An Inverse Generalized Conversion Filter for State Estimation in Nonlinear Adversarial Sensing Systems

In adversarial games involving intelligent sensing systems, inverse filtering plays an important role in the defender’s decision-making by estimating the opponent’s perception based on the defender’s sensor observations. Existing inverse nonlinear filters, such as the inverse quadrature Kalman filter and the inverse extended Kalman filter, are limited in their ability to fully exploit higher-order nonlinear information contained in sensor observations. To address this issue, this paper proposes an inverse generalized-conversion-based filter (I-GCF). Unlike conventional inverse filters, the proposed method not only extracts nonlinear information through deterministic sampling but also constructs a generalized optimal decorrelating transformation function to capture nonlinear observation information that cannot be obtained by the linear minimum mean-square error (LMMSE) estimator. As a result, it enhances the exploitation of higher-order nonlinear sensor information and improves the estimation accuracy and stability of inverse filtering in nonlinear sensing environments. Furthermore, this paper derives general expressions for the time complexities of both GCF and I-GCF, thereby further enriching their theoretical framework. Numerical results demonstrate that, in nonlinear environments, the proposed I-GCF achieves higher estimation accuracy and better stability than conventional inverse filters.