Acceleration Maneuvers Research Articles

Aircraft Approach Guidance Using Relative Loran-C Navigation

Precision navigation about a reference point using Loran-C can be achieved by subtracting the Loran Time Differences measured at the reference point from the received Time Differences, thus reducing by common-mode cancellation the effect of variations in signal propagation velocity; a potential application of this technique is aircraft final approach guidance. In addition to the classical Geometric Dilution of Precision, performance of Loran-C in this “relative navigation” mode is limited by reference datum accuracy, by the response of the receiver's tracking loops to noise and vehicle accelerations, and by local deformations in the shape of the Lines of Position grid. Optimization of the receiver's tracking loop bandwidth can result in an expected performance of 45 meters (2-σ) for a 0 dB signal to noise ratio and typical aircraft low-approach maneuvering accelerations. Ground-level measurements at this level of precision indicate the existence of a “grid microdeformation”: localized, repeatable distortions of the Lines of Position over distances much smaller than the carrier wavelength. It is concluded that 2-σ horizontal accuracies of 100 meters or less are realistically achievable with relative Loran-C if signal to noise ratio and maneuvering acceleration limits are specified. This accuracy is significantly better than that of VOR or NDB approach systems, but not as good as an ILS Localizer.

A 'current' statistical model and adaptive algorithm for estimating maneuvering targets

A model concept for maneuvering targets is proposed in this paper and a modified Rayleigh density is proposed to describe the current probability density of target maneuvering acceleration. The physical relation between the state (acceleration) estimate and the mean value of the state noise in the special case discussed here is also pointed out. Based on these two points, an adaptive Kalman filter for the mean and variance of the maneuvering acceleration is given. Some computer simulation results in oneand three-dimensional cases are given. The simulation results show that the proposed adaptive algorithm can estimate well the states of highly maneuvering targets.

A Direct Method for Estimating Tangential and Normal Accelerations of Maneuvering Targets in Three Dimensional Space

A nonlinear state model describing tangential and normal acceleration maneuvers of targets in three dimensional space is established. The magnitude of tangential and normal accelerations are modeled as modified Rayleigh-Markov processes, and the directive angle of normal acceleration is modeled as a uniform density with variable mean-value. In case only noisy position observation data are available, an adaptive extended Kalman filtering algorithm is developed and therefrom a direct method of estimating tangential and normal accelerations of maneuvring targets is obtained. some computational results are presented to confirm the effectiveness of this method.

Analytical Results for the x, y Kalman Tracking Filter

A two-dimensional x, y Kalman tracking filter is analyzed for a track-while-scan (TWS) operation when the radar sensor measures range and bearing (r, ?) at uniform sampling intervals T seconds apart. This development explicitly considers the coupling between the quantities measured by the sensor (r, ?) and the Cartesian x, y coordinate system selected for the tracking operation. The steadystate components of the gain and error covariance matrixes are analytically determined under the assumption of a white noise maneuver acceleration model in two dimensions. These results are verified by computer calculation of the Kalman filter matrix equations.

A Decision - Directed Adaptive Tracker

In the design of a tracking filter for air traffic control (ATC) applications, a maneuvering aircraft can be modelled by a linear system with random noise accelerations. A Kalman filter tracker, designed on the basis of a variance chosen according to the distribution of the potential maneuver accelerations, will maintain track during maneuvers and provide some improvement in position accuracy. However, during those portions of the flight path where the aircraft is not maneuvering, the tracking accuracy will not be as good as if no acceleration noise had been allowed in the tracking filter. In this paper, statistical decision theory is used to derive an optimal test for detecting the aircraft maneuver; a more practical suboptimal test is then deduced from the optimal test. As long as no maneuver is declared, a simpler filter, based on a constant-velocity model, is used to track the aircraft. When a maneuver is detected, the tracker is reinitialized using stored data, up-dated to the present time, and then normal tracking is resumed as new data arrives. In essence, the tracker performs on the basis of a piecewise linear model in which the breakpoints are defined on-line using the maneuver detector. Simulation results show that there is a significant improvement in tracking capability using the decision-directed adaptive tracker.

Separation theory in air traffic control system design

A general treatment of collision hazard is developed which expresses the relationship between separation standards, velocity and acceleration limits, surveillance accuracy, communication delays, sampling frequency, maneuver severity, and intervention frequency. An example of separation standards achievable through the use of an upgraded beacon system is given. The relations presented permit optimization of air traffic control systems with regard to collision safety and will permit comparisons between different proposed systems. They should assist in reviewing separation standards when changes in procedures, types of available data, or data accuracy are planned. Further, the procedures outlined could provide real-time assistance in hazard evaluation to the air traffic control process.

Statistical estimation in inertial navigation systems.

Although navigation systems have generally been developed by solving exactly the dynamic equations of motion, in reality the navigation problem is a statistical one since there are unpredictable errors in the measurements. The advent of very powerful navigation computers makes it possible by using statistical filtering techniques to retrieve more of the information contained in the navigation measurements. The navigation system is thus developed here as an information-filtering problem rather than a simulation of a deterministic physical system. The Kalman optimum linear filter is found to apply to the navigation problem if some technique is used to account for possible non-Gaussian maneuver accelerations. A major problem in the application of statistical techniques is the tremendous amount of computation required. Two methods are suggested which greatly reduce the amount of computation with a minimum degradation in the performance of the system. In one method, physical considerations are used to divide the total filter into smaller, simpler filters. In the other method, the optimum gains are precomputed and approximated by simple functions in the flight computer. The details are given for the alignment and calibration of an inertial platform using statistical filtering.