Standard Kalman Filter Research Articles

Robust tracking of moving objects using thermal camera and speeded up robust features descriptor

SummaryRobust methods based on nonlinear influence functions are often used to remove outliers from data. The article describes the design of an algorithm for tracking a moving object in a thermal image using a SURF descriptor and robust Kalman filter. However, given that the main shortfall of robust methods is reduced efficiency, tunable parameters of the robust influence function are used to achieve a balance between robustness and efficiency. The parameters adapt to the observed scene's current conditions, while their estimation is based on the calculated data outlier contamination factor. The outliers that contaminate the data are generally a result of various types of occlusions. The results show that the proposed solution achieves better performance than the standard Kalman filter or fixed‐parameter robust Kalman filter.

Effect of Pixelation on the Parameter Estimation of Single Molecule Trajectories.

The advent of single molecule microscopy has revolutionized biological investigations by providing a powerful tool for the study of intercellular and intracellular trafficking processes of protein molecules which was not available before through conventional microscopy. In practice, pixelated detectors are used to acquire the images of fluorescently labeled objects moving in cellular environments. Then, the acquired fluorescence microscopy images contain the numbers of the photons detected in each pixel, during an exposure time interval. Moreover, instead of having the exact locations of detection of the photons, we only know the pixel areas in which the photons impact the detector. These challenges make the analysis of single molecule trajectories, from pixelated images, a complex problem. Here, we investigate the effect of pixelation on the parameter estimation of single molecule trajectories. In particular, we develop a stochastic framework to calculate the maximum likelihood estimates of the parameters of a stochastic differential equation that describes the motion of the molecule in living cells. We also calculate the Fisher information matrix for this parameter estimation problem. The analytical results are complicated through the fact that the observation process in a microscope prohibits the use of standard Kalman filter type approaches. The analytical framework presented here is illustrated with examples of low photon count scenarios for which we rely on Monte Carlo methods to compute the associated probability distributions.

Adaptive extended Kalman filtering strategies for spacecraft formation relative navigation

The relative navigation problem for spacecraft formation flying missions in near-Earth orbit is addressed here through the design of two unique adaptive extended Kalman filter algorithms. The adaptive filters are capable of updating the internal noise characteristics of the Kalman filter in real time, and are viable in all orbit scenarios, including elliptical orbits subjected to perturbations. The first adaptive Kalman filter approach uses maximum likelihood estimation techniques to derive analytical adaptations laws, which are then improved through the novel inclusion of an intrinsic smoothing routine. The second approach uses an embedded fuzzy logic system based on a covariance-matching analysis of the filter residuals, where the fuzzy system has been specifically designed for the spacecraft navigation problem at hand. Numerical simulations of two spacecraft formations demonstrate that the proposed adaptive navigation algorithms are appreciably more robust to filter initialization errors, dynamics modelling deficiencies, and measurement noises than the standard Kalman filter.

The robust residual-based adaptive estimation Kalman filter method for strap-down inertial and geomagnetic tightly integrated navigation system.

When noise statistical characteristics of the system are unknown and there are outliers in the measurement information, the filtering accuracy of the strap-down inertial navigation system/geomagnetic navigation system (SINS/GNS) tightly integrated navigation system would decrease, and the filtering may diverge in severe cases. To solve this problem, a robust residual-based adaptive estimation Kalman filter (RRAEKF) method is proposed. In the RRAEKF method, the covariance matching technique is employed to detect whether the system is abnormal or not. When the system is judged to be abnormal, a weighted factor is constructed to identify and weight the wild value in the measurement information, eliminating the influence of the outliers on the filtering accuracy. To further improve the filtering accuracy of the integrated navigation system, a contraction factor is introduced to adaptively adjust the gain matrix of the filter algorithm, obtaining the optimal estimate of the state vector and covariance matrix. Simulation results demonstrate that compared with the standard extended Kalman filter method and residual-based adaptive estimation method, the space position errors of the SINS/GNS tightly integrated navigation system based on the proposed method are improved by 63.37% and 56.93%, respectively, in the case of time-varying noise and the presence of outliers.

Control Optimization of Stochastic Systems Based on Adaptive Correction CKF Algorithm

Standard cubature Kalman filter (CKF) algorithm has some disadvantages in stochastic system control, such as low control accuracy and poor robustness. This paper proposes a stochastic system control method based on adaptive correction CKF algorithm. Firstly, a nonlinear time-varying discrete stochastic system model with stochastic disturbances is constructed. The control model is established by using the CKF algorithm, the covariance matrix of standard CKF is optimized by square root filter, the adaptive correction of error covariance matrix is realized by adding memory factor to the filter, and the disturbance factors in nonlinear time-varying discrete stochastic systems are eliminated by multistep feedback predictive control strategy, so as to improve the robustness of the algorithm. Simulation results show that the state estimation accuracy of the proposed adaptive cubature Kalman filter algorithm is better than that of the standard cubature Kalman filter algorithm, and the proposed adaptive correction CKF algorithm has good control accuracy and robustness in the UAV control test.

Two-stage gradient-based iterative algorithm for bilinear stochastic systems over the moving data window

For the bilinear stochastic system, the difficulty of identification lies in the product of the state vector and input in the system. This paper studies the iterative estimation of the parameters and states for the bilinear state-space systems in the observer canonical form. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. Therefore, this paper proposes a state filter (SF) for the bilinear systems based on the extremum principle. By means of the hierarchical principle, we decompose the identification model into two sub-identification models by introducing two fictitious output variables. Then an SF two-stage gradient-based iterative algorithm is proposed to achieve the combined parameter and state estimation according to the gradient search. For the purpose of improving the identification performance, an SF two-stage moving data window gradient-based iterative algorithm is derived by increasing the data utilization. The numerical example demonstrates the validity of the proposed algorithms.

INS/Odometer Land Navigation by Accurate Measurement Modeling and Multiple-Model Adaptive Estimation

Land vehicle navigation based on inertial navigation system (INS) and odometers is a classical autonomous navigation application and has been extensively studied over the past several decades. In this work, we seriously analyze the error characteristics of the odometer (OD) pulses and investigate three types of odometer measurement models in the INS/OD integrated system. Specifically, in the pulse velocity model, a preliminary Kalman filter is designed to obtain accurate vehicle velocity from the accumulated pulses; the pulse increment model is accordingly obtained by integrating the pulse velocity; a new pulse accumulation model is proposed by augmenting the travelled distance into the system state. The three types of measurements, along with the nonhonolomic constraint (NHC), are implemented in the standard extended Kalman filter. In view of the motion-related pulse error characteristics, the multiple model adaptive estimation (MMAE) approach is exploited to further enhance the performance. Simulations and long-distance experiments are conducted to verify the feasibility and effectiveness of the proposed methods. It is shown that the standard pulse velocity measurement achieves the superior performance, whereas the accumulated pulse measurement is most favorable with the MMAE enhancement.

Adaptive [formula omitted] Kalman filter based random drift modeling and compensation method for ring laser gyroscope

This paper investigates the random drift influence on ring laser gyroscope (RLG) and proposes a random drift modeling and compensation method to improve the measurement accuracy of RLG. The traditional compensation method for random drift is the standard Kalman filter. However, it needs to know the accurate discrete-time state-space model and the statistic characteristics of process and measurement noises, which limits the performance of Kalman filter. Therefore, based on the autoregressive moving average (ARMA) model, this paper incorporates the H∞ technique and adaptive law design into the standard Kalman filter to deal with the system uncertainty and estimate the statistic characteristics of unknown noises. To test the performance of our proposed filter, the Allan variance method is adopted to analyze the random drift influence under different Kalman-type filters. The experimental results have been given to demonstrate that under the proposed adaptive H∞ Kalman filter, the influence of random drift on RLG output is largely reduced and the calibration accuracy for turntable is improved significantly.

Parameter identification of a differentiable Bouc-Wen model using constrained extended Kalman filter

Hysteresis is of critical importance to structural safety under severe dynamic loading conditions. One of the widely used hysteretic models for civil structures is the Bouc-Wen model, the effectiveness of which depends on suitable model parameters. The locally non-differentiable governing equation of the conventional Bouc-Wen model poses difficulty on existing identification algorithms, especially the extended Kalman filter, which relies on linearized system equations to propagate state estimates and covariance. In addition, the standard extended Kalman filter usually does not incorporate parameter constraints, and therefore may result in unreasonable estimates. In this article, a modified and differentiable Bouc-Wen model, together with a constrained extended Kalman filter (CEKF), is proposed to identify the hysteretic model parameters in a reliable way. The partial derivatives of the differentiable Bouc-Wen model with respect to hysteretic parameters can be easily calculated for implementing the identification algorithm. Constrained extended Kalman filter restricts the Kalman gain to ensure that the estimates of parameters satisfy constraints from physical laws. Parameter identification using simulated and experimental data collected from a four-story structure demonstrates that constrained extended Kalman filter can achieve more reliable identification results than the standard extended Kalman filter.

Multiple-Hypothesis Vision-Based Landing Autonomy

This paper presents a novel state estimation system for unmanned aerial vehicle landing. A novel vision algorithm that detects a portion of the marker is developed, and this algorithm extends the detectable range of the vision system for any known marker. A vision-aided navigation algorithm is derived within extended Kalman particle filter and Rao–Blackwellized particle filter frameworks in addition to a standard extended Kalman filter framework. These multihypothesis approaches not only deal well with a highly nonlinear and non-Gaussian distribution of the measurement errors of vision but also result in numerically stable filters. The computational costs are reduced compared to a naive implementation of particle filter, and these algorithms run in real time. This system is validated through numerical simulation, image-in-the-loop simulation, and flight tests.

A Marginal Adjustment Rank Histogram Filter for Non-Gaussian Ensemble Data Assimilation

AbstractAn extension to standard ensemble Kalman filter algorithms that can improve performance for non-Gaussian prior distributions, non-Gaussian likelihoods, and bounded state variables is described. The algorithm exploits the capability of the rank histogram filter (RHF) to represent arbitrary prior distributions for observed variables. The rank histogram algorithm can be applied directly to state variables to produce posterior marginal ensembles without the need for regression that is part of standard ensemble filters. These marginals are used to adjust the marginals obtained from a standard ensemble filter that uses regression to update state variables. The final posterior ensemble is obtained by doing an ordered replacement of the posterior marginal ensemble values from a standard ensemble filter with the values obtained from the rank histogram method applied directly to state variables; the algorithm is referred to as the marginal adjustment rank histogram filter (MARHF). Applications to idealized bivariate problems and low-order dynamical systems show that the MARHF can produce better results than standard ensemble methods for priors that are non-Gaussian. Like the original RHF, the MARHF can also make use of arbitrary non-Gaussian observation likelihoods. The MARHF also has advantages for problems with bounded state variables, for instance, the concentration of an atmospheric tracer. Bounds can be automatically respected in the posterior ensembles. With an efficient implementation of the MARHF, the additional cost has better scaling than the standard RHF.

Integrated navigation for doppler velocity log aided strapdown inertial navigation system based on robust IMM algorithm

Global navigation satellite system (GNSS) is the most widely used position, navigation and time service system. However, GNSS such as BeiDou Navigation Satellite System (BDS) cannot provide the external assistance information for the autonomous underwater vehicle (AUV) because of the blocking effect of water on electromagnetic wave. The uncertain and non-Gaussian characteristics of the measurement noise may degrade the performance of SINS/DVL integrated navigation under the standard Kalman filter (KF) framework. To solve this problem, this paper proposes a robust interacting multiple model algorithm (IMM-RKF) based on the Mahalanobis distance algorithm. Furthermore, two switching sub-models will depict the uncertain parameters. The contributions of the work presented here are twofold. First, this paper robustifies the IMM algorithm under non Gaussian condition, and second the research method is verified in the problem of SINS/DVL integrated navigation. Simulation experimental results for the problem of SINS/DVL integrated navigation under non-Gaussian and uncertain conditions demonstrate the validity and superiority of the proposed method.

Stubborn and Dead-Zone Redesign for Nonlinear Observers and Filters

We propose a redesign paradigm for stable estimators by introducing a saturation or a dead-zone nonlinearity with adaptive thresholds on the output injection term. Such nonlinearities allow improving the sensitivity to measurement noise in different scenarios (impulsive disturbances or persistent noise such as sensor bias), while preserving the asymptotic convergence properties of the original observer. These redesigns apply to a broad class of state estimators, including linear observers, observers for input-affine systems, observers for Lipschitz systems, observers based on the circle criterion, high-gain observers, standard and extended Kalman filters. Simulation results confirm the effectiveness of both the stubborn and dead-zone redesigns.

Adaptive Generalized Sidelobe Canceler Beamforming With Time-Varying Direction-of-Arrival Estimation for Arrayed Sensors

Adaptive generalized sidelobe cancelers (GSCs) have been widely used to enhance the desired signal and instantaneously suppress interference signal and noise. However, the GSC beamforming method must know the direction of arrival (DOA) of the desired signal in advance. In this paper, we consider the case of a sensor array application in free-field air in which the target signal source is moving, leading to a time-varying DOA problem. Through analysis of the GSC output error signal, we propose an effective method for estimating the time-varying DOA for a GSC. The new method avoids the intensive complexity requirements of conventional DOA estimation algorithms such as the multiple signal classification algorithm and estimation of signal parameters via rotational invariant techniques. In addition, the convergence performance of adaptive GSC algorithms suffers from an error signal in the presence of the desired signal. A simple augmented Kalman filter (AKF) is employed to calculate the beamformer’s weighting coefficients, removing the influence of the desired signal from the GSC output to improve the convergence performance. A simulation evaluation of the signal-to-interference-plus-noise ratio (SINR) revealed that the AKF algorithm combined with the new DOA tracking method has a better convergence rate and SINR performance than other adaptive GSC algorithms of similar complexity such as the standard Kalman filter and recursive least squares.

Modification of Standard Kalman Filter Based on Augmented Input Estimation and Deadbeat Dissipative FIR Filtering

ABSTRACT This paper presents modification of standard Kalman filter (KF) based on augmented input estimation (AIE) and deadbeat dissipative FIR filtering (DDFF) for maneuvering target tracking. Although KF is a well-known tool in estimation and tracking but it has two weaknesses, disability in maneuvering motions and lack of robustness against temporary model uncertainty. For the first problem, the AIE is proposed to cover both the non-maneuvering and maneuvering parts of motion and so the maneuver detection procedure is eliminated. This model with an input estimation (IE) approach is a special augmentation in the state space model which considers both the state vector and the unknown input vector as a new augmented state vector. Also, KF is based on infinite impulse response (IIR) structure and cannot be robust against temporary model uncertainty. Unlike IIR, finite impulse response (FIR) filter is robust and stable against model uncertainty. So, for the second problem, an extra type of FIR filter named DDFF is introduced in this paper that not only has the intrinsic properties of FIR but also can improve these features by tuning some weighting parameters. In the last examples of the paper, the advantages of the proposed model against other models are shown.

Acoustic Robust Velocity Measurement Algorithm Based on Variational Bayes Adaptive Kalman Filter

Acoustic Doppler velocity logs or acoustic Doppler current profilers, herein referred to as Doppler sonar, are important types of oceanographic instruments, which have been extensively used over the past 30 years. The precision of Doppler sonar is an important technical specification, which is a statement of velocity random error that partially or entirely averages out over a long period of time. This article focuses on acoustic robust velocity processing algorithm based on variational Bayes adaptive Kalman (VBAK) filter, known as the real-time estimation of velocity statistical characteristics, which may be contaminated by some unknown and nonstationary noise. It aims to solve the problem that the precision of the Doppler sonar is prone to be affected by the marine environment. The theory, simulation, and experimental results are compared with the standard Kalman filter algorithm. It shows that the VBAK algorithm may obtain a reasonable estimate of velocity even in the case of steep slope over 15° and the precision is effectively improved.

A correlational inference-based unscented total Kalman filter for integrated navigation

An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.

Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts

We introduce a new class of stochastic volatility models with autoregressive moving average (ARMA) innovations. The conditional mean process has a flexible form that can accommodate both a state space representation and a conventional dynamic regression. The ARMA component introduces serial dependence, which results in standard Kalman filter techniques not being directly applicable. To overcome this hurdle, we develop an efficient posterior simulator that builds on recently developed precision-based algorithms. We assess the usefulness of these new models in an inflation forecasting exercise across all G7 economies. We find that the new models generally provide competitive point and density forecasts compared to standard benchmarks, and are especially useful for Canada, France, Italy, and the U.S.

MULTI-FACTOR BUILDING DEFORMATION ANALYSIS AND PREDICTION MODEL BASED ON MULTI-SOURCE DATE

Abstract. Normally, when using standard Kalman filter to analyze and predict the buildings deformation, the influence of a single factor is generally considered, or some factors are selected subjectively. In many cases, the objective influence of multiple effective factors on the model cannot be really considered, which adversely affects the accuracy of the model prediction and then affects the adaptability and prediction accuracy of the model. Aim at this problem, in this paper, we introduced grey relational analysis to determine the factor choice by calculating the grey relational grade of each impact factor. Then, we regarded the selected factors as state input vectors. Finally, we incorporated the state input vectors into model to establish grey relational Kalman filter model with considering multi-factors. In addition, we compared and analyzed the grey relational Kalman filter model with the stepwise regression model and BP neural network model that both can take into consideration the influence of multiple factors. The result of example analysis shows that the grey relational Kalman filter model can effectively select the factor which has great influence on deformation into the model as the state input vector during the modeling process, and the prediction accuracy of the recursive algorithm of standard Kalman filter is improved. Compared with the stepwise regression model and BP neural network model, the self-adaptability of the grey relational Kalman filter model is improved and the accuracy of the prediction results is also higher.

Aircraft Trajectory Tracking Using Radar Equipment with Fuzzy Logic Algorithm

Radio-electronic means, including equipment for transmissions, radio-location, broadcasting, and navigation, allow the execution of various research missions and combat forces management. Determining the target coordinates and directing the armament towards them, obtaining and processing data about enemies, ensuring the navigation of ships, planes and outer atmospheric means, transmitting orders, decisions, reports and other necessary information for the armed forces; these are only some of the possibilities of radio-electronic technology. Fuzzy logic allows the linguistic description of the laws of command, operation and control of a system. When working with complex and nonlinear systems, it can often be observed that, as their complexity increases, there is a decrease in the significance of the details in describing the global behavior of the system. Even though such an approach may seem inadequate, it is often superior and less laborious than a rigorous mathematical approach. The main argument in favor of fuzzy set theory is to excel in operating with imprecise, vague notions. This article demonstrates the superiority of a fuzzy tracking system over the standard Kalman filter tracking system under the conditions of uneven accelerations and sudden change of direction of the targets, as well as in the case of failure to observe the target during successive scans. A cascading Kalman filtering algorithm was used to solve the speed ambiguity and to reduce the measurement error in real-time radar processing. The cascade filters are extended Kalman filters with controlled gain using fuzzy logic for tracking targets using radar equipment under difficult tracking conditions.