Method Of Measuring Differences Research Articles

Measurement Difference Method: A Universal Tool for Noise Identification

This article deals with noise identification of a system described by the linear time-varying state-space model using correlation methods. In particular, the stress is laid on the measurement difference method (MDM) as a universal tool allowing estimation of moments and parameters of the state and measurement noises. The recent results are summarized in a common framework and the full (and weighted) MDM implementation is developed. This implementation provides unbiased and weakly consistent estimate of an arbitrary raw or central moment of the state and measurement noises. The performance of the method is shown in a numerical study.

Poisson multi‐Bernoulli mixture filters with coloured measurement noise

To solve multitarget tracking (MTT) problems with coloured measurement noise, this study proposes a Poisson multi-Bernoulli mixture filter with coloured measurement noise (PMBM-CMN) and a robust PMBM-CMN filter. By using the measurement differencing method and state augmentation approach, the proposed PMBM-CMN filter transforms a state estimation problem with coloured measurement noise into a problem with white measurement noise. However, covariances of the true process and measurement noise in the proposed PMBM-CMN filter are time-varying and unknown, which may degrade the filtering performance. Therefore, a robust PMBM-CMN filter is proposed for estimating the augmented state, including the kinematic state, the predicted state covariance, and the white measurement noise covariance. For linear Gaussian systems, the augmented state is modelled as a Gaussian inverse Wishart inverse Wishart (GIWIW) distribution. The variational Bayesian method is also employed to guarantee the conjugacy of the GIWIW density. Simulation results demonstrate the ability of the PMBM-CMN filter to solve MTT problems with coloured measurement noise and show that the robust PMBM-CMN filter based on the GIWIW model (GIWIW-PMBM-CMN) has the best overall performance in comparison with existing state-of-the-art filters.

A new Gaussian approximate filter with colored non-stationary heavy-tailed measurement noise

The filtering issue of a nonlinear system with colored non-stationary heavy-tailed measurement noise (CNSHMN) is addressed in this study via designing a new Gaussian approximate filter. By utilizing the state expansion method and the measurement difference method, the nonlinear filtering problem with the one-step delayed state and the white non-stationary heavy-tailed measurement noise (NSHMN) after the difference is turned into the traditional nonlinear filtering problem with NSHMN. A Gaussian student t-mixed distribution (GSTM) with Bernoulli random variable is utilized to describe the differenced measurement noise. The state vector, intermediate random variables (IRV), mixed probability and Bernoulli random variable (BRV) are simultaneously inferred by introducing variational Bayesian (VB) technique. Target tracking simulation examples reveal that the proposed filter is superior to the existing methods in the nonlinear filtering issue of CNSHMN.

A Novel Student’s t-based Kalman Filter with Colored Measurement Noise

In this paper, a novel robust Student’s t-based Kalman filter (RSTKF) is proposed to solve the problem of a linear system with heavy-tailed process and measurement noises (HPMN) and colored measurement noise (CMN). The above problem is transformed into the filtering problem of a linear system with HPMN and white measurement noise after using the measurement differencing method and state augmentation approach. The augmentation state vector, the scale matrix and the auxiliary random variables are jointly estimated based on the variational Bayesian approach. Simulation results are provided to demonstrate the superiority of the proposed RSTKF by comparing with the existing filtering algorithms for systems with HPMN and CMN.

Performance Enhancement of GNSS/MEMS-IMU Tightly Integration Navigation System Using Multiple Receivers

Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS) are the most commonly used navigation systems. They both have unique advantages and disadvantages. GNSS is capable of generating precise navigation solutions while enough satellites are in view. However, the GNSS signals are sensitive to the environment. While the signals is attenuated, the GNSS receiver will fail to provide reliable navigation solutions. INS is an advanced navigation system built based on Newton's law. Due to the random noises contained in the Inertial Measurement Unit (IMU), the INS navigation solutions errors diverge over time. Therefore, effective integration of the two common systems can obtain better navigation results than any individual system. In this paper, for enhancing the GNSS/INS tightly integration system with low cost, multiple receivers were employed in the tight integration. Pseudo-range and Pseudo-range rates from the multiple receivers were employed to compose the measurement vector of the integration filter. In order to reduce the computation load, a measurement difference method was proposed. The state vector dimension could be reduced with the measurement difference scheme. Both simulation and field test were carried out for evaluating the performance of the proposed method. Since it was hard to obtain GNSS raw measurements from commercial receivers, self-developed DSP+FPGA (Digital Signal Processor, DSP; Field Programmable Gate Array, FPGA) based GNSS receivers were employed in the field test. The statistical analysis of the results showed that the positioning errors decreased with the receiver's amount increasing. In addition, a measurement difference method was proposed to reduce the state vector dimension for saving the computation load with the identical navigation solutions accuracy.

Estimation of Parameters of Gaussian Sum Distributed Noises in State-Space Models

The paper deals with the estimation of noise parameters of a linear time-varying system. In particular, the stress is laid on the state-space models, where the state and measurement noises are described by the Gaussian sum probability density functions. The recently introduced measurement difference method for the estimation of higher-order moments of the state and measurement noises is revised and, subsequently, extended for estimation of the parameters of the noise Gaussian sum densities with a special focus on the densities with two-components. The theoretical results are discussed and illustrated in a numerical example.

Improved Student’s t-Based Unscented Filter and its Application to Trajectory Estimation for Maneuvering Target

To estimate the systems with one-step randomly delayed measurement and time-correlated heavy-tailed measurement noises, on the basis of robust Student’s t based unscented filter (RSTUF), an improved Student’s t based unscented filter (ISTUF) is proposed. Referring to the measurement differencing method, a reformed measurement model was built. Then, by augmenting the system state vector, the conditional probability distribution of the measurement noise with respect to delayed measurement was taken into consideration. Based on the reformed measurement model and the augment state vector, a novel estimator was designed to solve the one-step randomly delayed problem. Maneuvering target tracking systems were used for simulation. Compared with unscented Kalman filter (UKF) or RSTUF, ISTUF had higher accuracy.

Convergence of Optimal Linear Estimator With Multiplicative and Time-Correlated Additive Measurement Noises

In this paper, the problem of convergence for the optimal linear estimator of discrete-time linear systems with multiplicative and time-correlated additive measurement noises is studied. By defining a new random vector that consists of the innovation, error, and part of the noise in the new measurement obtained from the measurement differencing method, we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose. It is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and, moreover, this fixed point can be obtained by solving a set of matrix equations.

A Novel Adaptive Kalman Filter With Colored Measurement Noise

In this paper, a novel variational Bayesian-based adaptive Kalman filter (VBAKF) is proposed to solve the problem of a linear state-space model with colored measurement noise and inaccurate noise covariance matrices. The filter problem of a linear state-space model with colored measurement noise and inaccurate noise covariance matrices is transformed into the filtering problem of a linear state-space model with white measurement noise and inaccurate noise covariance matrices using measurement differencing method and state augmentation approach. The augmentation state vector, corresponding predicted error covariance matrix and covariance matrix of white measurement noise are jointly estimated based on the variational Bayesian approach. The ability of addressing the colored measurement and inaccurate noise covariance matrices is demonstrated in the simulation of a target tracking example.

Noise Moment and Parameter Estimation of State-Space Model

The paper deals with the estimation of the moments and parameters of the state and measurement noises of a system described by a linear time-varying state-space model. In particular, a novel correlation measurement difference method is designed. The method is based on a statistical analysis of an augmented measurement prediction error leading to a system of linear matrix equations enabling higher-order noise moments estimation. The estimated moments, shown to converge to the true values, are then used for noise parameters computation. The theoretical results are discussed and illustrated in a numerical example.

State estimation for discrete-time Markov jump linear systems with time-correlated measurement noise

In this paper, the state estimation problem for discrete-time Markov jump linear systems affected by time-correlated measurement noise is considered where the time-correlated measurement noise is described by a linear system model with white noise. As a result, two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence. The first algorithm is optimal in the sense of minimum mean-square error, which is obtained based on the measurement differencing method, Bayes’ rule and some results derived in this paper. The second algorithm is a suboptimal algorithm obtained by using a lot of Gaussian hypotheses. The proposed suboptimal algorithm is finite-dimensionally computable and does not increase computational and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm.

Recursive filtering for discrete-time linear systems with fading measurement and time-correlated channel noise

This paper is concerned with the recursive filtering problem for discrete-time linear systems with fading measurement and time-correlated channel noise. The phenomenon of measurement fading appears in a random way and the fading phenomenon for each sensor is described by an individual random variable taking a value in a given interval. The time-correlated channel noise is depicted as a linear system model with white noise. Using the measurement differencing method and some results obtained in this paper, a recursive filtering algorithm for the system under consideration is proposed. The proposed algorithm is optimal in the sense of linear minimum mean-square error and does not increase computation and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed algorithm.

Maneuvering target tracking with colored noise

It is known that colored noise may degrade the performance of a tracking algorithm. A common remedy is to model colored noise as an autoregressive (AR) process and apply the measurement difference method. One problem with the approach is that the AR parameters are usually unknown. In this work, we propose a new method to adaptively estimate the AR parameters. It is shown that this method is simple and practically feasible. We incorporate oar method into the interacting multiple model (IMM) tracking algorithm and show that the performance is almost as good as that in the known parameters case.