Convolution PHD Filtering for Nonlinear Non-Gaussian Models

2011 ◽  
Vol 213 ◽  
pp. 344-348
Author(s):  
Jian Jun Yin ◽  
Jian Qiu Zhang
Keyword(s):  
Parallel Implementation ◽  
Gaussian Mixture ◽  
Probability Hypothesis Density ◽  
Gaussian Sum ◽  
Multi Target Tracking ◽  
Lower Complexity ◽  
Observation Noise ◽  
Non Gaussian ◽  
Convolution Filters ◽  
Cphd Filter

A novel probability hypothesis density (PHD) filter, called the Gaussian mixture convolution PHD (GMCPHD) filter was proposed. The PHD within the filter is approximated by a Gaussian sum, as in the Gaussian mixture PHD (GMPHD) filter, but the model may be non-Gaussian and nonlinear. This is implemented by a bank of convolution filters with Gaussian approximations to the predicted and posterior densities. The analysis results show the lower complexity, more amenable for parallel implementation of the GMCPHD filter than the convolution PHD (CPHD) filter and the ability to deal with complex observation model, small observation noise and non-Gaussian noise of the proposed filter over the existing Gaussian mixture particle PHD (GMPPHD) filter. The multi-target tracking simulation results verify the effectiveness of the proposed method.

scholarly journals Active Sonar Target Tracking Based on the GM-CPHD Filter Algorithm

2018 ◽  
Vol 36 (4) ◽  
pp. 656-663
Author(s):  
Xiao Chen ◽  
Yaan Li ◽  
Yuxing Li ◽  
Jing Yu
Keyword(s):  
Target Tracking ◽  
Detection Probability ◽  
Gaussian Mixture ◽  
Time Varying ◽  
Adaptive Detection ◽  
Probability Hypothesis Density ◽  
Active Sonar ◽  
Multi Target Tracking ◽  
Cphd Filter ◽  
The Relationship

The estimation of underwater multi-target state has always been the difficult problem of active sonar target tracking.In order to get the variable number of target and their state, the random finite set theory is applied to multi-target tracking system.This theory not only effectively avoids the problem of multi-target tracking data association, and also realizes the estimation of time-varying number of targets and their states.Due to Probability Hypothesis Density(PHD) recursion propagates cardnality distribution with only a single parameter, a new generalization of the PHD recursion called Cardinalized Probability Hypothesis Density(CPHD) recursion, which jointly propagates the intensity function and the cardnality distribution, while have a big computation than PHD.Also there did not have closed-form solution for PHD recursion and CPHD recursion, so for linear Gaussian multi-target tracking system, the Gaussian Mixture Probability Hypothesis Density and Gaussian Mixture Cardinalized Probability Hypothesis Density(GM-CPHD) filter algorithm is put forward.GM-CPHD is more accurate than GM-PHD in estimation of the time-varying number of targets.In this paper, we use the ellipse gate tracking strategy to reduce computation in GM-CPHD filtering algorithm.At the same time, according to the characteristics of underwater target tracking, using active sonar equation, we get the relationship between detection probability, distance and false alarm, when fixed false alarm, analytic formula of the relationship between adaptive detection probability and distance is obtained, we puts forward the adaptive detection probability GM-CPHD filtering algorithm.Simulation shows that the combination of ellipse tracking gate strategy and adaptive detection probability GM-CPHD filtering algorithm can realize the estimation of the time-varying number of targets and their state more accuracy in dense clutter environment.

scholarly journals Strong Tracking PHD Filter Based on Variational Bayesian with Inaccurate Process and Measurement Noise Covariance

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1126
Author(s):  
Zhentao Hu ◽  
Linlin Yang ◽  
Yong Jin ◽  
Han Wang ◽  
Shibo Yang
Keyword(s):  
Real Time ◽  
Gaussian Mixture ◽  
Measurement Noise ◽  
Tracking Accuracy ◽  
Process Noise ◽  
Probability Hypothesis Density ◽  
Measurement Noise Covariance ◽  
Multi Target Tracking ◽  
Noise Covariance ◽  
Fading Factor

Assuming that the measurement and process noise covariances are known, the probability hypothesis density (PHD) filter is effective in real-time multi-target tracking; however, noise covariance is often unknown and time-varying for an actual scene. To solve this problem, a strong tracking PHD filter based on Variational Bayes (VB) approximation is proposed in this paper. The measurement noise covariance is described in the linear system by the inverse Wishart (IW) distribution. Then, the fading factor in the strong tracking principle uses the optimal measurement noise covariance at the previous moment to control the state prediction covariance in real-time. The Gaussian IW (GIW) joint distribution adopts the VB approximation to jointly return the measurement noise covariance and the target state covariance. The simulation results show that, compared with the traditional Gaussian mixture PHD (GM-PHD) and the VB-adaptive PHD, the proposed algorithm has higher tracking accuracy and stronger robustness in a more reasonable calculation time.

scholarly journals Time-Matching Random Finite Set-Based Filter for Radar Multi-Target Tracking

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4416 ◽  
Author(s):  
Defu Jiang ◽  
Ming Liu ◽  
Yiyue Gao ◽  
Yang Gao ◽  
Wei Fu ◽  
...  
Keyword(s):  
Target Tracking ◽  
Gaussian Mixture ◽  
Bayesian Filtering ◽  
Probability Hypothesis Density ◽  
Random Finite Set ◽  
Bayesian Formulation ◽  
Multi Target Tracking ◽  
Finite Set ◽  
Density Filter ◽  
Bernoulli Filter

The random finite set (RFS) approach provides an elegant Bayesian formulation of the multi-target tracking (MTT) problem without the requirement of explicit data association. In order to improve the performance of the RFS-based filter in radar MTT applications, this paper proposes a time-matching Bayesian filtering framework to deal with the problem caused by the diversity of target sampling times. Based on this framework, we develop a time-matching joint generalized labeled multi-Bernoulli filter and a time-matching probability hypothesis density filter. Simulations are performed by their Gaussian mixture implementations. The results show that the proposed approach can improve the accuracy of target state estimation, as well as the robustness.

scholarly journals An Improved Gaussian Mixture CKF Algorithm under Non-Gaussian Observation Noise

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjian Wang ◽  
Cun Li
Keyword(s):  
Target Tracking ◽  
Computation Time ◽  
Velocity Model ◽  
Gaussian Mixture ◽  
Fast Tracking ◽  
Mixture Density ◽  
Cubature Kalman Filter ◽  
Observation Noise ◽  
Non Gaussian ◽  
Time Update

In order to solve the problems that the weight of Gaussian components of Gaussian mixture filter remains constant during the time update stage, an improved Gaussian Mixture Cubature Kalman Filter (IGMCKF) algorithm is designed by combining a Gaussian mixture density model with a CKF for target tracking. The algorithm adopts Gaussian mixture density function to approximately estimate the observation noise. The observation models based on Mini RadaScan for target tracking on offing are introduced, and the observation noise is modelled as glint noise. The Gaussian components are predicted and updated using CKF. A cost function is designed by integral square difference to update the weight of Gaussian components on the time update stage. Based on comparison experiments of constant angular velocity model and maneuver model with different algorithms, the proposed algorithm has the advantages of fast tracking response and high estimation precision, and the computation time should satisfy real-time target tracking requirements.

scholarly journals Improved Gaussian Mixture Probability Hypothesis Density for Tracking Closely Spaced Targets

2017 ◽  
Vol 63 (3) ◽  
pp. 247-254 ◽  
Author(s):  
Huanqing Zhang ◽  
Hongwei Ge ◽  
Jinlong Yang
Keyword(s):  
State Estimation ◽  
Analytic Solution ◽  
Gaussian Mixture ◽  
Multiple Target ◽  
Probability Hypothesis Density ◽  
Random Finite Set ◽  
Multi Target Tracking ◽  
Finite Set ◽  
Estimation Precision ◽  
Simulation Results

AbstractProbability hypothesis density (PHD) filter is a suboptimal Bayesian multi-target filter based on random finite set. The Gaussian mixture PHD filter is an analytic solution to the PHD filter for linear Gaussian multi-target models. However, when targets move near each other, the GM-PHD filter cannot correctly estimate the number of targets and their states. To solve the problem, a novel reweighting scheme for closely spaced targets is proposed under the framework of the GM-PHD filter, which can be able to correctly redistribute the weights of closely spaced targets, and effectively improve the multiple target state estimation precision. Simulation results demonstrate that the proposed algorithm can accurately estimate the number of targets and their states, and effectively improve the performance of multi-target tracking algorithm.

Carrier Phase-based RAIM Algorithm Using a Gaussian Sum Filter

2010 ◽  
Vol 64 (1) ◽  
pp. 75-90 ◽  
Author(s):  
Ho Yun ◽  
Youngsun Yun ◽  
Changdon Kee
Keyword(s):  
Gaussian Distribution ◽  
Carrier Phase ◽  
Phase Error ◽  
Critical Role ◽  
Gaussian Mixture ◽  
Error Distribution ◽  
Integrity Monitoring ◽  
Gaussian Sum ◽  
Carrier Phase Error ◽  
Non Gaussian

Carrier phase measurements are used to provide high-accuracy estimates of position. For safety-of-life navigation applications such as precision approach and landing, integrity plays a critical role. Carrier phase-based Receiver Autonomous Integrity Monitoring (CRAIM) has been investigated for many years (Pervan et al, 1998; Feng et al, 2007). Assuming that the carrier phase error has a Gaussian distribution, conventional CRAIM algorithms were directly derived from the Pseudorange-based RAIM (PRAIM). However, the actual carrier phase error does not exactly follow the Gaussian distribution, hence the performance of the conventional CRAIM algorithm is not optimal.To approach this problem, this paper proposes a new CRAIM algorithm that uses Gaussian sum filters. A Gaussian sum filter can deal with any non-Gaussian error distribution and accurately present the posterior distributions of states. In this paper, a new method of making a Gaussian mixture model, which follows the true error distribution, is introduced. Additionally an integrity monitoring algorithm, using a Gaussian sum filter, is described in detail. The simulation results show that the proposed algorithm can have about 18% smaller Minimum Detectable Bias (MDB) and generates about 20% lower protection levels than those of the conventional CRAIM algorithm. In other words, by considering a non-Gaussian carrier phase error distribution, the new algorithm can improve the accuracy and the availability.

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