Multi-autonomous underwater vehicles (AUVs) cooperative localization has become a research hotspot in the marine navigation field. In this paper, a filtering algorithm for slave AUV with compass failure is proposed based on ‘two-master-one slave’ cooperative localization model. In this algorithm, the course angle is unknown, and non-Gaussian measurement noise caused by measurement outliers is considered. The cooperative localization model is reconstructed, and a filtering algorithm is derived whose performance will not be affected by the unknown course angle. Moreover, the maximum information potential (MIP) criterion is introduced into a recursive model to deal with the non-Gaussian measurement noise in a complicated underwater environment. Simultaneously, the kernel bandwidth is adaptively adjusted by the innovation matrix and the measurement error covariance matrix. The proposed algorithm can accurately estimate the variation of the unknown course angle without expanding the dimension of state under the condition of non-Gaussian measurement noise. Finally, the proposed algorithm is verified through field experiments. The results show that the proposed algorithm has higher accuracy and robustness than other existing algorithms.

In this study, to cope with time-varying delay in acoustic communication under non-Gaussian noise caused by outliers, a novel robust delay filtering algorithm is proposed for cooperative localization of autonomous underwater vehicles (AUVs). First, the modified measurement equations of the nonlinear cooperative location system with time-varying delay are derived, and the delay caused by the information processing and propagation of the underwater acoustic modem is converted into measurement bias. Second, to improve the robustness of the system with outliers caused by abnormal measurement values of underwater acoustic communication and Doppler velocity log (DVL), the statistical similarity measure (SSM) is introduced to construct the cost function. This is accomplished by quantifying the similarity between the state vector and the predicted state vector, similarity between the delay measurement, and modified predicted delay measurement. Finally, the modified measurement noise variance is obtained by maximizing the cost function, and two algorithms for the approximate solution of the nonlinear cost function are presented. The proposed robust delayed algorithm alleviates the impacts of delayed measurement with outliers on localization accuracy. The effectiveness and potential of the proposed filter are verified by lake trials.

A novel robust filter called a Huber M-estimation delay Kalman filter is proposed for a strapdown inertial navigation system/ultra-short baseline (SINS/USBL) integrated navigation system to deal with time-varying delay in underwater acoustic communication and simultaneously cope with non-Gaussian noises induced by outliers. First, considering the influence of platform error angle, an SINS/USBL integrated navigation system is constructed and, according to the delay characteristics of USBL acoustic communication, a delay system model based on state inversion is derived to deal with the time-varying observations. Second, a linear recursive model based on the delay system model is constructed to update the posterior estimation and covariance matrix by combining it with Huber’s M-estimation theory whose performance has robustness when encountering outliers. Simultaneously, a fixed-point iteration method is introduced to obtain optimal estimation. The proposed algorithm not only solves the time-varying delay problem but also prevents outliers in the process and measurement noises. Simulation and experimental results verify that the proposed filter has improved accuracy and robustness compared with other existing filters.

In this paper, a novel robust Gaussian approximation smoother based on expectation-maximization (EM) algorithm is proposed for cooperative localization (CL) with faulty Doppler velocity log (DVL) and heavy-tailed measurement noise. In our model, the AUV velocity information that is not available due to DVL failure and the bias in the underwater acoustic modem are considered as unknown inputs. Then, the student’s t distribution is used to model the heavy-tailed measurement noise. An EM algorithm is also developed for the state space model with heavy-tailed measurement noise. The state, noise covariance matrices and auxiliary random variables are regarded as hidden variables to obtain the maximum likelihood estimation of unknown inputs. Gaussian smoother where modified process and measurement noise covariance are inferred by variational Bayesian (VB) approach is applied to estimate the state. The experimental results illustrate that given the heavy-tailed noise, the proposed method estimates the unknown input, and the state with a high level of accuracy. The proposed algorithm can be used as a backup algorithm for cooperative localization in cases where DVL is not available due to failure.

With active hydraulic fracturing performed since 2012, the Fuling shale gas field in China is one of the largest shale gas fields outside of North America. Recently, a Casing-in-Casing (CiC) refracturing treatment was successfully implemented, resulting in production beyond expectations. This was the first successful application of a CiC refracturing treatment in a horizontal shale gas well in this region, thus providing a new option for refracturing horizontal wells in China. Bullheading diversion refracturing with diverting balls was previously attempted in this field with high initial production observed; however, production was inconsistent and quickly declined. Therefore, the operator decided to attempt a CiC refracturing method in an understimulated candidate well. This involved installing and cementing 3.5-in. casing in 5.5-in. casing to effectively isolate the perforations, which enabled plugging and perforating operations in the reconstructed wellbore for an effective refracturing treatment. A customized refracturing design integrated the production profile, residual recoverable reserves, and the specific 5.5- × 3.5-in. reconstructed wellbore limitation. The length of the 3.5-in. casing was optimized to be as short as possible but still cover the original perforations, and high-performance slickwater was used to reduce pipe friction, thus increasing the treatment rate. An engineered breakdown approach was employed for improved fracture initiation. Additionally, more clusters were added between the original clusters and, based on production profile results, some of the original understimulated clusters with little proppant placement were reperforated. To overcome the impact of depleted fractures, a self-degradable particulate diverting agent was used to propagate new fractures, allowing access to new rock to increase total reserve recovery. The treatment in the reconstructed wellbore was successful, with 21 stages fractured in 12 days, achieving 100% placement of the designed proppant and fluid. A treatment rate of 7 to 12 m³/min from the toe to heel was executed as designed. Test production of 183,800 m³/D was also achieved with a recovery rate of 88.1%. Production has remained consistent and wellhead pressure has remained steady at a high level throughout the first two months of production. CiC refracturing technology helps overcome common disadvantages experienced with traditional refracturing techniques, such as poorly placed proppant and fluid and inconsistent production. CiC refracturing not only allows exploitation of bypassed reserves from original fractures, but also allows precise stimulation of new rock to obtain the highest reserve recovery. The successful implementation of this case study illustrates the reliability of CiC refracturing technology and provides valuable experience to be used during future regional horizontal well refracturing.