Cramér–Rao Bounds for Attitude Estimation Using Signals With Unknown Structure

Direction-of-arrival (DOA) estimation can be used for many different applications. In this paper the classical DOA estimation is modified to estimate the attitude of an antenna array when the DOAs of sources are given. Usually DOA attitude estimation assumes knowledge on the structure of the used signals. In this paper signals with an unknown structure are used for attitude estimation. The theoretical best performance is determined by deriving the Cramér-Rao lower bounds for attitude estimation based on two different signal models: the deterministic and stochastic signal model. Next, the attitude estimation performance of both signal models are compared to each other. It is shown that for high signal-to-noise ratios (SNRs) both models perform equally well. If the SNR drops, both models perform equally if the number of sources is low with respect to the number of antenna elements. For a large number of sources, the stochastic model outperforms the deterministic model unless the SNR drops too low. For very low SNRs, the deterministic outperforms the stochastic model regardless of the number of sources.