Variants of partial update augmented CLMS algorithm and their performance analysis

Naturally complex-valued information or those presented in complex domain are effectively processed by an augmented complex least-mean-square (ACLMS) algorithm. In some applications, the ACLMS algorithm may be too computationally and memory-intensive to implement. In this paper, a new algorithm, termed partial-update ACLMS (PU-ACLMS) algorithm is proposed, where only a fraction of the coefficient set is selected to update at each iteration. Doing so, two types of partial update schemes are presented referred to as the sequential and stochastic partial-updates, to reduce computational load and power consumption in the corresponding adaptive filter. The computational cost for full-update PU-ACLMS and its partial update implementations are discussed. Next, the steady-state mean and mean-square performance of PU-ACLMS for noncircular complex signals are analyzed and closed-form expressions of the steady-state excess mean-square error (EMSE) and mean-square deviation (MSD) are given. Then, employing the weighted energy-conservation relation, the EMSE and MSD learning curves are derived. The simulation results are verified and compared with those of theoretical predictions through numerical examples

Partial diffusion Kalman filtering for distributed state estimation in multiagent networks

Many problems in multiagent networks can be solved through distributed learning (state estimation) of linear dynamical systems. In this paper, we develop a partial-diffusion Kalman filtering (PDKF) algorithm, as a fully distributed solution for state estimation in the multiagent networks with limited communication resources. In the PDKF algorithm, every agent (node) is allowed to share only a subset of its intermediate estimate vectors with its neighbors at each iteration, reducing the amount of internode communications. We analyze the stability of the PDKF algorithm and show that the algorithm is stable and convergent in both mean and mean-square senses. We also derive a closed-form expression for the steady-state mean-square deviation criterion. Furthermore, we show theoretically and by numerical examples that the PDKF algorithm provides a trade-off between the estimation performance and the communication cost that is extremely profitable

Analysis of partial diffusion LMS for adaptive estimation over networks with noisy links

In partial diffusion-based least mean square (PDLMS) scheme, each node shares a part of its intermediate estimate vector with its neighbors at each iteration. In this paper, besides studying the general PDLMS scheme, we figure out how the noisy links deteriorate the network performance during the exchange of weight estimates. We investigate the steady state mean square deviation (MSD) and derive a theoretical expression for it. We also derive the mean and mean-square convergence conditions for the PDLMS algorithm in the presence of noisy links. Our analysis reveals that unlike the PDLMS with ideal links, the steady-state network MSD performance of the PDLMS algorithm is not improved as the number of entries communicated at each iteration increases. Strictly speaking, the noisy links condition imposes more complexity to the MSD derivation that has a noticeable effect on the overall performance. This term violates the trade-off between the communication cost and the estimation performance of the networks in comparison with the ideal links. Our simulation results substantiate the effect of noisy links on PDLMS algorithm and verify the theoretical findings. They match well with theory

Performance analysis of distributed Kalman filtering with partial diffusion over noisy network

The performance of partial diffusion Kalman filtering (PDKF) algorithm for the networks with noisy links is studied here. A closed-form expression for the steady-state mean square deviation is then derived and theoretically shown that when the links are noisy, the communication-performance tradeoff, reported for the PDKF algorithm, does not hold. Additionally, optimal selection of combination weights is investigated and a combination rule along with an adaptive implementation is motivated. The results confirm the theoretical outcome

State estimation in linear dynamical systems by partial update Kalman filtering

In this letter, we develop a partial update Kalman filtering (PUKF) algorithm to solve the state of a discrete-time linear stochastic dynamical system. In the proposed algorithm, only a subset of the state vector is updated at every iteration, which reduces its computational complexity, compared to the original KF algorithm. The required conditions for the stability of the algorithm are discussed. A closed-form expression for steady-state mean-square deviation is also derived. Numerical examples are used to validate the correctness of the provided analysis. They also reveal the PUKF algorithm exhibits a trade-off between the estimation accuracy and the computational load which is extremely profitable in practical applications

Energy-efficient diffusion Kalman filtering for multi-agent networks in IoT

Increasing the energy efficiency of an Internet of Things (IoT) system is a major challenge for its successful implementation. To reduce the computation and storage burden and enhance the efficiency of traditional IoT, an energy-efficient diffusion-based algorithm for state estimation in multi-agent networks is proposed in this paper. In the proposed algorithm (referred to as reduced-link diffusion Kalman filter (RL-diffKF)) the nodes (agents) can communicate only with a fraction of their neighbors and each node runs a local Kalman filter to estimate the state of a linear dynamic system. This algorithm results in a significant reduction in communication cost during both adaptation and aggregation processes albeit at the expense of possible degradation in the network performance. To justify the stability and convergence of the RL-diffKF algorithm, an in-depth analysis of the performance is reported. We also consider the problem of optimal selection of combination weights and use the idea of minimum variance estimation to analytically derive the adaptive combiners. The theoretical findings are verified through numerical simulations

Partial diffusion Kalman filter with adaptive combiners

Adaptive estimation of optimal combination weights for partial-diffusion Kalman filtering together with its mean convergence and stability analysis is proposed here. The simulations confirm its superior performance compared with the existing combiners. Sensor networks with limited accessible power highly benefit from this design

Demonstration of Universal Parametric Entangling Gates on a Multi-Qubit Lattice

We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gateset for a linear array of four superconducting qubits. An average process fidelity of $\mathcal{F}=93\%$ is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity against the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all such permutations, an average fidelity of $\mathcal{F}=91.6\pm2.6\%$ is observed. These results thus offer a path to a scalable architecture with high selectivity and low crosstalk