# Data Fusion Based on Adaptive Interacting Multiple Model for GPS/INS Integrated Navigation System
## 4 Real Ship Experiment and Its Performance Analysis
### Performance Analysis and Comparison of Proposed Algorithm  
To verify the performance of the proposed algorithm, the effectiveness of the proposed algorithm is testified by GPS is fused with low-cost INS. We investigate an alternative to the EKF, IMM filter, and AIMM filter data fusion technology with regard to the marine integrated navigation system, and INS/GPS integrated navigation system makes the most of the complete mathematical equations which contain the pseudo-range and Doppler measure value and INS provided measure value. The priori elevation dependent weighting method is described by the undifferenced measurement covariance at concrete elevation (el)  
\[r_{ii}=\sigma_{0}^{2}/(\sin(\mathrm{el}))^{2} \tag{24}\]  
in which \(\sigma_{0}\) represents the standard deviation, 0.3 m with regard to pseudo-ranges and 0.01 m/s with regard to Doppler observing data. First, an adaptive algorithm, which estimates the measurement covariance on line, is employed to enhance performance. Then, KF based on U-D filter will be introduced to update the filter with pseudo-range and Doppler observing data. In general, establishing a precise randomness model with regard to INS, which works better under various conditions, is very difficult. For addressing this problem, we not only propose a dual-model IMM filter method, but also set two process noise covariance matrices, namely, \(Q_{1}=4Q_{0}\) and \(Q_{s}=0.25Q_{0}\). Where \(Q_{0}\) is nominal covariance, which could be determined on the basis of the sensor detailed parameters. The dual-model IMM filter method was used when the preset value are confirmed by empirical data according to theory of probability. These probabilities can be represented as a Markov chain transfer matrix between these models  
\[[p_{ii}]=\left[ \begin{array}{cc}0.98&0.02\\ 0.02&0.98\end{array} \right] \tag{25}\]  
In fact, these values have little effect on the final results. With the aim to ameliorate the stability of the filter in the initial phase, it is crucial to consider the initial model probability of large process noise mode is a little larger. The initial model probabilities are 0.4 with regard to small process noise model, while 0.6 for large process noise model. Figure 5 shows a time series of positioning errors in the north, east, and down directions based on GPS/INS integration configurations. For purpose of testing the performance of AIMM filter, EKF and IMM with GPS/INS configuration are employed. As far as the positioning accuracy is concerned, the proposed adaptive IMM filter method reach significantly better results than the EKF and IMM filter method. Due to the imprecise statistical characteristics of the dynamic model and the measurement model, the EKF solutions comprise too much noise. Although a smoother track is shown from the navigation solution of AIMM filter, some abrupt positioning errors can be eliminated in the EKF framework. Furthermore, the traditional IMM filter fulfills lower precision if the priori measurement noise covariance is imprecise. In about 200-600 s, the navigation solution rapidly deviated from a 0.5 m error to almost a 3 m error. This is principally because multipath has the great ability of interference, and then the abnormal effects had done a great deal to influence the overweighed pseudo-range. Therefore, the positioning precision provided by GPS/INS-AIMM has a certain improvement for GPS/INS-IMM and GPS/INS. Figure 6 describes the position RMS (root mean square) error for EKF, IMM, and AIMM filters. As is evident from Figure 6, the AIMM can be ameliorate the positioning solutions of GPS/INS integrated navigation by 35.4%, 37.1%, and 31.7% in the north, east and down directions, respectively, in comparison with EKF filter. It is evident from the figure that east direction accomplishes the optimal performance owing to geometric configuration. Also, the AIMM solutions achieve the percentage improvement of 22.2%, 31.8%, and 11.9%, respectively, when IMM filter is used.