WSEAS Transactions on Signal Processing
Print ISSN: 1790-5052, E-ISSN: 2224-3488
Volume 22, 2026
Privacy-Preserving State Estimation: An Encrypted Extended Kalman Filter Using CKKS Homomorphic Encryption
Authors: , , ,
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Abstract: Fully Homomorphic Encryption (FHE) enables mathematical operations directly on encrypted data
without decryption. Any operation that a polynomial can approximate can, in principle, be executed under an
FHE scheme. To protect cyber-physical systems from eavesdropping on sensitive measurements, we integrate
CKKS, an FHE scheme for encrypted real and complex arithmetic, into a state estimator. The estimator is an
Extended Kalman Filter (EKF) that fuses GPS and Inertial Measurement Unit (IMU) data to estimate vehicle
position, velocity, linear acceleration, yaw angle, and turn rate. We implement CKKS using the Microsoft SEAL
library, which supports only a limited number of homomorphic arithmetic operations, creating major challenges
for EKF steps such as matrix inversion. We address these constraints with operation-efficient approximations and
structured compromises. Frobenius norm analysis shows that the encrypted EKF preserves the precision of the
plaintext EKF while reducing data exposure, at the cost of increased latency.
Keywords:
Cyber-physical systems security, Extended Kalman filter, Fully homomorphic encryption, Privacy-preserving computation, Secure state estimation, CKKS scheme
Pages: 108-124
DOI: 10.37394/232014.2026.22.9