ADAPTIVE DEVELOPMENT OF SVSF FOR A FEATURE-BASED SLAM ALGORITHM USING MAXIMUM LIKELIHOOD ESTIMATION AND EXPECTATION MAXIMIZATION

ABSTRACT: The smooth variable structure filter (SVSF) has been considered as the robust estimator. Like other filters, the SVSF needs an accurate system model and known noise statistics to approximate the posterior state. Unfortunately, the system cannot be accurately modeled, and the noise statistic is unknown in the real application. For these reasons, the performance of SVSF might be decreased or even led to divergence. Therefore, the enhancement of SVSF is required. This paper presents an Adaptive SVSF. Initially, SVSF is smoothed. To provide the ability to estimate the noise statistic, ASVSF is then derived based on maximum likelihood estimation (MLE) and expectation-maximization (EM). Additionally, the unbiased noise statistic is also approached. However, its covariance is complicatedly formulated. It might cause a negative definite symmetric matrix. Therefore, it is tuned based on the innovation covariance estimator (ICE). The ASVSF is designed to solve the online problem of Simultaneous Localization and Mapping (SLAM). Henceforth, it is termed as the ASVSF-SLAM algorithm. The proposed algorithm showed better accuracy and stability compared to the conventional algorithm in terms of root mean square error (RMSE) for both Estimated Path Coordinate (EPC) and Estimated Map Coordinate (EMC). ABSTRAK: Penapis struktur bolehubah lembut (SVSF) telah dianggap sebagai penganggar teguh. Seperti penapis lain, SVSF memerlukan model sistem yang tepat dan statistik hingar yang diketahui bagi menganggar keadaan posterior. Malangnya, sistem tidak dapat dimodelkan dengan tepat dan statistik hingar tidak diketahui dalam aplikasi sebenar. Atas sebab-sebab ini, prestasi SVSF mungkin berkurangan, bahkan berbeza. Oleh itu, memperbaharui SVSF adalah perlu. Kajian ini adalah mengenai SVSF Mudah Suai. Pada awalnya, SVSF dilembutkan. Bagi menyediakan keupayaan anggaran statistik hinggar, ASVSF dihasilkan terlebih dahulu berdasarkan anggaran kemungkinan maksimum (MLE) dan maksimum-harapan (EM). Tambahan, statistik hinggar yang tidak berat sebelah juga dibuat. Walau bagaimanapun, rumusan formula kovarians ini adalah kompleks. Ini mungkin menyebabkan matriks simetri menjadi negatif. Oleh itu, ia diselaraskan berdasarkan penganggar kovarians inovasi (ICE). ASVSF dibina bagi menyelesaikan masalah dalam talian Penempatan dan Pemetaan Serentak (SLAM) dalam talian. Oleh itu, ia disebut sebagai algoritma ASVSF-SLAM. Algoritma yang dicadangkan ini menunjukkan ketepatan dan kestabilan yang lebih baik berbanding algoritma konvensional dari segi ralat punca min kuasa dua (RMSE) bagi kedua-dua Koordinat Anggaran Laluan (EPC) dan Anggaran Koordinat Peta (EMC).

Motion State Estimation of Target Vehicle under Unknown Time-Varying Noises Based on Improved Square-Root Cubature Kalman Filter

In the advanced driver assistance system (ADAS), millimeter-wave radar is an important sensor to estimate the motion state of the target-vehicle. In this paper, the estimation of target-vehicle motion state includes two parts: the tracking of the target-vehicle and the identification of the target-vehicle motion state. In the unknown time-varying noise, non-linear target-vehicle tracking faces the problem of low precision. Based on the square-root cubature Kalman filter (SRCKF), the Sage–Husa noise statistic estimator and the fading memory exponential weighting method are combined to derive a time-varying noise statistic estimator for non-linear systems. A method of classifying the motion state of the target vehicle based on the time window is proposed by analyzing the transfer mechanism of the motion state of the target vehicle. The results of the vehicle test show that: (1) Compared with the Sage–Husa extended Kalman filtering (SH-EKF) and SRCKF algorithms, the maximum increase in filtering accuracy of longitudinal distance using the improved square-root cubature Kalman filter (ISRCKF) algorithm is 45.53% and 59.15%, respectively, and the maximum increase in filtering the accuracy of longitudinal speed using the ISRCKF algorithm is 23.53% and 29.09%, respectively. (2) The classification and recognition results of the target-vehicle motion state are consistent with the target-vehicle motion state.

A MAPAEKF-SLAM ALGORITHM WITH RECURSIVE MEAN AND COVARIANCE OF PROCESS AND MEASUREMENT NOISE STATISTIC

The most popular filtering method used for solving a Simultaneous Localization and Mapping is the Extended Kalman Filter. Essentially, it requires prior stochastic knowledge both the process and measurement noise statistic. In order to avoid this requirement, these noise statistics have been defined at the beginning and kept to be fixed for the whole process. Indeed, it will satisfy the desired robustness in the case of simulation. Oppositely, due to the continuous uncertainty affected by the dynamic system under time integration, this manner is strongly not recommended. The reason is, improperly defined noise will not only degrade the filter performance but also might lead the filter to divergence condition. For this reason, there has been a strong manner well-termed as an adaptive-based strategy that commonly used to equip the classical filter for having an ability to approximate the noise statistic. Of course, by knowing the closely responsive noise statistic, the robustness and accuracy of an EKF can increase. However, most of the existed Adaptive-EKF only considered that the process and measurement noise statistic are characteristically zero-mean and responsive covariances. Accordingly, the robustness of EKF can still be enhanced. This paper presents a proposed method named as a MAPAEKF-SLAM algorithm used for solving the SLAM problem of a mobile robot, Turtlebot2. Sequentially, a classical EKF was estimated using Maximum a Posteriori. However, due to the existence of unobserved value, EKF was also smoothed one time based on the fixed-interval smoothing method. This smoothing step aims to keep-up the derivation process under MAP creation. Realistically, this proposed method was simulated and compared to the conventional one. Finally, it has been showing better accuracy in terms of Root Mean Square Error (RMSE) of both Estimated Map Coordinate (EMC) and Estimated Path Coordinate (EPC).

Effect of spin-orbital interaction on continuous and jumpwise reversal magnetization in [Mn(II)(HL)(H2O)][Mn(III)(CN)6]·2H2O molecular ferrimagnet

Magnetic jumps were revealed during the magnetization reversal of [Mn(II)(HL)(H2O)][Mn(III)(CN)6]·2H2O molecular ferrimagnet. Amplitudes of the jumps were 0.01 – 0.1 % of the saturation magnetization. Fourier transform of the time series of jumps magnetization indicates that frequency spectrum is close to the white noise. Statistic distribution of the jumps versus time reveals the appearance of the most jumps at the beginning of the demagnetization. Effect of spin-orbit coupling on statistical distribution of magnetization jumps was considered by comparison of two compounds with different single ion anisotropies. The increase of spin-orbit interaction leads to the decrease of power of spectral density of magnetization jumps.

Time-Varying Noise Statistic Estimator Based Adaptive Simplex Cubature Kalman Filter

To address the problem that filtering accuracy is reduced with the inaccurate time-varying noise statistic in conventional cubature Kalman filter, a noise statistic estimator based adaptive simplex cubature Kalman filter is put forward in this paper. First, the simplex cubature rule is adopted to approximate the intractable nonlinear Gaussian weighted integral in the filter. Secondly, a suboptimal unbiased constant noise statistic estimator is derived based on the maximum a posteriori estimation criterion. For the time-varying noise, the above estimator is modified using an exponential weighted attenuation method to realize the oblivion of stale data which results in a fading memory estimator, which has the ability to estimate the time-varying noise statistic to revise the filter online. The simulation results indicate that the proposed filter can achieve higher accuracy than conventional filters with inaccurate noise statistic.

Data Processing with an Innovation Self-Adaptive Denoising Amalgamation Algorithm

The process noise and observation noise of a system are easily disturbed. It’s hard to know its statistic character. This paper proposes an innovation self-adaptive fading UPF algorithm to solve this problem. In the new algorithm, self-adaptive gradually vanishing UKF is used as weightiness density function of particle filter. New observation data is used to modify the error caused by state function of system and noise statistic parameter in time. What’s more, the new algorithm avoids traditional particle filter’s defect that it always gets part optimal solutions. Experiment results indicate that this new algorithm has a higher accuracy and robustness for the changeable noise statistics and non-linear system.

An Adaptive Unscented Kalman Filtering Algorithm for MEMS/GPS Integrated Navigation Systems

MEMS/GPS integrated navigation system has been widely used for land-vehicle navigation. This system exhibits large errors because of its nonlinear model and uncertain noise statistic characteristics. Based on the principles of the adaptive Kalman filtering (AKF) and unscented Kalman filtering (AUKF) algorithms, an adaptive unscented Kalman filtering (AUKF) algorithm is proposed. By using noise statistic estimator, the uncertain noise characteristics could be online estimated to adaptively compensate the time-varying noise characteristics. Employing the adaptive filtering principle into UKF, the nonlinearity of system can be restrained. Simulations are conducted for MEMS/GPS integrated navigation system. The results show that the performance of estimation is improved by the AUKF approach compared with both conventional AKF and UKF.

An Adaptive UKF Based SLAM Method for Unmanned Underwater Vehicle

This work proposes an improved unscented Kalman filter (UKF)-based simultaneous localization and mapping (SLAM) algorithm based on an adaptive unscented Kalman filter (AUKF) with a noise statistic estimator. The algorithm solves the issue that conventional UKF-SLAM algorithms have declining accuracy, with divergence occurring when the prior noise statistic is unknown and time-varying. The new SLAM algorithm performs an online estimation of the statistical parameters of unknown system noise by introducing a modified Sage-Husa noise statistic estimator. The algorithm also judges whether the filter is divergent and restrains potential filtering divergence using a covariance matching method. This approach reduces state estimation error, effectively improving navigation accuracy of the SLAM system. A line feature extraction is implemented through a Hough transform based on the ranging sonar model. Test results based on unmanned underwater vehicle (UUV) sea trial data indicate that the proposed AUKF-SLAM algorithm is valid and feasible and provides better accuracy than the standard UKF-SLAM system.