implementation suitable for discrete-time applications. A simulation analysis demonstrates the performance of the filter in the presence of noisy measurements and provides a comparison with existing techniques.

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“…ADAPTIVE ATTITUDE OBSERVER Following [12], an observer for the attitude dynamics (1) endowed with the measurement equation (3) can be defined as the systemṘ =RS(Ω(y))…”

Section: Disturbance Modelmentioning

confidence: 99%

Attitude tracking with adaptive rejection of rate gyro disturbances

Pisu

Serrani

2008

2008 American Control Conference

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Abstract-The classical attitude control problem for a rigid body is revisited under the assumption that measurements of the angular rates obtained by means of rate gyros are corrupted by harmonic disturbances, a setup of importance in several aerospace applications. The paper extends previous methods developed to compensate bias in angular rate measurements by accounting for a more general class of disturbances, and by allowing uncertainty in the inertial parameters. By resorting to adaptive observers designed on the basis of the internal model principle, it is shown how converging estimates of the angular velocity can be obtained, and used effectively in a passivity-based certainty-equivalence controller yielding global convergence within the chosen parametrization of the group of rotations. Since a persistence of excitation condition is not required for the convergence of the state estimates, only an upper bound on the number of distinct harmonic components of the disturbance is needed for the applicability of the method. I. PROBLEM DEFINITIONConsider the rotational dynamics of a rigid bodẏwith state (R, ω) ∈ SO(3) × R 3 , representing the orientation and angular velocity of a body-fixed frame with respect to an inertial frame, and control input u ∈ R 3 . The matrix S(·) denotes the skew-symmetric operator S(v)w := v×w, where v, w ∈ R 3 . The inertia matrix J(µ) ∈ R 3×3 is assumed to depend continuously on a vector of unknown parameters µ ranging over a given compact setfor the orientation and angular velocity of the body-fixed frame of (1) is provided by a smooth autonomous system of the form̟with state of importance in aerospace applications [1], and greatly simplify the analysis. The rotation matrix for the attitude error R e := R T d R ∈ SO(3) satisfies the kinematic equatioṅ R e = R e S(ω e ), where ω e := ω−R e T ω d denotes the angular velocity error resolved in the body frame.The classic attitude control problem [2] is loosely defined as that of finding a feedback control law such that all trajectories of the closed-loop system are bounded, and the tracking error satisfies (R e (t), ω e (t)) → (I 3 , 0) as t → ∞, for any given reference trajectory in the considered family of solutions of (2), and for all µ ∈ K µ . In this paper, the problem in question is revisited under the assumption that measurements of the rotation matrix R(t) are available, while measurements of ω(t) obtained by means of rate gyros are corrupted by additive harmonic noise. The considered setup arises frequently in the control of aerospace vehicles with significant aeroelastic effects [3], where structural vibrations are transmitted to the rate gyros through the coupling with the airframe, or in the attitude control of rigid of flexible satellites, where harmonic disturbance in the angular velocity measurements are produced by imbalance or mechanical defects in gyroscopes [4]- [6]. Dealing with uncertainties on the natural frequencies is a fundamental issue in applications to control of hypersonic vehicles, where the vibrational mo...

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Nonlinear observer design for integration of DGPS and INS

Cited by 16 publications

References 4 publications

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation

Attitude tracking with adaptive rejection of rate gyro disturbances

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