Adaptive IMM Filters for Maneuvering Target With Additive and Multiplicative Noises

The analysis of the influence of fluctuation stationary multiplicative (modulating) noise acting simultaneously with additive noise on the measurement accuracy of non-energy parameters of information signals is carried out. The term “low” level of noise with the combined effects of multiplicative and additive noise is clarified. It is shown that mathematical characteristics, bias, measurement errors and error dispersion can be used as characteristics of the accuracy of measuring signal parameters at a low level of noise. The structure of the optimal receiving device for measuring one information parameter with a random initial phase against the background of additive noise is obtained. An expression is obtained for the envelope of the signal at the output of the linear part of the optimal meter according to the desired information parameter. It is shown that at a low level of multiplicative and additive noise, the estimate of one parameter of the useful signal is unbiased, and its dispersion is the sum of two terms, the first takes into account the influence of additive noise, the second is multiplicative noise. Expressions are obtained for the variance of the estimation of the information parameter under the simultaneous effect of additive and multiplicative noise. The above expressions show that the variance of errors due to the presence of multiplicative noise significantly depends on the spectral characteristics of the noise modulation function. It is noted that slow multiplicative noise is the most dangerous.

The effects of both system additive and multiplicative noise on the X-, C-, and L-band synthetic aperture radar (SAR) data covering oil slicks are examined. Prior studies have attempted to characterize such oil slicks, primarily through analysis of polarimetric SAR data. In this article, we factor in system noise that is added to the backscattered signal, introducing artifacts that can easily be confused with random and volume scattering. This confusion occurs when additive and/or multiplicative system noise dominates the measured backscattered signal. Polarimetric features used in this article are shown to be affected by both additive and multiplicative system noise, some more than others. This article highlights the importance of considering specifically multiplicative noise in the estimation of the signal-to-noise ratio (SNR). The SNR based on additive noise should at least be above 10 dB and the SNR involving both additive and multiplicative noise should at least be above 0 dB. The SNR from TerraSAR-X (TS-X) and Radarsat-2 (RS-2) is below 0 dB for the majority of the oil slick pixels when considering both the additive and multiplicative noise, rendering these data unsuitable for any analysis of the scattering properties and characterization. These results are in contrast to the reduced impact of noise on oil slicks detected by the L-band UAVSAR system. In particular, we find that there is no need to invoke exotic scattering mechanisms to explain the characteristics of the data. We also recommend a noise subtraction for any polarimetric scattering analysis.

In some Global Positioning System (GPS) signal propagation environments, especially in the ionosphere and urban areas with heavy multipath, GPS signal encounters not only additive noise but also multiplicative noise. In this paper we compare and contrast the conventional GPS signal acquisition method which focuses on handling GPS signal acquisition with additive noise, with the enhanced GPS signal processing under multiplicative noise by proposing an extension of the GPS detection mechanism, to include the GPS detection model that explains detection of the GPS signal under additive and multiplicative noise. For this purpose, a novel GPS signal detection scheme based on high order cyclostationarity is proposed. The principle is introduced, the GPS signal detection structure is described, the ambiguity of initial PseudoRandom Noise (PRN) code phase and Doppler shift of GPS signal is analysed. From the simulation results, the received GPS signal at low power level, which is degraded by additive and multiplicative noise, can be detected under the condition that the received block of GPS data length is at least 1·6 ms and sampling frequency is at least 5 MHz.

The influence of fluctuating stationary multiplicative low level noise acting simultaneously with additive noise on the accuracy of measurement of non-energy information parameters of the signal is estimated. It is shown, that the degree of influence of multiplicative noise on the accuracy of frequency measurement is completely determined by the spectrum of the square of the signal envelope and the spectral characteristics of the noise modulation function. The influence of slow and fast multiplicative noise on the information parameters of the signal is analyzed. It is pointed out that the errors in measuring the time of arrival of the signal due to the presence of multiplicative noise depend on both the signal envelope and its phase structure. It is shown that the low-level multiplicative noise has a stronger effect on the accuracy of measurement of the arrival time than on the accuracy of measurement of the frequency of the useful signal. The influence of multiplicative and additive noise on the accuracy of measuring the non-energy parameters of the useful signal is quantified for practically important cases: for small purely phase distortions of the signal, a radio pulse with a bell-shaped envelope and a constant pulse-modulated frequency.

This paper focuses on adaptive Kalman filtering problem for linear systems with unknown covariances of both dynamic multiplicative noise (multiplicative measurement noise) and additive noises (additive process and measurement noises). A recursive-noise adaptive Kalman filter is proposed to estimate both states and covariances of noises by using the varaitional Bayesian (VB) inference and an indirect method. First, we characterize inverse Wishart priors for both measurement noise covariance and process noise covariance and employ the Student's t-distribution to represent the likelihood function, which is non-Gaussian and affected by mixing multiplicative noise and additive measurement noise. Then, an adaptive Kalman filtering for recursive both noise covariance matrices and dynamic state, is proposed following VB inference. Performance analysis for VB procedures and the proposed filter is provided to ensure the convergence and stability. A target tracking example is provided to validate the effectiveness of the proposed filtering algorithm.

Unsaturated piecewise bistable stochastic resonance with three kinds of asymmetries driven by multiplicative and additive noise

In this paper, We have studied the effects of intensity and correlation time of noises on the mean first-passage time in a picecewise nonlinear system driven by multiplicative and additive colored noises with colored cross-correlation. We derived the expression of the mean first-passage time (MFPT) by applying the unified colored approximation method and the steepest-descent approximation. Results show that the MFPT of the system exhibits a mono-peak structure and the “resonance” phenomena enhance with the increase of multiplicative noise intensity. The value of the peak decreases with increasing additive noise intensity and the correlation between the additive and multiplicative noises. However, the MFPT of the system increases with the increase of additive noise intensity. That is, the effects of the additive noise and the multiplicative noise on MFPT are different. Moreover, the negative and passive correlations play different roles in the MFPT.

We investigate the escape dynamics of an active Brownian particle (ABP) in a spatial cubic potential subject to the cross-correlated multiplicative noise and additive noise. Based on the Schweitzer–Ebeling–Tilch model, the effects of noise strength, cross-correlation intensity between noises, damping coefficient and potential amplitude on the mean escape time (MET) from a metastable potential state are analyzed. The results indicate that the MET exhibits a non-monotonic behavior with a maximum as a function of the intensities of the multiplicative and additive noises, identifying the occurrence of the noise enhanced stability (NES) effects induced by the multiplicative noise and by the additive noise. The increase of the cross-correlation strength always enhances the NES effect induced by the additive noise, regardless of the cross-correlation between noises is positive or negative. However, the positive and negative cross-correlation play an opposite role on the NES effect induced by the multiplicative noise. Moreover, the NES effects induced by the additive and multiplicative noises can be enhanced by the increase of the damping coefficient and the potential amplitude. A physical mechanism for the NES effect of the ABP can be understood as the fact that a certain amount of noise can stabilize the sojourn of the ABP in a limit cycle. Our results demonstrate that the cross-correlation between noises may provide a possible strategy for controlling the stability of active particle systems.

Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

Many healthy and pathological brain rhythms, including beta and gamma rhythms and essential tremor, are suspected to be induced by noise. This yields randomly occurring, brief epochs of higher amplitude oscillatory activity known as "bursts," the statistics of which are important for proper neural function. Here, we consider a more realistic model with both multiplicative and additive noise instead of only additive noise, to understand how state-dependent fluctuations further affect rhythm induction. For illustrative purposes, we calibrate the model at the lower end of the beta band that relates to movement; parameter tuning can extend the relevance of our analysis to the higher frequency gamma band or to lower frequency essential tremors. A stochastic Wilson-Cowan model for reciprocally as well as self-coupled excitatory (E) and inhibitory (I) populations is analyzed in the parameter regime where the noise-free dynamics spiral in to a fixed point. Noisy oscillations known as quasi-cycles are then generated by stochastic synaptic inputs. The corresponding dynamics of E and I local field potentials can be studied using linear stochastic differential equations subject to both additive and multiplicative noises. As the prevalence of bursts is proportional to the slow envelope of the E and I firing activities, we perform an envelope-phase decomposition using the stochastic averaging method. The resulting envelope dynamics are uni-directionally coupled to the phase dynamics as in the case of additive noise alone but both dynamics involve new noise-dependent terms. We derive the stationary probability and compute power spectral densities of envelope fluctuations. We find that multiplicative noise can enhance network synchronization by reducing the magnitude of the negative real part of the complex conjugate eigenvalues. Higher noise can lead to a "virtual limit cycle," where the deterministically stable eigenvalues around the fixed point acquire a positive real part, making the system act more like a noisy limit cycle rather than a quasi-cycle. Multiplicative noise can thus exacerbate synchronization and possibly contribute to the onset of symptoms in certain motor diseases.

We derive an optimum filter function to detect a target degraded by multiplicative noise and additive overlapping noise and placed in background noise. The filter is designed to maximize the metric peak-to-output energy, which is the ratio of the expected value squared of the output peak at the target position to the expected value of the average output energy. The optimum filter provides improved discrimination as well as robustness to input noise. One advantage of the filter described here over the homomorphic filters is that the additional preprocess on the input image, that is, the input logarithmic operation, is not required for reducing the effects of multiplicative noise. The performance of the filter is examined in terms of discrimination against background noise and robustness to multiplicative and additive input noise. Both multiplicative amplitude noise and multiplicative complex noise are considered.

In this paper, the modified potential function, the stationary probability distribution function (SPDF), the mean growth time and the mean degeneration time for a vegetation growth system with time delay are investigated, where the vegetation system is assumed to be disturbed by cross-correlated multiplicative and additive noises. The results reveal some fact that the multiplicative and additive noises can both reduce the stability and speed up the decline of the vegetation system, while the strength of the noise correlation and time delay can both enhance the stability of the vegetation and slow down the depression process of the ecological system. On the other hand, with regard to the impacts of noises and time delay on the mean development and degeneration processes of the ecological system, it is discovered that 1) in the development process of the vegetation population, the increase of the noise correlation strength and time delay will restrain the regime shift from the barren state to the boom one, while the increase of the additive noise can lead to the fast regime shift from the barren state to the boom one. 2) Conversely, in the depression process of the ecological system, the increase of the strength of the correlation noise and time delay will prevent the regime shift from the boom state to the barren one. Comparatively, the increase of the additive and multiplicative noises can accelerate the regime shift from the boom state to the barren state.

The paper addresses a parameter identification problem for discrete-time stochastic systems models with multiplicative and additive noises. Stochastic systems with additive and multiplicative noises are considered when solving many practical problems related to the processing of measurements information. The purpose of this work is to develop a numerically stable gradient-free instrumental method for solving the parameter identification problems for a class of mathematical models described by discrete-time linear stochastic systems with multiplicative and additive noises on the basis of metaheuristic optimization and singular value decomposition. We construct an identification criterion in the form of the negative log-likelihood function based on the values calculated by the newly proposed SVD-based Kalman-type filtering algorithm, taking into account the multiplicative noises in the equations of the state and measurements. Metaheuristic optimization algorithms such as the GA (genetic algorithm) and SA (simulated annealing) are used to minimize the identification criterion. Numerical experiments confirm the validity of the proposed method and its numerical stability compared with the usage of the conventional Kalman-type filtering algorithm.

INSAR images are inevitably contaminated by noise during the process of generation, transmission, compression, and reception. Noise not only affects the quality of the INSAR image, but also affects subsequent operations such as the design of corresponding filters, INSAR image segmentation, compression, restoration, and feature recognition. The INSAR image noise model is mainly divided into additive noise and multiplicative noise. Compared with additive noise, multiplicative noise is more complicated due to INSAR image correlation and non-Gaussian. Based on least squares algorithm system of additive and multiplicative mixed noise model, this paper proposes a method of using PCA to remove multiplicative gamma distribution noise. The pure noise coefficient is obtained by subtracting the original coefficient from the diagonal wavelet coefficient of the noisy image, and the mode of the local variance is calculated as the estimation value of the noise standard deviation. Experiments show that the proposed method can obtain more accurate estimation of noise; in particular in the case of less noise and more detailed image information, its effect is more obvious.

A typical bistable nonlinear system with multiplicative and additive noises can produce stochastic resonance (SR) by increasing the intensity of the additive noise or the multiplicative noise and it has been proved that SR can also be realized by tuning system parameters. We clearly demonstrate the equivalence between parameter-induced SR (PSR) and noise-induced SR in the presence of multiplicative and additive noises. By tuning several system parameters with fixed noise intensities, the SR is induced just as it is realized by tuning the additive noise or the multiplicative noise. It may be interesting to realize PSR when the noise intensity exceeds the resonance level, or when the characteristic of the noise is unknown.