State and measurement noise in positioning and tracking: Covariance matrices Estimation and Gaussianity Assessment

The paper presents the Noise covariance matrices Estimation with Gaussianity Assessment (NEGA) method that describes the noise characteristics of a linear time-varying state-space model. In particular, the motivation is placed on the state covariance matrices noise estimates combined with assessment of whether measurements noises are Gaussian or not. The proposed NEGA method, which belongs into the group of the correlation methods, provides unbiased and consistent noise covariance matrices estimate and hypothesis testing based decisions regarding the noises Gaussianity. Simultaneously conducting estimate and assessment is essential for an optimal design of any reliable and integrity-assured positioning and tracking algorithm. The proposed method applicability is extended for the nonlinear systems and thoroughly illustrated in numerical examples of both a nonlinear tracking example and a global navigation satellite system (GNSS) based positioning.