Correction to: Hidden AR process and adaptive Kalman filter

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.

Robust node position estimation algorithms for wireless sensor networks based on improved adaptive Kalman filters

In this paper, two types of adaptive Kalman filters are proposed by using the Grünwald-Letnikov (G-L) difference method to estimate the state information of continuous-time nonlinear fractional-order systems with unknown parameters and fractional-orders. An adaptive extended Kalman filter is designed by using the first-order Taylor expansion to deal with the nonlinear function in a nonlinear fractional-order system with unknown parameters and fractional-order. Based on the third-degree spherical-radial rule, an adaptive cubature Kalman filter as another adaptive fractional-order Kalman filter discussed in this paper is provided by the cubature points to deal with the nonlinear function. The augmented vector consisting of the unknown state vectors, parameters and fractional-order is constructed, and the corresponding augmented equation is established to solve the estimation problem with unknown parameters and fractional-order. The state estimations of nonlinear fractional-order systems with unknown parameters and fractional-orders are carried out by the augmented vector method. Finally, four examples are given to verify the effectiveness of the proposed adaptive Kalman filters with unknown parameters and fractional-orders in this paper.

Speech signal enhancement is one of the important and primary processes used in speech processing, speech recognitions and speaker recognitions. This paper proposed the fast processed method for speech signal enhancement, which is the second order implementation of the fast adaptive Kalman filtering. This proposed method improves the processing time of conventional second order adaptive Kalman filter as well as output SNR as compared to the fast adaptive Kalman filter. The Kalman filter's conventional algorithm uses defferent matrix operations to perform speech enhancement. These matrix operations increases the processing time and reduces the adaptability property of Kalman filter as well. Second order Adaptive Kalman Filter improves output SNR of conventional Kalman Filter, but this method almost doubles the matrix operation and further increases the performance time. This paper proposes the Fast Adaptive Second Order Kalman Filter, which reduced processing time of conventional second order Kalman Filter with effective output SNR. We can also say that this proposed algorithm improves the output SNR of First Ordered Fast Adaptive Kalman Filter.

The carrier-to-noise ratio (C/N0) is an important indicator of the signal quality of global navigation satellite system receivers. In a vector receiver, estimating C/N0 using a signal amplitude Kalman filter is a typical method. However, the classical Kalman filter (CKF) has a significant estimation delay if the signal power levels change suddenly. In a weak signal environment, it is difficult to estimate the measurement noise for CKF correctly. This article proposes the use of the adaptive strong tracking Kalman filter (ASTKF) to estimate C/N0. The estimator was evaluated via simulation experiments and a static field test. The results demonstrate that the ASTKF C/N0 estimator can track abrupt variations in C/N0 and the method can estimate the weak signal C/N0 correctly. When C/N0 jumps, the ASTKF estimation method shows a significant advantage over the adaptive Kalman filter (AKF) method in terms of the time delay. Compared with the popular C/N0 algorithms, the narrow-to-wideband power ratio (NWPR) method, and the variance summing method (VSM), the ASTKF C/N0 estimator can adopt a shorter averaging time, which reduces the hysteresis of the estimation results.

The integration of the BeiDou Navigation Satellite System(BDS) and the Inertial Navigation System(INS) can provide a more reliable and accurate navigation service than either system alone. The deeply coupled architecture for BDS and INS integration has more superior performance than the loosely coupled or the tightly coupled. Owing to the complicated dynamic scenario and the nonlinear system's noise uncertainty, the adaptive Kalman filter(AKF) algorithm is often adopted in the deep integration(DI) system. The adaptive Sage window methods including innovation-based adaptive estimation(IAE) and residual-based adaptive estimation(RAE) are widely applied in AKF algorithms, but they have several limitations. We propose an improved adaptive unscented Kalman filter(AUKF) based on forgetting-factor-weight smoothing and multi-factor adaptation to overcome these limitations. Compared with the Sage window methods, the improved AUKF algorithm is immune to the quantity change of the satellites concerning integration and more sensitive to present dynamic. Furthermore, it can reduce the computation and storage burden in implementation. A simulation test based on a software platform and the deeply integrated BDS/INS navigation system is carried out to evaluate the performance of the improved AUKF. Simulation results show that the improved AUKF algorithm outperforms the extended Kalman filter(EKF) and has a similar performance with the RAE-AUKF.

State-of-charge estimation of lead-acid batteries using an adaptive extended Kalman filter

This article presents a novel approach for adaptive nonlinear state estimation in a modified autoregressive time series with fixed coefficients, leveraging an adaptive polynomial Kalman filter (APKF). The proposed APKF dynamically adjusts the evolving system dynamics by selecting an appropriate autoregressive time‐series model corresponding to the optimal polynomial order, based on the minimum residual error. This dynamic selection enhances the robustness of the state estimation process, ensuring accurate predictions, even in the presence of varying system complexities and noise. The proposed methodology involves predicting the next state using polynomial extrapolation. Extensive simulations were conducted to validate the performance of the APKF, demonstrating its superiority in accurately estimating the true system state compared with traditional Kalman filtering methods. The root‐mean‐square error was evaluated for various combinations of standard deviations of sensor noise and process noise for different sample sizes. On average, the root‐mean‐square error value, which represents the disparity between the true sensor reading and estimate derived from the adaptive Kalman filter, was 35.31% more accurate than that of the traditional Kalman filter. The comparative analysis highlights the efficacy of the APKF, showing significant improvements in state estimation accuracy and noise resilience.

This paper presents relevant methods on navigation accuracy improvement of agricultural vehicle focusing on positioning accuracy and control precision. An adaptive kalman filtering, combination of Sage_Husa adaptive filtering and strong tracking kalman filtering based on strict convergence criterion, is adopted to improve filtering accuracy with strong ability of adaptive filtering and restraining filter divergence. A new variable-structure switching method to prevent PID controller from integrator windup can effectively solve the integral saturation phenomenon, which adopts a kind of adaptive adjustment rate to adjust the integral term of PID control algorithm. Finally, this paper puts the improved adaptive filtering and anti-windup variable-structure PID control technique into combination to effectively restrain interference and integral saturation, so as to achieve the purpose of improving system stability and control precision. The simulation and experiment results show that methods described above greatly enhance the capabilities of restraining filtering divergence and improving control precision.

This article introduces an augmented adaptive unscented Kalman filter (KF). The proposed novel technique is suitable to simultaneously estimate both the diagonal process noise covariance matrix and the unknown inputs, thus combining previously reported KF estimators for unknown inputs (dual or joint KF) and for covariance matrices (adaptive KF). A selective scaling method is also introduced to improve the convergence property of the suggested KF. The development of the novel KF is also motivated by a specific estimation problem related to crane systems. Cranes represent a special class of weight handling equipment as they are underactuated and described by nonlinear dynamics such that the load present oscillatory behavior. In addition to the increasing need for their automation in various industrial fields, these features also make them a benchmark system in control engineering with numerous control laws reported in the literature for sway elimination and trajectory tracking. A common issue to realize most of the advanced control laws on real, eventually industrial size cranes is the necessity to know the sway angle and frictions on the configuration variables. It is shown in simulation and also with real experiments on a reduced size overhead crane system that the suggested KF is suitable to estimate both the sway angles and the frictions.

The existing adaptive Kalman filters for tracking manoeuvring targets by wireless sensor networks can easily lose robustness when both the measurement and process noises are unknown and time‐varying, resulting in large positioning errors. To solve this problem, a wireless sensor network manoeuvring target tracking algorithm using a novel robust adaptive cubature Kalman filter is proposed. This innovative robust adaptive cubature Kalman filter consists of a derived third‐order biased noise statistic estimator and conventional cubature Kalman filter. This derived noise statistic estimator can simultaneously sense time‐varying and unknown measurement and process noises and ensure that the adaptive cubature Kalman filter's robustness is not lost. The robustness of the novel robust adaptive cubature Kalman filter is strictly proven in this study. Extensive practical experiments and numerical simulations show that the proposed robust adaptive cubature Kalman filter always has higher target tracking accuracy than other existing adaptive Kalman filters, regardless of whether the mobile target is manoeuvring or not, the noise is unknown or time‐varying, and the number of anchor nodes is few or many.

Interacting multiple model adaptive robust Kalman filter for process and measurement modeling errors simultaneously

The performance of the Kalman filter (KF), which is recognized as an outstanding tool for dynamic system state estimation, heavily depends on its parameter R, called the measurement noise covariance matrix. However, it's difficult to get the exact value of R before the filter starts, and the value of R is likely to change with the measurement environment when the filter is working. To solve this problem, a new parameter adaptive Kalman filter is proposed in this paper. In this new Kalman filter, the initial value of R is offline decided by Evolutionary Algorithm (EA), and the value of R decided by EA is online updated by Fuzzy Inference System (FIS). A simulation experiment based on target tracking is carried out, and the results demonstrate that the new adaptive Kalman filter proposed in this paper (HydGeFuzKF) has a stronger adaptability to time-varying measurement noises than regular Kalman filter (RegularKF), Sage-Husa adaptive Kalman filter (SageHusaKF), the adaptive Kalman filter only based on genetic algorithm (GeneticKF) and the adaptive Kalman filter only based on fuzzy inference system (FuzzyKF).

Adaptive hybrid Kalman filter for attitude motion parameters estimation of space non-cooperative tumbling target

The needle puncture technology is one of the simplest minimally invasive medical procedures. Due to the asymmetry of the needle tip, the lateral force exerted by the tissue causes the tip to deflect and reaches the target position. It is important to maintain the needle tip in a desired plane in 2D control. In the process of puncture, the position is measured and the posture of the needle tip needs to be estimated in real time. Three estimation algorithms for estimating the states of the needle tip are employed in this paper. The first algorithm is adaptive Kalman filter (AKF), which is applied to the statistical properties of the noise is not completely known. The second is unscented Kalman filter (UKF). The last one is the combination of AKF and UKF, called adaptive unscented Kalman filter (AUKF) which combines the advantages of both. It should be noted that AKF is based on the feedback linearization model, but UKF and AUKF are directly based on the nonlinear model. On the base of analysis of three estimation algorithms, we study the control method. In this work, we estimate the states via the three methods and analyze the results. The simulation results of the estimation algorithms and the control method illustrate the differences between the three algorithms.