Research On Estimation Performance Of Optic-electric Tracking Systems With Intermittent Observations And Filters Development

Optic-electric tracking systems are indispensable detection equipments in development of fire control systems. Fast acquiring targets and accuracy tracking targets depend on accuracy estimation of target motion parameters. However, during practical tracking processes, detection probability of optic-electric systems is always less than one, due to shading of obstacles (drifting clouds, etc), interference of weather conditions (fog, etc), limited detectability of detection equipments (laser, etc), faults of detection equipments and noises working environment, etc. Generally, estimation performance of optic-electric tracking systems with intermittent observations is analyzed using extrapolating technology with thoughts of complete observations. Recently, international scholars pay more attention to estimation theory with intermittent observations and obtain some valuable results, and basic theoretical system is established. Considering that estimation performance of optic-electric tracking systems degenerates significantly when there is a drop of detection probability with intermittent observations, based on requirements of engineering design and equipment development, using estimation theory of intermittent observations, thorough research on estimation performance and performance enhancement technology of optical-electric tracking systems with intermittent observations is conducted from fully exploiting angle redundant information, introducing angle velocity information and distributed networking of optic-electric tracking systems. Theoretical analysis and simulation research show that these technologies can effectively improve estimation performance of optical-electric tracking systems. The major research results are summed up as follows:(1) A residual test algorithm based on posterior confidence is presented. The new algorithm firstly adds a test threshold based on traditional residual test algorithm, and then the residuals between the two thresholds can be fuzzed by means of fuzzy membership function and the likelihood probability of residuals can be obtained, and combined with the prior detection information, the posterior confidence of detection data can be calculated. Therefore the detection situation of tracking system can be determined based on the calculated posterior confidence. Then, with intermittent observations, an unbiased converted measurement Kalman filtering (UCMKF) and a target tracking filtering of linear least unbiased estimation (BLUE) are designed based on the proposed residual test algorithm. The Cramer-Rao low bounds (CRLB) of tracking system is also presented under the statistic significance, and an upper and lower bound of average of estimation error covariance can be conveniently calculated with given detection probability.(2) The existence of critical detection probability of optic-electric tracking system is proved, and an upper and lower bound of critical detection probability is presented. The upper bound is described as the optimal solution of a nonlinear matrix inequality (NMI), and the lower bound is only related to eigenvalues of system state transition matrices. An iterative linear matrix inequality (ILMI) algorithm for solving the upper bound of critical detection probability is proposed by means of perturbation linearization. That provides theoretical basis for design of detection probability of optic-electric tracking system.(3) For optic-electric tracking system composed of laser range finder and precision angle measurement equipment with intermittent observations, a federated filter is designed based on the posterior confidence residual test algorithm. Firstly, the position detection channel of traditional optic-electric tracking systems is decomposed into two independent detection channels according to physical structure, and the CRLB model of the independent detection channels is presented. Then, target motion states are respectively estimated by use of the detection data of the two channels, and a global state estimate can be obtained by fusing the two state estimates. Finally, the information sharing of the federated filter is done according to the global state estimate and the posterior confidence of detection channels. Monte-Carlo simulation and measured data show that the proposed tracking filter can obviously improve estimation performance of tradition optic-electric tracking systems by mining redundant angle measurements without increasing any hardware cost, and the root mean square of estimate error (RMSE) of the proposed tracking filter is closed to the average CRLB of tracking systems.(4) A design idea, which is introducing angle velocity measurements of elevation and azimuth into traditional optic-electric tracking systems, is proposed, and a target tracking filter based on posterior confidence weighted fusion is designed with intermittent observations. Firstly, a measurement model for the new type of optic-electric tracking systems is built, and then using the nested conditioning method, the consistent estimate of the first two moments of converted measurement errors is derived. Secondly, for the four different detection cases of position and velocity detection channels, four sub-filters are designed respectively whose posterior confidences are calculated based on the detection cases of the channels, and then the output of the tracking filter is obtained by means of weighting the outputs of sub-filters with the corresponding posterior confidences. Finally, the statistic average of CRLB for tracking systems is presented. Monte-Carlo simulation results show that, with intermittent observations, the performance of optic-electric tracking systems with angle velocity measurements can be significantly improved as compared with that of traditional systems. Moreover, the RMSE of the designed tracking filter is closed to the average CRLB of tracking systems.(5) A distributed Kalman fusion algorithm is proposed for distributed optic-electric tracking systems with colored measurement noises. The principle of the algorithm is that system states are divided into two uncorrelated parts and then the two parts are sequentially treated by non-augmented state Kalman filtering and distributed state fusion. It is proved that the distributed state fusion is equivalent to centralized Kalman fusion. Furthermore, the influence on distributed tracking systems of feedback structure is analyzed, and a modified distributed Kalman fusion algorithm is given for distributed tracking systems with colored measurement noises and feedback. Theory analysis and Monte-Carlo simulation show that the estimation performance of the proposed distributed fusion filter can be obviously improved as compared with that of local tracking filters, and it can be conveniently applied in the situation of real-time processing.