Response surface approach is effective for robust parameter design. Previous response surface methodology assumes that the independent variables are measured without errors. However, this assumption might be violated due to the low capability of measurement system. This paper is concerned with applying response surface method for robust parameter design when there are measurement errors in variables. We present an unbiased estimator when there are some measurement errors and an optimal setting which is determined to minimize the expected quadratic loss. An example is illustrated to verify the effectiveness of the proposed approach. The results show that the proposed method can achieve better operating conditions under situations with measurement errors than the conventional method.

An inertially stabilized platform (ISP) is generally equipped with a position and orientation system (POS) to isolate attitude disturbances and to focus surveying sensors on interesting targets. However, rotation of the ISP will result in a time-varying lever arm between the measuring center of the inertial measurement unit (IMU) and the phase center of the Global Positioning System (GPS) antenna, making it difficult to measure and provide compensation. To avoid the complexity of manual measurement and improve surveying efficiency, we propose an automatic estimation method for the dynamic lever arm. With the aid of the ISP encoder data, we decompose the variable lever arm into two constant lever arms to be estimated on line. With a complete 21-dimensional state Kalman filter, we accurately and simultaneously accomplish navigation and dynamic lever arm calibration. Our observability analysis provides a valuable insight into the conditions under which the lever arms can be estimated, and we use the error distribution method to reveal which error sources are the most influential. The simulation results demonstrate that the dynamic lever arm can be estimated to within [0.0104; 0.0110; 0.0178] m, an accuracy that is equivalent to the positioning accuracy of Carrier-phase Differential GPS (CDGPS).

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