Tracking radar systems are used to measure the target’s relative position in range, azimuth angle, elevation angle, and velocity. In many real-world target tracking applications, the target states are often subjected to constraints arising from external limitations or inherent properties. Ideally, these constraints contain valuable information about target states in addition to the system models and measurements. Therefore, by proper incorporation of such constraints into the estimation process, the estimation accuracy can be improved. Consequently, various literatures where several model modification methods, in which the target state satisfies the constraints automatically based on projection techniques or direct elimination, have been published. However, these approaches are built on the premise that the constraints are perfectly known as prior information. To overcome this shortfall, researchers have formulated several approaches: such as LEC for the destination constraint and a noisy pseudo-measurement. Still, in some practical applications, the destination may also be observed by an imperfect sensor, resulting in destination information contaminated by noise. Moreover, direct utilization of the noisy destination information in the description of constraint relationships may cause constraint errors and result in the degradation of state estimates.
Overall, the direct use of available noise-corrupted destination information in the existing destination constrained filtering methods may lead to performance degradation. To address this limitation, researchers from the School of Electronics and Information Engineering at Harbin Institute of Technology in China: Professor Gongjian Zhou and Dr. Keyi Li together with Professor Thiagalingam Kirubarajan from the Department of Electrical and Computer Engineering at McMaster University in Canada investigated carefully the problem of state estimation with noisy destination information. Their focus was to treat the true destination as a state to be estimated along with the target state. Their work is currently published in the research journal, Signal Processing.
The research team first developed a novel way to formulate the destination constraint when the destination is known to be noisy by using the aforementioned approach of treating the true destination as a state to be estimated along with the target state. Secondly, based on the known trajectory shape, a new modeling method for the destination constraint was proposed. Lastly, two constrained-state estimation filters with augmented state vectors and augmented measurement vectors were proposed to produce the estimates of both the constrained target state and the constraint parameters.
In their approach, an uncertain destination constrained augmented state filter (UDC-ASF) with its state being augmented by destination, in which the unscented Kalman filter (UKF) was used to deal with the strong nonlinearity of the measurements, and was proposed to produce both constrained target state and destination estimates. Moreover, the unknown slope and the intercept of the straightline representing the destination constraint could also be augmented into the state vector and the two pseudo measurements which could also constructed in the process.
In summary, the study presented an in-depth investigation of the constrained state estimation problem with noisy prior information on destination position. Overall, the effectiveness and the superior performance of the proposed algorithms were demonstrated through Monte Carlo simulations with comparisons to an unconstrained filter and two existing destination-constrained filters.
Gongjian Zhou, Keyi Li, Thiagalingam Kirubarajan. Constrained state estimation using noisy destination information. Signal Processing, volume 166 (2020) 107226.