Study On Curve Fitting Prediction Models And Algorithms Of Target Tracking

Target tracking is a problem of state estimation for hybrid systems, namely, estimating the target state by use of sensor observations and finding the target position via filtering the random noise. From the perspective of data fusion, target tracking in essence is a process of fusing model and observation information, reducing the position estimation error, by choosing a filtering algorithm as accurate as possible. This dissertation is divided into two parts. The first part studies the motion models of target tracking, and attempts to build the prediction models by curve fitting method. The second part improves the nonlinear filtering algorithms from the perspective of information fusion.The main innovations of this dissertation are as follows:Firstly, Using weighted least squares fitting to the signal of polynomial prediction, this obtains the noise covariance of existing prediction coefficient. The results extended the range of application of literature [27] which used Lagrange multiplier of polynomial signal signals prediction, not required noise independent distribution, and with a general formula has given all the order number polynomial signals and all window length, it is more systematic to understand and describe the problems. Because to allow for noise covariance to exist, by increasing the length of the window, it can also smooth polynomial signal.Secondly, this dissertation analyzes the first and second order curve fitting prediction model and CV, CA model in the equivalent of the precision filter. At the same time, the curve fitting prediction model has the following advantages:(1) need not set sampling interval parameters, reduced dependence on the a priori knowledge;(2) because all components in the state space with the same dimension, makes the complexity of the noise matrix greatly reduce;(3) No mechanical analysis and concise form, easy to high order expansion. On this basis, this dissertation integrates one dimensional curve fitting prediction model with the interactive multiple model (IMM) algorithm. Since mechanical analysis to the target is unnecessary in the curve fitting prediction models, so it can flexibly design model collection according to curve order number. In addition, the curve fitting prediction model is introduced to high order FM signals in tracking filtering, thus this avoids the Wigner-Ville distribution difficult to overcome a cross problem.Thirdly, this dissertation investigates the coupled motion of target with tangential acceleration and constant normal acceleration in two-dimensional plane and three-dimensional space plane, then builds the high-dimensional curve fitting prediction model for the motion pattern above. The model can be compatible with the one-dimensional second-order curve fitting prediction models. For uniform circular motion in two-dimensional plane and three-dimensional space plane, since the curvature radius are equal everywhere, the model can also give unbiased prediction; For logarithmic spiral motion in two-dimensional plane and three-dimensional space plane, the model can give an approximate prediction. In virtue of prediction without knowing the turning angular velocity and the sample intervals, Compared with existing turning models, the model proposed in this dissertation is more adaptable, but compared to uncoupled model, it has higher precision of the filtering.Generally, observation vector of target tracking usually consists of angle and distance. Regarding those filtering systems where the subsets of observed value and state value constitutes a bijective function, this dissertation puts forward the reverse estimates the values of the states from observation and the predicted values of the state equations proceeding fusion to realize the filtering. In the observation noise is smaller, the method is better than the existing information filtering algorithms. According to fusion issue of the multi-observed values in the target tracking, combining reverse estimation with the particle filter (PF), by using merged the reverse estimation values as pseudo observation and each particle to do a Kalman filter, to drag particles cloud to bring latest global observation information into the proposal distribution. Simulation results show that we get better filter effect than that of standard particle filter (PF) and unscented particle filter (PF) in sensor network tracking scene.Subsequently, this dissertation makes use of an improved particle swarm optimization algorithm-Quantum-behaved Particle Swarm Optimization algorithm (QPSO) to find the peak point with maximum state posterior probability density of particle filter. Then, we sample new particles near the peak point and assign a weight to each particle. This sampling near the peak point with maximum state posterior probability density (SMSPP) particle filter algorithm proposed by this dissertation eliminates the generational relation between particles and makes particle concentration in a the most effective area of depicting posteriori probability density, Thus, SMSPP particle filter algorithm makes a new attempt in dealing with inherent problems of particle filter (PF) such as degradation and efficiency reduction of particles. According to the weak observation noise and posterior probability density gaussian hypothesis, specific practical maximum posteriori sampling particle filter algorithm were put forward, simulation results show that this method, compared with the traditional algorithm has its advantages.At last, this dissertation investigates the state dimension higher than observation dimension of nonlinear filtering problems. We get the pseudo-observation vector and the pseudo-observation matrix by splitting state predictive values from the posterior state estimation values. Then the dimension reduction for the nonlinear filter with different dimensions can be realized by fusing the pseudo-observation vector and the pseudo-observation matrix with the global predictive values. This method is more concise and intuitive than those existing marginal particle filter algorithms. Integrating this method with SMSPP particle filter algorithm proposed above, we achieve the optimization when the observation vector and state vector have different dimensions. It extends the scope of application for SMSPP particle filter algorithm.