Research On Constrained Nonlinear Filtering And Its Application For Target Tracking

Nonlinear dynamic systems are widely used in the fields of the rocket guidance and control,inertial navigation of aircraft and ships,satellite orbit and attitude estimation,radar or sonar detection and target tracking.In the past 20 years,many different nonlinear filtering theories have emerged,and among them,the unscented Kalman filtering and the particle filtering are the representative methods.Numerous practical dynamic systems involve constraints which arise from physical laws,mathematical properties,physical conditions,etc.How to establish a mathematical model which conforms to the physical principles and is consistent with the available measurement quantity,attribute and precision is a difficult and hot issue for the optimal control and estimation field.And then,the controllability and observability of the dynamic system can be improved.Yet,there is no unified principle and system for the compatibility,consistency,and redundancy between the constraints and physical models.Depending on the mathematical model features of the system and the statistical properties of the measurement error,the difficulty to solve the problem may be solved small,or it may be complicated to misunderstood fundamentally.Constrained nonlinear filtering techniques are currently involved less in target tracking and meanwhile are the key technical issues.The thesis focuses on the work that the soft constraints of the measurement information are constructed as the mathematical model and incorporated into the evolution of the nonlinear filtering algorithm.The proposed algorithms are applied for the bearings-only maneuvering target tracking,and the impact of the environment on the state estimation can be reduced and the filtering performance can be improved.The main achievements of the dissertation are given as follows:1.A constrained extended Kalman filtering(CEKF)algorithm for the nonlinear Gaussian mode is proposed.The traditional extended Kalman filtering algorithm linearizes the nonlinear function.The Kalman filter gain is no longer decoupled from the state prediction,and depends on the measurement sequence containing noise.Therefore,when the system nonlinearity is strong or the measurement uncertainty is large,it is difficult to obtain the theoretical steady state solution,which is easy to cause filter divergence.The proposed CEKF algorithm is similar to the traditional extended Kalman filter algorithm.The difference is that the statistical noise boundary constraint in the dynamic system is established as a mathematical model consistent with the measurement variance.The feasible domain is constructed based on the maximum posterior probability criterion,and the feasible set is selected to update.Simulation results show that the proposed algorithm effectively reduces the high-order truncation error of extended Kalman filter and enhances the computational stability of nonlinear dynamic systems.2.A constrained unscented Kalman filtering(CUKF)algorithm for the nonlinear Gaussian distribution mode is proposed.In the traditional unscented Kalman filtering(UKF)algorithm,in the view of the statistical point,the posterior distribution is approximated by selecting some Sigma points,it is restricted to the hypothesis that the state posterior should be a unimodal Gaussian distribution.Therefore,when the equivalent measurement likelihood is multi-peak distribution or the current measurement information is more accurate,the algorithm cannot effectively describe the true posterior distribution.In order to improve the credibility of the measurement information at the current moment,the proposed CUKF filtering algorithm constructs a feasible area by establishing a mathematical model for the soft-constrained information of the physical dynamic system,and constructs an objective function according to the nonlinear least-squares criterion.The sparse regularization operator is added to implement constrained optimization.In order to take advantage of the feedback of historical measurement information and the adaptability of current measurement information meanwhile,the CUKF filtering algorithm performs the unscented Kalman filtering update for state in the different sub-regions based on the original and modified prior probability density functions.The weighting factor is determined by the fuzzy logic function,and the true state posterior distribution is approximated by Gaussian mixture weighting.Simulation results show that compared with the traditional UKF algorithm,the proposed CUKF filtering algorithm effectively smooths the outliers of the update process,weakens the influence of the multimodal measurement likelihood distribution,and improves the dynamic system filtering accuracy.3.A constrained particle filtering(CAPF)algorithm for nonlinear non-Gaussian modes is proposed.Conventional particle filtering(PF)can effectively deal with nonlinear non-Gaussian problems.However,due to the lack of current measurement information,the particle degradation and sample impoverishment are serious.Considering the influence of the current measurement information on the update of the importance probability density function,the CAPF algorithm uses the auxiliary particle filtering(APF)algorithm framework to integrate the current statistical measurement with constrained noise and the target feature auxiliary variables into the update of the modified prior probability.Following the optimal Bayesian consideration of the measurement information at all times,the CAPF algorithm constructs a mixed importance density function based on the original and modified prior probability density functions with the fuzzy weighted factors.Thus,the feasible set with high likelihood probability is selected to approximate the true state posterior distribution.Simulation results show that compared with the traditional PF filtering algorithm,the proposed CAPF filtering algorithm improves the diversity and accuracy of real-time sequential importance sampling particles for the non-periodic sparse sampling scenarios.4.A constrained multiple model particle filtering(CMMPF)algorithm for nonlinear non-Gaussian dynamic multi-model models is proposed.Due to the uncertainty of the target maneuvering motion and the ambiguity of the measurement information,the multi-model filtering system has problems of the dynamic model switching delay and state estimation error.According to the Rao-Blackwellised theory,the proposed CMMPF filtering algorithm divides the maneuvering target tracking problem into two sub-prolbems: state model estimation and model state estimation;The state model is selected by the modified sequential importance resampling algorithm;The model state is estimated by the particle filtering with the bilateral limiting constraints and the assisted target spatial-time features;And the latter introduces the constraint prior konwledge to the dynamic model switching mechanism through the feedback mechanism.Compared with the traditional multiple model adaptive estimator(MMAE)algorithm and the interacting multiple model(IMM)filtering algorithm,the proposed CMMPF filtering algorithm effectively improves the efficiency and accuracy of dynamic model switching.The above four sections are complemented each other and comprise a systematic series of constrained nonlinear filtering algorithms.They provide some new views and the corresponding technical support for solving the bearings-only maneuvering target tracking problem in the complex environments.