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1

A signal processing technique for improving the accurancy of MEMS inertial sensors

Stubberud P. A., Stubberud A. R.

Systems Science

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2009

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Vol. 35, no 2

59-65

EN

Navigation, guidance and control for small space vehicles requires inertial measurement sensors which are small, inexpensive, low power, reliable and accurate. Micro-inertial sensors, such as MEMS gyroscopes, can provide small, inexpensive, low power devices; however, the accuracy of these devices is insufficient for many space applications. Signal processing methods can be used to provide the necessary accuracy. The individual outputs of many nominally identical micro-sensors can be combined to generate a single accurate measurement. An extended Kalman filter (EKF) which includes the dynamics of every sensor can be used for such a combination; however, the "curse of dimensionality" limits the number of sensors which can be used. In this paper, a new EKF technique for combining many sensors is proposed which, using a common nominal model for the micro-sensors and a single EKF with the state dimension of a single sensor, has accuracy comparable to the high dimensional EKF and is significantly more accurate than a single sensor. A simulation using the mathematical model of an existing micro-gyroscope was performed to compare the single EKF method to the multiple EKF method and the results presented.

2

Sequential estimation with multiple constraints

Stubberud S. C., Stubberud A. R.

Systems Science

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2004

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Vol. 30, no 4

51-60

EN

In previous work, a sequential estimator that incorporates constraints was developed. This technique created a parallel implementation of an unconstrained estimator that used a time series of measurements to continually update the estimate and a constrained estimator that at each time step used the unconstrained estimate and the constraint to create a constrained state estimate. The algorithm that was generated had one drawback to implementation in general. The constraint estimate equation was limited by linear independence in the number of constraints to the number of states in the system. For example, if the system has two states, then only two constraints can be allowed. In this paper, two implementations for handling multiple constraints are considered. The first is a least-squares approach to the problem. The second is an iterative approach.

3

An improved constrained nonlinear state estimator for target tracking

Stubberud A. R., Stubberud S. C.

Systems Science

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2004

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Vol. 30, no 4

31-39

EN

In a series of earlier papers, the first author developed an estimator which generates an optimal sequential estimate of the state of a linear discrete-time dynamic system in which the state is subject to an instantaneous constraint. In the third paper of the series, an extended estimator, based on the optimal linear estimator, was developed for the constrained nonlinear estimation problem. In this paper, the extended nonlinear estimator is revised. One of the critical steps in the development of an extended estimator is the quasi-linearization step. In this step, the terms in the Taylor series expansion which have been evaluated at some nominal state trajectory are instead evaluated at the most recent 'best' available state estimate. In developing the estimator, the point in the development at which the quasi-linearization takes place is not fixed. In the earlier paper, the quasi-linearization is performed about midway through the overall development. In this paper, the quasi-linearization is taken at the last possible point in the development. The result is an improved version of the extended constrained nonlinear sequential estimator.

4

Sequential target tracking using constrained nonlinear estimators

Stubberud A.R.

Systems Science

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2003

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Vol. 29, nr 2

17-29

EN

An estimator is presented which generates sequential estimates for nonlinear, time-variable discrete-time dynamic systems in which the system state estimates are subject to an instantaneous constraint. That is, at each sample time the state estimate is constrained to lie in a given region of the state space. This nonlinear sequential estimator is an extended version of an optimal sequential estimator for linear, time-variable discrete-time systems with state estimates constrained to a given region of the state space. The linear estimator was developed from a non-probabilistic weighted linear least squares basis with the constraints added through the mechanism of Lagrange multipliers; therefore, the estimator produces "hard" constraints on the state estimate. The solution of the constrained estimation problem, at each instant of time, requires only the unconstrained state estimate at that time instant and the instantaneous constraints which define the constraint region. If the unconstrained sequential estimate satisfies the constraints, then that solution is also the constrained solution. On the other hand, if the unconstrained estimate does not satisfy the constraints, then the constrained solution is generated from the solution of a set of static equations. The constrained estimation problem is thus reduced to a sequence of nonlinear programming problems. The estimator for the state of a nonlinear system was developed by quasi-linearization of the optimal constrained linear estimator. The estimates resulting from this estimator are "optimal in the small" for nonlinear systems and are optimal for linear systems.