State Estimation Algorithms Under Non-Ideal Conditions And Its Application In Angle-Only Relative Navigation

With the development of aerospace technology,space missions are becoming more and more complex.Relative navigation is the basis for realizing various space missions.Therefore,in order to ensure the smooth execution of space missions,higher requirements are imposed on relative navigation.The principle of relative navigation is to estimate the true state of the system by constructing an evolutionary model of the system state and using a series of sensor observations.The state estimation of the ideal system can be achieved through Kalman filtering.However,limited by the understanding of the actual system,the interference of external conditions in the communication process,and the limitations of the physical conditions inside the system,the system is often subject to non-ideal conditions such as model nonlinearity,correlated noises,randomly delayed measurements,and data packet loss.Therefore,the assumption of linear Gaussian required by the standard Kalman filtering algorithm is not satisfied,resulting in a decrease in estimation accuracy.In view of the above-mentioned different non-ideal conditions,scholars have designed estimation algorithms for corresponding scenarios,but the designed algorithms are often not universal.On the basis of the existing results,in this paper,the design of Gaussian filters under non-ideal conditions has been throughly studied.At the same time,considering that multi-sensor measurement helps to improve the estimation accuracy and robustness of the system,a centralized and distributed data fusion algorithm for multi-sensor systems under non-ideal conditions is designed,and the designed algorithm is applied to the space target angle-only relative navigation system.Based on the above discussion,the main contents of this article are summarized as follows:(1)The design of Gaussian filter for nonlinear systems with correlated noises is studied.Considering that randomly delayed measurements,data packet loss,and unknown interference can be modeled as multiplicative and additive noise,where the additive noise is divided into two cases of complex correlation and finite-step correlation,the design of filter under the Gaussian framework is given.Firstly,for the nonlinear system with synchronization correlated multiplicative and complex correlated additive noises,the process noise is augmented to the system state,and a Gaussian filter is designed based on the minimum mean square error estimation criterion.The numerical implementation is given based on third-degree spherical-radial rule.Then,the above-mentioned complex correlated additive noise is extended to finite-step correlated additive noise.Based on the projection theorem,the optimal filter is designed,and the corresponding numerical implementation is given based on the third-order spherical-radial rule.Finally,the analysis points out the necessity of designing Gaussian filtering algorithm for nonlinear systems.(2)Considering that in(1),the randomly delayed measurements and packet loss are modeled as noise,which cannot reflect the difference of the impact of non-ideal conditions on the system,the design of Gaussian filter under non-ideal conditions is discussed.Considering the limitation of communication bandwidth,a data packet is transmitted only once.At first,we studied the case where the data processing center received at most one data packet.Using two independent Bernoulli distributions to describe the one-step randomly delayed measurements and data packet loss,and the process and measurement noise are expanded to the state,a Gaussian filter is designed,and the corresponding numerical realization form is given based on the third-order spherical-radial rule.Then,reducing the communication bandwidth limit,it's considered that at most two data packets are received at the same time.By rebuilding the measurement model,and extending the contiguous state to the state increment of the system,the joint estimation is performed,and the corresponding numerical realization is given based on the third-order spherical-radial rule.Finally,the effectiveness of the designed algorithms is demonstrated through simulation examples.(3)Based on the research in(1)and(2),the data fusion problem of multi-sensor systems under non-ideal conditions is discussed.Considering that multi-sensor systems are conducive to improving the estimation accuracy and robustness,the centralized and distributed fusion estimator is designed for nonlinear systems with correlated noise and data packet loss.Firstly,considering that centralized fusion can obtain high-precision estimates,a centralized fusion filter,predictor,and smoother are designed.Besides,considering the implementation of the algorithm and the possible singular problems of matrix decomposition in the CKF algorithm,a numerical implementation based on SCKF is given.Then,considering the characteristics of distributed fusion that can improve the robustness of the system and facilitate fault isolation,a distributed fusion algorithm is designed,and the corresponding numerical realization is given based on the third-order spherical-radial rule.Finally,the proposed algorithms are all verified by simulation.(4)The relative navigation problem of space targets with angle-only condition under non-ideal conditions is studied.Firstly,considering that if the space target is a non-cooperative target,the information such as the center of mass,rotational inertia and angular velocity is unknown.The navigation system is built on the tracking satellite,and the corresponding kinematics and dynamics models are derived.Secondly,the observability of angle-only measurements during relative navigation is discussed,and it is clarified that if the camera offset is not applied,the distance blur problem will occur.By setting the camera offset installation,the observability of the system can be improved.Then,by constructing a relative navigation estimation model,and considering the multi-sensor measurements can improve the system robustness and estimation accuracy,based on the distributed fusion algorithm designed in Chapter 5,a relative navigation estimation algorithm is designed.Finally,it's verified that the proposed algorithm applied to the angle-only relative navigation system can get an effective estimate for space targets.