Covariance Feedback Research Articles

Real-time vision-inertial landing navigation for fixed-wing aircraft with CFC-CKF

Vision-inertial navigation offers a promising solution for aircraft to estimate ego-motion accurately in environments devoid of Global Navigation Satellite System (GNSS). However, existing approaches have limited adaptability for fixed-wing aircraft with high maneuverability and insufficient visual features, problems of low accuracy and subpar real-time arise. This paper introduces a novel vision-inertial heterogeneous data fusion methodology, aiming to enhance the navigation accuracy and computational efficiency of fixed-wing aircraft landing navigation. The visual front-end of the system extracts multi-scale infrared runway features and computes geo-reference runway image as observation. The infrared runway features are recognized efficiently and robustly by a lightweight end-to-end neural network from blurry infrared images, and the geo-reference runway is generated through projection of the runway’s prior geographical information and prior pose. The fusion back-end of the navigation system is the Covariance Feedback Control based Cubature Kalman Filter (CFC-CKF) framework, which tightly integrates visual observations and inertial measurements for zero-drift pose estimation and curbs the effect of inaccurate kinematic noise statistics. Finally, real flight experiments demonstrate that the algorithm can estimate the pose at a frequency of 100 Hz and fulfill the navigation accuracy requirements for high-speed landing of fixed-wing aircraft.

Capacity Optimization for Cell-Free MIMO Systems With Mean and Covariance Feedback

Capacity Optimization for Cell-Free MIMO Systems With Mean and Covariance Feedback

Cubature Kalman filter with closed-loop covariance feedback control for integrated INS/GNSS navigation

Cubature Kalman Filter (CKF) offers a promising solution to handle the data fusion of integrated nonlinear INS/GNSS (Inertial Navigation System/Global Navigation Satellite System) navigation. However, its accuracy is degraded by inaccurate kinematic noise statistics which originate from disturbances of system dynamics. This paper develops a method of closed-loop feedback covariance control to address the above problem of CKF. In this method, the posterior state and its covariance are fed back to the filtering process to constitute a closed-loop structure for CKF covariance propagation. Subsequently, based on the maximum likelihood principle, a control scheme of the prior state covariance is established by using the feedback state and covariance within an estimation window and further adopting a proportional coefficient to amplify the feedback terms in recent time steps for the full use of new information to reflect actual system characteristics. Since it does not directly use kinematic noise covariance, the proposed method can effectively avoid the adverse impact of inaccurate kinematic noise statistics on filtering solutions. Further, it can also guarantee the prior state covariance to be positive semi-definite without involving extra measures. The efficacy of the proposed method is validated by simulations and experiments for integrated INS/GNSS navigation.

A Covariance Feedback Approach to Covariance Control of Nonlinear Stochastic Systems

In this paper, the covariance control algorithm for nonlinear stochastic systems using covariance feedback is studied. Covariance control of nonlinear systems scenario involves the theory of covariance control based on the idea of the covariance feedback. Therefore, the proposed covariance control algorithm is derived for our case, firstly by applying the covariance control method and linear approximation of nonlinear systems, and then it is achieved by adopting this method for a class of nonlinear stochastic systems by using feedback linearization idea and a covariance feedback controller. The effectiveness of the proposed covariance feedback algorithm is studied using numerous simulations concerning different nonlinear case studies.

Adaptive Covariance Feedback Cubature Kalman Filtering for Continuous-Discrete Bearings-Only Tracking System

Bearings-only tracking is a continuous-discrete system, whose state of motion is in the continuous-time domain and the measurement is in the discrete-time domain. The unpredicted approximation errors are inevitable due to integration, discretization, and linearization of continuous model in many filtering methods. The adaptive covariance feedback framework is proposed for solving this kind of problem, in which the posterior covariance sequence is proved theoretically to be useful for prior covariance updating. In this framework, the covariance feedback framework is integrated with the continuous-discrete cubature Kalman filtering, and Chebyshev distance is applied to judge the proper condition for the start-up of the feedback channel. The numerical results illustrate the proposed method’s superior performance in accuracy and computational efficiency.

Optimal Transmission in MIMO Channels With Multiuser Interference

Cochannel interference is one of the inevitable deleterious components in designing and analyzing of a wireless network. The use of multiple antennas at both transmitting and receiving nodes is a promising technique to suppress and/or alleviate the effect of cochannel interference on capacity. In this paper, we assess the effects of both antenna correlation and cochannel interference on the ergodic capacity of multiple-input multiple-output channels with covariance feedback. In particular, we consider a general family of spatial fading correlation model-called unitary-independent-unitary -which encompasses most of zero-mean channels with arbitrary fading profiles including the popular separable correlation channel models. We derive the average minimum mean-square error and signal-to-interference-plus-noise ratio of the parallel spatial streams using Berezin’s supermathematics. We then put forth the structure of optimal input covariance matrix maximizing the mutual information connected with the necessary and sufficient conditions as a generalization of the noise-limited case, which is tested by a simple iterative algorithm. Together with the powerful supermathematical framework, the result in the paper enables us to quantify the multiuser MIMO interference effects on the capacity in terms of spatial correlation and interference power heterogeneity.

The Precoder Design with Covariance Feedback for Simultaneous Information and Energy Transmission Systems

We consider the optimal precoder design with the assumption that the transmitter only has channel covariance information, for the multi‐input multi‐output (MIMO) information and energy transmission system. The objective of the system design is to maximize the average system information rate, meanwhile meeting the minimum energy requirement of the energy receiver. Following this objective, we formulate the problem as a semidefinite programming (SDP) and further transform it into a dual problem. Two methods are proposed to solve this problem: the first method decomposes the transmission covariance as a product of precoders so that the constrained optimization becomes an unconstrained one, whereas the second method derives the structure of the optimal transmission covariance analytically. Both methods are proved to be convergent and their overheads and complexity are also analyzed. The achievable rate‐energy (R‐E) regions for the proposed methods are presented in the simulation. Under various system settings, the superiority of the proposed methods is shown by comparing with a few existing transmission schemes.

Power Control for Space–Time-Coded MIMO Systems With Imperfect Feedback Over Joint Transmit–Receive-Correlated Channel

In this paper, power adaptation strategies for minimizing bit error rate (BER) subject to an average power constraint for orthogonal space-time-coded multiple-input-multiple-output (MIMO) systems with mean and covariance feedback over joint transmit-receive-correlated channels are presented. We first develop an optimal spatial-only power control (PC) based on an approximated BER bound, which can include the mean feedback only and covariance feedback only as special cases. Using a newly defined fuzzy signal-to-noise ratio (FSNR) criterion, a suboptimal spatial PC scheme with a closed-form expression is derived. This FSNR-based power adaptation not only has less computational complexity but has a BER performance close to that of the optimal spatial-only PC scheme as well. Second, the degrees of freedom in temporal and spatial domains are exploited to derive a joint spatiotemporal PC (S-T-PC) with the use of the FSNR strategy to minimize the average BER subject to a long-term average power constraint with mean and covariance feedback. Simulation results show that the proposed two spatial-only PC schemes can provide a BER lower than that of equal power allocation and have almost the same performance as the existing spatial-only optimal scheme but with lower computational complexity. Moreover, they outperform the PC schemes with mean or covariance feedback only. Most importantly, the new joint S-T-PC scheme substantially outperforms all the spatial-only PC schemes.

Precoding methods for multi‐input multi‐ouput interference channels with channel covariance Feedback

Usually, instantaneous channel information is required by the transmitter for the precoding in multi-input multi-output interference channels. In the case of fast fading channels, the resultant additional overhead of the system will be high. Against this, this study considers the scenario where the channel is spatially correlated and the transmitter only has the covariance information of the channel so that the system overhead can be reduced. On the basis of maximum signal-to-interference-plus-noise ratio (SINR) criterion, the author proposes two precoding methods, including the iterative precoding and bisection search precoding methods. The first method solves the optimal precoder of a given user provided that others' precoders are known, so that the SINR can be increased gradually. Whereas the second method introduces an auxiliary variable, transforms the original non-convex problem into a convex one, and solves it by convex optimisation softwares. Both the proposed methods are proved to be convergent and their computation complexity and overheads are also analysed. Under various system settings, the proposed two methods are compared with a few existing precoding or joint transceiver methods by numerical method and computer simulation, and the superiority of the proposed methods is also shown in most cases.

Precoding design for STBC‐MIMO system with imperfect feedback in spatially correlated Rayleigh channel

By minimising the pairwise error probability (PEP) bound subject to the fixed power constraint, a suboptimal precoding scheme for space–time block-coded multiple-input–multiple-output (STBC-MIMO) systems with mean and covariance feedback in spatially correlated Rayleigh fading channels is developed, which can include the mean-feedback only and covariance-feedback only as its special cases. This scheme can achieve performances close to the existing optimal scheme while being more computationally efficient. The simulation results show that the proposed scheme can provide better performances than the conventional equal power scheme, and achieve almost the same performances as the existing optimal scheme.

MIMO Systems With Quantized Covariance Feedback

A unified approach is developed for the study of multi-input, multi-output (MIMO) systems under fast fading with quantized covariance feedback. In such systems, the receiver computes, using perfect channel state information (CSI), the covariance matrices to be adopted by the transmitter corresponding to the current channel realization, and feeds back a quantized version of this information to the transmitter using finite, say Nf, bits per channel realization. Our analysis is based on a geometric framework we developed in a companion paper for manifolds of positive semi-definite (covariance) matrices with various trace and rank constraints. That analysis applies to MIMO systems in a unified manner to optimal as well as various suboptimal precoding methods for obtaining input covariances. These include, for example, the capacity achieving spatio-temporal water-filling strategy, the incorporation of just spatial water-filling and reduced-rank beamforming with power allocation in both cases, as well as MIMO systems with antenna selection. For a given system strategy, including the one that achieves capacity, the gap between the communication rates in the perfect and quantized covariance cases is shown to be O(2-Nf/N), where N is the dimension of the particular Pn manifold used for quantization. This dimension depends on the precoding strategy adopted and strongly determines how quickly the communication rate with quantized covariance feedback approaches that with perfect CSI at the transmitter (CSIT). Our results show how the choice of covariance quantization manifold can be tailored to the available feedback rate in MIMO system design.

Capacity Bounds on MIMO Relay Channel With Covariance Feedback at the Transmitters

In this paper, the source and relay transmit covariance matrices are jointly optimized for a fading multiple-antenna relay channel when the transmitters only have partial channel state information (CSI) in the form of covariance feedback. For both full-duplex and half-duplex transmissions, we evaluate lower and upper bounds on the ergodic channel capacity. These bounds require a joint optimization over the source and relay transmit covariance matrices. The methods utilized in the previous literature cannot handle this joint optimization over the transmit covariance matrices for the system model considered in this paper. Therefore, we utilize matrix differential calculus and propose iterative algorithms that find the transmit covariance matrices to solve the joint optimization problem. In this method, there is no need to specify first the eigenvectors of the transmit covariance matrices. The algorithm updates both the eigenvectors and the eigenvalues at each iteration. Through simulations, we observe that lower and upper bounds are close to each other. However, the distance between the lower and upper bounds depends on the channel conditions. If the mutual information on the source-to-relay channel and the broadcast channel get closer to each other, the bounds on capacity also get closer.

Decentralised covariance control of dynamic routing in traffic networks: a covariance feedback approach

In this study, the authors propose a novel decentralised robust routing control strategy for average and covariance of queue length in a data network. The objective is to control the transitional behaviour of the data networks in response to new traffic load. For each node, the authors design a local state feedback controller based on minimising the worst case of the queue length. The authors then propose an innovative model for covariance of the queue length in each node. To control the average of queue length, local delay-dependent robust controllers are designed based on an equivalent descriptor representation and linear matrix inequalities (LMIs). For covariance control of the queue length, the authors first show that the covariance control problem is equivalent to a standard disturbance rejection problem. Then the authors propose a covariance feedback control law. To investigate the effectiveness of the proposed methodology an example is also presented and extensive simulation results are conducted. Simulation results indicate that the proposed method significantly improves the packet loss and system response time and is able to efficiently control the transient conditions in each.

Robust stochastic moment control via genetic-pole placement in communication network parameter setting

In this paper, the problems of stochastic robust approximate covariance assignment and robust covariance feedback stabilization, which are applied to variable parameters of additive increase/multiplicative decrease (AIMD) networks, are considered. The main idea of the developed algorithm is to use the parameter settings of an AIMD network congestion control scheme, where parameters may assign the desired network’s window covariance, with respect to the current network conditions. The aim is to search for the optimal AIMD parameters of a feedback gain matrix such that the objective functions defined via appropriate robustness measures and covariance assignment constraints can be optimized using an adaptive genetic algorithm (AGA). It is shown that the results can be used to develop tools for analyzing the behavior of AIMD communication networks. Quality of service (QoS) and other performance measures of the network have been improved by using the proposed congestion control. The accuracy of the controller is demonstrated by using MATLAB and NS software programs.

Covariance control for stochastic uncertain multivariable systems via sliding mode control strategy

The main idea proposed in this study is based on converting continuous-time covariance matrix differential equations of a multivariable system into a new uncertain deterministic linear system. The closed-loop form of the new state covariance equations is derived by converting the covariance matrix Riccati equation to a new linear deterministic vector state space system. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies can be applied to it. Using a sliding mode control strategy, the uncertain interconnection terms satisfying a matching condition are nullified and the closed-loop covariance system is asymptotically stable. This is accomplished by applying a control strategy composed of sliding mode and covariance feedback control for each local subsystem.

Beamforming Capacity Optimization for MISO Systems with Both Mean and Covariance Feedback

The beamforming capacity optimization problem in MISO systems, when the transmitter has both mean and covariance feedback of the channel, has been tackled only with the SNR maximization approach, which is known to give a sub-optimal solution. Numerical solutions of the full rank input covariance matrix, presented in the literature, are capable of tracking the beamforming vector only if it is the optimal capacity achieving solution. In this paper, we solve the beamforming capacity optimization problem by following an analytical approach that projects the beamforming vector on an orthonormal basis defined by the eigenvectors of the channel covariance matrix. The proposed formulation reduces the complexity of calculating the solution and provides intuition into the problem itself. In particular, we express the necessary conditions for beamforming capacity maximization as a system of two equations, which can be solved numerically very efficiently using the secant method. Surprisingly, our indicative numerical results for the 2 x 1 and 10 x 1 MISO systems, showed that for some cases the performance gain through beamforming capacity optimization compared to the SNR maximization approach can reach 0.4 bps/Hz. This means that the SNR maximization solution deviates considerably from the optimal beamforming vector. Finally, the optimality of the SNR maximization solution is also examined.

Effective Capacity Maximization in Multi-Antenna Channels with Covariance Feedback

The tradeoff between average transmission rate and average delay is important for the system design of future wireless communication systems. In double-correlated multiple antenna channels, the spatial degrees of freedom allow to optimize the transmit strategy under throughput/delay priority. In this work, we maximize the effective capacity of a MIMO system with covariance feedback. Interestingly, the larger the delay requirement is, the more spatial degrees of freedom are used to avoid low instantaneous transmission rates. This fact is shown analytically by deriving a closed-form expression for the beamforming optimality range as a function of the spatial correlation, the SNR, and the QoS exponent. Numerical simulations illustrate the average effective capacity optimization and confirm the theoretical results.

New scheme for discrete observer design with estimation error covariance assignment

This article presents an innovative method for solving an estimation error covariance assignment problem to design an observer for a stochastic linear system. In the proposed method, the covariance assignment problem is converted to the problem of finding an extra noise-like input to the observer. Using appropriate matrix manipulation, the Riccati equation of the estimation error covariance assignment problem, is converted to a new deterministic linear state-space model. Also, the extra noise-like input to the observer is modelled as an input to the new deterministic linear state-space model. Therefore, all the conventional and well-defined control strategies could be applied and there is no need to solve a complicated Riccati equation. Moreover, using the proposed method, a multi-objective estimation error covariance tracking problem would be easily converted to the problem of controlling a standard deterministic linear state-space system. Based on the integral control method, which is applied to the new state-space model, formulations for the proposed covariance feedback law are presented. The control law results in a stable closed-loop covariance system and assigns a pre-specified covariance matrix to the estimation errors.

Optimal transmit strategy of a two-hop decode-and-forward MIMO relay system with mean and covariance feedback

This letter proposes an optimal transmit strategy to maximize the cut-set bound on the ergodic capacity for the two-hop decode-and-forward (DF) MIMO relay system with the mean and covariance feedback. Upon the analysis of the ergodic capacity, we show that the optimal transmit beamforming directions in the first hop are along the eigenvectors of the difference between the source-relay channel and the source-destination channel. In the second hop, the relay should transmit along the eigenvectors of the relay-destination channel. Using the optimization theory, we then investigate the optimal power allocation for the source and the relay with the constraint of the total transmit power. Simulation results are then presented for illustration.

State covariance assignment problem

Covariance control theory provides a parameterisation of all controllers which assign a specified state covariance matrix to the closed-loop system according to different requirements on system performance. In this study, an innovative scheme for covariance system description based on the original linear stochastic system is proposed. The main idea of the proposed scheme is based on a special rearrangement of the corresponding covariance matrix Riccati equation to a new linear deterministic state space system. The variances of the states and cross-covariance between each two states of the original system would be the states of the new covariance system. By some mathematical manipulations, the covariance assignment problem is reformulated as a standard disturbance rejection problem. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies can be applied on it. Results are presented by a covariance feedback control law based on an integral control action applied to the new covariance system. The control law causes a stable closed-loop system and assigns a pre-specified state covariance matrix to the states of the closed-loop system.