While linear covariance analysis is widely used for navigation system design and analysis, it is often overlooked as a tool for closed-loop guidance navigation and control (GN&C) system design and analysis. This article presents an overview of the techniques and methods required to develop a linear covariance analysis tool for a close-loop GN&C system. Then, using a simple nonlinear closed-loop GN&C problem as a guide, the capabilities of linear covariance analysis for the design and analysis of closed-loop systems are demonstrated. It is shown that linear covariance can be accurately applied to a closedloop system with time-to-go guidance, dead-reckoning navigation, and a Kalman filter for state estimation. The accuracy and efficiency of linear covariance analysis is shown by direct comparison to Monte Carlo analysis results, and the value of linear covariance analysis is highlighted by presenting several analysis capabilities that are often required in the design and analysis of closed-loop GN&C systems. It is also shown how the efficiency of linear covariance enables new design methodologies, one of which is presented in this article, that would otherwise be prohibitive with Monte Carlo analysis.

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The Back‐Projection Algorithm (BPA) is a time‐domain‐matched filtering technique to form synthetic aperture radar (SAR) images. To produce high‐quality BPA images, precise navigation data for the radar platform must be known. Errors in position, velocity, or attitude result in improperly formed images that are corrupted by shifting and blurring. The contribution of this paper is the development of analytical expressions that characterise the relationship between navigation errors and image formation errors from an inertial navigation point of view, where trajectory estimation errors in position, velocity, and attitude propagate through time and cause compounding errors in the vehicle state vector. These analytical expressions are verified via simulated image formation and real‐data image formation.

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Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout the synthetic aperture. The proposed neural network approach is able to learn to predict the initial errors on both simulated and real SAR image data.