Gas path performance analysis of aircraft engines involves the use of flight data and engine mathematical models to estimate component health parameters, which play crucial roles in increasing engine safety and reducing maintenance costs. Gas path performance analysis generally faces the problem of having many parameters to estimate (including health parameters and sensor bias errors) and few sensor measurement points. Existing health parameter estimation methods usually perform dimensionality reduction on the parameters to be estimated and cannot comprehensively and accurately estimate all the parameters. To address the issue of having few sensor measurement points as system outputs, this study uses measurement data from multiple proximate steady-state operating conditions to form an augmented system output vector, which makes the number of available system outputs greater than the number of parameters to be estimated. The homogenization of the engine model under proximate operating conditions leads to low parameter identifiability. Therefore, this study analyzes the inherent mechanism of large deviations in parameter estimation results from a linear perspective and proposes a multistage nonlinear parameter identification method that combines biased/unbiased estimation. The proposed method can accurately estimate health parameters and sensor bias errors on the basis of measurement data from proximate operating conditions. Using the JT9D engine as an example for simulation verification, the traditional gas path performance analysis method can estimate 10 health parameters with a maximum error of 2.2% (relative to the nominal values) using 10 output measurements. When 3 proximate steady-state operating conditions are used and the maximum distance between operating conditions is 4% in terms of low-pressure relative conversion speed, 23 parameters can be accurately estimated, including 10 health parameters and 13 sensor measurement bias errors, with the maximum error of the health parameters being less than 0.1%.