Abstract: ‍ ‍To address the detection challenges posed by the low observability and high maneuverability of unmanned aerial vehicle （UAV） targets in complex electromagnetic environments， we propose a heuristic search-based detection method in polarimetric radar for UAV. By establishing a heuristic search framework that integrates kinematic， acceleration， and polarimetric-energy-consistency constraints， this approach effectively overcomes the limitations of high computational complexity and poor adaptability to maneuvering inherent in conventional multi-frame detection methods. First， we constructed a three-dimensional state space based on the time-range-velocity data matrix derived from short-time Fourier transform-processed radar signals. Second， we designed a multi-constraint heuristic function. We established kinematic constraints on a velocity-range mapping model through kinematic equations to derive inter-frame reachable regions for search space compression. We also incorporated acceleration constraints including penalty terms to suppress non-physical maneuver trajectories. And we set polarimetric-energy-consistency constraints to realize a cross-validation mechanism combining geometric mean and minimum value criteria by leveraging the energy focusing characteristics of dual-polarization channels. Finally， we unified these three constraints into a heuristic-function-based evaluation criterion via linear weighting， with dynamic pruning and path optimization achieved through the greedy best-first search method. Simulation results demonstrate that the proposed method achieves detection rates exceeding 80% for constant-velocity targets， uniformly accelerated targets， and time-varying accelerated targets when the signal-to-noise ratio exceeds 5 dB， significantly outperforming traditional detection methods featuring constant false alarm rate. Furthermore， the required signal-to-noise ratio for attaining trajectory correctness rates greater than 80% was reduced by over 5 dB compared to conventional approaches. Validation using real measured data demonstrates continuous trajectory detection capability for both fixed-wing and rotary-wing UAV under fluctuating signal-to-noise ratio conditions. Both simulation analysis and real measured data validation confirm that the proposed multi-constraint heuristic search mechanism enables effective detection of complex maneuvering UAV through synergistic optimization of physical principles and observational data.