Abstract: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 p… Show more
“…However, there are azimuth and elevation biases among corresponding axes of both frames. According to [4], all the attitude biases can be equivalent to measurement errors at time instance k as:…”
Section: Mathematical Descriptionmentioning
confidence: 99%
“…Usually two kinds of state vectors can be used: (1) equations which contain target states and systematic biases [2], [3]; and (2) only systematic biases are contained. However, since the existence of the dependence between the initial target states and systematic biases, the usage of the former equation set is not appropriate (high computation burden and slow convergence speed) [4].…”
Registration is the act or process of simultaneously entering information about radar offset biases and attitude biases of Inertial Navigation System (INS) in a common reference frame known as radar registration frame. The variables that describe the registration are defined as radar offset biases and attitude biases. The mathematical relationship that shows the formal relation among the registration variables or radar offset biases and attitude biases is defined as the registration equation(s). For mobile 2-, 3-D radar networks, in order to improve the accuracy of the registration equations, the earth-centered earth-fixed (ECEF) coordinate system is used as the intermediate frame to get to the registration frame. Since a 2-D radar model has no comprehensive 3-D information of the target when establishing the registration equations, three different methods are discussed, each method differently and uniquely pinpoints to a reference point. The latter instead of the true target coordinates is used to establish the registration equations. The errors of the reference points are unavoidable and will be embodied in the estimation errors of all the biases. The mobile 2-D radar network registration in ECEF frame can also be included in this methodology. Simulation results show that all three methods can be applied well for registration, and for a certain condition, one of them outperforms the others.
“…However, there are azimuth and elevation biases among corresponding axes of both frames. According to [4], all the attitude biases can be equivalent to measurement errors at time instance k as:…”
Section: Mathematical Descriptionmentioning
confidence: 99%
“…Usually two kinds of state vectors can be used: (1) equations which contain target states and systematic biases [2], [3]; and (2) only systematic biases are contained. However, since the existence of the dependence between the initial target states and systematic biases, the usage of the former equation set is not appropriate (high computation burden and slow convergence speed) [4].…”
Registration is the act or process of simultaneously entering information about radar offset biases and attitude biases of Inertial Navigation System (INS) in a common reference frame known as radar registration frame. The variables that describe the registration are defined as radar offset biases and attitude biases. The mathematical relationship that shows the formal relation among the registration variables or radar offset biases and attitude biases is defined as the registration equation(s). For mobile 2-, 3-D radar networks, in order to improve the accuracy of the registration equations, the earth-centered earth-fixed (ECEF) coordinate system is used as the intermediate frame to get to the registration frame. Since a 2-D radar model has no comprehensive 3-D information of the target when establishing the registration equations, three different methods are discussed, each method differently and uniquely pinpoints to a reference point. The latter instead of the true target coordinates is used to establish the registration equations. The errors of the reference points are unavoidable and will be embodied in the estimation errors of all the biases. The mobile 2-D radar network registration in ECEF frame can also be included in this methodology. Simulation results show that all three methods can be applied well for registration, and for a certain condition, one of them outperforms the others.
“…For UGSP mobile radar, the measurement frame is parallel to the body frame (see Figure 1(a)). Its y axis denotes zero-degree azimuth, and clock-wise direction denotes the increment of azimuth.The subscript “ p ” (so-called “platform”) was used to identify body frame, and “ s ” denotes sensor frame. ENU frame has the same origin with the body frame; its x, y , and z axis denotes east, north, and up, respectively. Earth-centred Earth-fixed (ECEF) frame (Progri, 2011; 2014) has its origin located at the centre of the earth (Wang et al, 2013): its x- axis passes through the Greenwich meridian, its z- axis coincides with the Earth's axis of rotation and its y- axis lies in the equatorial plane to form a right-handed coordinate system.Figure 1.Illustration of UGSP mobile radar. (a) Illustration of body frame and sensor frame; (b) Conversion from body frame to ENU frame.…”
For mobile radars installed on a gyro-stabilised platform (GSP) that can steadily follow an East-North-Up (ENU) frame, attitude biases (ABs) of the platform and offset biases (OBs) of the radar are linear dependent variables. Therefore ABs and OBs are unobservable in the linearized registration equations; however, when combining them as new variables, the system becomes observable, and this model has been called the unified registration model (URM). Unlike GSP mobile radars, un-stabilised GSP (or UGSP) mobile radars are installed on the platform directly and rotate with the platform simultaneously. For UGSP, it is testified that both types of biases are independent and observable because the time-varying attitude angles (AAs) 1 of the platform are included in the registration equations, which destroy the dependencies of both kinds of biases and lead us to propose a completely different linearized registration model-the All Augmented Model (AAM). AAM employs all OBs and ABs in the state vector and a Kalman filter (KF) to produce their estimates. Numerical simulation results show that the estimated performance of AAM is close to the Cramér-Rao lower bound (CRLB) and that the Root Mean Square Errors (RMSEs) of the rectified measurements by using AAM are more than 500 m smaller than by URM in all directions.
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“…So, in noisy circumstances or variables with slowly varying linear dependent coefficients in the registration equations, this SVD criterion can only give the qualitative instead of the exact dependent relations among different variables. Besides the methods above, the optimized bias estimation model (OBEM) was proposed by Wang et al [8], where it was verified that when the azimuth and yaw biases are combined as one variable, the registration model is observable. The attitude bias conversion model (ABCM) [7] is proposed to explicitly establish nonlinear registration equations using linear dependencies among all biases.…”
Section: Introductionmentioning
confidence: 99%
“…From the control theory perspective of view, for nonlinear control system with zero input control items, the linearized model can be used directly to construct observability matrix (OM) to analyze the OoS [9]. Furthermore, Wang et al [8] converted the ABs of the platform into radar measurement errors (MEs) by three analytical expressions. These expressions contain the TCs as well as the ABs as variables.…”
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.
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