Yingting Luo

Globally Optimal Multisensor Distributed Random Parameter Matrices Kalman Filtering Fusion with Applications

This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.

Globally Optimal Distributed Kalman Fusion With Local Out-of-Sequence-Measurement Updates

In a distributed multisensor fusion systems, observations produced by sensors can arrive at local processors out of sequence. The resulting problem at the central processor/fusion center-how to update current estimate using multiple local out-of-sequence-measurement (OOSM) updates - is a nonstandard distributed estimation problem. In this note, based on the centralized update algorithm with multiple asynchronous (1-step-lag) OOSMs see we firstly deduce the optimal distributed fusion update algorithm with multiple local asynchronous (1-step-lag) OOSM updates, which is proved, under some regularity conditions, to be equivalent to the corresponding optimal centralized update algorithm with all-sensor 1-step-lag OOSMs. Then, we propose an optimal distributed fusion update algorithm with multiple local arbitrary-step-lag OOSM updates.

Optimal Distributed Kalman Filtering Fusion Algorithm Without Invertibility of Estimation Error and Sensor Noise Covariances

Although the globally optimal distributed Kalman filtering fusion has been proposed and studied for more than twenty years, the invertibility of estimation error and measurement noise covariances has been always a restrictive assumption to derive a globally optimal distributed Kalman filtering fusion equivalent to the centralized Kalman filtering fusion. This letter proposes an optimal distributed Kalman filtering fusion algorithm for general dynamic systems without invertibility of estimation error and measurement noise covariances. The new algorithm uses the convex combination fusion, whose fusion weights are recursively given. Computer experiments show that the performance of this fusion algorithm is very likely to be equivalent to that of the centralized Kalman filtering fusion. In practice, the new fusion algorithm can be applied to any distributed Kalman filtering fusion, such as the equality constrained distributed Kalman filtering fusion.

Novel Data Association Algorithm Based on Integrated Random Coefficient Matrices Kalman Filtering

We present a novel data association algorithm based on an integrated random coefficient matrices Kalman filtering (DAIRKF) for the multiple targets and sensors tracking association problem. The basic idea of this algorithm is to integrate all targets and measurements which need to be associated to a new whole system. Then the random coefficient matrices Kalman filtering is applied to this integrated dynamic system to derive the estimates of these target states. Since this algorithm violates some independence conditions for the optimality of the random coefficient matrices Kalman filtering, it is suboptimal in the mean square error (MSE) sense. Nevertheless, in some degree, there is still a correct theoretical basis in DAIRKF and the idea of this algorithm is significantly different from that of joint probabilistic data association (JPDA). Moreover, we can extend the single-sensor DAIRKF algorithm to a multisensor DAIRKF (MSDAIRKF) algorithm with high survivability in poor environment. The computation burden of MSDAIRKF grows linearly as the number of sensors increases. Numerical examples show that the new algorithm works significantly better than JPDA in many cases.

Globally optimal distributed Kalman filtering fusion

The goal of this paper is to give a survey of the previous works on the globally optimal distributed Kalman filtering fusion with classical and nonclassical dynamic systems. Then, we summarize some of our recent results on nonclassical and unideal dynamic systems, including dynamic systems with feedback and cross-correlated sensor measurement noises, dynamic systems with random parameter matrices, and dynamic systems with out-of-sequence or asynchronous measurements. The global optimality in this paper means that the distributed Kalman filtering fusion is exactly equal to the corresponding centralized optimal Kalman filtering fusion. Therefore, not only all of the proposed fusion algorithms here are distributed, but performance as good as that of the corresponding optimal centralized fusion algorithms is achieved. There also exist many papers for other fusion optimality (e.g., the optimal convex linear estimation/compression fusion) discussion, which are not involved in this paper.

Minimizing Euclidian State Estimation Error for Linear Uncertain Dynamic Systems Based on Multisensor and Multi-Algorithm Fusion

In this paper, a multisensor linear dynamic system with model uncertainty and bounded noises is considered. Based on previously developed set-valued estimation methods in terms of convex optimization, we propose several efficient algorithms of centralized sensor fusion, distributed sensor fusion, and multi-algorithm fusion to minimize the Euclidian estimation error of the state vector. Obviously, an ellipsoid/box with a larger “size” cannot be in general guaranteed to contain another ellipsoid/box with a smaller “size” since centers and shapes of the two ellipsoids/boxes may be different from each other. This fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids/boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives. Then intersection fusion of these estimation ellipsoids/boxes yields a final Euclidian-error-minimized state estimate. Numerical examples show that the new method with multi-algorithm at both the sensors and the fusion center can significantly reduce the Euclidian estimation error of the state.

Integrated optimization methods in multisensor decision and estimation fusion

This paper presents a significant integrated optimization point of view behind the following three successful decision and estimation fusion results: 1) a unified fusion rule for networked sensor decision systems; 2) optimal sensor data quantization for estimation fusion and 3) integrated multi-target data association tracking systems. More precisely speaking, the integrated optimization method in 1) derives a unified objective function optimizing only sensor rules given a unified fusion rule; the method in 2) derives a unified objective function optimizing both the sensor quantization rule and the final estimation in the MSE sense, and the method in 3) integrates all associated targets and their valid observations into a whole random measurement matrix dynamic system so that the optimal random matrix Kalman filtering can be applied to estimate the states of all associated targets.

Globally optimal flight path update with adding or removing out-of-sequence measurements

In a multisensor target tracking system, observations produced by sensors can arrive at a central processor out of sequence. There have been some state estimate update algorithms for out-of-sequence measurements (OOSMs). In this paper, we propose a flight path update algorithm for a sequence with arbitrary delayed OOSMs. The new algorithm has three advantages: 1) it is a globally optimal recursive algorithm; 2) it is an algorithm for arbitrary delayed OOSMs including the case of interlaced OOSMs with less storages, compared with the optimal state update algorithm in [19]; 3) it can update the current whole flight path other than only the current single state with less computation, i.e., the dimension of the matrices which need to be inverted is not more than that of the state in process of updating the past ℓ (lag steps) estimates and corresponding error covariances. Besides, this algorithm can be easily modified to derive a globally optimal flight path update with removing an earlier (incorrectly associated) measurement.

A novel model for linear dynamic system with random delays

This paper explores a novel model to describe linear dynamic system with random delays. Compared with the existing research, the probabilities of random delays in the novel model are calculated by conditional probabilities. Therefore, the process noises and measurements noises in the new model for random delay problems are infinitely correlated. By treating the model as random parameter matrices Kalman filtering with one-step correlated noises approximately, the new state estimators are presented. Numerical examples show that the new estimators work better than the existing algorithm in many cases.