A novel augmented Kalman filter with mixed norm constraint for impact force identification

When the impact location is unknown, classical Kalman filter-based force identification fails to provide accurate estimation. By exploiting the spatial sparsity of impact forces, the compressed sensing-embedded augmented Kalman filter with l₁ norm constraint (CSAKF-1) improves solution accuracy. However, it fails to handle severely ill-conditioned problems due to insufficient sparsity-promoting ability of the l₁ norm. Given that non-convex regularization offers better sparsity promotion than convex alternatives, this paper develops a compressed sensing-embedded augmented Kalman filter with mixed norm constraint (CSAKF-m) for impact force identification. The pseudo-measurement technique is applied to enforce the sparsity. Considering the nonlinearity of the mixed norm, we first extend the pseudo measurement technique to handle nonlinear penalty functions and then propose the CSAKF-m algorithm. The property of the pseudo-measurement technique in reducing estimation uncertainty is demonstrated. Comprehensive validation through simulation studies and experiments highlights the advantages of the CSAKF-m algorithm over the l₁-constrained baseline (CSAKF-1). The CSAKF-m algorithm maintains stability under partial measurement configurations, demonstrates strong robustness to measurement noise, and effectively identifies multi-source forces. The proposed algorithm achieves a significant improvement in estimation accuracy with only a modest increase in computational cost.