# Automatic Estimation of Dynamic Lever Arms for a Position and Orientation System
## 1 Introduction  
Airborne earth observation takes the aircraft as the platform, and it uses remote sensing load such as synthesize aperture radar (SAR) and charge coupled device (CCD) array camera to acquire a wide range, highly accurate and multilayered space-time information of global surface and deep earth [1]. A position and orientation system (POS) is a dedicated strapdown inertial navigation system (SINS)/Global Positioning System (GPS) integrated system for airborne remote sensing [2]. As a direct georeferencing (DG) system, the POS provides the ability to directly relate the data collected by a remote sensing system to earth without using traditional ground-based measurements [3]. To improve mapping accuracy and efficiency, the POS is required to provide the position information to centimeter-level accuracy, and orientation data to sub-arcminute accuracy in either real-time navigation or post-mission, such as the current state-of-the-art airborne system POS AV610 [3, 4]. This is primarily accomplished by the inertial measurement unit (IMU) integrated with a Carrier-phase Differential GPS (CDGPS). The key algorithm for POS is still SINS/GPS integrated navigation [5, 6]. For the loosely-coupled integration method discussed here, the positions and velocities of the SINS and GPS solutions are compared, and the resulting differences are used as the measurement values for a Kalman filter [7, 8]. Due to the extremely high positioning accuracy of a CDGPS, typically 1-2 cm plus 1 ppm of baselineseparation in real-time kinematic (RTK) or post-processing [9; 10], many overlooked errors must be treated seriously. Among these, the time and space asynchronies are the dominant error sources. The time asynchrony means the time delay of the GPS position and the velocity information with respect to the SINS data in real-time systems, which will badly influence the accuracy of the SINS/GPS navigation solution. Based on one pulse per second (1 PPS) of the GPS, which can deliver very high time accuracies such as 20 ns, the time delay can be significantly attenuated by the professional time synchronization technology [11]. The space asynchrony means the lever arm between the GPS antenna and the IMU. Generally, the GPS antenna is mounted on the roof of the plane for better GPS satellite visibility [7; 12], while the IMU is installed inside the plane cabin or under the aircraft belly as close to the surveying sensors as possible to weaken the influence of flexural deformation. Therefore, the phase center of the GPS antenna and the measuring center of the IMU are separated by a lever arm. Since the lever arm in length is usually several meters, it severely deteriorates measurement values under angular excitations if no compensation is provided. Many efforts have been devoted to improving SINS/GPS integration accuracy by attenuating the lever arm uncertainty. One method is manual measurement by a total station [13; 14], which can obtain the length of the lever arm with sufficient accuracy, but suffers from complicated operation. Furthermore, it is a difficult task in itself to determine the phase center of a GPS antenna and the sensing center of an IMU. Repeated measurements are inevitable if the GPS antenna or IMU is replaced or remounted. The other method is automatic identification of the lever arm by the SINS/GPS integration navigation [1; 15; 16; 17; 18; 19; 20], in which the lever arm is extended as an error state of the Kalman filter to be estimated, while the vehicle maneuvers. The latter method is simple and effective, but practical only if the lever arm is constant. To maintain imaging quality, aerial surveying sensors are required to move in a straight line with a given direction, but a plane may deviate from the ideal motion trajectory, due to gusts, air turbulence, or flight control errors [7; 21].