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In view that traditional dynamic Allan variance (DAVAR) method is difficult to make a good balance between dynamic tracking capabilities and the confidence of the estimation. And the reason is the use of a rectangular window with the fixed window length to intercept the original signal. So an improved dynamic Allan variance method was proposed. Compared with the traditional Allan variance method, this method can adjust the window length of the rectangular window adaptively. The data in the beginning and terminal interval was extended with the inverted mirror extension method to improve the utilization rate of the interval data. And the sliding kurtosis contribution coefficient and kurtosis were introduced to adjust the length of the rectangular window by sensing the content of shock signal in terminal interval. The method analyzed the window length change factor in different stable conditions and adjusted the rectangular window’s window length according to the kurtosis, sliding kurtosis contribution coefficient. The test results show that the more the kurtosis stability threshold was close to 3, the stronger the dynamic tracking ability of DAVAR would be. But the kurtosis stability threshold was too close to 3, there was a misjudgement in kurtosis analysis of signal stability, resulting in distortion of DAVAR analysis results. When using the improved DAVAR method, the kurtosis stability threshold can be close to 3 to improve the tracking ability and the estimation confidence in stable interval. Therefore, it solved the problem that the dynamic Allan variance tracking ability and confidence level were difficult to take into account, and also solved the problem of misjudgement in the stability analysis of kurtosis.

Compared with the non-redundant inertial navigation system (INS), the redundant INS (RINS) has more error parameters and the system is more complicated. The calibration methods for non-redundant INS are unable to be adopted by RINS directly. Meanwhile, the inner lever arm effect of accelerometers is more severe in RINS, which is not supposed to be ignored in the error compensation. To solve the problems above, this paper proposes a novel calibration method for accelerometers in RINS. First, the paper analyses and models the bias, scale factor error, installation angle error and lever arm error. Based on the error model, two Kalman filters are designed to estimate the error parameters. The calibration is divided into two steps: the bias, scale factor error and installation angle error are calibrated by the static multi-position experiment first, and then the lever arm error is calibrated by the rotation experiment. Experiments prove that the proposed method can effectively calibrate the deterministic error of the accelerometers, that the estimation errors are controlled at 1 × 10 −4 level. Further, the paper studies and optimizes the turntable rotation scheme in the lever arm error calibration experiment, and proposes the design principles for the rotation scheme. Comparing with the casually designed scheme, the optimized procedure can improve the accuracy by almost an order of magnitude as well as the time-consumption being shortened by 40%. The design principles are applicable to the other inertial navigation systems to improve the calibration accuracy and reduces the time cost.

In view of the large output noise and low precision of the Micro-electro-mechanical Systems (MEMS) gyroscope, the virtual gyroscope technology was used to fuse the data of the MEMS gyroscope to improve its output precision. Random error model in the conventional virtual gyroscopes contained an angular rate random walk and angle random walk ignoring other noise items and the virtual gyroscope technology can not compensate all random errors of MEMS gyroscope. So, the improved virtual gyroscope technology based on the autoregressive moving average (ARMA) model was proposed. First, the conventional virtual gyroscope technology was used to model the random error of three MEMS gyroscopes, and the data fusion was carried out by a Kalman filter to get the output of the virtual gyroscope. After that, the ARMA model was used to model the output of the virtual gyroscope, the random error model was improved with the ARMA model, and the Kalman filter was designed based on the improved random error model for data fusion of the MEMS gyroscopes. The experimental results showed that the 1σ standard deviation of the output of the virtual gyroscope based on the ARMA model was 1.4 times lower than that of the conventional virtual gyroscope output.

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