In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which appears in pseudo-inverse matrix operations is employed as an objective function of the problem in the present extended approach. The procedure for the maximization of the determinant of the corresponding matrix is proved to be mathematically the same as that of the previously proposed QR method when the number of sensors is less than that of state variables (undersampling). On the other hand, the authors have developed a new algorithm for when the number of sensors is greater than that of state variables (oversampling). Then, a unified formulation of the two algorithms is derived, and the lower bound of the objective function given by this algorithm is shown using the monotone submodularity of the objective function. The effectiveness of the proposed algorithm on the problem using real datasets is demonstrated by comparing with the results of other algorithms. The numerical results show that the proposed algorithm improves the estimation error by approximately 10% compared with the conventional methods in the oversampling case, where the estimation error is defined as the ratio of the difference between the reconstructed data and the full observation data to the full observation. For the NOAA-SST sensor problem, which has more than ten thousand sensor candidate points, the proposed algorithm selects the sensor positions in few seconds, which required several hours with the other algorithms in the oversampling case on a 3.40 GHz computer.

The problem of selecting an optimal set of sensors estimating a high-dimensional data is considered. Objective functions based on D-, A-, and E-optimality criteria of optimal design are adopted to greedy methods, that maximize the determinant, minimize the trace of the inverse, and maximize the minimum eigenvalue of the Fisher information matrix, respectively. First, the Fisher information matrix is derived depending on the numbers of latent state variables and sensors. Then, a unified formulation of the objective function based on A-optimality is introduced and proved to be submodular, which provides the lower bound on the performance of the greedy method. Next, greedy methods based on D-, A-, and E-optimality are applied to randomly generated systems and a practical dataset concerning the global climate; these correspond to an almost ideal and a practical case in terms of statistics, respectively. The D- and A-optimality-based greedy methods select better sensors. The E-optimality-based greedy method does not select better sensors in terms of the index of E-optimality in the oversample case, while the A-optimality-based greedy method unexpectedly does so in terms of the index of E-optimality. The poor performance of the E-optimality-based greedy method is due to the lack of submodularity in the E-optimality index and the better performance of the A-optimality-based greedy method is due to the relation between A- and E-optimality. Indices of D- and A-optimality seem to be important in the ideal case where the statistics for the system are well known, and therefore, the D- and A-optimality-based greedy methods are suitable for accurate reconstruction. On the other hand, the index of E-optimality seems to be critical in the more practical case where the statistics for the system are not well known, and therefore, the A-optimality-based greedy method performs best because of its superiority in terms of the index of E-optimality.

A vector-measurement-sensor problem for the least squares estimation is considered, by extending a previous novel approach in this paper. An extension of the vector-measurement-sensor selection of the greedy algorithm is proposed and is applied to particle-image-velocimetry data to reconstruct the full state based on the information given by sparse vector-measurement sensors.

The present study proposes a sensor selection method based on the proximal splitting algorithm and the A-optimal design of experiment using the alternating direction method of multipliers (ADMM) algorithm. The performance of the proposed method was evaluated with a random sensor problem and compared with previously proposed methods, such as the greedy and convex relaxation methods. The performance of the proposed method is better than the existing greedy and convex relaxation methods in terms of the A-optimality criterion. Although, the proposed method requires a longer computational time than the greedy method, it is quite shorter than that of convex relaxation method in large-scale problems. Then the proposed method was applied to the data-driven sparse-sensor-selection problem. The dataset adopted was the National Oceanic and Atmospheric Administration optimum interpolation sea surface temperature dataset. At a number of sensors larger than that of the latent variables, the proposed method showed similar and better performance compared with previously proposed methods in terms of the A-optimality criterion and reconstruction error.

The regression characteristics of axial-injection end-burning hybrid rocket were experimentally investigated using a laboratory-scale motor. The axial-injection end-burning type fuel grains were made by high-accuracy three-dimensional printing. Firing tests were conducted using gaseous oxygen as the oxidizer at a chamber pressure range of 0.10 to 0.43 MPa. Results of 15 static firings tests show that fuel regression rate increases as the chamber pressure rises, and fuel regression rate decreases as the oxidizer port velocity increases. A data reduction method was developed to avoid the difficulty in calculating oxidizer-to-fuel ratio. A simplified fuel regression model based on the granular diffusion flame model is developed to investigate regression characteristics. The trend in results as calculated using the granular diffusion flame model agrees with that in experimentally observe values. However, this does not hold true in tests with varying oxidizer port velocity. A granular diffusion flame model only takes into account simple solid propellant regression. Therefore, modification of the model is needed for calculating the fuel regression rate of an end-burning hybrid rocket.