Observability analysis of piece-wise constant systems. II.Application to inertial navigation in-flight alignment [militaryapplications]

For pt.I see ibid., vol.28, no.4, p.1056-67, Oct. 1992. The method of analyzing the observability of time-varying linear systems as piecewise constant systems (PWCS) is applied to the analysis of in-flight alignment (IFA) of inertial navigation systems (INS) whose estimability is known to be enhanced by maneuvers. The validity of this approach to the analysis of IFA is proven. The analysis lays the theoretical background to, and clearly demonstrates the observability enhancement of, IFA. The analytic conclusions are confirmed by covariance simulations. Although INS IFA was handled to various degrees in the past, a comprehensive control theoretic approach to the problem is introduced. The analysis yields practical conclusions and a procedure previously unknown     

Attitude Determination from Vector Observations: Quaternion Estimation

Two recursive estimation algorithms, which use pairs of measured vectors to yield minimum variance estimates of the quaternion of rotation, are presented. The nonlinear relations between the direction cosine matrix and the quaternion are linearized, and a variant of the extended Kalman filter is used to estimate the difference between the quaternion and its estimate. With each measurement this estimate is updated and added to the whole quaternion estimate. This operation constitutes a full state reset in the estimation process. Filter tuning is needed to obtain a converging filter. The second algorithm presented uses the normality property of the quaternion of rotation to obtain, in a straightforward design, a filter which converges, with a smaller error, to a normal quaternion. This algorithm changes the state but not the covariance computation of the original algorithm and implies only a partial reset. Results of Monte-Carlo simulation runs are presented which demonstrate the superiority of the normalized quaternion.     

Navigation Computation in Terrestrial Strapdown Inertial Navigation Systems

The problem of computing the translational velocity and position relative to earth, which has to be solved by the processor of a strapdown inertial navigation system is discussed. Several approaches are briefly examined with consideration given to the form in which the sensor data are generated and to the computational burden involved in each approach. A computational scheme is finally selected in which the computation is divided into three rate levels. The differential equations of this scheme are developed and the assumptions on which the development is founded are stated. Three variants of the basic scheme are presented, each based on a different level of simplifying assumptions. The main purpose of this work is to develop the differential equations to be solved at each stage of the computation, rather than the numerical implementation of the solution. This work supplies the theoretical background for some of the numerical methods which are now being used.     

The Psi-Angle Error Equation in Strapdown Inertial Navigation Systems

A detailed development is presented of the psi-angle vector differential equation as applied to the error analysis of strapdown inertial navigation systems. The coordinate systems involved and the psi misalignment vector are clearly defined. It is proven that apart from a sign change the psi-angle differential equation in the error analysis of strapdown inertial navigation systems is identical to the one used in conventional gimbaled inertial navigation systems.     

Batch Recursive Data Compression Schemes for INS Error Estimation

Application of new data compression schemes to aided inertial navigation systems is presented. The need for data compression is motivated by the fact that the external aiding system generates frequent but inaccurate position measurements, which have to be processed by a processor whose computation capability is limited. Two new data compression techniques are presented and their efficiency is demonstrated through covariance simulation runs as well as computational complexity analysis. These schemes are characterized by their ability to process batches of measurements recursively and efficiently. It is demonstrated that the resulting estimation accuracy is comparable to that produced by a Kalman filter which processes optimally the same amount of data, while the required computational effort is reduced.