Development of a fuzzy logic-based adaptive Kalman filter

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

A fuzzy logic adaptive Kalman filtering methodology was developed for the automatic control of an irrigation canal system under unknown disturbances (water withdrawals) acting in the canal. Using a linearized finite difference model of open channel flow, the canal operation problem was formulated as an optimal control problem and an algorithm for gate opening in the presence of arbitrary external disturbances (changes in flow rates) was derived. Based on the linear optimal control theory, the linear quadratic regulator (LQR), assuming all the state variables (flow depths and flow rates) were available, was designed to generate control input (optimal gate opening). As it was expensive to measure all the state variables (flow rates and flow depths) in a canal system, a fuzzy logic adaptive Kalman filter and traditional Kalman filter were designed to estimate the values for the state variables that were not measured but were needed in the feedback loop. The performances of the state estimators designed using the fuzzy logic adaptive Kalman filter methodology and the traditional Kalman filtering technique were compared with the results obtained using the LQR (target loop function). The results of the present study indicated that the performance of the fuzzy logic adaptive Kalman filter was far superior to the performance of the observer design based upon the traditional Kalman filter approach. The obvious advantages of the fuzzy logic adaptive Kalman filter were the prevention of filter divergence and ease of implementation. As the fuzzy logic adaptive Kalman filter requires smaller number of state variables for the acceptable accuracy therefore, it would need less computational effort in the control of irrigation canals. Copyright © 2009 John Wiley & Sons, Ltd.

The paper proposes a new Kalman filtering (KF) algorithm called VBI-MCKF that combines the variational Bayesian inference (VBI)-based KF algorithm and the maximum correntropy KF (MCKF) for visual tracking problem. The VBI-based KF algorithm works to estimate the unknown measurement noise covariance matrix (MNCM) and process noise covariance matrix (PNCM), and the MCKF works to deal with non-Gaussian process noise and measurement noise. In order to cater for the visual tracking target scenario, where the MNCM and PNCM are unknown and non-Gaussian, we modify the VBI-based KF algorithm to work for suddenly occurring outliers and modify the MCKF work for small bandwidth. Simulations show that the proposed VBI-MCKF algorithm performs well when both covariance matrices of Gaussian process noise and non-Gaussian measurement noise are unknown or inaccurate.

A novel intelligent adaptive Kalman Filter for estimating the Submarine's velocity: With experimental evaluation

Visual servoing has been around for decades, but time delay is still one of the most troublesome problems to achieve target tracking. To circumvent the problem, in this paper, the Kalman filter is employed to estimate the future position of the object. In order to introduce the Kalman filter, accurate time delays, which include the processing lag and the motion lag, need to be obtained. Thus, the delays of the visual control servoing systems are discussed and a generic timing model for the system is provided. Then, we present a current statistical model for a moving target. A fuzzy adaptive Kalman filter, which is evolved from the Kalman filter, is introduced based on the current statistical model. Finally, a two DOF visual controller based variable structure control law for micro-manipulation is presented. The results show that the proposed adaptive Kalman filter can improve the ability to track moving targets.

Flowmeter is an instrument for measuring the flow rate of fluid, which is widely used in industrial, agricultural, environmental and other fields. However, the signal of flowmeter is often affected by various noises and interferences, which reduces the measurement accuracy. In order to improve the signal quality of flowmeter, this paper proposes a flowmeter signal processing method based on adaptive Kalman filter. This method uses the advantages of Kalman filter, combined with adaptive algorithm, dynamically adjusts the process noise covariance matrix and measurement noise covariance matrix, and realizes the effective filtering and estimation of flowmeter signal. This research takes the water flow signal processing based on Kalman filter as an example, and verifies the effectiveness and superiority of this method through simulation and experiment. The results show that this method can effectively suppress the noise and interference in the flowmeter signal, improve the measurement accuracy and stability of the flowmeter, and is suitable for different working conditions and different types of flowmeters.

According to the poor adaptive ability of traditional filter algorithm in the estimatio n for traffic state and travel time with Kalman filter, an improved fuzzy adaptive Kalman filtering method was pro posed. The new interest of observation noise was defined, and the fuzzy logic was used to adjust the importance weights of system noise and observation noise through on-line monitoring the interest changes, which changed the trust and utilization degree of the model for the observation information, and this made the filter eventually tend to be stable. To guarantee the real-time performance of system, a direct input - output fuzzy membership function matching method was put forward to take the place of fuzzy reasoning. The method was tested on the urban expressway in Guangzhou by using real-time detection data, and the result show that the traffic state es timation model had better tracking ability than conventional Kalman filter, and results of travel time prediction show that there was a sligh t difference between the prediction value and that of actual observation in free traffic flow state, and the relative error was under 1 5% in traffic congested state. The precision and applicability of this method were acceptable, and it can be used to provide a basis for travel time of urban expressway in traffic control and guidance system.

Real-time state of charge estimation for electric vehicle power batteries using optimized filter

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.

This paper designs a new adaptive Kalman filter (KF) to solve the filtering problem of with unknown noise statistics. The estimation error of the process noise covariance matrix will destroy the state estimation, and the state estimation error will reduce the estimation of the process noise covariance matrix, thus affecting the stability and optimality of the filter. In addition, most adaptive KF algorithms adopt the measurement method of single sensor, which is easy to cause the shortage of measurement data and affect the accuracy of the algorithm. Therefore, we propose a measurement sequence fusion adaptive Kalman filter (MSFAKF) algorithm to solve this series of problems. Based on MSFAKF algorithm, the estimation of process noise covariance and measurement noise covariance are obtained by measurement fusion sequence and innovation sequence respectively. Under certain conditions, the stability of MSFAKF algorithm is proved, and the filtering result converges to that of ideal KF with known second moment of noise. Simulation experiment shows that MSFAKF algorithm has the characteristics of fast convergence speed, high accuracy and strong adaptability.

For autonomous vehicles, navigation systems must be accurate enough to provide lane-level localization. Highaccuracy sensors are available but not cost-effective for production use. Although prone to significant error in poor circumstances, even low-cost GPS systems are able to correct Inertial Navigation Systems (INS) to limit the effects of dead reckoning error over short periods between sufficiently accurate GPS updates. Kalman filters (KF) are a standard approach for GPS/INS integration, but require careful tuning in order to achieve quality results. This creates a motivation for a KF which is able to adapt to different sensors and circumstances on its own. Typically for adaptive filters, either the process (Q) or measurement (R) noise covariance matrix is adapted, and the other is fixed to values estimated a priori. We show that by adapting Q based on the state-correction sequence and R based on GPS receiver-reported standard deviation, our filter reduces GPS root-mean-squared error by 23% in comparison to raw GPS, with 15% from only adapting R.

Adaptive Kalman filtering is widely used in data fusion and integration. This paper highlights the use of fuzzy inference system in INS/GPS integration for adaptation of the measurement noise covariance matrix, while the process covariance matrix is known. Selection of initial measurement noise covariance matrix, training process and an innovative adaption approach are investigated. A strapdown INS equipped with high quality inertial sensors and an accurate GPS receiver is evaluated in several tests, and the results confirm that tuning the measurement noise covariance matrix in neuro-fuzzy adaptive Kalman filtering approach outperforms the conventional Kalman filter in INS/GPS integration.

This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on Square-Root Unscented Kalman Filter (SRUKF), the traditional Maybeck’s estimator is modified and extended to the nonlinear systems, the estimation of square root of the process noise covariance matrix Q or measurement noise covariance matrix R is obtained straightforwardly. Then the positive semi-definiteness of Q or R is guaranteed, some shortcomings of traditional Maybeck’s algorithm are overcome, so the stability and accuracy of the filter is improved greatly.

In the scenario of high dynamics and low C/N0, the discriminator output of a GNSS tracking loop is noisy and nonlinear. The traditional method uses a fixed-gain loop filter for error estimation, which is prone to lose lock and causes inaccurate navigation and positioning. This paper proposes a cascaded adaptive vector tracking method based on the KF+EKF architecture through the GNSS Software defined receiver in the signal tracking module and the navigation solution module. The linear relationships between the pseudo-range error and the code phase error, the pseudo-range rate error and the carrier frequency error are obtained as the measurement, and the navigation filter estimation is performed. The signal C/N0 ratio and innovation sequence are used to adjust the measurement noise covariance matrix and the process noise covariance matrix, respectively. Then, the estimated error value is used to correct the navigation parameters and fed back to the local code/carrier NCO. The field vehicle test results show that, in the case of sufficient satellite signals, the positioning error of the proposed method has a slight advantage compared with the traditional method. When there is signal occlusion or interference, the traditional method cannot achieve accurate positioning. However, the proposed method can maintain the same accuracy for the positioning results.

Transfer alignment is an initialization of the missile INS prior to launch using data provided by master INS or GPS/INS system in aircraft. Generally, Kalman filter is applied to estimate misalignment attitude. Unfortunately, the Kalman filter provides optimal estimates only if the system model is accurate and filter noise is white and accurately obtained. Considering the complicated vibrated air environment, these demands can not be satisfied all the time. Therefore, after establishing a 12-state velocity matching transfer alignment model, an improved adaptive method is derived on the basis of the study on traditional adaptive Kalman filter such as Sage-Husa and intense adaptive filter. The improved adaptive filter is aimed at modifying the model and noise matrix with the process of filtering according to the practical measurement data. Numerical simulations show that with this improved adaptive filter under a "s" turn maneuver, transfer alignment Kalman filter keeps good working condition under large range of P, Q and R, and reaches good performance on estimating precise and convergent speed.