Shuli Sun

Brief paper: Optimal linear estimation for systems with multiple packet dropouts

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with multiple packet dropouts. Based on a packet dropout model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are computed recursively in terms of the solution of a Riccati difference equation of dimension equal to the order of the system state plus that of the measurement output. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. Simulation results show the effectiveness of the proposed optimal linear estimators.

Optimal Full-Order and Reduced-Order Estimators for Discrete-Time Systems With Multiple Packet Dropouts

This paper is concerned with the estimation problem for discrete-time stochastic linear systems with multiple packet dropouts. Based on a recently developed model for multiple-packet dropouts, the original system is transferred to a stochastic parameter system by augmentation of the state and measurement. The optimal full-order linear filter of the form of employing the received outputs at the current and last time instants is investigated. The solution to the optimal linear filter is given in terms of a Riccati difference equation governed by packet arrival rate. The optimal filter is reduced to the standard Kalman filter when there are no packet dropouts. The steady-state filter is also studied. A sufficient condition for the existence of the steady-state filter is given and the asymptotic stability of the optimal filter is analyzed. At last, a reduced-order filter is investigated.

Optimal Filtering for Systems With Multiple Packet Dropouts

This paper is concerned with the optimal filtering problem for discrete-time stochastic linear systems with multiple packet dropouts, where the number of consecutive packet dropouts is limited by a known upper bound. Without resorting to state augmentation, the system is converted to one with measurement delays and a moving average (MV) colored measurement noise. An unbiased optimal filter is developed in the linear least-mean-square sense. Its solution depends on the recursion of a Riccati equation and a Lyapunov equation. A numerical example shows the effectiveness of the proposed filter.

Multiple-Level Quantized Innovation Kalman Filter

Abstract In this paper, we study a general multiple-level quantized innovation Kalman filter (MLQ-KF) for estimation of linear dynamic stochastic systems. First, given a multi-level quantization of innovation, we derive the corresponding MMSE filter in terms of the given quantization levels under the assumption that the innovation is approximately Gaussian. By optimizing the filter with respect to the quantization levels, we obtain an optimal quantization scheme and the corresponding optimal MLQ-KF. The optimal filter is given in terms of a simple Riccati difference equation as in the standard Kalman filter. For the case of 1-bit transmission, our proposed optimal filter gives a better performance than the sign-of-innovation filter (SOI-KF) Ribeiro et al. [2006]. The convergence of the MLQ-KF to the standard Kalman filter is established.

Quantized Kalman Filtering

This paper is concerned with the estimation problem for a dynamic stochastic estimation in a sensor network. Firstly, the quantized Kalman filter based on the quantized observations (QKFQO) is presented. Approximate solutions for two optimal bandwidth scheduling problems are given, where the tradeoff between the number of quantization levels or the bandwidth constraint and the energy consumption is considered. However, for a large observed output, quantizing observations will result in large information loss under the limited bandwidth. To reduce the information loss, another quantized Kalman filter based on quantized innovations (QKFQI) is developed, which requires that the fusion center broadcast the one-step prediction of state and innovation variances to the tasking sensor nodes. Compared with QKFQO, QKFQI has better accuracy. Simulations show the effectiveness.

Quantized filtering of linear stochastic systems

>> In this paper we investigate a general multi-level quantized filter of linear stochastic systems. For a given multi-level quantization and under the Gaussian assumption on the predicted density, a quantized innovations filter that achieves the minimum mean square error is derived. The filter is given in terms of quantization thresholds and a simple modified Riccati difference equation. By optimizing the filtering error covariance with respect to quantization thresholds, the associated optimal thresholds and the corresponding filter are obtained. Furthermore, the convergence of the filter to the standard Kalman filter is established. We also discuss the design of a robust minimax quantized filter when the innovation covariance is not exactly known. Simulation and experimental results illustrate the effectiveness and advantages of the proposed quantized filter.In this paper we investigate a general multi-level quantized filter of linear stochastic systems. For a given multi-level quantization and under the Gaussian assumption on the predicted density, a quantized innovations filter that achieves the minimum mean square error is derived. The filter is given in terms of quantization thresholds and a simple modified Riccati difference equation. By optimizing the filtering error covariance with respect to quantization thresholds, the associated optimal thresholds and the corresponding filter are obtained. Furthermore, the convergence of the filter to the standard Kalman filter is established. We also discuss the design of a robust minimax quantized filter when the innovation covariance is not exactly known. Simulation and experimental results illustrate the effectiveness and advantages of the proposed quantized filter.

Optimal linear estimators for systems with multiple random measurement delays and packet dropouts

This article is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with possible multiple random measurement delays and packet dropouts, where the largest random delay is limited within a known bound and packet dropouts can be infinite. A new model is constructed to describe the phenomena of multiple random delays and packet dropouts by employing some random variables of Bernoulli distribution. By state augmentation, the system with random delays and packet dropouts is transferred to a system with random parameters. Based on the new model, the least mean square optimal linear estimators including filter, predictor and smoother are easily obtained via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state estimators is given. An example shows the effectiveness of the proposed algorithms.

Distributed fusion estimation for multi-sensor asynchronous sampling systems with correlated noises

ABSTRACT This paper is concerned with the distributed fusion estimation problem for a class of multi-sensor asynchronous sampling systems with correlated noises. The state updates uniformly and the sensors sample randomly. Based on the measurement augmentation method, the asynchronous sampling system is transformed to the synchronous sampling one. Local filter is designed by using an innovation analysis approach. Then, the filtering error cross-covariance matrix between any two local filters is derived. Finally, the optimal distributed fusion filter is proposed by using matrix-weighted fusion algorithm in the linear minimum variance sense. Simulation results show the effectiveness of the proposed algorithms.

Optimal and suboptimal prior filters with bounded multiple packet dropouts

This paper is concerned with the filtering problem for discrete-time stochastic linear system with bounded multiple packet dropouts. An optimal prior filter is developed in linear unbiased minimum variance sense. Its solution depends on the recursion of a Riccati equation and a Lyapunov equation, which involves the complex computation of multiple sums by some correlated terms. To reduce the computational cost, a suboptimal prior filter is presented. Furthermore, the proposed optimal and suboptimal filters are reduced to the standard Kalman filters when there are no packet dropouts. A simulation shows the effectiveness of the proposed algorithms.

Pole-assignment fixed-interval Kalman smoother with an exponential stability

Using the innovation analysis method in the time domain, based on the autoregressive moving average (ARMA) innovation model and white noise estimators, a pole-assignment fixed-interval steady-state Kalman smoother is presented for discrete-time linear stochastic systems. It avoids the computation of the optimal initial smoothing estimate, and can rapidly eliminate the effect of arbitrary initial smoothing estimate by assigning the poles of the smoother, with an exponentially decaying rate. Several simulation examples show its effectiveness.