Enhanced GNSS Navigation Using a Centered Error Entropy Extended Kalman Filter in Non-Gaussian Noise Environments.

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.

The past decade has seen the rapid development of information theoretic learning and its applications in signal processing and machine learning. Specifically, minimum error entropy (MEE) and maximum correntropy criterion (MCC) have been widely studied in the literature. Although MEE and MCC are applied in many branches of knowledge and could outperform statistical criteria (such as mean square error), they have not been compared with each other from theoretical point of view. In some cases, MEE and MCC perform similarly to each other; however, under some conditions (e.g., in non-Gaussian environments), they act differently. This letter derives a new information theoretic relation between MEE and MCC, leading to better understanding of the theoretical differences, and illustrates the findings in a common example.

Minimum total complex error entropy for adaptive filter

In the case of a non-linear system, the dynamic state of the targets (position, velocity, and acceleration) is estimated by an extended Kalman filter (EKF). The theory of EKF is established on the assumption that measurements follow Gaussian distribution. However, in practice, this assumption falls short and limits the application of EKF. In literature, to deal with the non-Gaussianity, the maximum correntropy criterion (MCC)-based EKF (EKF-MCC) has been studied well. The MCC, an information-theoretic criterion, claims to effectively deal with the system's non-Gaussianity. Nevertheless, like EKF, EKF-MCC also approximates the known system non-linearity with a Jacobian. The Jacobian provides the first-order approximation of the non-linearity and hinders the estimation accuracy achieved by EKF-MCC, particularly for complex target motion models. Therefore, in this work, firstly, we propose to use EKF-MCC for estimating the dynamic state of the target from non-Gaussian measurement. After that, utilizing MCC, we propose reproducing kernel Hilbert space (RKHS) based non-linear estimation of system non-linearity and using it with EKF-MCC. Amid non-linear estimation utilizing MCC, the proposed filter is named EKF-MCC-RKHS. The simulation performed to estimate the dynamic states of the complex constant acceleration (CA) target motion model validates the superiority of EKF-MCC-RKHS over recently introduced EKF-MCC and traditional EKF.

Continuous discrete minimum error entropy Kalman filter in non-Gaussian noises system

With the growing size of the system, this distributed Kalman filter (DKF) is widely used in multi-sensor networks. However, it is difficult for DKF to accurately estimate state values in non-Gaussian noise environments. In this paper, a regression equation is first constructed to contain all sensor node information. Then, by bringing the minimum error entropy with fiducial points (MEEF) standard into the process of information fusion, a robust algorithm named centralized MEEF KF (CMEEF-KF) is presented, which is robust to non-Gaussian noise and unusual data. Furthermore, to overcome the communication burden of CMEEF-KF in sensor networks, the distributed MEEF-KF (DMEEF-KF) is developed, which construct a framework of consensus average method for node information fusion. Specifically, each sensor only exchanges the key information with its neighborhoods. In addition, in order to make the algorithm able to cope with the nonlinear state estimation problem, the distributed MEEF extended Kalman filter is also proposed. Eventually, the effectiveness of the suggested algorithms is demonstrated by land vehicle navigation and power system tracking state estimation using a 10-node sensor network.

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or α-stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise.

For enhancing the robustness of the Kalman filter in the presence of non-Gaussian noise or measurement outliers within a nonlinear state-space model, a robust filter based on mixed correlation entropy is proposed in this paper. The mixed correlation entropy cost function is utilized as a replacement for the second-order function used in the Kalman filter for measurement fitting errors in the Global Positioning System (GPS). Leveraging entropy theory with kernel functions, a novel robust filtering algorithm is designed by using the maximum correntropy criterion (MCC). While it has been demonstrated, the MCC-based robust filters are feasible for handling non-Gaussian noise and the default kernel in the original MCC, such as the Gaussian kernel, which may not be sufficient for dealing with more complex data encountered in many practical problems. The selection of kernel parameters for MCC-based filters becomes challenging when an adaptive kernel is not used. Therefore, there is a need to design algorithms, which are insensitive to kernel parameters for handling the measurement outliers. In this paper, the robust filters based on double-Gaussian mixture correntropy are proposed and combined with the nonlinear filtering algorithms, replacing filtering methods that rely solely on the minimum mean square criterion. Finally, the algorithm’s robustness is validated through simulation experiments under a certain degree of accuracy. The solutions suggested may outperform the current robust approaches, according to simulation findings, which can achieve better performance for GPS navigation applications.

The Global Navigation Satellite Systems (GNSS) applications are growing and more pervasive in the modern society. The presence of multi-constellation GNSS receivers able to use signals coming from different systems like the american Global Positioning System (GPS), the european Galileo, the Chinese Beidou and the russian GLONASS, permits to have more accuracy in position solution. All the receivers provide always more reliable solution but it is important to monitor the possible presence of problems in the position computation. These problems could be caused by the presence of impairments given by unintentional sources like multipath generated by the environment or intentional sources like spoofing attacks. In this thesis we focus on design algorithms at signal processing level used to assist Integrity operations in terms of Fault Detection and Exclusion (FDE). These are standalone algorithms all implemented in a software receiver without using external information. The first step was the creation of a detector for correlation distortion due to the multipath with his limitations. Once the detection is performed a quality index for the signal is computed and a decision about the exclusion of a specific Satellite Vehicle (SV) is taken. The exclusion could be not feasible so an alternative approach could be the inflation of the variance of the error models used in the position computation. The quality signal can be even used for spoofinng applications and a novel mitigation technique is developed and presented. In addition, the mitigation of the multipath can be reached at pseudoranges level by using new method to compute the position solution. The main contributions of this thesis are: the development of a multipath, or more in general, impairments detector at signal processing level; the creation of an index to measure the quality of a signal based on the detector's output; the description of a novel signal processing method for detection and mitigation of spoofing effects, based on the use of linear regression algorithms; An alternative method to compute the Position Velocity and Time (PVT) solution by using different well known algorithms in order to mitigate the effects of the multipath on the position domain.

Autonomous Underwater Vehicles (AUVs) need accurate navigation and positioning data to carry out their operations in challenging marine environments. However, non-Gaussian environmental noise and sensor outliers in underwater environments degrade the positioning accuracy and stability of traditional algorithms. In such circumstances, the typical Unscented Kalman Filter (UKF) performs worse according to the Minimum Mean Square Error (MMSE) criteria. To reduce non-Gaussian environmental disturbances, a Maximum Correntropy Criterion (MCC) is created. This study extends the MCUKF by utilizing a mixture correntropy framework and an effective iterative optimization technique, and an improved Sage-Husa filtering mechanism is integrated into the iterative algorithm to address time-varying noise dynamics in complex scenarios. These changes increase the algorithm's resilience and flexibility in demanding underwater conditions. The algorithm's capability is confirmed using simulation and sea experiments, which show notable gains in Root Mean Square Error and navigation accuracy. Experimental results show that the proposed method outperforms other existing algorithms in terms of navigation accuracy performance in our simulations and experiments. To guarantee algorithm performance and resilience for the non-Gaussian time-varying measurement noise issue that AUVs encounter in intricate maritime settings, and to additionally enhance the precision and dependability of localization, this study uses the MCC-UKF to combat the environment's non-Gaussian noise, and the Levenberg-Marguardt iterative method to improve reliability of numbers and estimation precision, while the Maximum Mixture Correntropy Criterion (MMCC) serves the purpose of improve the filter flexibility and convergence speed, and finally, the improved Sage-Husa algorithm is combined to improve the robustness to time-varying noise. The following are the study's primary contributions. (1) In our study, we suggest an enhanced UKF algorithm that combines the MCC and iterated cost function, and adopt a Levenberg-Marquardt optimization strategy to accelerate the convergence. The mixture correntropy criterion was added in the construction of the LMIMC-UKF framework in order to achieve the synergistic enhancement of convergence performance and calculate accuracy. (2) Targeting the issue of time-varying environment noise interference, a fusion approach of iterative tuning and improved Sage-Husa filtering is suggested to achieve the systematic improvement of algorithm robustness. (3) By combining the Monte Carlo simulation with maritime measurement data, the algorithm's technical viability is confirmed, and the parameter sensitivity is quantitatively examined by methodical simulation tests. According to the results, the suggested algorithm performs noticeably better than the current maximum correntropy filtering techniques in terms of anti-interference capability, iteration speed, and navigation accuracy.

본 논문은 비가우시안 노이즈가 존재하는 수중환경에서 비선형 필터 기법에 따른 2차원 위치 추정에 관한 연구 내용이다. 최근 위치 추정을 위한 필터로 확장형 칼만필터(EKF: Extended Kalman filter)가 많이 사용되고 있다. 하지만, 수중과 같은 비가우시안 노이즈가 존재하는 비선형 시스템에서는 많은 문제점을 가지고 있다. 따라서 본 논문에서는 상태변이의 예측을 기반으로한 EKF를 대신하여 통계적 발생인자 에 기반을 둔 분포 재해석 기법을 이용한 2차원 파티클필터 (TDPF: Two-Dimension Particle Filter)를 제안한다. 모의 실험을 통하여 Non-Gaussian Noise 가 존재하는 수중환경에서 제안하는 TDPF의 성능을 EKF와 비교분석하였으며 TDPF가 EKF보다 정확한 위치 추정결과를 제공하는 것을 확인하였다. This paper has considered the location estimation problem in two dimension space by using a non-linear filter under non-Gaussian noise in underwater acoustic sensor networks(UASNs). Recently, the extended Kalman filter (EKF) is widely used in location estimation. However, the EKF has a lot of problems in the non-linear system under the non-gaussian noise environment like underwater environment. In this paper, we propose the improved Two-Dimension Particle Filter (TDPF) using the re-interpretation distribution techniques based on the maximum likelihood (ML). Through the simulation, we compared and analyzed the proposed TDPF with the EKF under the non-Gaussian underwater sensor networks. Finally, we determined that the TDPF's result shows more accurate localization than EKF's result.

Novel robust minimum error entropy wasserstein distribution kalman filter under model uncertainty and non-gaussian noise

Methods for decoding movements from neural spike counts using adaptive filters often rely on minimizing the mean-squared error. However, for non-Gaussian distribution of errors, this approach is not optimal for performance. Therefore, rather than using probabilistic modeling, we propose an alternate non-parametric approach. In order to extract more structure from the input signal (neuronal spike counts) we propose using minimum error entropy (MEE), an information-theoretic approach that minimizes the error entropy as part of an iterative cost function. However, the disadvantage of using MEE as the cost function for adaptive filters is the increase in computational complexity. In this paper we present a comparison between the decoding performance of the analytic Wiener filter and a linear filter trained with MEE, which is then mapped to a parallel architecture in reconfigurable hardware tailored to the computational needs of the MEE filter. We observe considerable speedup from the hardware design. The adaptation of filter weights for the multiple-input, multiple-output linear filters, necessary in motor decoding, is a highly parallelizable algorithm. It can be decomposed into many independent computational blocks with a parallel architecture readily mapped to a field-programmable gate array (FPGA) and scales to large numbers of neurons. By pipelining and parallelizing independent computations in the algorithm, the proposed parallel architecture has sublinear increases in execution time with respect to both window size and filter order.

This study addresses the state estimation problem for the preceding vehicle in vehicle-to-vehicle (V2V) cooperative perception, with the objective of balancing estimation accuracy against communication load under constraints of limited bandwidth and non-Gaussian noise interference. To this end, an extended Kalman filtering algorithm is proposed that integrates an event-triggered (ET) mechanism with the maximum correntropy criterion (MCC). The event-triggered mechanism adaptively regulates communication frequency, significantly reducing network load while preserving estimation performance. Meanwhile, the maximum correntropy criterion enhances the filter’s robustness against non-Gaussian noise, enabling high-precision state estimation under limited communication resources. Simulation results under double lane-change and continuous sinusoidal steering scenarios show that, compared to conventional extended Kalman filtering and existing event-triggered robust filtering methods, the proposed algorithm achieves better estimation accuracy and stability in non-Gaussian noise environments. Moreover, it reduces the average communication load by approximately 68% without compromising estimation performance. This work provides an effective solution for state estimation in V2V cooperative perception that combines high robustness with high communication efficiency.