Joint Self-Calibration of Receiver Geometry, Timing, and Target Positions for Multistatic Radar Autofocus

Near-field multistatic radar imaging assumes that the transmitter, receiver, and target positions, as well as the receiver time references, are known exactly. In practice they are known only approximately: receiver positions and clocks carry small survey and synchronization errors, and target locations used to initialize or refine an image are themselves approximate. This paper develops a joint self-calibration framework that estimates small corrections to receiver positions, receiver clock biases, and target positions from the same bistatic echo delays used for imaging, and ties the correction directly to image sharpness rather than to parameter accuracy alone. We derive the linearized observation model relating delay residuals to these corrections, and give a regularized (maximum a posteriori) weighted least-squares estimator that explicitly separates measurement noise from prior parameter uncertainty. We characterize the identifiability of this estimator progressively, from a single anchor (the transmitter alone, which leaves an exact three-dimensional rotational null space) to two anchors (transmitter plus one additional point, which reduces the null space to a one-parameter rotation about a fixed axis) to three anchors (transmitter, one target, and one receiver, in general position, which removes the continuous ambiguity entirely). We additionally treat the dual problem of localizing an unknown transmitter from a small number of exactly known anchors—receivers, targets, or time samples of a single moving platform—and show that collinear or coplanar anchor geometries leave an exact, uncorrectable continuous or discrete ambiguity, respectively, regardless of how many such anchors are used, with the coplanar case notably invisible to a standard rank or conditioning check. We then reformulate the calibration objective directly in terms of coherent multistatic image sharpness, evaluated using the matched-filter score already used for image formation, and propose a two-stage algorithm: a coarse linear delay-residual solve followed by phase-coherent sharpness refinement. Numerical experiments verify the predicted identifiability transitions via the singular value spectrum of the linearized system, demonstrate quadratic convergence of the proposed estimator, verify the transmitter-localization ambiguity structure—including an exact mirror-twin solution for coplanar anchors, reproducing all range measurements to floating-point precision—and demonstrate the effect of self-calibration on a simulated multistatic image of an extended (eagle-shaped) target, including the incremental effect of bandwidth, aperture/frequency windowing, and CLEAN deconvolution on the recognizability of the resulting image, as well as on the resolvability of multiple simultaneous discrete targets (two instances of the same target). We relate this formulation to, and distinguish it from, the existing literature on time-of-arrival sensor network self-calibration and on joint target-localization/clock-bias estimation, which largely target single moving targets, anchor-free minimal-data solvability, or localization accuracy rather than multistatic image focus.