Recursive Bias Estimation and Orbit Determination

Abstract

O RBIT determination algorithms are designed to estimate satellite position and inertial velocity from unbiased sensor measurements. Static and dynamic measurement biases, which are low-frequency systematic errors, cause biases in both position and velocity estimates that can significantly degrade track accuracy. As only the random error statistics are characterized, the filter covariance usually underestimates the biased track error statistics. Track biases and covariance fidelity are important issues for correlation and fusion of multiple sensor tracks [1,2]. Many algorithms have been developed [3–10] for estimation of bias parameters in the system dynamics, in the measurements, or in both. Generally, bias parameters are estimated jointly with the position and velocity states. Depending on the number of bias parameters, this approach can be computationally intensive, the system covariance matrix can become ill conditioned, and bias-state observability and separability can be problematic. Alternatively, two-step techniques extract bias parameters from the track measurement residuals. For current radar systems, measurement biases are calibrated by tracking one metric satellite having an accurate ephemeris, or by tracking many satellites with less accurate ephemerides [9]. Range and angle biases are calibrated after (not during) the data collection (s). A noteworthy exception is a real-time algorithm for angle bias estimation in wideband radars [10]. In this Note, an iterated 12-state extended Kalman filter EKF(12) is formulated for simultaneous (real-time) orbit determination and bias estimation. Orbit position and velocity states are augmented with six dynamic (rather than static) bias states that model radar orientation biases and radar range-angle measurement biases. Biasstate observability and separability are enhanced by physical models for the bias dynamics and by careful characterization of bias effects in the measurement residuals. For example, random and certain environmental (i.e., tropospheric) bias errors are intrinsic to the radar measurements, whereas radar orientation biases corrupt the transformation of the prior position estimate from inertial to radar coordinates. Performance evaluations will demonstrate accurate real-time state estimates and excellent covariance fidelity, which are essential for radar-to-radar track correlation and fusion. II. Sensor Models