Boundedness of covariance estimates of extended Kalman filtering with directional measurements and linear state dynamics

In wildlife telemetry and several other applications, dynamical systems arise where all of the measurements consist of angles. In this paper we treat the problem of classical extended Kalman filtering in this situation, and analyze the equation that describes the covariance estimates of the measurement error. It is shown that under some mild hypotheses the error covariance remains bounded by bounds which can be precomputed from noise and system data, and that the upper bound tends to zero when the state and measurement covariance tend to zero