Self-Calibration of Array Errors via Semidefinite Programming for High-Accuracy Indoor Localization with 5G Picocell Base Stations

The evolution toward 5G-Advanced and 6G networks necessitates high-accuracy indoor positioning for applications such as Internet of Things (IoT) and digital twins. However, existing technologies like ultrawideband (UWB) and Wi-Fi face challenges in cost, coverage, and accuracy, especially in multi-path environments. This paper proposes a novel framework for sub-meter-level indoor positioning using 5G picocell base stations (gNBs). First, a Semidefinite Programming-based Joint Array Calibration (SDP-JAC) algorithm mitigates gain-phase errors in compact arrays by reformulating array calibration as a covariance matrix structure-constrained optimization which is solved via semidefinite programming to avoid local optima. Second, a dual-stage phase compensation scheme integrates noise subspace projection with adaptive regularization to achieve globally optimal phase error estimates for multipath suppression. Finally, a Multi-Base-Station Weighted Fusion Localization (MBS-WFL) framework enhances positioning accuracy by employing a hierarchical scoring strategy to adaptively select the optimal gNB subset. Simulations demonstrate that the proposed method achieves a 90% cumulative probability of positioning errors below 1 meter at SNRs ≥ 0 dB, outperforming conventional algorithms and complying with 3GPP R17 standards. This work provides a deployable, cost-effective solution for 5G-Advanced integrated sensing and communication (ISAC) networks without requiring dedicated hardware.