Statistically Linearized Estimation of Reentry Trajectories

Several filters are applied to the problem of state estimation from inertial measurements of reentry drag. This is a highly nonlinear problem of practical significance. It is found that a filter based on the technique of statistical linearization performs better than the extended Kalman in this application. This is believed to be the first application of the statistically linearized filter to a practical dynamics problem. A sensitivity analysis is performed to demonstrate the relative insensitivity of this filter to modeling errors and approximations.     

In-Flight Alignment and Calibration of Inertial Measurement Units?Part I: General Formulation

This is the first part of a two-part paper which summarizes work pursued by the author in 1966 [1]. The paper describes the application of minimum-variance estimation techniques for in-flight alignment and calibration of an inertial measurement unit (IMU) relative to another IMU and/or some other reference. The first part formulates the problem, and the second part [2] reports numerical results and analyses. The approach taken is to cast the problem into the framework of Kalman-Bucy estimation theory, where velocity and position differences between the two IMU's are used as observations and the IMU parameters of interest become part of the state vector. Instrument quantization and computer roundoff errors are considered as measurement noise, and environmental induced random accelerations are considered as state noise. Typical applications of the technique presented might include the alignment and calibration of IMU's on aircraft carriers, the initialization of rockets or rocket airplanes which are launched from the wing of a mother ship, the alignment and calibration of IMU's which are only used in the latter phases of rocket flight, and for the initialization/updating of SST guidance systems.     

Optimal Aircraft Go?Around and Flare Maneuvers

This paper analyzes in detail two of the critical aircraft maneuvers associated with approach and landing: the go-around maneuver and the flare maneuver. Optimal solutions that include state and control variable constraints are obtained for both problems. Two algorithms are given for computation of the minimum and maximum altitude loss associated with the pilot-controlled go-around maneuver. A matrix operator is obtained that can be used for in-flight computation of the altitude loss on a small general-purpose digital computer. The flare optimization presented is for a cost functional that includes both the longitudinal touchdown dispersion and the normal acceleration. A closed-loop mechanization is given that approximates the optimal trajectory. A second matrix operator which can be used for prediction of the longitudinal touchdown point is obtained. Uncertainties are also obtained for the purpose of establishing a prediction confidence level. It is proposed that these prediction techniques should be incorporated into a decision making performance monitor. This monitor could provide the pilot with a continuous assessment of the approach and could generate a preflare decision on whether or not to commit the aircraft to the flare maneuver.     

Optimum Alignment of an Inertial Autonavigator

The performance of an inertial autonavigator can only be as good as the accuracy to which the system is initially aligned. Optical methods of alignment can be performed with high precision; however, this technique requires external equipment and is subject to some physical constraints, such as land-based operation. The general problem discussed here is the use of an automatic azimuth alignment technique known as gyrocompassing. In the use of the gyrocompassing technique to obtain azimuth alignment, accuracies are degraded considerably by two dominant error sources, the level axis controlling gyro drift rate and the imperfections of reference or independent velocity information. Consequently, an optimum performance controller is developed for driving the system in this mechanization and is based on a priori knowledge of the second-order statistics of the system error sources. The performance criteria will be to minimize the mean square azimuth error.     

Ensembling clocks of Global Positioning System

The Global Positioning System (GPS) is a satellite navigation system capable of providing 15-m position accuracy. Its system time reference is currently one of the monitor station clocks. Using a simple two-clock example, it is shown analytically that improved reference time stability and overall state estimation accuracy can be achieved by constructing GPS time as an ensemble of all system clocks and that the problem of covariance divergence can be handled by the introduction of pseudomeasurement processing