Tracking technique for manoeuvring target with correlated measurement noises and unknown parameters

Response variability is often correlated across populations of neurons, and these noise correlations may play a role in information coding. In previous studies, this possibility has been examined from the encoding and decoding perspectives. Here we used d prime and related information measures to examine how studies of noise correlations from these two perspectives are related. We found that for a pair of neurons, the effect of noise correlations on information decoding can be zero when the effect of noise correlations on the information encoded obtains its largest positive or negative values. Furthermore, there can be no effect of noise correlations on the information encoded when it has an effect on information decoding. We also measured the effect of noise correlations on information encoding and decoding in simultaneously recorded neurons in the supplementary motor area to see how well d prime accounted for the information actually present in the neural responses and to see how noise correlations affected encoding and decoding in real data. These analyses showed that d prime provides an accurate measure of information encoding and decoding in our population of neurons. We also found that the effect of noise correlations on information encoding was somewhat larger than the effect of noise correlations on information decoding, but both were relatively small. Finally, as predicted theoretically, the effects of correlations were slightly greater for larger ensembles (3-8 neurons) than for pairs of neurons.

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

For multi-sensor system with colored measurement noises, using the observation transformation, the system can be converted into an equivalent system with correlated measurement noises. Based on this method, using the classical Kalman filtering, this paper proposed a covariance intersection (CI) fusion Kalman estimator, which can handle the fused filtering, prediction and smoothing problems. The advantage of the proposed method is that it can avoid the computation of the cross co-variances among the local filtering errors and can reduce the computational burden significantly, as well as the CI fusion algorithm can be used in the uncertain system with unknown cross covariances. Based on classical Kalman filtering theory, the centralized fusion and three weighted fusion (weighted by matrices, scalars and diagonal) estimators are also presented respectively. Their accuracy comparisons are given. The geometric interpretations based on covariance ellipses are also given. A Monte-Carlo simulation example shows that the accuracy relations.

This paper considers a Fractional Sampling (FS) technique to enhance the Spectrum Sensing (SS) efficiency of a Cognitive Radio (CR) using a decision statistic based on asymptotic Random Matrix Theory (RMT). Firstly, the effect of noise correlation on eigenvalue based SS is studied analytically and by numerical evaluation. Secondly, new bounds for the Standard Condition Number (SCN) are proposed to enhance the SS efficiency in correlated noise scenarios. It is shown that proposed FS method can enhance SS efficiency up to certain FS rates at the expense of receiver complexity and no performance advantage is obtained if the FS rate is increased beyond this limit. As a result, a method for determining the operating point for the FS rate in terms of sensing performance and complexity is suggested.

In a recent paper, equations were derived for the state estimation and the error covariance of a linear discrete-time delayed system involving correlated noises. However, there appears to be a fundamental mistake in the procedure given and this is corrected.

An adaptive target tracking scheme using two Kalman filters in series is presented. The first filter is a priori designed to cope with all possible target maneuvers, The second filter is controlled adaptively to suppress measurement noise, A pseudosystem concept is applied that have an influence on the Kalman filter algorithms of both filters. This includes the decomposition of the first filter state covariance into a system noise part and a measurement noise part and the inclusion of the covariance between the state estimates of the two filters in the second filter gain and covariance algorithms. The covariance between the state estimates is recursively calculated and accounts for the serially correlated measurement noise of the second filter. The qualitative merits of the method are discussed, Results from computer simulations are included to demonstrate performance obtained.

An analytical solution is presented for a discrete-time, steady-state Kalman filter with correlated measurement noise. The measurement model is a first-order Markov process, characterized by variance and correlation parameters. The analytical results are used to study the effect of a correlation on steady-state tracking accuracies. >

For multi-target tracking, the IMM (interactive multiple model) algorithm has been proposed. The IMM is expected to reduce tracking errors for both nonmaneuvering and maneuvering targets. However, the IMM requires a heavy computational burden, because it utilizes multiple Kalman filters in parallel. On the other hand, the Kalman filter with a turning acceleration estimator, which can adapt a maneuvering target, has been proposed. The Kalman filter with a turning acceleration estimator is a single two-stage type filter and has a problem of setting threshold for the maneuver detector. In this paper, we propose the hybrid filter with a constant-velocity (CV) filter and a turning acceleration estimation filter. The proposed filter does not require a maneuver detector, because it integrates the outputs of two filters using the likelihood of each filter. And its computational requirement is smaller than the IMM, since it consists of only two Kalman based filters. The proposed method can prevent deteriorating tracking accuracy by reducing the risk of maneuver misdetection when a target maneuvers. We evaluate the performance of the proposed filter by computer simulation, and show the effectiveness of the proposed filter, comparing with the conventional Kalman filter and the two-stage Kalman filter.

In federated design of ultra-tight GPS/INS integrated system, the baseband signal pre-processing is completed in a single pre-filter assigned for each channel. As the state space model of this single pre-filter includes the code tracking errors coupled with carrier tracking errors, ionospheric errors and normalized signal amplitude, the carrier tracking process may be destroyed. Also, the measurement noises are not independent any longer after passing through the code and carrier discriminators. Therefore, we propose a double-filter-based pre-filter model that distributes the carrier and code tracking into two independent filters: a conventional pre-filter, where the normalized signal amplitude is excluded from the state space and tracks only the code signal, and a 3-dimension state filter, tracking the carrier signal. The measurement information from both filters is a scalar quantity, which removes most of the noise correlation. To further improve the performance of the double-filter-based pre-filter model, we propose a modified Kalman filter algorithm. Simulation and field tests have been conducted, and the performance analysis has been done for the following configurations in a vector-tracking mode: double-filter model with modified Kalman filter, double-filter model with conventional Kalman filter and traditional single-filter model. The preliminary analysis indicates that the double-filter model with modified Kalman filter shows the best performance in tracking and navigation domains, while the traditional single-filter model shows a sub-optimal performance.

New results are given for the bit error probability for binary DPSK modulation over both terrestrial and satellite channels taking into account noise correlation and power imbalance. The new expressions are remarkably simpler than their previously published counterparts. For the terrestrial channel, the results are in closed form in terms of tabulated functions and, for the hard-limiting satellite channel, both in terms of integrals readily evaluated by quadrature and in terms of infinite series. Using the results, it is shown that the error rate does not depend on the noise correlation (down-link in the satellite case) so long as the a priori symbol probabilities are equal, thereby solving an "open problem" posed by Lee, French, and Hong. Also, the satellite case in which each of the up-link and down-link channels contains nonzero noise correlations is briefly treated.

The magnetic recording channel is often equalised to the PR4 partial response. Viterbi detection is used to detect the recorded data, but suffers a loss owing to the effects of noise correlation. The use of coding on the PR4 magnetic recording channel to reduce the effects of noise correlation is proposed. This is shown to achieve a gain in effective SNR over an uncoded channel. Parity codes are shown to be one method of achieving this. The read data is decoded with a soft decision Viterbi detector. The performance of the method is verified through simulations.

For the multisensor linear discrete time-invariant systems with correlated measurement noises and with different measurement matrices, based on the linear unbiased minimum variance criterion, a weighted measurement fusion Kalman filtering algorithm is presented. It is identical to that obtained by the Weighted Least Squares(WLS) method, and is numerically identical to the centralized fusion Kalman filtering algorithm, so that it has the global optimality. The optimal weights are given by the Lagrange multiplier method, but its computation burden is large. In order to reduce the computational burden, a reduced dimension weighted measurement fusion Kalman filtering algorithm is derived, which avoids the Lagrange multiplier method, and can significantly reduced the computational burden. The comparison of computational count between two algorithms is given. A simulation example shows effectiveness and correctness of the proposed algorithm.

This letter considers the problem of robust angle of arrival (AOA) source localization in the presence of correlated noise and outliers based on nonconvex sparse optimization. To maintain the total convexity of the cost function while using the nonconvex penalty, we propose to regularize the correlation matrix weighted cost by generalized minimax concave (GMC) function. Then the alternating direction forward-backward splitting algorithm (ADFBS) is proposed to estimate outliers and source position simultaneously. To counter the bias problem of ADFBS, a new ADFBS based instrumental-variable estimator (IVADFBS) is developed. The IVADFBS is observed to produce nearly unbiased estimates with lower mean squared errors.

For the multisensor system with identical measurement matrix and correlated measurement noises, by correlated method, the online estimators of the noise statistics are obtained. Based on modern time series analysis method, a self-tuning weighted measurement fusion Wiener filter is presented, which avoids Lyapunov and Riccati equations, reduces the computational burden and is suitable for real time application. By dynamic error system analysis (DESA) method, it is rigorously proved that the proposed self-tuning Wiener filter converges to the optimal Wiener filter in a realization or with probability one, i.e. it has asymptotical global optimality. A simulation example for a target tracking systems with 3 sensors shows its effectiveness.

The problem of delay estimation is considered. The approach taken generally considers nonstationary signals and correlated measurement noises. The signals are described as the output of a finite dimensional linear system driven by white noise. The estimator is conceptually equivalent to two blocks. The first has the structure of a Kalman-Bucy filter for signals with delays [9]. The second minimizes the log-likelihood function. When stationary, long observation interval (SLOT) [7] assumptions are considered, the cross-correlator array receiver [1] is recovered. The results of the paper are then a generalization of the classical solution.