Besides offset biases (such as range, the gain of range, azimuth, and elevation biases), for mobile radars, platform attitude biases (such as yaw, pitch, and roll biases) induced by the accumulated errors of the Inertial Measurement Units (IMU) of the Inertial Navigation System (INS) can also influence radar measurements. Both kinds of biases are coupled. Based on the analyses of the coupling influences and the observability of 3-D radars' error registration model, in the article, an Attitude Bias Conversion Model (ABCM) based on Square Root Unscented Kalman Filter (SRUKF) is proposed. ABCM can estimate 3-D radars' absolute offset biases under the influences of platform attitude biases. It converts platform attitude biases into radar measurement errors, by which the target East-North-Up (ENU) coordinates can be obtained from radar measurements directly without using the rotation transformation, which was usually used in the transition from platform frame to ENU considering attitude biases. In addition, SRUKF can avoid the inaccurate estimations caused by linearization, and it can weaken the adverse influences of the poor attitude bias estimation results in the application of ABCM. Theoretical derivations and simulation results show that 1) ABCM-SRUKF can improve elevation bias estimate accuracy to about 0·8 degree in the mean square error sense; 2) linearization is not the main reason for poor estimation of attitude biases; and 3) unobservability is the main reason. K E Y

For mobile radar, offset biases and attitude biases influence radar measurements simultaneously. Attitude biases generated from the errors of the inertial navigation system (INS) of the platform can be converted into equivalent radar measurement errors by three analytical expressions (range, azimuth, and elevation, resp.). These expressions are unique and embody the dependences between the offset and attitude biases. The dependences indicate that all the attitude biases can be viewed as and merged into some kind of offset biases. Based on this, a unified registration model (URM) is proposed which only contains radar "offset biases" in the form of system variables in the registration equations, where, in fact, the "offset biases" contain the influences of the attitude biases. URM has the same form as the registration model of stationary radar network where no attitude biases exist. URM can compensate radar offset and attitude biases simultaneously and has minor computation burden compared with other registration models for mobile radar network.

For mobile 3-D radar installed on a gyro-stabilized platform, its measurements are usually contaminated by the systematic biases which contain radar offset biases (i.e., range, azimuth and elevation biases) and attitude biases (i.e., yaw, pitch and roll biases) of the platform because of the errors in the Inertial Measurement Units (IMU). Systematic biases can NOT be removed by a single radar itself; however, fortunately, they can be estimated by using two different radar measurements of the same target. The process of estimating systematic biases and then compensating radar measurements is called error registration. In this paper, the registration models are established first, then, the equivalent radar measurement error expressions caused by the attitude biases are derived and the dependencies among attitude biases and offset biases are analysed by using the observable matrix criterion. Based on the analyses above, an Optimized Bias Estimation Model (OBEM) is proposed for registration. OBEM uses the subtraction of azimuth and yaw bias as one variable and omits roll and pitch biases in the state vector, which decreases the dimension of the state vector from fourteen of the All Augmented Model (AAM), (which uses all the systematic biases of both radars as state vector) to eight and has about 80% reduction in calculation costs. Also, OBEM can decrease the coupling influences of roll and pitch biases and improve the estimation performance of radar elevation bias. Monte Carlo experiments were made. Numerical results showed that the bias estimation accuracies and the rectified radar raw measurement accuracies can be improved. K E Y WO R D S1. Error Registration.2. Attitude Bias. 3. All Augmented Model (AAM). 4. Optimized Bias Estimation Model (OBEM).