Sensitivity of back‐projection algorithm (BPA) synthetic aperture radar (SAR) image formation to initial position, velocity, and attitude navigation errors

Abstract

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.

GPS-Denied Navigation Aided by Synthetic Aperture Radar Using the Range-Doppler Algorithm

“…This dependence means that errors in trajectory estimation will result in errors in the final SAR image. For example, position estimation errors cause imaged targets to shift in, and some types of velocity or attitude estimation errors cause imaged targets to both shift and blur (Lindstrom et al, 2022). In this research, the errors induced on the image by trajectory estimation errors are exploited to recover navigation information lost during GPS denial.…”

“…For the research in this paper, azimuth FM rate errors were introduced into the SAR imaging system when forward velocity or attitude errors (which induce additional velocity errors) were present. Such errors result in a blurred image if not corrected by an autofocusing algorithm (Lindstrom et al, 2022). To express azimuth FM errors, let K amf be the azimuth FM rate with an error included such that K K K amf a = +∆ where K ∆ is the amount of error present in K amf .…”

Gps-Denied Navigation Using Sar Images And Neural Networks

“…Simulated data is generated from flight and radar software developed in MATLAB. The software has the capability to generate a flight trajectory, populate the ground with radar targets, and form both truth and distorted SAR images via the BPA from synthesized radar data [20,33]. For the real datasets, the radar data is obtained from flight tests of the Space Dynamics Laboratory X-band radar system.…”

“…For the simple case of constant horizontal position errors, identification of SAR image shifts with respect to an a priori SAR map provide easily exploitable information regarding position errors. When velocity and attitude errors are included, however, the mapping from initial errors to image distortions is more complex [19,20].…”

“…The task of correcting errors in the estimated trajectory is, therefore, reduced to determining the nine errors at the beginning of the time interval of interest. A more detailed discussion of the inertial navigation framework and error modeling is provided in [19,20]. Previous sensitivity studies discovered the complex and seemingly ambiguous relationship between the nine initial navigation errors and the induced SAR image distortions, summarized in Table 1 [19].…”