A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with i...A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.展开更多
Traditional strapdown inertial navigation system （SINS） algorithm studies are based on ideal measurements from gy- ros and accelerometers, while in the actual strapdown inertial measurement unit （SIMU）, time-async...Traditional strapdown inertial navigation system （SINS） algorithm studies are based on ideal measurements from gy- ros and accelerometers, while in the actual strapdown inertial measurement unit （SIMU）, time-asynchrony between each iner- tial sensor is inevitable. Testing principles and methods for time- asynchrony parameter identification are studied. Under the single- axis swaying environment, the relationships between the SINS platform drift rate and the gyro time-asynchrony are derived using the SINS attitude error equation. It is found that the gyro time- asynchrony error can be considered as a kind of pseudo-coning motion error caused by data processing. After gyro testing and synchronization, the single-axis tumble test method is introduced for the testing of each accelerometer time-asynchrony with respect to the ideal gyro triad. Accelerometer time-asynchrony parame- ter identification models are established using SINS specific force equation. Finally, all of the relative time-asynchrony parameters between inertial sensors are well identified by using fiber optic gyro SIMU as experimental verification.展开更多
文摘A pseudo-cone in ℝ^(n) is a nonempty closed convex set K not containing the origin and such thatλK⊆K for allλ≥1.It is called a C-pseudo-cone if C is its recession cone,where C is a pointed closed convex cone with interior points.The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies,but it may be infinite.After proving a necessary condition for cone-volume measures of C-pseudo-cones,we introduce suitable weights for cone-volume measures,yielding finite measures.Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.
基金supported by the National Natural Science Foundation of China(61273333)
文摘Traditional strapdown inertial navigation system （SINS） algorithm studies are based on ideal measurements from gy- ros and accelerometers, while in the actual strapdown inertial measurement unit （SIMU）, time-asynchrony between each iner- tial sensor is inevitable. Testing principles and methods for time- asynchrony parameter identification are studied. Under the single- axis swaying environment, the relationships between the SINS platform drift rate and the gyro time-asynchrony are derived using the SINS attitude error equation. It is found that the gyro time- asynchrony error can be considered as a kind of pseudo-coning motion error caused by data processing. After gyro testing and synchronization, the single-axis tumble test method is introduced for the testing of each accelerometer time-asynchrony with respect to the ideal gyro triad. Accelerometer time-asynchrony parame- ter identification models are established using SINS specific force equation. Finally, all of the relative time-asynchrony parameters between inertial sensors are well identified by using fiber optic gyro SIMU as experimental verification.
