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In the target tracking system, sensor measurements may arrive at the fusion center out of sequence because of the different communication delays, which results in the Out-of-Sequence Measurement(OOSM) problem. In order to solve one-step-lag OOSM problem with corrected process noise and measurement noise in nonlinear system, a new algorithm has been proposed. By combing the framework of the forward prediction filtering, wipe off the correlation, and use Particle filtering to estimate the state. Simulations verify the effectiveness of the proposed algorithm. Introduction In a centralized multi-sensor target tracking system, various sensors have different sampling rates, pretreatment time and communication delay , measurement synchronizations are difficult to ensure, which can cause measurement from the same target arrive to the fusion center out of sync, the asynchronous problem occurred [1,2,3]. Further, there will be a phenomenon that the measurement observed earlier arrives later, which can be called OOSM(Out-of-Sequence Measurement) phenomenon. And the traditional filtering algorithm cannot directly handle these OOSM, need to study the corresponding filter algorithm. At present, the most suitable for the real-time processing of OOSM is direct update method, using OOSM and target state estimator in full stored to update the current state estimation, working out a new state estimation and estimation error covariance matrix [5]. On account of the small storage volume and calculated amount of direct update method, and no lag output, scholars have proposed the A1, B1, AA1 linear filtering algorithm to deal with OOSM. For weakly nonlinear Gaussian system, [4] discusses EKF-A1 algorithm, linearize the nonlinear system, and apply the existed A1 algorithm to it . The above algorithm is relatively simple, but there may be a larger filtering error. UT transform was proposed to solve jacobian matrix or hessian matrix of nonlinear measurement equations, but this method cannot apply to the situation that the system equations is nonlinear, and the approximation error is bigger. For strongly nonlinear system, particle filter was presented to solve the OOSM problem in [6][9], but process and measurement noise was not taken a sufficient consideration. When observations in common environment, may be interfered by the same noise, the process noise and measurement noise is often corrected. Some algorithms were raised to address the corrected problem in [7][8], but they worked only when the system was linear. Aiming at this, under the forward prediction framework, nonlinear system equations are identical transformation to be uncorrected, and then update the state with particle filter. Algorithm can effectively deal with one-step-lag OOSM problem. Formulation of the problem Consider a target dynamic model evolving from 1 k t − to k t ( ) , 1 1 , 1 , 1 k k k k k k k k x f x w − − − − = + Γ (1) ( ) k k k k z h x v = + (2) where, , 1 k k f − is the state transition matrix to time k t from time 1 k t − , ( ) k h  is the measurement 5th International Conference on Advanced Materials and Computer Science (ICAMCS 2016) © 2016. The authors Published by Atlantis Press 791 matrix, 1 k− Γ is noise input matrix, , 1 k k w − is the process noise for this interval, k v is the measurement noise, k z is the measurement of sensor at time k t , the process and measurement noise is white gaussian noise. Assumption 1 , 1 k k w − and k v is corrected, its statistical characteristics are as follows ( ) ( ) , 1 , 1 , 1 ,Cov , T k k k k j j k kj E w q w w Q δ − − − = = ( ) ( ) ,Cov , T k k j k kj E v r v v R δ = = ( ) , 1 Cov , T k k j k kj w v S δ − = where, k Q is the negative definite symmetric matrix, k R is symmetric positively defective matrix, kj δ is kronecker δ − function. Assumption 2 The initial state ( ) 0 x is not corrected to , 1 k k w − or k v , its statistical characteristics are as follows ( ) 0 0 x̂ E x = ( ) ( ) ( ) ( ) ( ) 0 0 0 0 ˆ ˆ 0 0 T P Cov x E x x x x   = = − −   by (1) ( ) , , , k k d d k d k d x f x w = +Γ (3) At time k t one has | | ˆ | , | k k k k k k k k x E x Z P Cov x Z           (4) where k Z is the cumulative set of measurement at time k t . Subsequently, the earlier measurement from time d t , denoted from now on with discrete time notation as d , ( ) d d d d z h x v = + (5) arrives after the state estimate (4) has been calculated. As shown in fig.1. The problem is as follows: update the posteriori distribution ( ) 1: | k k p x z with OOSM d z , to obtain ( ) 1: | , k k d p x z z , so that the latest state estimate and the covariance matrix can be calculated. The arrival time of the measurement The observe time of the measurement Zk-1 Zk-2 Zk Zd tk-1 tk-2 tk td Fig.1 One-step-lag OOSM situation Algorithm design Aiming at last given nonlinear discrete system, considering the same time process noise and measurement noise corrected situation, put forward to solve the problems of the one-step-lag OOSM filtering algorithm. Solve the corrected process noise and measurement noise The measurement equation can be rewritten as ( ) 0 k k k k z h x v − − = (6) then (1) can be expressed as

Update Algorithm on One-Step-Lag Out-of-Sequence Measurement with Correlated Noise Based on Particle Filter