Research Of Filter Algrithms For Non-ideal Measurements

Filtering is a method to estimate the random signal from noisy measurements,which is widely used in detection,target tracking and navigation.However,in the actual application nowaday,due to wide use of network circumstances and influences of some unpredictable factors,heavy-tailed non-Gaussian measurement noise may appear;due to the limitation of sensor bandwidth,network congestion often occurs;due to the influences of transmission medium,transmission mechanism and unreliable network,transmission signal will inevitablely appear the phenomena of one-step randomly delayed measurement,missing measurement and censored measurement.The uncertain measurements mentioned above are different from the measurement forms used by the tranditional filters,and we define them non-ideal measurements.The appearance of these measurements makes the standard measurement model need to modify,and the tranditional filters also need to be modify accordingly to adapt to these measurement models.In this paper,we will investigate the measurement models and filter algorithms mentioned above,including measurement noises with heavy-tailed distribution;robust filter algorithms for linear and nonlinear discrete systems under this kind of noise;lower bound of variance of robust filtering estimation for linear systems;recursive estimation for censored sensor system with one-step transmission delay or transmission loss;a robust marginal particle filter algorithm and a robust particle filter for one-step randomly delayed measurements and heavy-tailed measurement noise.The specific research work is as follows:For the problem of static and non-static heavy-tailed measurement noise model,Student's t distribution,Gaussian-Student's t mixed distribution and skewed Student's t distribution are used to build model respectively,then the statistical properties of these distributions are derived.For the cases with censored sensor and system measurement uncertainties,Tobit measurement model is defined;and the measurement uncertainties such as one-step random measurement delay,measurement loss,random measurement matrix and multiplicative measurement noise are given;in addition,the tranditional filtering theroy to be modified is also described.For the filtering problem of linear discrete system with non-ideal heavy-tailed measurement noise,which is modeled as Student's t-distribution.Variational Bayes(VB)method can decompose the estimation of multivariate parameters into univariate estimation.An approximate Kalman filter(KF)algorithm is designed by using this VB method.The recursive formula for the approximate posterior PDFs of parameters and states is derived in detail.Then,the asymptotic Bayesian Cramer-Rao lower bounds for the proposed filter are given.Numerical simulations verify the superior performance of the proposed filter and the correctness of proposed variance lower bounds under time-varying measurement noise.The efficiency of the proposed filter is also demonstrated by a real shipborne test data of SINS / Doppler integrated navigation.For the filtering problem of non-ideal measurements of random one-step transmission delay and censoring in sensor networks,these two random phenomena are described by two Bernoulli random variable squences,in which the censored variable is dependent on the delay variable.The probability of the transmission signal being uncensored is given by the local approximations using a priori and a posteriori of the state estimation.Then,a novel measurement model that incorporates both the censoring random matrix and the signal delay is established.Based on this model,an optimal recursive estimation method is proposed for systems with specified two uncertainties by making use of an innovation analysis approach and a weighted conditional expectation formula.The superior performance of the proposed method will be verified by a typical oscillator simulation example.For the problem of transmission loss and measurement censoring in sensor networks system,random transmission loss is described by a Bernoulli variable set.Then,the standard Tobit measurement model is modified by using censoring random matrix and translation transformation.Uncensored probability of latent measurement is computed,which includes the case of pure noise for the lost measurement.From this probability,an optimal recursive estimation method is derived by innovative analysis and total expectation rule.The effectiveness of our proposed method is demonstated by the oscillator simulation and comparison with other existing algorithms.For the problem of non-ideal measurement noise of time-varying or outlier in nonlinear discrete system,Student-t distribution is used to model the measurement noise.Combined with variational Bayes,a novel particle filter(PF)is designed,which can estimate all parameters of t-distributed measurement distribution including mean parameter as well as state.Further,particle filter with noise correlation at the same epoch,which is applicable for time variant measurement noise,is developed.For verifying the performances of the proposed algorithms,the simulations on the typical univariate non-stationary growth model are performed under the different noise conditions in detail.The outcomes show that the proposed algorithms have the superior performances to the compared ones.In navigation or target tracking,for the problem that the state equation is linear,the measurement equation is nonlinear,and the variance of Gaussian white noise is time-varying,two Rao–Blackwellised particle filters are developed.The mixed state is estimated by KF and PF alternately,and measurement variance is estimated by VB.Simulation on example of target tracking demonstrates that the performance of proposed method is superior to that of the Rao-Blackwellised particle filter only when variance of measurement noise is time-variant.Finally,a robust particle filter algorithm for nonlinear systems with one-step randomly delayed measurements and outlier corrupted measurement noise is investigated.To address the issue of measurement outliers,a Student's t distribution is utilized to model the measurement noise.The random delay uncertainty is identified by a Bernoulli random variable,based on which the measurement likelihood PDF with weighted sum of two t-distributions is transformed into an exponential multiplication form.The state estimation is obtained by Bayesian recursion.Then,by using variational Bayesian approach,the latent random variables and Bernoulli random variable are estimated together.The superior performance of our proposed method is verified through a typical example by comparing with existing particle filters that consider random measurement delay and heavy-tailed measurement noise seperately.