Aircraft System Identification Program Using Least Squares or Recursive Least Squares Estimation

Aircraft system identification is the process of estimating mathematical model parameters for flight vehicles using flight data, where aerodynamic derivatives (such as lift coefficient, drag coefficient, etc.) are key parameters. Least Squares (LS) and Recursive Least Squares (RLS) are two commonly used parameter estimation methods.

Least Squares (LS) Principle: Solves static parameters by minimizing the sum of squared errors between observed data and model predictions in a single batch operation. Implementation approach: Requires constructing a linear regression equation where design matrix columns represent flight states (angle of attack, velocity) and output vector contains aerodynamic force data. The normal equations (X^T X)β = X^T y are solved using matrix inversion or QR decomposition. Application scenario: Suitable for offline batch data processing, requires storing all historical data, computationally intensive but produces stable results. Aircraft implementation: Pre-collected flight states and corresponding aerodynamic data are used to build regression equations for derivative estimation.

Recursive Least Squares (RLS) Principle: Introduces recursive mechanism based on LS, updating parameter estimates incrementally using only new data without reprocessing historical data. Algorithm advantage: Ideal for real-time identification with low memory footprint, allows historical data weighting adjustment through forgetting factors. Code implementation: Typically involves initializing covariance matrix P and parameter vector θ, then updating with each new data point using P(k+1) = [P(k) - P(k)φ(k)φ(k)^T P(k)/(λ + φ(k)^T P(k)φ(k))]/λ and θ(k+1) = θ(k) + P(k+1)φ(k)[y(k) - φ(k)^T θ(k)] where φ is the regressor vector and λ is the forgetting factor. Aircraft dynamic response: Continuously processes flight sensor data streams to rapidly track aerodynamic parameter changes (such as derivative discontinuities after stall).

Implementation considerations Data preprocessing (outlier removal, filtering for noise reduction) is crucial for both methods. RLS requires careful forgetting factor selection: too small causes parameter oscillation, too large reduces tracking sensitivity. Aerodynamic derivatives often exhibit coupled nonlinear relationships; problem simplification can be achieved by incorporating model structure (e.g., separating longitudinal/lateral-directional equations).

Extension directions include implementing more robust adaptive algorithms (such as weighted RLS) or combining neural networks to handle strong nonlinear effects.