Multiple hypothesis tracking based on the Shiryayev sequential probability ratio test

Sequential sampling plans based on the negative binomial distribution were developed for egg mass density of spruce budworm, Choristoneura fumiferana (Clemens), in Michigan's Upper Peninsula. Plans developed were modifications of Wald's sequential probability ratio test (SPRT) based on Monte Carlo simulation. Parameters of the negative binomial distribution were estimated by the maximum likelihood method. Sampling models developed classify egg mass populations into low and high categories using the number of egg masses on whole branch samples of balsam fir, Abies balsamifera (L.) Voss. Plans are presented for three pairs of population density hypotheses to give forest pest managers the flexibility to select a plan that best meets management objectives. Monte Carlo estimates indicated that Wald's average sample number (ASN) and operating characteristic (OC) equations underestimated the actual ASN values, and the actual alpha and beta error probabilities were smaller than the values prescribed by Wald's equations. Errors were sufficiently large to have serious economic implications during implementation of plans developed from Wald's approximate procedure. The sequential plans developed by modifying the decision boundaries of Wald's SPRT using the Monte Carlo procedure had error probabilities, OC functions, and ASN values that were approximately equal to those desired.

Multi-static active sonar systems detect contacts of interest by transmitting coherent waveforms and detecting the echoes on one or more receiving sensors. When a target of interest is in a region where its echoes are detectable by more than one receiver it can, in general, be declared sooner by combining the measurements from all sensors. The track detection schemes used in active sonar systems are often based on the Wald Sequential Probability Ratio Test (SPRT) and take as input the amplitudes of the target echoes associated to the track and where the statistical models for the amplitude of a target echo usually depend on a signal-to-noise ratio (SNR) parameter. The Multi-Static Adaptive Track Detector (MSATD) is an SPRT based track detection scheme that uses estimates of target aspect derived from track state estimates and a model of bi-static target strength to adapt the parameters in the distribution for target echo amplitude. Essentially, the SUM detector is modified to use different values for SNR parameter at each sensor. The SNR parameters are determined using a model of bistatic target strength and estimates of the target aspect observed by each sensor computed from the current track state estimate. The theoretical improvement in system track detection performance (i.e., probability of detection and latency) afforded by the proposed method is also presented; theoretically exact expressions for probability of detection and latency are evaluated numerically for all three track detection schemes for a system of one source and two receivers

In this paper, an algorithm for tracking multiple maneuvering targets by Multiple Hypothesis Tracking (MHT) with nonlinear non-Gaussian Kalman filter is investigated. The main challenges in multiple maneuvering targets tracking are the nonlinearity and non -Gaussianity problems. The Multiple Hypothesis Tracking (MHT) is used to detect the multiple targets in maneuverable and non-maneuverable modes. The computational requirements increase exponentially with number of tracks, the backscan depth and this can be reduced by careful design and tuning of MHT. The 1-backscan MHT algorithm is a good compromise between the two conflicting requirements of good tracking performance and limitation of computation time. The nonlinear non-Gaussian Kalman filter is used to track the target with high maneuver rate. The nonlinear non-Gaussian Kalman filter is implemented in MHT to give less probability of missing the target. The 1-backscan MHT with nonlinear non-Gaussian Kalman filter is free from computational burden by using simple probability concepts. This method of tracking also shows the reduction in the overshoot of root mean square error (RMSE).

Statistical data analysis includes several phases. First, there is the phase of data collection. Second, there is the phase of analysis and inference. The two phases are interconnected. There are two types of data analysis. One type is called parametric and the other type is nonparametric. In the present paper, we discuss parametric inference. In parametric inference, we model the results of a given experiment as realization of random variables having a particular distribution, which is specified by its parameters. A random sample is a sequence of independent and identically distributed (i.i.d.) random variables. Statistics are functions of the data in the sample, which do not involve unknown parameters. A statistical inference is based on statistics of a given sample. We discuss two kinds of parametric inference. Estimating the values of parameters, or testing hypotheses concerning the parameters in either kind of inference, we are concerned with the accuracy and precision of the results. In estimation of parameters, the results are precise if, with high probability, they belong to a specified neighborhoods of the parameters. In testing hypotheses, one has to decide which one of two or several hypotheses should be accepted. Hypotheses which are not accepted are rejected. We distinguish between two types of errors. Type I error is the one committed by rejecting a correct hypothesis. Type II is that of accepting a wrong hypothesis. It is desired that both types of errors will occur simultaneously with small probabilities. Both precision in estimation or small error probabilities in testing depend on the statistics used (estimators or test functions) and on the sample size. In this paper, we present sampling procedures that attain the desired objectives. In Sec. 2, we discuss estimation of the parameters of a binomial distribution. In Sec. 3, more general results about estimation of expected values are presented. In Sec. 4, we discuss the Wald Sequential Probability Ratio Test (SPRT), which has optimal properties for testing two simple hypotheses.

A non-parametric sequential rank-sum probability ratio test method for binary hypothesis testing

Hypothesis formation is a major computational burden for any multiple hypotheses tracking (MHT) method. In particular, a track-oriented MHT method defines compatible tracks to be tracks not sharing common observations and then re-forms hypotheses from compatible tracks after each new scan of data is received. The Cheap Joint Probabilistic Data Association (CJPDA) method provides an efficient means for computing approximate hypothesis probabilities. This paper presents a method of extending CJPDA calculations in order to eliminate low probability track branches in a track-oriented MHT method. The method is tested using IRST data. This approach reduces the number of tracks in a cluster and the resultant computations required for hypothesis formation. It is also suggested that the use of CJPDA methods can reduce assignment matrix sizes and resultant computations for the hypothesis-oriented (Reid’s algorithm) MHT implementation.

In multi-target tracking, Multiple Hypothesis Tracking (MHT) can effectively solve the data association problem. However, traditional MHT can not make full use of motion information. In this work, we combine MHT with Interactive Multiple Model (IMM) estimator and feature fusion. New algorithm greatly improves the tracking performance due to the fact that IMM estimator provides better estimation and feature information enhances the accuracy of data association. The new algorithm is tested by tracking tropical fish in fish container. Experimental result shows that this algorithm can significantly reduce tracking lost rate and restrain the noises with higher computational effectiveness when compares with traditional MHT.

A new approach for multitarget detection and tracking with Doppler ambiguity is presented. Ambiguous Doppler measurements, in addition to the position measurements, are directly used in data association and tracking. Based on the unscented Kalman filter (UKF), the multiple hypothesis tracking (MHT) algorithm and the probabilistic data association (PDA) algorithm, three different methods for solving the ambiguity, independent of the choice of particular pulse repetition frequency (PRF) values, in the tracking level are proposed. First, the UKF is modified to handle explicitly the ambiguous Doppler measurement. It is shown that the modified UKF can achieve better tracking performance than the standard UKF. On the other hand, the MHT and PDA algorithms, both of which are usually used to solve the measurement-to-track association problem, are modified here to handle the Doppler ambiguity problem. Simulations are performed to demonstrate the effectiveness of the new algorithms.

Multiple Object Tracking (MOT) has attracted increasing attention due to its academic and commercial potential. However, it still remains challenging due to factors like data association ambiguity and abrupt appearance changes. To address these issues, we extended the multiple hypothesis tracking (MHT) by incorporating the appearance features which extracted from faster region convolutional neural network (Faster-RCNN). Additionally, a principal component analysis method was introduced to update discriminative appearance features. Thus, the data association ambiguity can be reduced surprisingly by exploiting Faster-RCNN, which means fewer hypothesis for MHT. Meanwhile, the issue of abrupt appearance changes can be addressed by modeling discriminative appearance feature based-on MHT. Many experiments on MOT benchmark show competitive performance of the proposed approach in comparison with other state-of-art tracking methods.

The com flea beetle, Chaetocnenw pulicaria Melsheimer, is an important pest of sweet com because it transmits Erwinia stewartii (Smith) Dye, the causal pathogen of Stewart’s wilt. Our goal was to quantify corn flea beetle distribution within and between sweet com plants and develop a sampling method that would be compatible with an existing sampling plan for lepidopteran pests. From plant emergence to tile 5th fully emerged leaf stage, >50% of the com flea beetles were recorded on the uppermost fully emerged leaf and the whorl leaves. For more mature sweet corn, 40-50% of the com flea beetles were recorded on leaves 4-6. The between-plant distribution pattern of adult com flea beetles fit a negative binomial distribution and was aggregated. The Wald sequential probability ratio test was used to develop sequential sampling plans for different combinations of type I and II errors, and 2 sets of decision rule boundaries. The sampling plans were validated and the effect of truncation at 100 samples examined by Monte Carlo simulation techniques. With the upper boundary of the decision rule set at the current threshold, the sampling plan would be reasonably cost effective and compatible with the lepidopteran sampling plan, although the type II error is relatively high.

Interacting multiple model (IMM) filtering and multiple hypothesis tracking (MHT) represent the most accurate methods currently available for tracking multiple maneuvering targets in cluttered environments. Although these methods are complex, modern computational capabilities make their combined implementation feasible for modern tracking systems. This paper discusses alternative approaches for developing a combined IMM/MHT tracking system and describes specific implementations that have been developed for radar and IRST applications. Simulation results for both radar and IRST systems are presented. Track maintenance and accuracy performance for the IMM/MHT system is compared with that obtained from an MHT tracker using a conventional filtering approach. Results indicate that the improvements in data association derived from the use of IMM filtering with MHT may be comparable to the well known IMM improvements in track accuracy. The addition of multiple filter models to MHT data association has the potential to significantly increase computational requirements. Thus, several compromises, described in this paper, have been developed in order to assure computational feasibility. Preliminary estimates of computational requirements are given in order to demonstrate implementation feasibility.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, we present a novel 2-D laser-based global localization approach for mobile robots, which is composed of geometrical relationship construction, a new structural unit encoding scheme (SUES), and an extended multiple hypothesis tracking (MHT) algorithm. Different from existing methods, we construct a 3-D "directional endpoint" feature encapsulating both the endpoint and the direction of a line segment; on this basis, a novel and efficient online structural unit encoding scheme (SUES) is proposed to describe the geometric relationship between the two directional endpoint features with some robustness to dynamic disturbances. Note that SUES presented in this paper is different from the bag-of-words scheme in two aspects: 1) SUES quantizes the geometrical relationship without offline training for vocabulary and 2) SUES is independent of the quality of the vocabulary. By factoring the global localization problem into a discrete pose estimation problem, the MHT is extended on the basis of SUES and odometry information to gradually restore the global robot pose. Different from the classical MHT framework, the extended MHT takes the independent observation results as the a priori, while the likelihood term is composed of consecutive candidate poses and the odometry information. Evaluations are carried out by using both publicly available data sets and self-recorded data sets. Comparative experimental results with respect to the adaptive Monte Carlo localization are presented to show the superior performance of the proposed approach in terms of success ratio and efficiency.

This paper presents a detailed analysis of the computational complexity of multiple hypothesis tracking (MHT). The result shows that the computational complexity of MHT is dominated by the number of hypotheses. Track merging and pruning are also analyzed. The results of this paper provide a new efficient tool for selecting parameters for an MHT tracker and predicting its complexity.

Because computers (except for parallel computers) generate simulation outputs sequentially, we recommend sequential probability ratio tests (SPRTs) for the statistical analysis of these outputs. However, until now simulation analysts have ignored SPRTs. To change this situation, we review SPRTs for the simplest case; namely, the case of choosing between two hypothesized values for the mean simulation output. For this case, the classic SPRT of Wald (Wald A. Sequential tests of statistical hypotheses. Ann Math Stat 1945; 16: 117–186) allows general types of distribution, including normal distributions with known variances. A modification permits unknown variances that are estimated. Hall (Hall WJ. Some sequential analogs of Stein’s two-stage test. Biometrika 1962; 49: 367–378) developed a SPRT that assumes normal distributions with unknown variances estimated from a pilot sample. A modification uses a fully sequential variance estimator. In this paper, we quantify the performance of the various SPRTs, using several Monte Carlo experiments. In experiment #1, simulation outputs are normal. Whereas Wald’s SPRT with estimated variance gives too high error rates, Hall’s original and modified SPRTs are “conservative”; that is, the actual error rates are smaller than those prespecified (nominal). Furthermore, our experiment shows that the most efficient SPRT is Hall’s modified SPRT. In experiment #2, we estimate the robustness of these SPRTs for non-normal output. For these two experiments, we provide details on their design and analysis; these details may also be useful for simulation experiments in general.

In medical, health, and sports sciences, researchers desire a device with high reliability and validity. This article focuses on reliability and validity studies with n subjects and m ≥2 repeated measurements per subject. High statistical power can be achieved by increasing n or m, and increasing m is often easier than increasing n in practice unless m is too high to result in systematic bias. The sequential probability ratio test (SPRT) is a useful statistical method which can conclude a null hypothesis H0 or an alternative hypothesis H1 with 50% of the required sample size of a non-sequential test on average. The traditional SPRT requires the likelihood function for each observed random variable, and it can be a practical burden for evaluating the likelihood ratio after each observation of a subject. Instead, m observed random variables per subject can be transformed into a test statistic which has a known sampling distribution under H0 and under H1. This allows us to formulate a SPRT based on a sequence of test statistics. In this article, three types of study are considered: reliabilityof a device, reliability of a device relative to a criterion device, and validity of a device relative to a  criterion device. Using SPRT for testing the reliability of a device, for small m, results in an average sample size of about 50% of the fixed sample size for a non-sequential test. For comparing a device to criterion, the average sample size approaches to 60% approximately as m increases. The SPRT tolerates violation of normality assumption for validity study, but it does not for reliability study.