A novel interacting multiple model algorithm

Abstract

For maneuvering target tracking, the interacting multiple model (IMM) algorithm employs a fixed model set. The performance of this algorithm depends on the model set adopted. The result of using too many models is as bad as the case of too few models. Therefore, a variable structure IMM (VSIMM) was presented and applied to ground target tracking. This algorithm improves performance and reduces computational load with using auxiliary information. But it is difficult to extend the VSIMM to other scenario (for example, aerial target), where there is not auxiliary information such as a map. A novel interacting multiple model (Novel-IMM) algorithm was presented to solve the problem of model set adaptation without auxiliary information. The Novel-IMM algorithm consists of N independent IMM filters operating in parallel, and each independent IMM filter also consists of multiple sub-filters, which operate interactively. In every time index, only one IMM output of a certain model set is used; but for a long time, the algorithm will alternatively choose an output of the model set to be the optimum final output. The Novel-IMM approach was illustrated in detail with an aerial complex maneuvering target tracking example.

Introduction

Computing the optimal state estimate for a jump Markov system requires exponential complexity, and hence, practical filtering algorithms are necessarily suboptimal. In target tracking literatures, suboptimal multiple model filtering algorithms, such as the interacting multiple model (IMM) method, are widely used for state estimation of such systems [1]. The IMM estimation has received a great deal of attention in recent years due to its unique power and great success in handling problems with both structural and parametric uncertainties and/or changes, and in decomposing a complex problem into simpler sub-problems, ranging from target tracking to fault detection and isolation, and from biomedical signal processing to process control [2], [3]. The application of IMM filters for detection and diagnosis of anticipated reaction wheel failures in the attitude control system has been described and developed in Refs. [4], [5]. The IMM method for fault detection of railway vehicle from the measurement of the lateral acceleration of bogie and body and from rate of bogie has been described in Refs. [6], [7].

The IMM algorithm, which uses a fixed set of models, usually performs reasonably well for problems with a small model set. Many practical problems, however, involve more than just a small number of models [8]. When these algorithms are applied to solve target tracking problems, it happens that only using a small number of models cannot get satisfying result. At any time, the target trajectory evolves according to one of a finite number of predetermined model set. This requires that the model set include as many models as necessary to handle the varying target motion characteristics. But this cannot improve the performance successfully. The result of using too many models is as bad as the case of too few models. As demonstrated in Ref. [9], using more models makes it no better. In fact, the performance will deteriorate if too many models are used due to the excessive “competition” from the “unnecessary” (excess) models. The dilemma is that more models have to be used to improve the accuracy, but the use of too many models would degrade the performance [10].

Several modified IMM algorithms were proposed for improvement of performance or computation efficiency in recent years. A selected filter IMM (SFIMM) algorithm which uses a subset of filters with the specific subset chosen using decision rules was presented to improve computation efficiency of maneuvering target tracking [11]. A variable structure IMM (VSIMM) algorithm was presented to solve the dilemma where the model set not only differs across targets, but also varies with time for a given target [2], [3]. Not only does VSIMM inherit the effective cooperation strategies of the IMM and the superior output processing of the AMM (autonomous multiple model), but it also adapts to the outside world by producing new elemental filters if the existing ones are not good enough and by eliminating those elemental filters that are harmful. This algorithm works successfully in ground target tracking where the model set adapts sequentially according to the target position and the road network configuration [12], [13], [14], [15].

The major objective of the MM is to achieve best modeling accuracy with a minimum number of models. Here VSIMM estimation has certain advantages. In a general setting, the problem of efficient model set design for MM estimation is still open, Researches in the field of VSIMM focus on the efficient model set design [16], [17], [18] and model set adaptation algorithms [1], [3], [19], [20], which includes the decision for activating a candidate model as well as terminating the model in effect. In general, those decisions should consist of a set of complex rules based on both a priori and a posteriori information about the current system mode in effect, but there are not unified theories and practical methods to guide us how to use these rules. These theories about model adaptation is much more challenging [21], [22]. So the advantages in all presented model set adaptation methods based on the statistical hypothesis testing have been surprisingly limited. In addition, it is very difficult to realize the VSIMM without the auxiliary information.

A novel interacting multiple model (Novel-IMM) algorithm has been presented in this paper to solve the problem of model set adaptation without auxiliary information. This method adopts independent parallel model set method but not a serial model set adaptation which is adopted in VSIMM. It consists of N independent IMM filters operating in parallel, and each independent IMM filter also consists of multiple sub-filters, which operate interactively. In every time index, only one IMM output of a certain model set is used; but for a long time, the algorithm alternatively chooses an output of the model set to be the optimum final output. The method does not use the decision for model activation and the decision for termination of the model in effect. The computer simulations illustrate the Novel-IMM could improve the performance of target tracking.