Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

This paper proposes a novel strong tracking filter (STF), which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF) based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF) algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP). Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments

Continuous stirred tank reactor fault detection using higher degree Cubature Kalman filter

Continuous Stirred Tank Reactor (CSTR) plays a major role in chemical industries, it ensures the process of mixing reactants according to the attended specification to produce a specific output. It is a complex process that usually represent with nonlinear model for benchmarking. Any abnormality, disturbance and unusual condition can easily interrupt the operations, especially fault. And this problem need to detect and rectify as soon as possible. A good knowledge based fault detection using available model require a good error residual between the measurement and the estimated state. Kalman filter is an example of a good estimator, and has been exploited in many researches to detect fault. In this paper, Higher degree Cubature Kalman Filter (HDCKF) is proposed as a method for fault detection by estimation the current state. Cubature Kalman filter (CKF) is an extension of the Kalman filter with the main purpose is to estimate process and measurement state with high nonlinearities. It is based on spherical radial integration to estimate current state by generating cubature points with specific value. Conventional CKF use 3rd degree spherical and 3rd degree radial, here we implement Higher Degree CKF (HDCKF) to have better accuracy as compared to conventional CKF. High accuracy is required to ensure no false alarm is detected and furthermore good computational cost will improve its detection. Finally, a numerical example of CSTR fault detection using HDCKF is presented. Implementation of HDCKF for fault detection is compared with other filter to show effective results

Driver behaviour modelling of vehicles at signalized intersection with heterogeneous traffic

Roads network is composed of mid-blocks and intersections. The part where two roads cross is called an intersection whereas the straight sections without intersection or any other interuptions is called mid-block. It can be observed that the vehicles on the mid-blocks tend to achieve their free-flow speeds while those at the intersections are forced to decelerate. Modelling of these sections needs to separate the intersections from mid-block. Further, drivers behave differently at these two locations. Present study attempts to separate the intersection zone of influence (IZOI) and mid-block using the manoeuvring characteristics of drivers in terms of acceleration/deceleration. These were captured through a global positioning system (GPS) device in the vehicle after sighting a red signal at the intersection. Further, this study also tried to observe whether different classes of drivers such as aggressive, normal or timid drivers, based on acceleration/deceleration behaviour exists. A junction with 1-km straight stretch in R. K. Puram New Delhi (India) was chosen for the study to find the IZOI. After identifying IZOI a video data was collected in Mumbai (India) for a stretch more than 200-m long near intersection where the red signal was visible; This enabled observing the driver behaviour more closely. Around 900 drivers of different modes were analysed to understand their behaviour. It was found that cars start reducing its speed at 160 m, motorized three-wheelers at 124 m and buses start reducing their speeds at 98 m distance from the intersection. The driver behaviours were distinct in each of the mode (Bus, Car and motorized-there-wheelers), but it emerges that the drivers cannot be classified into finite number of clusters based on the fitted normal distribution. Thus it can be seen that there are no clearly demcarcated driver behaviours irrespective of the vehicle type, such as aggressive, normal and timid categories as the intersection approaches. A normal distribution model can classify the drivers satisfactorily

Filtragem Não Linear Adaptativa e Seguimento Radar Ótimo de Veículos Aeroespaciais

A filtragem não-linear é um dos tópicos mais importantes e complexos em engenharia, especialmente quando aplicada a situações de tempo-real em ambientes altamente não-lineares. Este é o cenário da maioria das aplicações aeroespaciais nomeadamente, aviso de colisão, seguimento radar, vigilância, orientação, navegação e controlo de veículos aeroespaciais, sendo que o principal objetivo é a estimação dos estados de um determinado alvo (seja este uma aeronave, satélite, míssil ou outro) a partir de medições ruidosas. A maior dificuldade está em desenvolver métodos que sejam capazes de lidar não só com a não-linearidade dos modelos, mas também com as incertezas associadas aos instrumentos de medições e às perturbações existentes no meio envolvente que afetam diretamente o sistema e, na sua maioria, são difíceis de prever e computar. Uma das estratégias mais utilizadas para garantir o ajuste dinâmico e ótimo dos métodos de filtragem face a todas estas adversidades é a implementação de algoritmos adaptativos. Assim sendo, a abordagem mais utilizada para lidar com esta problemática é a filtragem de Kalman. O seu sucesso, principalmente na área de engenharia, deve-se na sua maioria ao filtro de Kalman estendido (EKF – Extended Kalman Filter). Este assenta no pressuposto de que a linearização é suficiente para representar localmente a não-linearidade do sistema e, por conseguinte, o algoritmo utiliza o modelo linearizad0 em substituição ao modelo original não-linear. A linearização é um processo relativamente fácil de compreender e aplicar, o que justifica a popularidade do filtro. Contudo, ao lidar com sistemas altamente não-lineares, o EKF tende a apresentar algumas limitações, tais como, estimativas erráticas, comportamentos instáveis e por vezes até divergentes. De forma a colmatar algumas destas limitações, esta tese apresenta um filtro de Kalman estendido melhorado e adaptativo, denominado por improved Extended Kalman Filter (iEKF), onde para além da adaptabilidade clássica das matrizes de ruído, é proposto uso da norma de Frobenius como fator de correção da estimativa da covariância a priori e é também proposto um novo ponto de linearização. Desta forma, o iEKF adapta as matrizes de transição dos modelos através do novo ponto de linearização e adapta as informações estatísticas através da matriz de covariância proposta. A principal intenção é manter a simplicidade e estrutura pelo qual o EKF é conhecido, porém melhorar o seu desempenho e precisão com conceitos simples, eficazes e adaptativos. Um outro foco desta tese é analisar o desempenho da filtragem no seguimento radar. Assim sendo, tanto o EKF como o iEKF foram implementados e analisados em quatro aplicações deste âmbito, sendo estas: a estimação de uma órbita de um satélite artificial, a estimação de uma transferência orbital (transferência de Hohmann), a estimação de uma reentrada na atmosfera, e por fim, a estimação da trajetória de uma aeronave comercial, em que objetivo é estimar a posição e velocidade do veículo. Tanto o EKF como o iEKF foram analisados e comparados com base no RMSE (Root Mean Square Error). Os resultados demonstram que o iEKF fornece estimativas superiores. O algoritmo é, em geral, mais preciso, estável e confiável, demonstrando ser uma alternativa conveniente ao clássico EKF. Em suma, esta tese propõe um novo método de filtragem não-linear adaptativo, denominado por iEKF. Os resultados indicam que este deve ser tido em consideração para a estimação de estados não-linear tanto para o seguimento radar, como para qualquer outra área que necessidade de um algoritmo de filtragem eficiente.Nonlinear filtering is an important and complex topic in engineering, especially when applied to real-time applications with a highly nonlinear environment. This scenario involves most aerospace applications, such as surveillance, guidance, navigation, attitude control, collision warning and target tracking, where the main objective consists of estimating the states of a moving target (aircraft, satellite, missile, spacecraft, etc.) based on noisy measurements. The challenge is to develop methods that are capable to cope, not only with the nonlinearities of the models but also with the instrumental inaccuracies related to the data acquisition system and the environmental perturbations that are unwanted and, in most cases, difficult to compute. One of the promising strategies to dynamically adjust and guarantee filter optimality is the computation of adaptative algorithms. A very well-known framework to deal with those problems is the Kalman filter algorithms, whose success in engineering applications is mostly due to the Extended Kalman Filter (EKF). The EKF is based on the assumption that a local linearization of the system may be a sufficient description of nonlinearities, therefore the linearized model is used instead of the original nonlinear function. Such approximations are easy to understand and apply, which explains the popularity of the filter. However, when dealing with highly nonlinear systems, the EKF estimates suffer serious problems, such as unstable and quickly divergent behaviours and/or erratic estimates. To address those limitations, this thesis proposes an improved Extended Kalman filter (iEKF) with an adaptative structure, where a new Jacobian matrix expansion point is proposed, and a Frobenius norm of the covariance matrix is suggested as a correction factor for the a priori estimates. Therefore, the iEKF does not only update the statistical information based on the proposed covariance matrix but also updates the state and measurements transitions matrices based on the new Jacobian expansion point. The core idea is to maintain the EKF structure and simplicity but improve the overall performance with simple yet effective concepts. Another objective of this thesis was to evaluate the performance of the filtering methods on radar tracking applications. Thus, the effectiveness of EKF and iEKF were analysed and compared in four radar tracking applications: an artificial satellite orbit estimation, a Hohmann orbit transfer, an atmospheric reentry estimation, and a commercial aircraft trajectory estimation, where the position and velocity of the aerospace vehicle were computed. The EKF and iEKF were compared based on the RMSE (Root Mean Square Error). Simulations results suggest that the iEKF provides a considerably higher accuracy on the overall results. The algorithm is more precise, stable, and reliable, which make it an attractive alternative to the classic EKF. In summary, this thesis proposed an improved Extended Kalman Filter with an adaptative structure. This algorithm is a promising method for nonlinear state estimation, not only for radar tracking applications but any applications that require an efficient nonlinear filter

Interacting Multiple Model (IMM) Fifth-Degree Spherical Simplex-Radial Cubature Kalman Filter for Maneuvering Target Tracking

For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF) is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM) filter and the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF). The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with the interacting multiple model unscented Kalman filter (IMMUKF), the interacting multiple model cubature Kalman filter (IMMCKF) and the interacting multiple model fifth-degree cubature Kalman filter (IMM5thCKF)

Mixed-Degree Spherical Simplex-Radial Cubature Kalman Filter

Conventional low degree spherical simplex-radial cubature Kalman filters often generate low filtering accuracy or even diverge for handling highly nonlinear systems. The high-degree Kalman filters can improve filtering accuracy at the cost of increasing computational complexity; nevertheless their stability will be influenced by the negative weights existing in the high-dimensional systems. To efficiently improve filtering accuracy and stability, a novel mixed-degree spherical simplex-radial cubature Kalman filter (MSSRCKF) is proposed in this paper. The accuracy analysis shows that the true posterior mean and covariance calculated by the proposed MSSRCKF can agree accurately with the third-order moment and the second-order moment, respectively. Simulation results show that, in comparison with the conventional spherical simplex-radial cubature Kalman filters that are based on the same degrees, the proposed MSSRCKF can perform superior results from the aspects of filtering accuracy and computational complexity