Shunyi Zhao

Minimum variance unbiased FIR filter for discrete time-variant systems

This paper is concerned with the minimum variance unbiased (MVU) finite impulse response (FIR) filtering problem for linear system described by discrete time-variant state-space models. An MVU FIR filter is derived by minimizing the variance from the unbiased FIR (UFIR) filter. The relationship between the filter gains of MVU FIR, UFIR and optimal FIR (OFIR) filters is derived analytically, and the mean square errors (MSEs) of different FIR filters are compared to provide an insight into the estimation performance. Simulations provided verify that errors in the MVU FIR filter are in between the UFIR and OFIR filters. It is also shown that the MVU FIR filter can offer optimal estimates without a prior knowledge of the initial state, and exhibits better robustness against temporary modeling uncertainties than the Kalman filter.

Linear Optimal Unbiased Filter for Time-Variant Systems Without Apriori Information on Initial Conditions

In this technical note, an optimal unbiased filter (OUF) is derived for time-variant systems to relax the initial condition assumption in Kalman filter (KF). By minimizing the mean square errors subject to the unbiasedness condition a solution is derived in a batch computation form first. To facilitate the on-line application, a recursive realization is further developed. The effect of removing the initial condition assumption on the estimation performance is analysed, and we show that the proposed algorithm converges to the KF asymptotically. Two-state harmonic model and four-state moving target tracking model are employed to demonstrate that the OUF can improve transient estimation performance significantly and can be used in place of the KF when the apriori information about the initial state values is not available.

Fault Detection and Diagnosis of Multiple-Model Systems With Mismodeled Transition Probabilities

This paper proposes an improved interacting multiple-model (I2MM) algorithm with inaccurate transition probabilities (TPs) for fault detection and diagnosis (FDD). We first study the influence of inaccurate TPs by inspecting the expectation and covariances of residual error vectors in the traditional IMM method. It shows that Kalman filters can be retained as subfilters in the presence of mismodeled TPs, and the effect of TPs can be removed naturally if all of the probabilities of true modes are equal to one. In view of this, a modification operator is proposed to make the real mode probabilities heuristically approach one. The modification degree is governed by a parameter determined by the online measurements. When the modification parameter calculated is identical to one, the I2MM method reduces to the conventional IMM algorithm. An experiment designed through a ball-and-tube testbed is presented to demonstrate that the I2MM-based FDD method can provide more reliable FDD results and reduce the possibility of false alarms.

Detection and Diagnosis of Multiple Faults With Uncertain Modeling Parameters

In this brief, a fault-detection and diagnosis method is proposed for the stochastic hybrid system with the consideration of model parameter uncertainty. To negate the effect of model uncertainty, a compensation step is introduced, which uses a compensation parameter to adjust the degree of dependence of the filtering on the model or the measurements. To determine the compensator parameter governing the degree of dependence, an orthogonality principle between the estimation error and the residual is applied. Numerical simulations with a second-order tracking system and a pilot-scale experiment study on a quadruple water tank system are conducted to demonstrate the effectiveness of the proposed approach.

Localization of Indoor Mobile Robot Using Minimum Variance Unbiased FIR Filter

The demand of indoor localization has recently grown quickly in industries. In general, a localization system is required to be reliable, fast, and have high accuracy. In this paper, the ultrawideband (UWB) technique is combined with the inertial navigation sensor (INS) to form a coupled UWB/INS localization framework, which inherits the advantages from both components. A minimum variance unbiased finite impulse response (MVU FIR) method is then applied to obtain accurate position and velocity estimations from noisy measurements. Two experiments and several simulations are conducted. Compared with the traditional Kalman filter (KF) and particle filter, the MVU FIR filter exhibits better immunity to the errors about a priori knowledge of noise variances. It can handle the kidnapped problem, and recover from some extreme failures satisfactorily. Moreover, the MVU FIR filtering algorithm is fast and easily implementable. Its online computational time is even lower than that of the KF, which is favorable in localization applications.Note to Practitioners—For indoor robot localization, an effective filtering algorithm can improve the accuracy significantly. Existing and commonly used filtering approaches suffer from weak robustness to the imprecise a priori knowledge of noise variances used, unsatisfied performance when dealing with sudden behaviors of robot, and large online computational load. This paper suggests a new practical method to estimate the current state using finite past measurements with a finite impulse response filter gain computed off-line. By testing it within the coupled ultrawideband/inertial navigation sensor localization framework under different operating conditions, we demonstrate that the proposed method can effectively overcome the above problems, providing fast, accurate, and reliable estimation in a practical environment.

Iterative Residual Generator for Fault Detection With Linear Time-Invariant State–Space Models

In this paper, an iterative residual generator (IRG) is proposed for discrete time-invariant state–space model with the aim of detecting faulty signals. By minimizing the mean square errors subject to unbiasedness constraint, a new filter with finite impulse response structure is derived. The resulting IRG is then obtained by extracting residual signal from the batch filter through several predictor/corrector iterations. It shows that IRG can provide a zero-mean Gaussian process regardless of previous estimation errors. More importantly, it includes the residual generation process in the Kalman filter as its special case. With the chi-square test, a numerical example is simulated to demonstrate that IRG can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults, and the estimation horizon length in IRG serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm.

Bayesian state estimation on finite horizons: The case of linear state–space model☆

Abstract The finite impulse response (FIR) filter and infinite impulse response filter including the Kalman filter (KF) are generally considered as two different types of state estimation methods. In this paper, the sequential Bayesian philosophy is extended to a filter design using a fixed amount of most recent measurements, with the aim of exploiting the FIR structure and unifying some basic FIR filters with the KF. Specifically, the conditional mean and covariance of the posterior probability density functions are first derived to show the FIR counterpart of the KF. To remove the dependence on initial states, the corresponding likelihood is further maximized and realized iteratively. It shows that the maximum likelihood modification unifies the existing unbiased FIR filters by tuning a weighting matrix. Moreover, it converges to the Kalman estimate with the increase of horizon length, and can thus be considered as a link between the FIR filtering and the KF. Several important properties including stability and robustness against errors of noise statistics are illustrated. Finally, a moving target tracking example and an experiment with a three degrees-of-freedom helicopter system are introduced to demonstrate effectiveness.