State estimation using an extended Kalman filter with privacy-protected observed inputs

Abstract

In this paper, we focus on the parameter estimation of dynamic state-space models using privacy-protected data. We consider an scenario with two parties: on one side, the data owner, which provides privacy-protected observations to, on the other side, an algorithm owner, that processes them to learn the system's state vector. We combine additive homomorphic encryption and Secure Multiparty Computation protocols to develop secure functions (multiplication, division, matrix inversion) that keep all the intermediate values encrypted in order to effectively preserve the data privacy. As an application, we consider a tracking problem, in which a Extended Kalman Filter estimates the position, velocity and acceleration of a moving target in a collaborative environment where encrypted distance measurements are used.

Privacy in Distributed Computations based on Real Number Secret Sharing

“…We can information theoretically verify that the information leak caused by a share decreases as the numerical value of p ∈ P increases. Consider for instance P = {1, 2, 3} and t = 2, then according to (12), the shares of s are Then, assuming s, c 1 , and c 2 are independent and Gaussian distributed with mean value zero and variance σ 2 s , σ 2 c1 , and σ 2 c2 , respectively, then…”

“…Regarding the complexities, as seen, Algorithm 5 uses 12 multiplications and one inversion, which amounts to 27 interactive operations, independent of the dimension of the matrices. [12] does not provide the complexity for their solution, thus, we provide here an underestimation of the number of interactive operations which lies around 10M + l + 1, where M is the dimension of the matrix R in (46) and l is the number of bits used to represent the numbers (which in the simulations by [12] is at least 24 bits).…”

“…7 it is seen that the difference in result from the privacy preserving solution and the non-private solution lies around the third decimal. In comparison, the difference for the solution in [12] lies before the decimal point.…”

“…Scenarios where a problem of this form appears, could for instance be traffic monitoring [8], medical monitoring [9], and consumption forecasting [10]. The problem of privacy preserving Kalman filtering has already been studied for instance in [11] that uses a form of data compression to preserve privacy of measurements, [12] that base the privacy on a combination of homomorphic encryption and secure multiparty computation techniques, and [13] that relies on differential privacy. These existing works all suffer from a degradation in output utility compared to the none-privacy preserving solution due to noise insertion or to the previously mentioned rounding of reals to integers.…”

“…We will show that a privacy aware Kalman filter based on our real number secret sharing scheme achieves significantly improved output utility. Furthermore, we compare our privacy preserving Kalman filter to the one proposed in [12] and show that ours has a reduction in computation and communication overhead.…”