Algorithms for Mobile Nodes Self-Localisation in Wireless Ad Hoc Networks

大学人工智能英语教材翻译IntroductionIn recent years, artificial intelligence (AI) has become a ubiquitous presence in our lives, revolutionizing various industries and fields. To meet the growing demand for AI professionals, universities have started offering courses and developing textbooks on the subject. This article aims to translate key contents of a university-level AI English textbook into Chinese, providing students with a comprehensive resource to enhance their understanding of this rapidly evolving field.Chapter 1: Introduction to Artificial Intelligence人工智能简介Artificial intelligence, often referred to as AI, is a branch of computer science that focuses on the creation of intelligent machines capable of performing tasks that typically require human intelligence. AI can be divided into two categories: narrow AI, which is designed to perform a specific task, and general AI, which aims to replicate human-level intelligence across a wide range of domains.Chapter 2: Machine Learning机器学习Machine learning is a subset of AI that enables computers to learn and improve from experience without being explicitly programmed. It involves the development of algorithms and models that allow computers to analyze and interpret data, identify patterns, and make predictions or decisions basedon the observed information. Supervised learning, unsupervised learning, and reinforcement learning are the three main types of machine learning techniques.Chapter 3: Neural Networks神经网络Neural networks are a fundamental concept in AI. Inspired by the structure and function of the human brain, neural networks consist of interconnected nodes or artificial neurons. These networks learn from training data by adjusting the connections between nodes to optimize their performance. Deep learning, a subfield of AI, utilizes neural networks with multiple layers to solve complex problems and achieve higher accuracy in tasks such as image recognition and natural language processing.Chapter 4: Natural Language Processing自然语言处理Natural language processing (NLP) focuses on enabling computers to interact and understand human language in a natural and meaningful way. It involves the development of algorithms and models that can process, analyze, and generate human language, enabling tasks such as machine translation, sentiment analysis, and chatbot development. NLP plays a crucial role in bridging the gap between humans and AI systems.Chapter 5: Computer Vision计算机视觉Computer vision is an interdisciplinary field that deals with the extraction, analysis, and understanding of visual information from images or videos. Through the use of AI techniques, computers can recognize objects, detect and track motion, and perform tasks such as facial recognition and image classification. Computer vision has various applications, including autonomous vehicles, surveillance systems, and augmented reality.Chapter 6: Robotics and Artificial Intelligence机器人与人工智能The integration of AI and robotics has led to significant advancements in the field of robotics. AI-powered robots can perceive their environment, make autonomous decisions, and interact with humans and other robots effectively. This chapter explores the role of AI in robotics, discussing topics such as robot perception, robot control, and human-robot interaction.Chapter 7: Ethical and Social Implications of AI人工智能的伦理和社会影响As AI continues to advance, ethical considerations and potential societal impact become increasingly important. This chapter delves into the ethical dilemmas surrounding AI, including privacy concerns, biases in AI systems, and the impact of AI on employment and workforce. It emphasizes the need for responsible development and deployment of AI technologies, ensuring that they benefit humanity and uphold ethical standards.ConclusionIn conclusion, this article has provided a translated overview of key topics in a university-level AI English textbook. By familiarizing themselves with these concepts, students can deepen their understanding of artificial intelligence and its various applications. Moreover, this translation serves as a valuable resource for educators and researchers in the Chinese-speaking community who seek to expand their knowledge in this rapidly advancing field. With the continued development of AI, it is imperative to bridge language barriers and foster global collaboration in order to drive innovation and ensure responsible AI implementation.。

普林斯顿算法
普林斯顿算法是一种用于解决最短路径问题的一种经典算法，也称为迪杰斯特拉算法。

它是一种贪婪算法，逐步构建最短路径树，从起始节点开始，依次选择与当前节点距离最近的节点，并更新该节点到其他节点的距离。

通过不断选择最短路径上的节点，最终得到起点到各个节点的最短路径。

普林斯顿算法的基本步骤如下：
1. 创建一个距离列表distances，用于保存起始节点到各个节点的最短距离，初始值为无穷大（表示未知路径）。

2. 创建一个前驱列表predecessors，用于保存路径上每个节点
的前驱节点，初始值为None。

3. 将起始节点的距离设置为0，即distances[start_node] = 0。

4. 选择距离最短且未被访问的节点作为当前节点。

5. 更新当前节点到邻居节点的距离，如果新的距离比原来的距离小，则更新距离和前驱节点。

6. 标记当前节点为已访问。

7. 重复步骤4-6直到所有节点都被访问。

8. 根据distances和predecessors构建最短路径。

普林斯顿算法的时间复杂度为O(V^2)，其中V为节点数。

它
适用于处理节点数不太大的图，但在节点数非常大时，性能可能较差。

为了提高效率，还有一种优化的算法称为堆优化的迪杰斯特拉算法，它使用优先队列来选择最短距离的节点，使得时间复杂度降为O((V+E)logV)，其中E为边数。

随着科技的发展三代人购物方式的英语作文全文共3篇示例，供读者参考篇1The Evolution of Shopping: A Generational Shift Driven by TechnologyShopping, a fundamental aspect of human society, has undergone remarkable transformations across generations, shaped by the relentless march of technology. From the traditional brick-and-mortar stores of our grandparents' era to the seamless online experiences of today's youth, the way we acquire goods and services has been revolutionized. This essay delves into the contrasting shopping experiences of three distinct generations, illuminating how technological advancements have reshaped our purchasing behaviors and expectations.Generation 1: The Brick-and-Mortar EraFor our grandparents, shopping was an inherently physical and social experience. They grew up in a time when retail therapy meant strolling through bustling downtown districts or traversing the aisles of department stores. The mere act of goingshopping was an event, often accompanied by family members or friends, fostering a sense of community and camaraderie.The shopping experience of this generation was deeply rooted in personal interactions. Salespeople were not just facilitators of transactions but trusted advisors, offering guidance and expertise on products and services. Our grandparents valued the opportunity to touch, feel, and inspect items before making a purchase, relying heavily on their senses to evaluate quality and authenticity.Moreover, shopping was a leisurely activity, with time dedicated to browsing, comparing options, and savoring the entire process. Window shopping was a beloved pastime, allowing our grandparents to admire the latest fashions and coveted items without the pressure of immediate acquisition.Generation 2: The Dawn of ConvenienceAs technology advanced, our parents' generation witnessed the emergence of new shopping paradigms that prioritized convenience and efficiency. The rise of suburban shopping malls and big-box retailers reshaped the shopping landscape, offering a wider array of products under one roof.While personal interactions with salespeople became less frequent, this generation embraced the convenience ofself-service shopping. They could browse through extensive merchandise displays, read product descriptions, and make informed decisions without the need for constant assistance.The advent of catalogs and home shopping networks introduced a novel way of shopping from the comfort of one's home. Our parents could peruse catalogs, place orders over the phone, and eagerly await the arrival of their purchases, a precursor to the online shopping experiences of today.Technology also ushered in the era of debit and credit cards, streamlining the payment process and enabling our parents to make purchases without the need for cash or checks. This newfound convenience, coupled with the proliferation of shopping malls and big-box stores, fostered a culture of impulse buying and leisure shopping.Generation 3: The Digital NativesFor today's youth, dubbed the "digital natives," shopping has transcended physical boundaries and become an immersive, technology-driven experience. The rise of e-commerce platforms and online marketplaces has revolutionized the way we discover, research, and acquire products and services.With a few taps or clicks, this generation can access a vast array of products from the comfort of their homes or on-the-go via mobile devices. Online shopping has become a seamless and personalized journey, with algorithms tailoring recommendations based on browsing history and preferences.Social media and influencer marketing have emerged as powerful forces shaping the shopping habits of digital natives. Peer recommendations, unboxing videos, and social media influencers have become trusted sources of product information, often superseding traditional advertising channels.Moreover, this generation values convenience, speed, and transparency. One-click purchases, fast shipping options, and easy returns have become the norm, catering to their desire for instant gratification and hassle-free experiences.Technological advancements have also introduced innovative shopping experiences, such as augmented reality (AR) and virtual reality (VR). Digital natives can virtually "try on" clothing or visualize furniture in their living spaces, blurring the lines between the physical and digital realms.ConclusionThe evolution of shopping across three generations is a testament to the profound impact of technology on our daily lives. From the tactile and social experiences of our grandparents to the convenience-driven era of our parents, and the immersive digital realm embraced by today's youth, each generation has adapted to the prevailing technological landscape.While the allure of brick-and-mortar stores and personal interactions may never fade entirely, the future of shopping lies in seamless omnichannel experiences that blend the best of physical and digital worlds. As technology continues to advance, we can expect even more innovative and personalized shopping journeys, catering to our ever-evolving needs and preferences.Ultimately, the evolution of shopping reflects our human capacity for adaptation and our insatiable pursuit of convenience, efficiency, and personalization. As we embrace the marvels of technology, we must also cherish the enduring joy of the shopping experience – a timeless ritual that transcends generations and connects us to our shared human experiences.篇2The Evolution of Shopping: A Generational Shift Catalyzed by TechnologyAs I ponder upon the stark differences in shopping habits between my grandparents, parents, and myself, I can't help but marvel at the profound impact technology has had on our lives. What was once a simple errand has metamorphosed into a multifaceted experience, transcending mere transactions and reshaping the very fabric of how we acquire goods and services.My grandparents, raised in a era where brick-and-mortar stores reigned supreme, embodied a shopping ethos that was deeply rooted in tradition and personal interaction. For them, the act of physically visiting a store held a certain charm – a ritual that allowed them to immerse themselves in the sights, sounds, and even the aromas that accompanied the shopping experience.I vividly recall the stories my grandmother would regale me with, tales of meticulously planning her trips to the local market or the downtown shopping district. The anticipation would build as she carefully crafted her shopping list, a testament to her resourcefulness and frugality. Once at the store, she would relish the opportunity to engage with shopkeepers, exchanging pleasantries and seeking their expertise on the products she intended to purchase.My grandfather, on the other hand, found solace in the camaraderie that blossomed among fellow patrons as they awaited their turn at the checkout counter. These chance encounters often evolved into lively discussions, fostering a sense of community that extended far beyond the confines of the store itself.For my grandparents, shopping was an event – a chance to immerse themselves in the vibrant tapestry of human interaction while procuring the necessities of daily life. Their approach was deliberate, unhurried, and infused with a deep appreciation for the tangible nature of the shopping experience.As time marched on, my parents' generation ushered in a new era of shopping, one that was shaped by the advent of technological advancements. The proliferation of malls andbig-box retailers revolutionized the way they approached the act of acquiring goods and services.Gone were the days of leisurely strolls through quaint marketplaces; instead, my parents embraced the convenience and efficiency that these modern shopping meccas offered. Vast parking lots and sprawling complexes became the new playgrounds, where they could indulge in a one-stop-shopexperience, their carts brimming with an array of products from diverse retailers under one roof.Technology's influence extended beyond the physical shopping environment, as my parents eagerly embraced the emergence of online shopping. With a few clicks of a button, they could browse virtual aisles, compare prices, and have their purchases delivered straight to their doorstep – a convenience that was once unimaginable.Yet, despite the allure of these technological advancements, my parents still maintained a connection to the traditional shopping experience. They would often blend their online ventures with occasional trips to brick-and-mortar stores, seeking to strike a balance between convenience and the tactile joy of physically examining and trying on merchandise.As I came of age in a world increasingly dominated by digital technologies, my shopping habits have undergone a seismic shift, one that would likely bewilder and intrigue my grandparents and parents alike. For my generation, the boundaries between the physical and virtual realms have become blurred, giving rise to a seamless, omnichannel shopping experience.With the ubiquity of smartphones and the ever-expanding reach of the internet, I can now shop anytime, anywhere, with a mere swipe or tap on my mobile device. Online marketplaces have become vast emporiums, offering an unprecedented array of products from around the globe, all accessible at my fingertips.The rise of social media has further transformed the shopping landscape, with influencers and targeted advertising shaping my purchasing decisions in ways that were once unimaginable. Algorithms and personalized recommendations have become trusted advisors, curating products tailored to my preferences and browsing history.Moreover, the integration of augmented reality and virtual try-on technologies has revolutionized the way I evaluate potential purchases. I can now visualize how a piece of furniture would look in my living room or try on a pair of shoes without ever stepping foot in a physical store.Yet, despite the allure of these digital conveniences, I still find myself drawn to the tangible experience ofbrick-and-mortar shopping on occasion. There is a certain thrill in physically exploring a store, immersing myself in its ambiance,and engaging with knowledgeable sales associates who can offer personalized recommendations and insights.As I reflect on the generational divide in shopping habits, I am struck by the profound impact of technological advancements. What began as a simple transaction has evolved into a multifaceted experience, one that seamlessly blends the convenience of digital platforms with the enduring allure of physical exploration.While my grandparents' generation found solace in the rituals and human connections that accompanied traditional shopping, my parents' era ushered in a new era of convenience and efficiency. And now, my generation stands at the precipice of a truly revolutionary shopping paradigm, where the boundaries between the physical and virtual worlds have become increasingly blurred.As technology continues to shape our lives, it is clear that the act of shopping will continue to evolve, adapting to our ever-changing needs and desires. Perhaps the future will bring even more immersive and personalized experiences, blending the best of both worlds – the convenience of digital platforms and the sensory delights of physical exploration.Regardless of the path that lies ahead, one thing remains certain: the way we shop has become an indelible reflection of the times in which we live, a tapestry woven from the threads of technological progress and our enduring human desire for both convenience and connection.篇3As a student, here is an essay on "The Evolution of Shopping Methods Across Three Generations with Technological Advancements," written in English, approximately 2000 words:The Evolution of Shopping Methods Across Three Generations with Technological AdvancementsShopping, a ubiquitous activity that has been an integral part of human existence for centuries, has undergone a remarkable transformation with the advent of technology. From the traditional brick-and-mortar stores to the rise ofe-commerce, and now the emergence of immersive shopping experiences, the way we shop has evolved significantly across three generations. This essay delves into the contrasting shopping experiences of Baby Boomers, Generation X, and Millennials, highlighting how technological advancements have shaped and reshaped the retail landscape.Baby Boomers: The Traditional Shopping ExperienceBorn between 1946 and 1964, Baby Boomers grew up in an era when shopping was a physical experience. The retail landscape was dominated by department stores, local markets, and mom-and-pop shops. Shopping was a social activity, an opportunity to interact with salespeople, try on clothes, and browse through aisles filled with merchandise.For Baby Boomers, the shopping experience was a tactile one. They could touch, feel, and inspect products before making a purchase. The act of browsing through stores and window shopping was a form of entertainment, a way to spend leisure time. Shopping malls became popular gathering places, where families could enjoy a day out, grab a bite to eat, and indulge in retail therapy.However, this generation also experienced the early stages of technological disruption in the retail sector. The introduction of credit cards and catalogs opened up new avenues for purchasing goods without physically visiting a store. Nevertheless, the traditional shopping experience remained the predominant mode of consumption for Baby Boomers.Generation X: The Rise of E-CommerceBorn between 1965 and 1980, Generation X witnessed a pivotal shift in shopping methods with the advent of the internet and the rise of e-commerce. This generation was at the forefront of adopting online shopping, which offered convenience, accessibility, and a wider range of choices.E-commerce platforms like Amazon, eBay, and early online retailers revolutionized the way Generation X shopped. No longer confined to physical stores, they could browse and purchase products from the comfort of their homes or offices. Online shopping allowed for comparison shopping, access to reviews, and the ability to find niche or hard-to-find items with just a few clicks.While the traditional in-store experience still held value for Generation X, online shopping became increasingly popular due to its time-saving and hassle-free nature. This generation embraced the convenience of having products delivered straight to their doorsteps, saving them the effort of battling traffic and crowded malls.Millennials: The Immersive Shopping ExperienceBorn between 1981 and 1996, Millennials are the true digital natives, growing up in an era where technology has permeated every aspect of life, including shopping. For this generation, thelines between online and offline shopping have blurred, creating an immersive and interconnected shopping experience.Millennials have embraced the concept of "omnichannel" shopping, seamlessly transitioning between physical stores,e-commerce platforms, and mobile apps. They expect a consistent and personalized experience across all channels, with the ability to research products online, make purchases via their smartphones, and pick up or return items in-store.Social media has become a powerful influencer in the shopping habits of Millennials. Influencer marketing,user-generated content, and peer recommendations play a significant role in their purchasing decisions. They seek authenticity, transparency, and a sense of connection with the brands they support.Moreover, Millennials have embraced the concept of experiential shopping, where the act of shopping is not just about acquiring products but also about creating memorable experiences. Pop-up stores, interactive displays, and immersive virtual reality (VR) experiences have become increasingly popular among this generation, blending entertainment and retail in innovative ways.The Future of Shopping: Seamless Integration and PersonalizationAs we look towards the future, the evolution of shopping methods is likely to continue, driven by technological advancements and changing consumer preferences. The lines between online and offline shopping will become even more blurred, creating a seamless and integrated shopping experience.Artificial intelligence (AI) and machine learning will play a crucial role in personalization, offering tailored recommendations based on individual preferences and purchasing behaviors. Virtual and augmented reality technologies will further enhance the immersive shopping experience, allowing consumers to virtually try on clothes, visualize furniture in their homes, or explore virtual showrooms.Moreover, the rise of the Internet of Things (IoT) and smart home devices will enable seamless replenishment of household items, with appliances automatically reordering consumables when running low.ConclusionThe evolution of shopping methods across three generations – Baby Boomers, Generation X, and Millennials – has been a fascinating journey shaped by technological advancements. From the traditional brick-and-mortar stores to the rise of e-commerce and the emergence of immersive shopping experiences, each generation has adapted to and embraced new ways of shopping.As we move forward, the future of shopping will likely be characterized by a seamless integration of online and offline channels, personalized experiences driven by AI and data analytics, and the continued exploration of immersive technologies like VR and AR. Regardless of the generation, the desire for convenience, choice, and unique experiences will remain at the forefront of consumer expectations, shaping the ever-evolving retail landscape.。

算法作文素材Algorithms have become an integral part of our daily lives, influencing everything from social media feeds to autonomous vehicles. 算法已经成为我们日常生活中不可或缺的一部分，影响着从社交媒体到自动驾驶车辆的方方面面。

These complex mathematical instructions dictate how technology functions, often making decisions for us without our awareness. 这些复杂的数学指令指导着技术的运作，通常在我们不知情的情况下为我们做出决策。

One of the benefits of algorithms is their ability to sift through vast amounts of data quickly and efficiently. 算法的好处之一是它们能够快速而有效地筛选大量数据。

However, this efficiency can also lead to issues of bias and discrimination, as algorithms are often programmed with the biases of their creators. 然而，这种效率也可能导致偏见和歧视的问题，因为算法往往被编程了其创造者的偏见。

For example, a study by the University of Washington found that online ads for high-paying jobs were shown more frequently to men than women. 例如，华盛顿大学的一项研究发现，高薪工作的在线广告更频繁地展示给男性而不是女性。

广东省东莞市第四高级中学2024-2025学年高三上学期11月期中英语试题一、阅读理解Environmental charities play a crucial role in preserving our planet for future generations. Here’s a look at how a few of these organizations are making a difference.Sierra Club Foundation (SCF)The SCF has been a leader in environmental conservation for over a century. With a focus on wildlife protection and habitat restoration, the foundation has helped establish numerous national parks and wildlife reserves. They also run educational programs to raise awareness about environmental issues.Friends of the Earth (FOE)Friends of the Earth is an international network of environmental organizations that advocate for the protection of the natural world. They are known for their activism and persuading efforts, pushing for stronger environmental laws and corporate responsibility. FOE also provides resources to help individuals make sustainable choices.Environmental Defense Fund (EDF)The EDF is a global organization dedicated to addressing climate change and preserving biodiversity. They use science, economics, and law to find environmental solutions that work with industry and government. Their initiatives have led to significant policy changes and corporate responsibility improvements.Ecology and Environment Foundation (EEF)The EEF is a charitable organization that focuses on community-based conservation projects. They work closely with local communities to develop sustainable practices that protect the environment and improve livelihoods. By empowering individuals and communities, EEF aims to create lasting change.1．What is the primary mission of the Sierra Club Foundation?A．Relying on stronger environmental laws.B．Setting up national parks and wildlife reserves.C．Providing resources for sustainable living.D．Appealing to corporate responsibility.2．How does the Environmental Defense Fund (EDF) mainly operate?A．Through community-based conservation projects.B．By using science, economics, and law to find solutions.C．By running educational programs for the public.D．By selling goods and asking for help.3．What is a unique approach of the Ecology and Environment Foundation (EEF)?A．Working with industry and government to create policy changes.B．Advocating for the protection of the natural world through activism.C．Using science and economics to address climate change.D．Granting rights of local communities to develop sustainable practices.Sandra Cisneros was born in Chicago in 1954 to a Mexican American family. As the only girl in a family of seven children, she often felt like she had “seven fathers,” because her six brothers, as well as her father, tried to control her. Feeling shy and unimportant, she retreated (躲避) into books. Despite her love of reading, she did not do well in elementary school because she was too shy to participate.In high school, with the encouragement of one particular teacher, Cisneros improved her grades and worked for the school literary magazine. Her father encouraged her to go to college because he thought it would be a good way for her to find a husband. Cisneros did attend college, but instead of searching for a husband, she found a teacher who helped her join the famous graduate writing program at the University of Iowa. At the university’s Writers’ Workshop, however, she felt lonely — a Mexican American from a poor neighborhood among students from wealthy families. The feeling of being so different helped Cisneros find her “creative voice”.“It was not until this moment when I considered myself truly different that my writing acquired a voice. I knew I was a Mexican woman, but I didn’t think it had anything to do with why I felt so much imbalance in my life, but it had everything to do with it! That’s when I decided I would write about something my classmates couldn’t write about.”Cisneros published her first work, The House on Mango Street, when she was twenty-nine.The book talks about a young Mexican American girl growing up in a Spanish-speaking area in Chicago, much like the neighborhoods in which Cisneros lived as a child. The book won an award in 1985 and has been used in classes from high school to graduate school level. Since then, Cisneros has published several books of poetry, a children’s book and a short-story collection. 4．What can we know about Cisneros in her childhood?A．Her brothers disliked her.B．She felt herself a nobody.C．She was too shy to go to school.D．She did not meet any good teachers.5．The graduate program gave Cisneros a chance to ________.A．run away from her family B．develop her writing styleC．make a lot of friends D．search for a husband6．According to Cisneros, what was the key factor in her success?A．Her childhood experience.B．Her training in the Workshop.C．Her feeling of being different.D．Her early years in college.7．What do we learn about The House on Mango Street?A．It enjoys great popularity among students.B．It is a book of poetry written by Cisneros.C．It wasn’t a success as it was written in Spanish.D．It won an award when Cisneros was twenty-nine.The news industry has had a rough decade. Print readership is steadily decreasing, newspapers are closing, and journalists with decades of experience are being laid off. In response, major newspapers have made significant changes. They’re attempting to defeat declining reader interest by shortening stories, creating clickbait (诱饵性标题), and most especially, using social media to their advantage.With the rise of social media sites, many people have claimed that we are entering a new age in which news must be delivered in 140 characters or fewer. People’s ability to focus onlong-form content and engage in deep reading has also been declining due to the endless distractions and excessive information in today’s world. This change in reading habits has led to a preference for short, easily understood news pieces that can be quickly consumed. To interest a more specific and generally younger readership, newspapers have revised content, prioritizing articles that are visually appealing instead of having depth.But, in reality, there is still a demand for in-depth reporting. In this era of misinformation and clickbait, readers are seeking reliable sources of news that provide context, analysis, and accountability. Depth reporting explores the fundamental causes, involves multiple views, and uncovers the hidden truths that shape our world, helping readers get a more comprehensive understanding of complex matters.While social media have changed the way we consume news, the quality of news remains essential for the public. It’s crucial for the news industry to achieve a balance between catering to changing reader preferences while also maintaining the integrity (完整性) of news. This means providing both quick updates and in-depth analysis, and using social media to promote their content, but not at the expense of accuracy or integrity. By doing so, news organizations can ensure that they remain relevant and trusted sources of information in a rapidly changing media environment.8．What problem does traditional news industry face?A．The decline of readership.B．The lack of long-form stories.C．The spread of unreliable information.D．The shortage of experienced journalists.9．What does the underlined word “prioritizing” in paragraph 2 probably mean?A．Checking out.B．Cutting down.C．Paying no attention to.D．Attaching importance to.10．What do we know from paragraph 3?A．People’s need for in-depth reporting is decreasing.B．Social media has played a key role in promoting hidden facts.C．Clickbait greatly increases readers’ interests in exploring truths.D．In-depth reporting can improve comprehension of complex issues.11．What is the main idea of the last paragraph?A．A focus on quick updates and popular topics.B．Preference for multiple perspectives and shorter articles.C．A balance between readers’ preferences and the quality of news.D．Importance of news sources and accuracy of contents.About ten years ago, logging into Facebook, Twitter, or Instagram would mostly show posts from friends and family in the order they were posted. Today, these platforms present a mix of content, tailored by algorithms (算法) to match users’ interests, whether it’s plants, sports, cats, or politics.Kyle Chayka, a writer for The New Yorker, discusses this topic in his book, Filterworld. He explains that algorithms analyze user data to predict and influence what they will likely engage with. This means that instead of a simple, chronological feed, users encounter a dynamic stream, constantly adapting to their preferences. Chayka examines how these algorithmic recommendations control what we consume, from music and movies to food and travel destinations. He argues that this machine-driven selection process has turned us into passive consumers, making our preferences and tastes more similar.Chayka points out that algorithms make us passive by always showing us content that we’re unlikely to click away from but won’t find too unexpected or challenging. This constant stream of recommendations reduces our exposure to diverse or challenging content, subtly shaping our preferences and behaviors.Moreover, Chayka points out that algorithms also pressure content creators, like musicians and artists, to tailor their work to fit these digital platforms. For instance, musicians on Spotify or TikTok might focus on creating catchy hooks at the beginning of their songs to grab the listener’s attention.Despite the strong presence of these algorithms, Chayka believes that regulation could reduce their influence. He suggests that if Meta, the parent company of Facebook, were required to separate its various services, like Instagram or WhatsApp, and make them compete with each other, it could give users more control and choice over their digital consumption.In summary, the change from simple, time-ordered social. media posts to algorithm-drivencontent has a big impact on both the viewers and the creators, influencing what we see, hear, and even think. Chayka’s insights highlight the need for greater awareness and potentially more regulation in our increasingly digital world.12．According to the text, how have social media platforms changed in the past ten years?A．They show posts in a time-based order.B．They prioritize posts from friends and family.C．They make adjustments to satisfy users’ needs.D．They provide more content to meet different needs.13．What does Kyle Chayka think of algorithmic recommendations?A．They make users more active consumers.B．They shape users’ preferences and behaviors.C．They reduce the influence of content creators.D．They expose users to diverse and challenging content.14．How do algorithms influence musicians’ work on digital platforms?A．By encouraging musicians to create longer songs.B．By discouraging musicians from using catchy hooks.C．By giving musicians more control and choice over their music.D．By requiring musicians to create their work to fit the platforms.15．What can be concluded from the text?A．Tech companies should have more departments.B．Social media algorithms give content creators less opportunities.C．Social media algorithms flatten our culture by making decisions for us.D．Network platforms have increased the common recommendations for 10 years.Art is all around us. It can be found everywhere, including fancy galleries, people’s living rooms, and on the sides of buildings. So, why is art important?It promotes expression and creativity. As humans, we’re naturally drawn to art as a form of expression and communication. 16 It’s a way for them to express themselves before they’re able to speak. In fact, participation in the arts may even assist kids with language, motor skills, and visual learning development.17 When someone applies for a job, there are certain skills they need to have like data analysis or bookkeeping. However, many employers also understand the very important need for the skills which are hard to measure and often difficult to define. Some examples include a person’s ability to adapt to change, think creatively, or collaborate with team members.It provides historical context. 18 This is why people devote their lives to studying cave art, Shakespearean plays, and so much more. When we take the time to dive into art created in the past, we can learn about other generations and eras. We can study art to find out what those before us were facing and how they overcame it. 19In therapy(疗法)settings, art also provides an opportunity for digging deeper and expressing emotions that are difficult to discuss. 20 In one important study, children between 6 and 12 were asked to draw a house as a distraction after thinking about something upsetting. This group was able to improve their mood when compared with children who were instructed to draw the negative event or simply copy another drawing.A．These are its major benefits.B．Children love to draw, sing, and dance.C．Art and human history go hand-in-hand.D．How does it have an impact on our life?E．It helps all of us develop necessary soft skills.F．It can help people handle both their past and present problems.G．Similarly, future generations will learn about our current events through our art.二、完形填空My mother has always been one of those rare people that sees the good in everyone and does good things. She’s had her ups and downs but has always 21 a positive, sunny outlook on life and been very 22 to people.One day, my little sister fell and hurt her ankle, desperately needing a 23 to the hospital emergency room. My mother immediately 24 into crisis mode, packed my sister into the car, and drove to our local hospital. In such a 25 , my mother didn’t call to tell my father. When she got to the hospital, she realized she needed to 26 with my father immediately.While waiting for my sister to be examined, my mother 27 her way to the pay phone to place her call. She put her coin in, called my father and told him everything. After she hung up, the phone 28 several additional coins that Mom wasn’t owed.Realizing that the phone was 29 , my mother decided to leave the 30 coins by the phone. She told us that in a crisis, people might not remember to bring 31 with them to make that emergency call.I’ve often thought about her 32 from an adult’s perspective. I realize that someone seeing the money by he phone may have 33 taken it because not everyone was as 34 as my mother. But I like to believe that my mother’s faith was 35 and that someone who needed them found the coins waiting there.21．A．tolerated B．anticipated C．maintained D．expressed 22．A．patient B．helpful C．honest D．polite 23．A．rest B．stay C．lift D．visit24．A．cut B．shifted C．looked D．stuck 25．A．rush B．way C．relief D．process 26．A．come along B．keep in line C．make up D．get in touch 27．A．made B．felt C．picked D．gave 28．A．found B．returned C．collected D．charged 29．A．smart B．ready C．convenient D．broken 30．A．different B．ancient C．extra D．rare31．A．luck B．phones C．change D．chances 32．A．opportunity B．decision C．appointment D．encounter 33．A．simply B．suddenly C．obviously D．gradually 34．A．thoughtful B．grateful C．hopeful D．successful 35．A．hard-won B．newly-built C．well-placed D．deeply-rooted三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

Accurate Passive Location Estimation Using TOA MeasurementsJunyang Shen,Andreas F.Molisch,Fellow,IEEE,and Jussi Salmi,Member,IEEEAbstract—Localization of objects is fast becoming a major aspect of wireless technologies,with applications in logistics, surveillance,and emergency response.Time-of-arrival(TOA) localization is ideally suited for high-precision localization of objects in particular in indoor environments,where GPS is not available.This paper considers the case where one transmitter and multiple,distributed,receivers are used to estimate the location of a passive(reflecting)object.It furthermore focuses on the situation when the transmitter and receivers can be synchronized,so that TOA(as opposed to time-difference-of-arrival(TDOA))information can be used.We propose a novel, Two-Step estimation(TSE)algorithm for the localization of the object.We then derive the Cramer-Rao Lower Bound(CRLB) for TOA and show that it is an order of magnitude lower than the CRLB of TDOA in typical setups.The TSE algorithm achieves the CRLB when the TOA measurements are subject to small Gaussian-distributed errors,which is verified by analytical and simulation results.Moreover,practical measurement results show that the estimation error variance of TSE can be33dB lower than that of TDOA based algorithms.Index Terms—TOA,TDOA,location estimation,CRLB.I.I NTRODUCTIONO BJECT location estimation has recently received inten-sive interests for a large variety of applications.For example,localization of people in smoke-filled buildings can be life-saving[1];positioning techniques also provide useful location information for search-and-rescue[2],logistics[3], and security applications such as localization of intruders[4].A variety of localization techniques have been proposed in the literature,which differ by the type of information and system parameters that are used.The three most important kinds utilize the received signal strength(RSS)[5],angle of arrival(AOA)[6],and signal propagation time[7],[8],[9], respectively.RSS algorithms use the received signal power for object positioning;their accuracies are limited by the fading of wireless signals[5].AOA algorithms require either directional antennas or receiver antenna arrays1.Signal-propagation-time based algorithms estimate the object location using the time it takes the signal to travel from the transmitter to the target and from there to the receivers.They achieve very accurate Manuscript received April15,2011;revised September28,2011and Jan-uary18,2012;accepted February12,2012.The associate editor coordinating the review of this paper and approving it for publication was X.Wang.J.Shen and A.F.Molisch are,and J.Salmi was with the Department of Electrical Engineering,Viterbi School of Engineering,University of Southern California(e-mail:{junyangs,molisch,salmi}@).J.Salmi is currently with Aalto University,SMARAD CoE,Espoo,Finland.This paper is partially supported by the Office of Naval Research(ONR) under grant10599363.Part of this work was presented in the IEEE Int.Conference on Ultrawide-band Communications2011.Digital Object Identifier10.1109/TWC.2012.040412.1106971Note that AOA does not provide better estimation accuracy than the signal propagation time based methods[10].estimation of object location if combined with high-precision timing measurement techniques[11],such as ultrawideband (UWB)signaling,which allows centimeter and even sub-millimeter accuracy,see[12],[13],and Section VII.Due to such merits,the UWB range determination is an ideal candidate for short-range object location systems and also forms the basis for the localization of sensor nodes in the IEEE802.15.4a standard[14].The algorithms based on signal propagation time can be fur-ther classified into Time of Arrival(TOA)and Time Difference of Arrival(TDOA).TOA algorithms employ the information of the absolute signal travel time from the transmitter to the target and thence to the receivers.The term“TOA”can be used in two different cases:1)there is no synchronization between transmitters and receivers and then clock bias between them exist;2)there is synchronization between transmitters and receivers and then clock bias between them does not exist. In this paper,we consider the second situation with the synchronization between the transmitter and receivers.Such synchronization can be done by cable connections between the devices,or sophisticated wireless synchronization algo-rithms[15].TDOA is employed if there is no synchronization between the transmitter and the receivers.In that case,only the receivers are synchronized.Receivers do not know the signal travel time and therefore employ the difference of signal travel times between the receivers.It is intuitive that TOA has better performance than the TDOA,since the TDOA loses information about the signal departure time[7].The TDOA/TOA positioning problems can furthermore be divided into“active”and“passive”object cases.“Active”means that the object itself is the transmitter,while“passive”means that it is not the transmitter nor receiver,but a separate (reflecting/scattering)object that just interacts with the signal stemming from a separate transmitter2.There are numerous papers on the TOA/TDOA location estimation for“active”objects.Regarding TDOA,the two-stage method[16]and the Approximate Maximum Likelihood Estimation[17]are shown to be able to achieve the Cramer-Rao Lower Bound(CRLB)of“active”TDOA[8].As we know,the CRLB sets the lower bound of the estimation error variance of any un-biased method.Two important TOA methods of“active”object positioning are the Least-Square Method[18]and the Approximate Maximum Likelihood Es-timation Method[17],both of which achieve the CRLB of “active”TOA.“Active”object estimation methods are used, e.g,for cellular handsets,WLAN,satellite positioning,and active RFID.2The definitions of“active”and“passive”here are different from those in radar literature.In radar literature,“passive radar”does not transmit signals and only detects transmission while“active radar”transmits signals toward targets.1536-1276/12$31.00c 2012IEEE“Passive”positioning is necessary in many practical situa-tions like crime-prevention surveillance,assets tracking,and medical patient monitoring,where the target to be localized is neither transmitter nor receiver,but a separate(reflect-ing/scattering)object.The TDOA positioning algorithms for “passive”objects are essentially the same as for“active”objects.For TOA,however,the synchronization creates a fundamental difference between“active”and“passive”cases. Regarding the“passive”object positioning,to the best of our knowledge,no TOA algorithms have been developed.This paper aims tofill this gap by proposing a TOA algorithm for passive object location estimation,which furthermore achieves the CRLB of“passive”TOA.The key contributions are:•A novel,two step estimation(TSE)method for the passive TOA based location estimation.It borrows an idea from the TDOA algorithm of[16].•CRLB for passive TOA based location estimation.When the TOA measurement error is Gaussian and small,we prove that the TSE can achieve the CRLB.Besides,it is also shown that the estimated target locations by TSE are Gaussian random variables whose covariance matrix is the inverse of the Fisher Information Matrix(FIM)related to the CRLB.We also show that in typical situations the CRLB of TOA is much lower than that of TDOA.•Experimental study of the performances of TSE.With one transmitter and three receivers equipped with UWB antennas,we perform100experimental measurements with an aluminium pole as the target.After extracting the signal travel time by high-resolution algorithms,the location of the target is evaluated by TSE.We show that the variance of estimated target location by TSE is much (33dB)lower than that by the TDOA method in[16]. The remainder of this paper is organized as follows.Section II presents the architecture of positioning system.Section III derives the TSE,followed by comparison between CRLB of TOA and TDOA algorithms in Section IV.Section V analyzes the performance of TSE.Section VI presents the simulations results.Section VII evaluates the performance of TSE based on UWB measurement.Finally Section VIII draws the conclusions.Notation:Throughout this paper,a variable with“hat”ˆ•denotes the measured/estimated values,and the“bar”¯•denotes the mean value.Bold letters denote vectors/matrices. E(•)is the expectation operator.If not particularly specified,“TOA”in this paper denotes the“TOA”for a passive object.II.A RCHITECTURE OF L OCALIZATION S YSTEMIn this section,wefirst discuss the challenges of localization systems,and present the focus of this paper.Then,the system model of individual localization is discussed.A.Challenges for target localizationFor easy understanding,we consider an intruder localization system using UWB signals.Note that the intruder detection can also be performed using other methods such as the Device-free Passive(DfP)approach[19]and Radio Frequency Identification(RFID)method[20].However,both the DfP and RFID methods are based on preliminary environmental measurement information like“Radio Map Construction”[19] and“fingerprints”[20].On the other hand,the TOA based approach considered in our framework does not require the preliminary efforts for obtaining environmental information. With this example,we show the challenges of target po-sitioning system:Multiple Source Separation,Indirect Path Detection and Individual Target Localization.The intruder detection system localizes,and then directs a camera to capture the photo of the targets(intruders).This localization system consists of one transmitter and several receivers.The transmitter transmits signals which are reflected by the targets,then,the receivers localize the targets based on the received signals.Multiple Source Separation:If there are more than one intruders,the system needs to localize each of them.With multiple targets,each receiver receives impulses from several objects.Only the information(such as TOA)extracted from impulses reflected by the same target should be combined for localization.Thus,the Multiple Source Separation is very important for target localization and several techniques have been proposed for this purpose.In[21],a pattern recognition scheme is used to perform the Multiple Source Separation. Video imaging and blind source separation techniques are employed for target separation in[22].Indirect Path Detection:The transmitted signals are not only reflected by the intruders,but also by surrounding objects,such as walls and tables.To reduce the adverse impact of non-target objects in the localization of target, the localization process consists of two steps.In the initial/first stage,the system measures and then stores the channel impulses without the intruders.These impulses are reflected by non-target objects,which is referred to as reflectors here.The radio signal paths existing without the target are called background paths.When the intruders are present,the system performs the second measurement. To obtain the impulses related to the intruders,the system subtracts the second measurement with thefirst one. The remaining impulses after the subtraction can be through one of the following paths:a)transmitter-intruders-receivers,b)transmitter-reflectors-intruders-receivers,c) transmitter-intruders-reflectors-receivers,d)transmitter-reflectors-intruders-reflectors-receivers3.Thefirst kind of paths are called direct paths and the rest are called indirect paths.In most situations,only direct paths can be used for localization.In the literature,there are several methods proposed for indirect path identification[23],[24]. Individual Target Localization:After the Multiple Source Separation and Indirect Path Detection,the positioning system knows the signal impulses through the direct paths for each target.Then,the system extracts the characteristics of direct paths such as TOA and AOA.Based on these characteristics, the targets arefinally localized.Most researches on Individual Target Localization assumes that Multiple Source Separation and Indirect Path Detection are perfectly performed such as [16],[25]and[26].Note that the three challenges sometimes 3Note that here we omit the impulses having two or more interactions with the intruder because of the resulted low signal-to-noise radio(SNR)by multiple reflections.Cable for synchronizationFig.1.Illustration of TOA based Location Estimation System Model.are jointly addressed,so that the target locations are estimated in one step such as the method presented in [27].In this paper,we focus on the Individual Target Local-ization,under the same framework of [16],[25]and [26],assuming that Multiple Source Separation and Indirect Path Detection are perfectly performed in prior.In addition,we only use the TOA information for localization,which achieves very high accuracy with ultra-wideband signals.The method to ex-tract TOA information using background channel cancelation is described in details in [28]and also Section VII.B.System Model of Individual LocalizationFor ease of exposition,we consider the passive object (target)location estimation problem in a two-dimensional plane as shown in Fig.1.There is a target whose location [x,y ]is to be estimated by a system with one transmitter and M receivers.Without loss of generality,let the location of the transmitter be [0,0],and the location of the i th receiver be [a i ,b i ],1≤i ≤M .The transmitter transmits an impulse;the receivers subsequently receive the signal copies reflected from the target and other objects.We adopt the assumption also made in [16],[17]that the target reflects the signal into all ing (wired)backbone connections be-tween the transmitter and receivers,or high-accuracy wireless synchronization algorithms,the transmitter and receivers are synchronized.The errors of cable synchronization are negli-gible compared with the TOA measurement errors.Thus,at the estimation center,signal travel times can be obtained by comparing the departure time at the transmitter and the arrival time at the receivers.Let the TOA from the transmitter via the target to the i th receiver be t i ,and r i =c 0t i ,where c 0is the speed of light,1≤i ≤M .Then,r i = x 2+y 2+(x −a i )2+(y −b i )2i =1,...M.(1)For future use we define r =[r 1,r 2,...,r M ].Assuming each measurement involves an error,we haver i −ˆri =e i ,1≤i ≤M,where r i is the true value,ˆr i is the measured value and e i is the measurement error.In our model,the indirect paths areignored and we assume e i to be zero mean.The estimation system tries to find the [ˆx ,ˆy ],that best fits the above equations in the sense of minimizing the error varianceΔ=E [(ˆx −x )2+(ˆy −y )2].(2)Assuming the e i are Gaussian-distributed variables with zeromean and variances σ2i ,the conditional probability functionof the observations ˆr are formulated as follows:p (ˆr |z )=Ni =11√2πσi ·exp −(ˆr i −( x 2+y 2+ (x −a i )2+(y −b i )2))22σ2i,(3)where z =[x,y ].III.TSE M ETHODIn this section,we present the two steps of TSE andsummarize them in Algorithm 1.In the first step of TSE,we assume x ,y , x 2+y 2are independent of each other,and obtain temporary results for the target location based on this assumption.In the second step,we remove the assumption and update the estimation results.A.Step 1of TSEIn the first step of TSE,we obtain an initial estimate of[x,y, x 2+y 2],which is performed in two stages:Stage A and Stage B.The basic idea here is to utilize the linear approximation [16][29]to simplify the problem,considering that TOA measurement errors are small with UWB signals.Let v =x 2+y 2,taking the squares of both sides of (1)leads to2a i x +2b i y −2r i v =a 2i +b 2i −r 2i .Since r i −ˆr i =e i ,it follows that−a 2i +b 2i −ˆr 2i 2+a i x +b i y −ˆr i v=e i (v −ˆr i )−e 2i 2=e i (v −ˆr i )−O (e 2i ).(4)where O (•)is the Big O Notation meaning that f (α)=O (g (α))if and only if there exits a positive real number M and a real number αsuch that|f (α)|≤M |g (α)|for all α>α0.If e i is small,we can omit the second or higher order terms O (e 2i )in Eqn (4).In the following of this paper,we do this,leaving the linear (first order)term.Since there are M such equations,we can express them in a matrix form as followsh −S θ=Be +O (e 2)≈Be ,(5)whereh=⎡⎢⎢⎢⎢⎣−a21+b21−ˆr212−a22+b22−ˆr222...−a2M+b2M−ˆr2M2⎤⎥⎥⎥⎥⎦,S=−⎡⎢⎢⎢⎣a1b1−ˆr1a2b2−ˆr2...a Mb M−ˆr M⎤⎥⎥⎥⎦,θ=[x,y,v]T,e=[e1,e2,...,e M]T,andB=v·I−diag([r1,r2,...,r M]),(6) where O(e2)=[O(e21),O(e22),...,O(e2M)]T and diag(a) denotes the diagonal matrix with elements of vector a on its diagonal.For notational convenience,we define the error vectorϕ=h−Sθ.(7) According to(5)and(7),the mean ofϕis zero,and its covariance matrix is given byΨ=E(ϕϕT)=E(Bee T B T)+E(O(e2)e T B T)+E(Be O(e2)T)+E(O(e2)O(e2)T)≈¯BQ¯B T(8)where Q=diag[σ21,σ22,...,σ2M].Because¯B depends on the true values r,which are not obtainable,we use B(derived from the measurementsˆr)in our calculations.From(5)and the definition ofϕ,it follows thatϕis a vector of Gaussian variables;thus,the probability density function (pdf)ofϕgivenθisp(ϕ|θ)≈1(2π)M2|Ψ|12exp(−12ϕTΨ−1ϕ)=1(2π)M2|Ψ|12exp(−12(h−Sθ)TΨ−1(h−Sθ)).Then,lnp(ϕ|θ)≈−12(h−Sθ)TΨ−1(h−Sθ)+ln|Ψ|−M2ln2π(9)We assume for the moment that x,y,v are independent of each other(this clearly non-fulfilled assumption will be relaxed in the second step of the algorithm).Then,according to(9),the optimumθthat maximizes p(ϕ|θ)is equivalent to the one minimizingΠ=(h−Sθ)TΨ−1(h−Sθ)+ln|Ψ|. IfΨis a constant,the optimumθto minimizeΠsatisfies dΠdθθ=0.Taking the derivative ofΠoverθ,we havedΠdθθ=−2S TΨ−1h+2S TΨ−1Sθ.Fig.2.Illustration of estimation ofθin step1of TSE.Thus,the optimumθsatisfiesˆθ=arg minθ{Π}=(S TΨ−1S)−1S TΨ−1h,(10)which provides[ˆx,ˆy].Note that(10)also provides the leastsquares solution for non-Gaussian errors.However,for our problem,Ψis a function ofθsince Bdepends on the(unknown)values[x,y].For this reason,themaximum-likelihood(ML)estimation method in(10)can notbe directly used.Tofind the optimumθ,we perform theestimation in two stages:Stage A and Stage B.In Stage A,themissing data(Ψ)is calculated given the estimate of parameters(θ).Note thatθprovides the values of[x,y]and thus thevalue of B,therefore,Ψcan be calculated usingθby(8).In the Stage B,the parameters(θ)are updated according to(10)to maximize the likelihood function(which is equivalentto minimizingΠ).These two stages are iterated until con-vergence.Simulations in Section V show that commonly oneiteration is enough for TSE to closely approach the CRLB,which indicates that the global optimum is reached.B.Step2of TSEIn the above calculations,ˆθcontains three componentsˆx,ˆy andˆv.They were previously assumed to be independent;however,ˆx andˆy are clearly not independent ofˆv.As amatter of fact,we wish to eliminateˆv;this will be achievedby treatingˆx,ˆy,andˆv as random variables,and,knowing thelinear mapping of their squared values,the problem can besolved using the LS solution.Letˆθ=⎡⎣ˆxˆyˆv⎤⎦=⎡⎣x+n1y+n2v+n3⎤⎦(11)where n i(i=1,2,3)are the estimation errors of thefirststep.Obviously,the estimator(10)is an unbiased one,and themean of n i is zero.Before proceeding,we need the following Lemma.Lemma 1:By omitting the second or higher order errors,the covariance of ˆθcan be approximated as cov (ˆθ)=E (nn T )≈(¯S T Ψ−1¯S )−1.(12)where n =[n 1,n 2,n 3]T ,and Ψand ¯S(the mean value of S )use the true/mean values of x ,y,and r i .Proof:Please refer to the Appendix.Note that since the true values of x ,y,and r i are not obtain-able,we use the estimated/measured values in the calculationof cov (ˆθ).Let us now construct a vector g as followsg =ˆΘ−G Υ,(13)where ˆΘ=[ˆx 2,ˆy 2,ˆv 2]T ,Υ=[x 2,y 2]T and G =⎡⎣100111⎤⎦.Note that here ˆΘis the square of estimation result ˆθfrom the first step containing the estimated values ˆx ,ˆy and ˆv .Υis the vector to be estimated.If ˆΘis obtained without error,g =0and the location of the target is perfectly obtained.However,the error inevitably exists and we need to estimate Υ.Recalling that v =x 2+y 2,substituting (11)into (13),and omitting the second-order terms n 21,n 22,n 23,it follows that,g =⎡⎣2xn 1+O (n 21)2yn 2+O (n 22)2vn 3+O (n 23)⎤⎦≈⎡⎣2xn 12yn 22vn 3⎤⎦.Besides,following similar procedure as that in computing(8),we haveΩ=E (gg T )≈4¯D cov (ˆθ)¯D ,(14)where ¯D =diag ([¯x ,¯y ,¯v ]).Since x ,y are not known,¯Dis calculated as ˆD using the estimated values ˆx ,ˆy from the firststep.The vector g can be approximated as a vector of Gaussian variables.Thus the maximum likelihood estimation of Υis theone minimizing (ˆΘ−G Υ)T Ω−1(ˆΘ−G Υ),expressed by ˆΥ=(G T Ω−1G )−1G T Ω−1ˆΘ.(15)The value of Ωis calculated according to (14)using the valuesof ˆx and ˆy in the first step.Finally,the estimation of target location z is obtained byˆz =[ˆx ,ˆy ]=[±ˆΥ1,± ˆΥ2],(16)where ˆΥi is the i th item of Υ,i =1,2.To choose the correct one among the four values in (16),we can test the square error as followsχ=M i =1( ˆx 2+ˆy 2+ (ˆx −a i )2+(ˆy −b i )−ˆr i )2.(17)The value of z that minimizes χis considered as the final estimate of the target location.In summary,the procedure of TSE is listed in Algorithm 1:Note that one should avoid placing the receivers on a line,since in this case (S T Ψ−1S )−1can become nearly singular,and solving (10)is not accurate.Algorithm 1TSE Location Estimation Method1.In the first step,use algorithm as shown in Fig.2to obtain ˆθ,2.In the second step,use the values of ˆx and ˆy from ˆθ,generate ˆΘand D ,and calculate Ω.Then,calculate the value of ˆΥby (15),3.Among the four candidate values of ˆz =[ˆx ,ˆy ]obtained by (16),choose the one minimizing (17)as the final estimate for target location.IV.C OMPARISON OF CRLB BETWEEN TDOA AND TOA In this section,we derive the CRLB of TOA based estima-tion algorithms and show that it is much lower (can be 30dB lower)than the CRLB of TDOA algorithms.The CRLB of “active”TOA localization has been studied in [30].The “passive”localization has been studied before under the model of multistatic radar [31],[32],[33].The difference between our model and the radar model is that in our model the localization error is a function of errors of TOA measurements,while in the radar model the localization error is a function of signal SNR and waveform.The CRLB is related to the 2×2Fisher Information Matrix (FIM)[34],J ,whose components J 11,J 12,J 21,J 22are defined in (18)–(20)as follows J 11=−E (∂2ln(p (ˆr |z ))∂x 2)=ΣM i =11σ2i (x −a i (x −a i )2+(y −b i )2+xx 2+y2)2,(18)J 12=J 21=−E (∂2ln(p (ˆr |z ))∂x∂y )=ΣM i =11σ2i (x −a i (x −a i )2+(y −b i )2+x x 2+y 2)×(y −b i (x −a i )2+(y −b i )2+yx 2+y 2),(19)J 22=−E (∂2ln(p (ˆr |z ))∂y 2)=ΣM i =11σ2i (y −b i (x −a i )2+(y −b i )2+yx 2+y2)2.(20)This can be expressed asJ =U T Q −1U ,(21)where Q is defined after Eqn.(8),and the entries of U in the first and second column are{U }i,1=x ¯r i −a ix 2+y 2(x −a i )2+(y −b i )2 x 2+y 2,(22)and{U }i,2=y ¯r i −b ix 2+y 2(x −a i )2+(y −b i )2 x 2+y 2,(23)with ¯r i =(x −a i )2+(y −b i )2+ x 2+y 2.The CRLB sets the lower bound for the variance of esti-mation error of TOA algorithms,which can be expressed as [34]E [(ˆx −x )2+(ˆy −y )2]≥ J −1 1,1+J −1 2,2=CRLB T OA ,(24)where ˆx and ˆy are the estimated values of x and y ,respec-tively,and J −1 i,j is the (i,j )th element of the inverse matrix of J in (21).For the TDOA estimation,its CRLB has been derived in [16].The difference of signal travel time between several receivers are considered:(x −a i )2+(y −b i )2−(x −a 1)2+(y −b 1)2=r i −r 1=l i ,2≤i ≤M.(25)Let l =[l 2,l 3,...,l M ]T ,and t be the observa-tions/measurements of l ,then,the conditional probability density function of t is p (t |z )=1(2π)(M −1)/2|Z |12×exp(−12(t −l )T Z −1(t −l )),where Z is the correlation matrix of t ,Z =E (tt T ).Then,the FIM is expressed as [16]ˇJ=ˇU T Z −1ˇU (26)where ˇUis a M −1×2matrix defined as ˇU i,1=x −a i (x −a i )2+(y −b i )2−x −a 1(x −a 1)2+(y −b 1)2,ˇUi,2=y −b i (x −a i )2+(y −b i )2−y −b 1(x −a 1)2+(y −b 1)2.The CRLB sets the lower bound for the variance of esti-mation error of TDOA algorithms,which can be expressed as [34]:E [(ˆx −x )2+(ˆy −y )2]≥ ˇJ −1 1,1+ ˇJ −1 2,2=CRLB T DOA .(27)Note that the correlation matrix Q for TOA is different from the correlation matrix Z for TDOA.Assume the variance of TOA measurement at i th (1≤i ≤M )receiver is σ2i ,it follows that:Q (i,j )=σ2i i =j,0i =j.and Z (i,j )= σ21+σ2i +1i =j,σ21i =j.As an example,we consider a scenario wherethere is a transmitter at [0,0],and four receivers at [−6,2],[6.2,1.4],[1.5,4],[2,2.3].The range of the targetlocations is 1≤x ≤10,1≤y ≤10.The ratio of CRLB of TOA over that of TDOA is plotted in Fig.3.Fig.3(a)shows the contour plot while Fig.3(b)shows the color-coded plot.It can be observed that the CRLB of TOA is always —in most cases significantly —lower than that of TDOA.xy(a )xy0.10.20.30.40.50.60.70.80.9Fig.3.CRLB ratio of passive TOA over passive TDOA estimation:(a)contour plot;(b)pcolor plot.V.P ERFORMANCE OF TSEIn this section,we first prove that the TSE can achieve the CRLB of TOA algorithms by showing that the estimation error variance of TSE is the same as the CRLB of TOA algorithms.In addition,we show that,for small TOA error regions,the estimated target location is approximately a Gaussian random variable whose covariance matrix is the inverse of the Fisher Information Matrix (FIM),which in turn is related to the CRLB.Similar to the reasoning in Lemma 1,we can obtain the variance of error in the estimation of Υas follows:cov (ˆΥ)≈(G T Ω−1G )−1.(28)Let ˆx =x +e x ,ˆy=y +e y ,and insert them into Υ,omitting the second order errors,we obtainˆΥ1−x 2=2xe x +O (e 2x )≈2xe x ˆΥ2−y 2=2ye y +O (e 2y)≈2ye y (29)Then,the variance of the final estimate of target location ˆzis cov (ˆz )=E (e x e ye x e y )≈14C −1E ( Υ1−x 2Υ2−y 2Υ1−x 2Υ2−y 2 )C −1=14C −1cov (ˆΥ)C −1,(30)where C = x 00y.Substituting (14),(28),(12)and (8)into (30),we can rewrite cov (ˆz )as cov (ˆz )≈(W T Q −1W )−1(31)where W =B −1¯SD−1GC .Since we are computing an error variance,B (19),¯S(5)and D (14)are calculated using the true (mean)value of x ,y and r i .Using (19)and (1),we can rewrite B =−diag ([d 1,d 2,...,d M ]),whered i=(x−a i)2+(y−b i)2.Then B−1¯SD−1is given by B−1¯SD−1=⎡⎢⎢⎢⎢⎢⎣a1xd1b1yd1−¯r1√x2+y2d1a2xd2b2yd2−¯r2√x2+y2d2.........a Mxd Mb Myd M−¯r M√x2+y2d M⎤⎥⎥⎥⎥⎥⎦.(32)Consequently,we obtain the entries of W as{W}i,1=x¯r i−a ix2+y2(x−a i)2+(y−b i)2x2+y2,(33){W}i,2=y¯r i −b ix2+y2(x−a i)2+(y−b i)2x2+y2.(34)where{W}i,j denotes the entry at the i th row and j th column.From this we can see that W=paring(21)and (31),it followscov(ˆz)≈J−1.(35) Then,E[(ˆx−x)2+(ˆy−y)2]≈J−11,1+J−12,2.Therefore,the variance of the estimation error is the same as the CRLB.In the following,wefirst employ an example to show that[ˆx,ˆy]obtained by TSE are Gaussian distributed with covariance matrix J−1,and then give the explanation for this phenomenon.Let the transmitter be at[0,0],target at[0.699, 4.874]and four receivers at[-1,1],[2,1],[-31.1]and[4 0].The signal travel distance variance at four receivers are [0.1000,0.1300,0.1200,0.0950]×10−4.The two dimensional probability density function(PDF)of[ˆx,ˆy]is shown in Fig.4 (a).To verify the Gaussianity of[ˆx,ˆy],the difference between the PDF of[ˆx,ˆy]and the PDF of Gaussian distribution with mean[¯x,¯y]and covariance J−1is plotted in Fig.4(b).The Gaussianity of[ˆx,ˆy]can be explained as follows.Eqn.(35)means that the covariance of thefinal estimation of target location is the FIM related to CRLB.We could further study the distribution of[e x,e y].The basic idea is that by omitting the second or high order and nonlinear errors,[e x,e y]can be written as linear function of e:1)According to(29),[e x,e y]are approximately lineartransformations ofˆΥ.2)(15)means thatˆΥis approximately a linear transfor-mation ofˆΘ.Here we could omit the nonlinear errors occurred in the estimate/calculation ofΩ.3)According to(11),ˆΘ≈¯θ2+2¯θn+n2,thus,omittingthe second order error,thus,ˆΘis approximately a linear transformation of n.4)(10)and(39)mean that n is approximately a lineartransformation of e.Here we could omit the nonlinear errors accrued in the estimate of S andΨ.Thus,we could approximately write[e x,e y]as a linear trans-formation of e,thus,[e x,e y]can be approximated as Gaussian variables.Fig.4.(a):PDF of[ˆx,ˆy]by TSE(b):difference between the PDF of[ˆx,ˆy] by TSE and PDF of Gaussian distribution with mean[¯x,¯y]and covariance J−1.Fig.5.Simulation results of TSE for thefirst configuration.VI.S IMULATION R ESULTSIn this section,wefirst compare the performance of TSE with that TDOA algorithm proposed in[16]and CRLBs.Then, we show the performance of TSE at high TOA measurement error scenario.For comparison,the performance of a Quasi-Newton iterative method[35]is shown.To verify our theoretical analysis,six different system con-figurations are simulated.The transmitter is at[0,0]for all six configurations,and the receiver locations and error variances are listed in Table I.Figures5,6and7show simulation results comparing the distance to the target(Configuration1vs. Configuration2),the receiver separation(Configuration3vs. Configuration4)and the number of receivers(Configuration5 vs.Configuration6),respectively4.In eachfigure,10000trails are simulated and the estimation variance of TSE estimate is compared with the CRLB of TDOA and TOA based localization schemes.For comparison,the simulation results of error variance of the TDOA method proposed in[16]are also drawn in eachfigure.It can be observed that1)The localization error of TSE can closely approach theCRLB of TOA based positioning algorithms.4During the simulations,only one iteration is used for the calculation of B(19).。