The time derivative of this vector is the sum of the inertially measurable angular velocity vector and of the inertially nonmeasurable noncommutativity rate vector. It is precisely this noncommutativity rate vector that causes the computational problems when numerically integrating the direction cosine matrix. The orientation vector formulation allows the noncommutativity contribution to be isolated and, therefore, treated separately and advantageously. An orientation vector mechanization is presented for a strapdown inertial system. Further, an example is given of the application of this formulation to a typical rigid body rotation problem.

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Show Context Citation Context The tim Hol, Laurens Slot, Henk Luinge " Abstract—This paper applies the second order Taylor approximation to model the nonlinear uncertainty of acceleration rotation for MEMS based strapdown integration.

Filtering solutions for tracking comprising inertial sensors require a good statistical modeling of the inertial measurements.

The nonli The nonlinearity results in an umbrella-shape probability density distribution, and causes net downward vertical acceleration bias, which can not be estimated by traditional methods using only the first order approximation. This in turn leads to increasing vertical velocity and position errors after double integration which is significant for MEMS grade inertial sensors.

Moreover, the analytical second order nonlinear term is applied in an extended Kalman filter EKF framework and compared with a normal EKF. It is expected that having a better linearization model for inertial sensors will benefit the overall estimation when integrated with other sensors. Finally conclusions are given in section VI. We first introduce the coordin Sensing power transfer between the human body and the environment by Peter H. Eng , " Abstract—The power transferred between the human body and the environment at any time and the work performed are impor-tant quantities to be estimated when evaluating and optimizing the physical interaction between the human body and the environment in sports, physical labor, and rehabilitation.

It is the objective of the current paper to present a concept for estimating power transfer between the human body and the environment during free motions and using sensors at the interface, not requiring measurement sys-tems in the environment, and to experimentally demonstrate this principle.

Mass and spring loads were moved by hand over a fixed height difference via varying free movement trajectories. Kine-matic and kinetic quantities were measured in the handle between the hand and the load. The orientation was estimated from the angular velocity, using the initial orientation as a begin condition.

The accelerometer signals were expressed in global coordinates using this orientation infor-mation. Velocity was estimated by integrating acceleration in global coordinates, obtained by adding gravitational acceleration to the accelerometer signals. Zero start and end velocities were used as begin and end conditions. Power was calculated as the sum of the inner products of velocity and force and of angular velocity and moment, and work was estimated by integrating power over time.

The principle of estimating power transfer demonstrated in this pa-per can be used in future interfaces between the human body and the environment instrumented with body-mounted miniature 3-D force and acceleration sensors. Index Terms—Ambulatory sensing, force sensing, inertial move-ment sensing, power estimation, work estimation. The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results.

First, the class of bilinear stochastic systems or linear systems with multiplicative noise is discussed. The stochastic stability of bi The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a solvable Lie group, necessary and sufficient conditions for stochastic stability are derived.

Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups are also discussed. The study of estimation problems involving bilinear systems is motivated by several practical applications involving rotational processes in three dimensions. Two classes of estimation problems are considered. First it is proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations.

Finally, the theory of harmonic analysis is used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces. Powered by:.


A New Mathematical Formulation for Strapdown Inertial Navigation

Gardalar From This Paper Topics from this paper. Post on Aug views. Unfortunately, at the timethere was no sustaining external interest in this work and theresults never became widely known. Citations Publications citing this paper.


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