Abstract
In order to solve the problems of particle degradation and difficulty in selecting importance density function in particle filter algorithm, a robust interacting multiple model unscented particle filter algorithm is presented, which is based on the advantages of interacting multiple model and particle filter algorithms. This algorithm can use the unscented transformation to get the particles that contain the latest measurement information of each model and calculate the robust equivalent weight function. This robust factor is designed to adjust the estimation and variance, and the important distribution function adaptively obtained is closer to the true distribution. Then, the particles weights can be flexibly adjusted in real time by using Euclidean distance to improve the computational efficiency during the resampling process. In addition, this filter process can comprehensively describe the uncertainty of the statistics characteristic of observation noise between different models. The diversity of available particles is increased, and the filter precision is improved. The proposed algorithm is applied to the SINS/GPS integrated navigation system, and the simulation analysis results demonstrate that the algorithm can effectively improve the filter performance and the calculation precision in positioning of integrated navigation system; thus, it provides a new method for nonlinear model filter.
Highlights
2.3. e Main Steps of interacting multiple model unscented particle filter (IMMUPF) Algorithm. e IMM estimation algorithm is an iterative recursive projection method
Robust Interacting Multiple Model Unscented Particle Filter e proposed robust interacting multiple model unscented particle filter algorithm improves the robust adjustment capability of the system model by modifying the measurement and state covariance in real time, so as to ensure the accuracy of the calculation. e IMM process can take into consideration the probability of each model by Markov transition probability. e basic design idea of the algorithm is as follows: firstly, these groups of corresponding particles are interacted as inputs to each model, and this process can reinitialize the filter input value; secondly, the unscented transformation is carried out for each model, and at the time k the Sigma point is calculated to obtain the estimations with the latest measurement information
The model is matched with the robust unscented particle filter; thirdly, in the resampling process, the calculated weights of the particles can be adjusted by the Euclidean distance to increase the weights of the useful particles; it can update the corresponding model probability and calculate the output interaction for the particle sets of each model; the state estimation is realized by constantly cyclic updating of the particles
Summary
Calculate the Sigma point χik and that of the particle weight ωik. In the process of time update, χij,k−1 is sampling calculated strategy, according and χij,k/k−1 to is the sigma point calculated by the nonlinear state transfer function f(·), so as to obtain one-step state prediction xk/k−1 and covariance matrix Pk/k−1, χij,k/k−1 fχij,k−1, ωk−1; j 0, . . . , 2N, 2N xik/k−1 ωmj χij,k/k−1, j 0. Combined with the UPF algorithm above, the interacting multiple model unscented particle filter (IMMUPF) algorithm [20, 21] is obtained as follows: For k 0, draw N sampling points according to the initial mean and variance xi0 ∼ p(xo), where i 1, 2, . (6) Combined output: e weighted sum calculation is completed for the m models corresponding particle sets. It can complete input interaction for the corresponding particles of each model by using the IMMUPF algorithm formulae [12] and [13]. Step 4: For k time, calculate the robust equivalent weight function and adjust particles completed unscented transformation, get xik∗ and Pik∗ , as follows,. If the reciprocal function is taken, it is defined as variance expansion factor function
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