Robustness failure interpretation, diagnostics, and improvement strategy of L 1 -norm estimation

L1-norm estimation is robust for geodetic gross error processing, yet not always guaranteed, vaguely attributed to least squares leverage points. This paper investigates interpretation, diagnostics, and improvement of such failure. The robustness failpoint of L1-norm estimation (RFP-L1) is explained using influence functions and L1-norm adjustment model. Two RFP-L1 identification methods and a robustness enhancement strategy (RF-L1) are proposed. Leveling and regression experiments validate them. Results show L1-norm estimation fails when gross errors occur in RFP-L1, which cannot be reflected in residuals, causing severe parameter deviation. RFP-L1 diagnosis and RF-L1 strategy identify such observations, suppress bias and restore gross error detectability.