Certifying Kalman Filters

Formal code certification is a rigorous approach to demonstrate software quality. Its basicidea is to require that code producers provide formal certificates, or proofs, that their codesatisfies certain quality properties. In this paper, we focus on certifying software developed forstate estimation of dynamic systems, which is an important problem found in spacecraft, aircraft,geophysical, and in many other applications. The most common way of solving state estimationproblems consists of using Kalman filters, which are stochastic, recursive algorithms providingstatistically optimal estimates of the state of a system based on noisy sensor measurements. Wepresent a certifier for Kalman filter programs, which is a program that takes as input a programclaiming to implement a Kalman filter together with a specification of that Kalman filter, aswell as a certificate under the form of assertions and proof scripts merged within the programvia annotations, and tells whether the code correctly implements the state estimation problemspecified. We tested our certifier on three Kalman filters: simple Kalman filter, informationfilter and extended Kalman filter. So far we have played both the role of the producer of theseprograms and the role of the consumer, but our next step is to merge the presented technologywith AutoFilter, a state estimation program sysnthesis system developed by researchers atNASA Ames, the idea being to have AutoFilter synthesize the correctness certificates togetherwith the code.