John D. Glass

A MIMO radar benchmarking environment

With the growing amount of research being devoted to the concept of multiple-input multiple-output (MIMO) radar, there has been a lack of a common simulation and benchmarking environment for determining the viability and cost-effectiveness of MIMO radar architectures and algorithms. To this end, GTRI has developed a MIMO Benchmark environment to serve this purpose, which is to be made publically available to researchers in order to compare the performance of MIMO techniques with those of more conventional phased array radar systems. This paper describes the problem that the MIMO Benchmark is intended to be used to assist in solving, in the form of a new challenge problem for the MIMO community, as well as providing a summary of the architecture of the MIMO Benchmark infrastructure.123

MIMO radar resource allocation using posterior Cramér-Rao lower bounds

A technique is presented that will determine an efficient set of transmitters in a MIMO radar event based on tracking accuracy and energy consumption.123 The posterior Cramér-Rao lower bound (PCRLB) will provide the means of determining these optimal transmitters by placing a bound on the variance of the track state estimate. This is a predictive PCRLB since it is calculated before any measurements are taken. Optimal transmitters are chosen by minimizing a proposed cost function that incorporates the PCRLB, along with number of transmitters in the MIMO event. To account for measurement origin uncertainty, an information reduction factor (IRF) will be incorporated in the calculation of the PCRLB for each predicted measurement. Since the complexity of the cost calculation increases exponentially with the number of sensors, several approximations are made for the calculation of the PCRLB and IRF. The jacobian matrix for the sine space measurement equations are derived for use in the calculation of the PCRLB. This resource allocation scheme is evaluated using the GTRI/ONR MIMO Radar Benchmark with metrics including track completeness ratio and total cumulative energy consumption.

IMM estimators with unbiased mixing for tracking targets performing coordinated turns

The tracking of highly maneuvering targets using an interacting multiple model (IMM) estimator is considered. Two IMM estimators are evaluated: one which incorporates a horizontal coordinated turn model and one which incorporates a 3D coordinated turn model. An objective comparison of the track performances achievable with the two IMM estimators is given in the paper. Since the models in each IMM have different state dimensions, special care must be taken during the mixing stage to prevent biases. Previously, an unbiased mixing procedure was developed for an IMM estimator with two modes, and this work extends the previous result to an IMM estimator with three modes. Performance assessment of the IMM estimators was performed using a high fidelity radar simulation and benchmark scenarios. Results show that both IMM estimators provide performance enhancements over the default solution during horizontal turns. However, the IMM estimator that incorporates a 3D coordinated turn model performed better during vertical maneuvers.

Detection of rayleigh targets using adjacent matched filter samples

The matched filter maximizes signal-to-noise ratio (SNR) at its output. To determine the presence of a target, traditional radar detection compares the observed SNR at samples of the matched filter output to a specified threshold. However, sample rates often used in practice result in two or more adjacent samples with target energy. Therefore, traditional radar detection ignores a key piece of information - the correlation between samples. Using an explicit model of adjacent matched filter samples and the functional form of the matched filter response, the average log likelihood ratio test (ALLRT) is derived assuming a Rayleigh target with pulse-to-pulse fluctuations. Furthermore, key features relevant to the design of a detector are investigated. In particular, the ALLRT detector provides robustness against the negative effects of range bin straddling, and in some cases outperforms traditional detectors that use oversampled matched filter outputs.

Range estimation using adjacent matched filter samples

By jointly considering multiple adjacent matched filter samples, target localization can be more accurate than considering only a single sample. For sub-bin range estimation, a power-weighted centroid is typically the method of choice due to its simplicity. However, centroiding does not consider the correlation between adjacent samples, and is hence sub-optimal. By making assumptions on the structure of the transmitted pulse, a closed-form maximum likelihood estimator (MLE) for range can be found. The derived MLE is compared to centroiding using mean squared error (MSE) as the performance metric. Numerical simulations show that the MLE outperforms centroiding in all practical cases. Detection threshold values based on observed signal-to-noise ratio are provided for several practical false alarm probabilities.

Monopulse DOA estimation using adjacent matched filter samples

In modern surveillance radar systems, amplitude comparison monopulse techniques improve target angle estimation. By comparing the difference and sum of returns from two squinted sub-beams, an angle estimate can be formed. Radars using pulse compression techniques typically use a sampled version of the matched filter output for detection and estimation purposes, and the target energy is often assumed to be contained in a single sample. In practice this assumption is often not valid; target energy is usually contained in multiple adjacent samples, and the correlation between matched filter samples is ignored. Recently, the correlation between matched filter samples has been shown useful for a variety of estimation purposes such as resolving multiple targets and fine estimation of target range. In this work, we use an explicit model for multiple adjacent matched filter samples of the sum and difference channels of a monopulse radar system, and find maximum likelihood estimates of direction of arrival for a single target. With an emphasis on low signal-to-noise and off-boresight targets, performances of the maximum likelihood estimator and generalized maximum likelihood estimator are compared to conventional monopulse techniques that use the real part of the monopulse ratio.

Tracking with MIMO radar: A baseline solution

This paper describes a baseline target tracking system implemented using the GTRI/ONR Multiple-Input Multiple-Output (MIMO) Radar Benchmark platform. MIMO radar systems have been garnering a significant amount of attention for their potential to improve overall radar performance in comparison to existing systems. While there is much in the current literature regarding the performance and parameter design of MIMO radar target tracking systems, there is little that describes a complete target tracking solution. Such a solution would integrate measurement processing, data assignment, and track filtering into a single unit. The “MIMO tracker” described in this paper aims to provide a starting point for such tracking solutions. Although naive in some respects, this MIMO tracker provides a comparison tool for new MIMO target tracking algorithms. The results of running the tracker with the scenarios provided in the GTRI/ONR MIMO Radar Benchmark are also presented.

MIMO radar target tracking using the probability hypothesis density filter

Target tracking in a widely spread multiple input multiple output (MIMO) radar system requires joint processing of several measurements from multiple sensors. The probability hypothesis density (PHD) filter provides a promising framework to process these measurements, since it does not require any measurement-to-track associations. Furthermore, the PHD filter naturally handles a multi-target environment because of the lack of explicit data association. We implement a PHD filter in the GTRI/ONR MIMO Benchmark, and compare results against the Benchmarks default solution. We assume a linear Gaussian target model so that the posterior target intensity at any time step is a Gaussian mixture (GM). Under this assumption, the PHD filter has closed-form recursions and target state extraction is simplified. This paper focuses on our implementation of the GM-PHD filter in the MIMO Benchmark, along with practical issues such as track labeling and applying the filter for the case of multiple sensors.

Detection of unresolved Rayleigh targets using adjacent bins

Amplitude comparison monopulse systems provide angular localization of a target. When multiple targets in the illuminating beam occupy a single resolution cell, then the targets are unresolved. When knowledge of the presence of unresolved targets is known a-priori, then estimators derived in existing literature can be used for angle localization of the targets. However, the presence of unresolved targets is often not known a-priori, and in these cases typical single-target DOA estimators can fail. Detection of unresolved targets has been treated in existing literature for the case of a single range sample, ignoring range straddling. In recent literature, range and angle estimators exploiting range straddling show estimation performance enhancements in the single and multiple target cases. In those works, the correlation between adjacent bins, which is ignored in traditional radar literature, is used in the estimation of multiple targets. In this work, we expand upon recent literature by revisiting the topic of detection of unresolved targets with a signal model that includes range straddling. We use the generalized likelihood ratio test (GLRT) for the hypothesis test of multiple targets vs. a single target. A performance comparison with existing algorithms is provided. Results suggest that the proposed GLRT can provide significant benefits over existing approaches for the detection of unresolved targets.

Joint-Bin Monopulse Processing of Rayleigh Targets

Amplitude comparison monopulse systems provide precision angle localization of a target. In practice, the in-phase part of the monopulse ratio is commonly used for direction-of-arrival (DOA) estimation due to simplicity and computational speed, but it suffers poor performance for off-boresight and/or low signal-to-noise ratio (SNR) targets. Target energy is typically assumed to be contained in a single range bin, while in practice the matched filter sampling process often results in multiple adjacent matched filter samples with target energy. In the traditional radar literature, this is called bin straddling and is typically treated as a nuisance-an undesired loss of signal energy. Recent literature has addressed bin straddling for DOA and range estimation for the case of multiple unresolved targets. However, error variance reports on those target estimates, which are required by target tracking algorithms, are not provided. Furthermore, target strength is assumed to be a known parameter, which is often not valid in practice. Here, we explicitly incorporate sampling into the statistical model for sum and difference channel signal samples, and derive estimators for the unknown range and unknown DOA of a single Rayleigh target. Closed-form Cramér-Rao lower bounds (CRLBs) on those estimators are provided. Furthermore, we propose the generalized CRLB (GCRLB) as an error variance report, and SNRs required for statistical efficiency and variance consistency are provided.