Determinant Of Fisher Information Matrix Research Articles

Optimal Measurement of Drone Swarm in RSS-Based Passive Localization With Region Constraints

Passive geolocation by multiple unmanned aerial vehicles (UAVs) covers a wide range of military and civilian applications including rescue, wild life tracking and electronic warfare. The sensor-target geometry is known to significantly affect the localization precision. The existing optimal sensor placement strategies mainly work on the cases without any constraints on the sensor locations. However, UAVs cannot fly/hover simply in arbitrary region due to realistic constraints, such as the geographical limitations, the security issues, and the max flying speed. In this paper, optimal geometrical configurations of UAVs in received signal strength (RSS)-based localization under region constraints are investigated. Employing the D-optimal criteria, i.e., maximizing the determinant of Fisher information matrix (FIM), such optimal problem is formulated. Based on the rigorous algebra and geometrical derivations, optimal and also closed-form configurations of UAVs under different flying states are proposed. Finally, the effectiveness and practicality of the proposed configurations are demonstrated by simulation examples.

Observation-Driven Multiple UAV Coordinated Standoff Target Tracking Based on Model Predictive Control

An observation-driven method for coordinated standoff target tracking based on Model Predictive Control (MPC) is proposed to improve observation of multiple Unmanned Aerial Vehicles (UAVs) while approaching or loitering over a target. After acquiring a fusion estimate of the target state, each UAV locally measures the observation capability of the entire UAV system with the Fisher Information Matrix (FIM) determinant in the decentralized architecture. To facilitate observation optimization, only the FIM determinant is adopted to derive the performance function and control constraints for coordinated standoff tracking. Additionally, a modified iterative scheme is introduced to improve the iterative efficiency, and a consistent circular direction control is established to maintain long-term observation performance when the UAV approaches its target. Sufficient experiments with simulated and real trajectories validate that the proposed method can improve observation of the UAV system for target tracking and adaptively optimize UAV trajectories according to sensor performance and UAV-target geometry.

Using Frame Theory for Optimal Placement of New Added Anchors in Location Estimation Wireless Networks

The relative geometry of the anchors and the emitter plays an important role in the estimation accuracy of the emitter location. In this article, it is assumed that there are a number of anchors with known location in a 2-D wireless network. Each anchor either measures the distance between itself and the emitter or it measures the look angle to the emitter. Knowing the location of the anchors, the emitter location can be estimated using these noisy measurements. It is assumed that one wants to add a number of new anchors to this network to improve the accuracy of estimating the emitter location. In this article, we have used the frame theory to obtain an algorithm which proposes the optimum location of the new anchors in the network. The optimization criterion for anchors placement is maximizing the Fisher information matrix determinant, which is equivalent to minimizing the trace of the Cramér–Rao lower bound in our assumed problem. Numerical simulations confirm the ability of the proposed algorithm to find the optimal location for new anchors.

Underwater Bearing Only Tracking Using Optimal Observer Maneuver Strategies

This paper considers the problem of tracking a uniform moving source using noisy bearing measurements obtained from a distant observer. Observer trajectory optimization plays a central role in this problem, with the objective to minimize the estimation error of the target state. The Bearing Only Tracking (BOT) of passive targets is mainly focused on the observer maneuver with known trajectories and rarely focused on the future prediction of observer states using adaptive optimization strategies. In this paper, observer paths using one-step ahead optimization based on a performance index are devised which are potentially useful for longer horizon observer trajectory planning in passive tracking. This performance index is the function of source parameters termed as the determinant of Error Covariance Matrix (ECM) which is numerically more efficient than the determinant of Fisher Information Matrix (FIM). The determinant of the FIM requires the calculation of future values for target states and measurements rather than the current values, which is not feasible for Kalman like filters. Therefore, in this paper, the optimization technique is implemented using the state error covariance which is readily available through Kalman filter equations and does require separate numerical calculations. Due to optimal observer maneuver, the performance of the proposed algorithm does not depend on the initial conditions as compared to the conventional tracking methods. The efficiency of the evolutionary algorithm is calculated in terms of range, position and velocity errors and simulation results show 4% fewer estimation errors for ECM based optimization than the determinant of the FIM method.

Distributed power allocation for cognitive tracking based on non-cooperative game in decentralized netted radar

The traditional centralized power allocation method for cognitive tracking in the netted radar can achieve the best resource utilization efficiency and target tracking performance. However, this method has poor robustness, low fault tolerance, and a high bandwidth requirement. In order to address this challenge, we propose a decentralized distributed power allocation method based on the non-cooperative game for multi-target tracking. Firstly, we model the power allocation problem for decentralized netted radar as a non-cooperative game problem and consider each radar node in the radar network as a player in the game. Then, we employ the determinant of Fisher information matrix to evaluate target tracking accuracy and use it to construct the utility function of the non-cooperative game based on the game rule. Finally, we propose an iterative distributed computing method to solve the Nash equilibrium. Meanwhile, we theoretically prove the Nash equilibrium solution's existence and uniqueness. Numerical simulation results show that the tracking performance of the proposed method is superior to the uniform and random power allocation method. Simultaneously, the tracking performance of the proposed method is close to the centralized power allocation method with a much lower computational load.

Optimal observation configuration of UAVs based on angle and range measurements and cooperative target tracking in three-dimensional space

This article investigates the optimal observation configuration of unmanned aerial vehicles (UAVs) based on angle and range measurements, and generalizes predecessors' researches in two dimensions into three dimensions. The relative geometry of the UAVs-target will significantly affect the state estimation performance of the target, the cost function based on the Fisher information matrix (FIM) is used to derive the FIM determinant of UAVs' observation in three-dimensional space, and the optimal observation geometric configuration that maximizes the determinant of the FIM is obtained. It is shown that the optimal observation configuration of the UAVs-target is usually not unique, and the optimal observation configuration is proved for two UAVs and three UAVs in three-dimension. The long-range over-the-horizon target tracking is simulated and analyzed based on the analysis of optimal observation configuration for two UAVs. The simulation results show that the theoretical analysis and control algorithm can effectively improve the positioning accuracy of the target. It can provide a helpful reference for the design of over-the-horizon target localization based on UAVs.

Optimal sensor placement for source localization based on RSSD

Source localization based on the received signal strength (RSS) has received great interest due to its low cost and simple implementation. In this paper we consider the source localization problem based on the received signal strength difference (RSSD) with unknown transmitted power of the source using spatially separated sensors. It is well- known that the relative sensor-source geometry (SSG) plays a significant role in localization performance. For this issue, the fisher information matrix (FIM) which inherently is a function of relative SSG is derived. Then for different scenarios the SSG based on the maximization of determinant of FIM is investigated to obtain the optimal sensor placement. Finally, computer simulations are used to study the performance of various sensor placements. Both theoretical analysis and simulation results reveal the ability of the proposed sensor- source geometries.

Multi-objective optimization design of accelerated degradation test based on Wiener process

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown parameters are solved by a two-step maximum likelihood estimation method. Considering both the accuracies of life estimation and the model parameter estimation, a multi-objective optimization model is established with the optimization goals of the minimum asymptotic variance of P-quantile of lifetime and the maximum determinant of Fisher information matrix. The Pareto solutions are set by the multi-objective genetic algorithm, and the test configurations for multi-objectives are obtained. Under the step stress accelerated degradation test and the constant stress accelerated degradation test, the effectiveness of the proposed method is verified by an optimization example of LEDs accelerated degradation test.

Sensor placement for RSSD-based localization: Optimal angular placement and sequential sensor placement

Energy-based localization has received great interest due to its low cost and simple implementation. It is well-known that sensor placement around the source plays a significant role in localization performance. This paper considers source localization based on the received signal strength difference (RSSD). Then, we propose two methods for sensor placement using maximization of the determinant of Fisher information matrix (FIM). The first one is based on the Gradient optimization method in which our optimization metric is a function of angular locations of all sensors, and the output of this method is optimal angular sensor separation which is called the optimal angular placement (OAP). In the second approach, we obtain the optimization metric as a function of single variable for each sensor in which the sensors are arranged in step-by-step manner, this method is called sequential sensor placement (SSP) in our study. At the end of this paper, simulation results reveal the ability of the proposed sensor placements.

Copula based constant-stress PALT using tampered failure rate model with dependent competing risks

PurposeAccelerated life tests (ALTs) are used to make timely assessments of the lifetime distribution of highly reliable materials and components. Life test under accelerated environmental conditions may be fully accelerated or partially accelerated. In fully accelerated life testing, all the test units are run at accelerated condition, while in partially accelerated life testing, they are both run at normal and accelerated conditions. The products can fail due to one of the several possible causes of failure which need not be independent. The purpose of this paper is to design constant-stress PALT with dependent competing causes of failure using the tampered failure rate model.Design/methodology/approachGumbel–Hougaard copula is used to model and measure the dependence between the life times of competing causes of failure. The use of the copula simplifies the model specification and gives a general class of distributions with the same dependent structure and arbitrary marginal distributions.FindingsThe optimal plan consists in finding optimum allocation of test units in different chambers by minimizing the reciprocal of the determinant of Fisher Information Matrix. The confidence interval for the estimated values of the design parameters has been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.Originality/valueThe model formulated can help reliability engineers obtain reliability estimates quickly of high reliability products that are likely to last for several years.

An accelerated life test plan for a two-component parallel system under ramp-stress loading using masked data

PurposeMost of the literature on the design of accelerated life test (ALT) plan focus on a single system (subsystem) totally disregarding its internal configuration. Many a times it is not possible to identify the components that cause the system failure or that the cause can only be identified by a subset of its components resulting in a masked observation. The purpose of this paper is to deal with the planning of ramp-stress accelerated life testing for a high-reliability parallel system comprising two dependent components using masked failure data. Such a testing may prove to be useful in a twin-engine aircraft. A ramp-stress results when stress applied on the system increases linearly with time.Design/methodology/approachA parallel system with two dependent components is taken with dependency modeled by Gumbel-Hougaard copula. The stress-life relationship is modeled using inverse power law, and cumulative exposure model is assumed to model the effect of changing stress. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding optimal stress rate using D-optimality criterion.FindingsThe optimal plan consists in finding optimal stress rate using D-optimality criterion by minimizing the reciprocal of the determinant of Fisher information matrix. The proposed plan has been explained using a numerical example and carrying out a sensitivity analysis.Originality/valueThe model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

Optimal Plan for Step-Stress Accelerated Life Test with Two Stress Variables for Lognormal Data

A simple step-stress accelerated life testing plan with two stress variables is considered, when the failure times in each level of stress follow the lognormal distribution. The lognormal distribution is commonly used to model certain types of data that arise in several fields of engineering such as, for example, different types of lifetime data or coefficients of wear and friction. The problem of choosing the optimal times to change the stress level is investigated by minimizing the asymptotic variance of the reliability estimate and maximizing the determinant of Fisher information matrix. In this paper, we obtain the optimal bivariate step-stress accelerated life test using both the criteria. Due to the nonlinearity and complexity of problem, the particle swarm optimization algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and the optimization ability is more. To illustrate the effect of the initial estimates on the optimal values, sensitivity analysis is performed. Finally, numerical studies are discussed to illustrate the proposed criterion. Simulation results show that the proposed optimum plan is robust.

Optimal sensor configuration for positioning seafloor geodetic node

This paper deals with the optimal acoustic sensor configuration for positioning seafloor geodetic node. We use the determinant of Fisher Information Matrix (FIM) to measure the performance of different sensor configuration. This criteria is calculated in both 2D and 3D scenarios on a more practical assumption that range observations have different weights depending on their value, instead of identical weights. Then the uncertainty of initial node position is also taken into consideration for the calculation of determinant of FIM which was often neglected in the optimizing process. We present a kind of optimal configurations based on the maximum of determinant (FIM), which is circular and has different optimal radius at each corresponding scenario. Simulative experiments are carried out to demonstrate the optimal configuration. Practical experiments in South China Sea can further prove the relationship between positioning accuracy, configuration and determinant of FIM.

Optimum modified ramp-stress ALT plan with competing causes of failure

PurposeAccelerated life test is undertaken to induce early failure in high-reliability products likely to last for several years. Most of these products are exposed to several fatal risk factors and fail due to one of them. Examples include solar lighting device with two failure modes: capacitor failure, and controller failure. It is necessary to assess each risk factor in the presence of other risk factors as each one cannot be studied in isolation. The purpose of this paper is to explore formulation of optimum time-censored accelerated life test model under modified ramp-stress loading when different failure causes have independent exponential life distributions.Design/methodology/approachThe modified ramp-stress uses one test chamber in place of the various chambers used in the normal ramp-stress accelerate life test thus saving experimental cost. The stress-life relationship is modeled by inverse power law, and for each failure cause, a cumulative exposure model is assumed. The method of maximum likelihood is used for estimating design parameters. The optimal plan consists in finding out relevant experimental variables, namely, stress rate and stress rate change point(s).FindingsThe optimal plan is devised using D-optimality criterion which consists in finding out optimal stress rate and optimal stress rate change point by maximizing logarithm of determinant of Fisher information matrix to the base 10. This criterion is motivated by the fact that the volume of joint confidence region of model parameters is inversely proportional to square root of determinant of Fisher information matrix. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.Originality/valueThe model formulated can help reliability engineers obtain reliability estimates quickly of high-reliability products that are likely to last for several years.

Two-Phase Optimal Guidance Law considering Impact Angle Constraint with Bearings-Only Measurements

The implementation of advanced guidance laws with bearings-only measurements requires estimation of the range information. To improve estimation accuracy and satisfy the impact angle constraint, this paper proposes a two-phase optimal guidance law consisting of an observing phase and an attacking phase. In the observing phase, the determinant of Fisher information matrix is maximized to achieve the optimal observability and a suboptimal solution expressed by leading angle is derived analytically. Then, a terminal sliding-mode guidance law is designed to track the desired leading angle. In the followed attacking phase, an optimal guidance law is integrated with a switching term to satisfy both the impact angle constraint and the field-of-view constraint. Finally, comparison studies of the proposed guidance law and a traditional optimal guidance law are conducted on stationary targets and maneuvering targets cases. Simulation results demonstrate that the proposed guidance law is able to improve the range observability and achieve better terminal performances including impact angle accuracy and miss distance.

Multi-Stress Equivalent Optimum Design for Ramp-Stress Accelerated Life Test Plans Based on D-Efficiency

Due to time and cost limitations, multi-stress accelerated life tests (ALTs) have been gradually applied in the fields of experimental design and reliability estimation for highly reliable and long-life products. To develop more efficient and concise test plans, it is necessary to study an equivalent experimental design method to create an equivalent conversion approach for different ALT plans. This paper presents the equivalent optimum design method combined with D-efficiency and asymptotic variance. In this method, the Fisher information matrix determinant is proposed as the equivalent feature variable. D-efficiency is a new equivalent criterion applied in the ALT design method and is measured using the ratio of Fisher information matrix determinants. The objective is to minimize the test time at a given efficiency and under asymptotic variance constraints without loss of test estimation accuracy. Based on the proposed equivalent method, a constant-stress ALT plan was successfully converted into its equivalent step-stress or ramp-stress ALT plan. Finally, an example is presented to demonstrate the equivalent ALT design of an electrical product with two stresses. The constant-stress ALT is equivalently designed for the ramp-stress ALT plan, and the sensitivity of the D-efficiency is analyzed. The results show that the proposed equivalent test scheme can shorten test time while achieving the same estimation accuracy.

On the optimal anchor placement in single-hop sensor localization

In wireless sensor networks, the problem of anchor (whose locations are a priori known) placement plays a vital role in improving the estimation accuracy of sensor (whose locations are unknown and need to be determined) locations. This paper deals with single-hop sensor localization from a novel perspective. On the one hand, unlike existing studies relying on ideal independent identically distributed (i.i.d.) noises in distance measurements, namely distance-independent noises, this paper defines a more realistic noise model in the sense that the noise variance is a function of sensor-to-anchor distances, namely distance-dependent noises. On the other hand, other than evaluating the localization performance for sensors at deterministic locations, a statistical approach is adopted by assuming a uniform and random distribution within a unit disk for the sensor location and evaluating the mean value of the associated Fisher information matrix determinant as the optimality metric for anchor placement. Through this metric, the optimal anchor placement is investigated from both theoretical and simulative perspectives. In the literature of optimal anchor placement with distance-independent noises, it has been addressed or conjectured to be true that it is optimal to have anchors equally spaced on the boundary. However, after a thorough analysis, it is shown that this conclusion is generally incorrect, but approaches to be true provided that the number of anchors goes to infinity. This study not only provides useful guidance for optimally deploying anchors in practice, but also yields valuable insights for future research on optimal anchor placement.

Optimality Analysis of Sensor‐Target Geometries for Bearing‐Only Passive Localization in Three Dimensional Space

Optimality analysis of sensor to target observation geometry for bearing-only passive localization is of practical significance in engineering and military applications and this paper generalized predecessors’ researches in two-dimensions into three dimensional space. Based on the principles of Cramer-Rao lower bound (CRLB), Fisher information matrix (FIM) and the determinant of FIM derived by Cauchy-Binet formula, this paper configured the optimal observation geometry resulted from maximizing the determinant of FIM. Optimal observation geometry theorems and corresponding propositions were proved for N ≥ 2 sensors in three dimensions. One conjecture was proposed, i.e., when each range of N( N ≥ 4) sensors to the single target is identical, configuring the optimal geometry is equivalent to distributing N points uniformly on a unit sphere, which is one of the worldwide difficult problem. Studies in this paper can provide helpful reference for passive sensor deployment, route planning of detection platform and so on.

Optimal Byzantine attack strategy for distributed localisation with M ‐ary quantised data

The distributed localisation with M-ary quantised data at sensor nodes is investigated in the presence of Byzantines from the attacker's perspective. The Byzantine nodes attack the network by transmitting falsified data to the fusion centre (FC) to deteriorate the performance of the distributed target localisation, where the independent and probabilistic Byzantine attack model is considered. By making the determinant of Fisher information matrix be zero, the optimal Byzantine attack strategy, which makes the FC incapable of estimating target location using the data at sensor nodes, is found. Numerical results show that the security performance of the distributed localisation improves sharply as the number of quantisation bits increases. Moreover, the security performance also increases tremendously as the attack probability decreases. Hence, the Byzantine attacker faces a trade-off between the performance damage and the hazard to be identified.

Orbit optimization of Mars orbiters for entry navigation: From an observability point of view

In this paper, the observability of orbiter-based Mars entry navigation is investigated and its application to the orbit optimization of Mars orbiters is demonstrated. An observability analysis of Mars entry navigation processing of range measurements to multiple orbiters based on Fisher information matrix is conducted. The determinant of Fisher information matrix is derived to quantify the degree of observability. The orbit optimization method based on the observability analysis is then proposed. Two navigation scenarios using three and four orbiters are considered in simulations. To verify the advantages of navigation performance, the orbiter-based and ground beacon-based navigation schemes are comparatively analyzed. In the simulation, an Extended Kalman Filter is used to examine the navigation accuracy. It is concluded that the proposed orbit optimization method is able to optimize the orbits of Mars orbiters with the maximum degree of observability. For the Mars entry navigation based on orbiters, a better configuration which is a main contributor to the observability, can be achieved. The navigation performance is more excellent than the ground beacon-based navigation. However, a diminishing return of navigation accuracy is obtained solely by increasing the number of orbiters.