Optimum Steady State Position, Velocity, and Acceleration Estimation Using Noisy Sampled Position Data

Ramachandra, K. V.; Division, Radar C

doi:10.1109/taes.1987.310865

Cited by 27 publications

(8 citation statements)

References 3 publications

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“…255-257, pp. 318-320]) or 3 (as in [27]). To circumvent this dimensional mismatch to higher dimensional real applications that may be hard-wired to a fixed dimension n,we can achieve the dimension n sought by augmenting to obtain the requisite matrices and vectors as a concatenation of several lower dimensional test problems with solutions that are also already known.…”

Section: Aggregation/augmentation Of Lower Order Results Into Highermentioning

confidence: 99%

“…20). Moreover, idempotent matrices could be used as the system matrix in obtaining closedform solutions for both the continuous-time and discrete-time Riccati equations since there is no restriction that system matrices be stable in these applications but other closed-form expressions [31, [4], [26], [27] are superior for software cross-checking in this specialized Riccati verification role (see [4, Table 1, App.] for, respectively, a recommended collection of tests and a way to avoid having to solve for the roots of an associated biquadratic polynomial otherwise encountered in seeking to utilize the result of [27] as a software test case availing a conveniently known answer both before and after a periodic measurement).…”

Section: What About Its Use As Solutions To Matrix Lyapunov and Riccatimentioning

confidence: 99%

“…One benefit of dealing with an idempotent system matrix, A, as occurs here, is that the Kalman "rank test for controllability" (as the standard regularity condition that must be satisfied before an optimal control can be sought) degenerates into a much more tractable expression for the Controllability Grammian as (27) that one must check the rank of, where its being of rank n establishes that the system is controllable. However, in the case of the present 2-dimensional example, there is no actual reduction in complexity (but there would be if the second matrix of Eq.…”

Section: Verifying Finite Horizon Lq/lqg Optimal Control Solutionsmentioning

confidence: 99%

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Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

Kerr¹

2001

SPIE Proceedings

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We alert the reader here to a variety of structural properties associated with idempotent matrices that make them extremely useful in the verification/validation testing of general purpose control and estimation related software. A rigorous general methodology is provided here along with its rationale to justify use of idempotent matrices in conjunction with other tests (for expedient full functional coverage) as the basis of a coherent general strategy of software validation for these particular types of applications. The techniques espoused here are universal and independent of the constructs of particular computer languages and were honed from years of experience in crosschecking Kalman filter implementations in several diverse commercial and military applications. While standard Kalman filter implementation equations were originally derived by Rudolf E. Kalman in 1960 using the Projection Theorem in a Hubert Space context (with prescribed inner product related to expectations), there are now comparable Kalman filter results for systems described by partial differential equations (e.g., arising in some approaches to image restoration or with some distributed sensor situations for environmental toxic effluent monitoring) involving a type of Riccati-like PDE equation to be solved for the estimation error. The natural framework for such infinite dimensional PDE formulations is within a Banach Space (being norm-based) and there are generalizations of idempotent matrices similar to those offered herein for these spaces as well that allow closed-form test solutions for infinite dimensional linear systems to verify and confirm proper PDE implementations in S/W code. Other closed-form test case extensions discussed earlier by the author have been specifically tailored for S/W verification of multichannel maximum entropy power spectral estimation algorithms and of approximate nonlinear estimation implementations of Extended Kalman filtering and for Batch Least Squares (BLS) filters, respectively.

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Section: Aggregation/augmentation Of Lower Order Results Into Highermentioning

confidence: 99%

Section: What About Its Use As Solutions To Matrix Lyapunov and Riccatimentioning

confidence: 99%

Section: Verifying Finite Horizon Lq/lqg Optimal Control Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

Kerr¹

2001

SPIE Proceedings

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“…Target dynamics is assumed to be linear in the Local Inertial Cartesian Coordinate System (LICCS) [10]. A state variable model can express a discrete-time equation of target motion, given by [11] …”

Section: A Local Sensor Modelmentioning

confidence: 99%

Multi-sensor track fusion via Multiple-Model Adaptive Filter

Fong

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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A Multiple-Model Adaptive Filter (MMAF) is developed for use in multi-sensor track fusion systems for target tracking. The architecture of hierarchical fusion consists of several local processors and a global processor. Each local processor collects measurement data from a sensor and then using Kalman filter performs tracking function. The global processor utilizes the MMAF which consists of Information Matrix Filter (IMF) with two levels of common process noise and a decision logic switch to aggregate the outputs of local processors. The switch is designed by adopting the modified probabilistic neural network to compute the probability of each IMF for providing the switching capability to respond target dynamics. The resulting filter has better tracking performance than each individual IMF. Simulation results are included to demonstrate the effectiveness of proposed algorithm.

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“…Target dynamics is assumed to be linear in the Local Inertial Cartesian Coordinate System (LICCS). A state variable model [6] can express a discrete-time equation of target motion, given by…”

Section: Sensor-level Local Processorsmentioning

confidence: 99%

Integrated Track-to-Track Fusion with Modified Probabilistic Neural Network

Fong

2006

2006 CIE International Conference on Radar

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Utilization of information acquired from a sensor network to improve the tracking accuracy is one of the most important issues in sensor network research. An approach that consists of sensor-based filtering algorithms, local processors and global processor is employed to describe the distributed fusion problem when several sensors execute surveillance over the certain area. For sensor tracking systems, each filtering algorithm utilized in the Reference Cartesian Coordinate System (RCCS) is presented for target tracking when the radar measures range, bearing and elevation angle in the Spherical Coordinate System (SCS). For local processors, each track-to-track fusion algorithm is used to merge two tracks representing the same target. The number of 2-combinations of a set with N distinct sensors is considered for central track fusion. For global processor, a Bayesian method with SemiMarkov process is employed to develop the Modified Probabilistic Neural Network (MPNN) algorithm to compute the weights of local processors. By using local processor weights, the subsequent data fusion is executed to combine the corresponding joint state estimates. Simulation results are presented comparing the performance of the global MPNN algorithm with the local-level fusion algorithm and with the sensor-level filtering algorithm.

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Optimum Steady State Position, Velocity, and Acceleration Estimation Using Noisy Sampled Position Data

Cited by 27 publications

References 3 publications

Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

Exact methodology for testing linear system software using idempotent matrices and other closed-form analytic results

Multi-sensor track fusion via Multiple-Model Adaptive Filter

Integrated Track-to-Track Fusion with Modified Probabilistic Neural Network

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