CRLB for Estimation of 3D Sensor Biases in Spherical Coordinates and Its Attainability
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In order to carry out data fusion, it is crucial to account for the imprecision of sensor measurements due to systematic errors. This requires estimation of the sensor measurement biases. In this paper, we consider a three-dimensional multisensor–multitarget maximum likelihood bias estimation approach for both additive and multiplicative biases in the measurements. Multiplicative biases can more accurately represent real biases in many sensors; however, they increase the complexity of the estimation problem. By converting biased measurements into pseudo-measurements of the biases, it is possible to estimate biases separately from target state estimation. The conversion of the spherical measurements to Cartesian measurements, which has to be done using the unbiased conversion, is the key that allows estimation of the sensor biases without having to estimate the states of the targets of opportunity. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. We evaluate the Cramér–Rao lower bound on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Through the use of the iterated least squares, it is proved that it is possible to achieve statistically efficient estimates.
