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Although percentage bands are useful and many trading systems have been created using them, they have a number of problems Bollinger explains: By addressing those problems, I was led to create Bollinger Bands The first problem was that you needed different width bands from stock to stock Some stocks need bands that are 2 to 3 percent wide, and some stocks need bands that are 7 to 10 percent wide Because the bands varied, depending on the stock and time period, Bollinger said using them was very time consuming, primarily because you had to draw them by hand Perhaps the worst problem with percentage bands, he says, was they allowed your emotions to enter the trading process, which is a disaster, as we all know He says that percentage bands were designed based on data the trader wanted to include, a very subjective process I was looking for a system that could set the bands automatically, Bollinger says At the time, he was an options trader and was very concerned with how options were priced, which was based on calculating volatility: In those days, we believed that volatility was a fixed number We thought it was part of the property of a security In other words, once volatility was calculated for a security, it wouldn t be revised No one bothered to calculate it more than once a year, because it was believed that volatility didn t change, he says Fortunately, Bollinger had access to an early version of a spreadsheet called SuperCalc using the old CP/M [Control Program for Microcomputers] operating system One day I copied the volatility formula on the spreadsheet and saw for the first time that volatility was actually a dynamic number, he explains It was changing all the time And I said, That s interesting! That s when he realized he could use the volatility calculation to make the percentage bands more adaptive to real-life market conditions Over the course of a few months, with trial and error and different forms of volatility calculations, I came up with Bollinger Bands, notes Bollinger At the time, he knew he had a valuable tool, but he didn t think others would recognize it The way it was introduced to the public was through a television interview I did on the Financial News Network in the early 1980s, he says I showed a chart that had my indicator on it I said we are projecting that the market will rally from the lower band to the upper band in a relatively short.

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The analysis in 5 assumes that the estimator design model is an exact model of the navigation system error dynamics That assumption is optimistic In the design process, a series of modeling tradeo s may be considered for various reasons including computational loading Due to such tradeo s and the fact that any mathematical model is only an approximation to the actual physical system, the estimator design model will not exactly match the real system Therefore, the analyst should be interested in analyzing the robustness of the system performance to discrepancies between the actual and model systems In addition, the designer may be interested in considering how the system performance would change under di erent sets of design choices, for example, changing the quality of a sensor 6 presents both a method to study the robustness of the system performance to model errors and a method that allows the designer to consider each source of system error separately to determine its contribution to the overall error budget

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time The interviewer asked me, What do you call those bands I actually didn t have a name for them, so I said, My trading bands Then I quickly blurted out, Bollinger Bands And that s how they got named

s 2 6 will have presented various theoretical topics which can be combined to provide a classical theory for the design and analysis of aided navigation systems 7 combines together the various theoretical concepts within simple navigation examples to illustrate the key concepts of the approach This understanding is the stepping o point for Part II of the text It is critical to understand the basic theory and overall approach prior to attempting more complex and higher dimensional real world navigation systems 7 will discuss the complementary lter with applications and exercises The complementary lter framework relates well to aided navigation system design Within this framework it is natural to focus on key ideas such as the complementary nature of sensors, observability, and linearized models for stochastic error variables Researchers might be tempted to investigate more advanced concepts such as particle lters, neural networks, or fuzzy estimators Such advanced

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topics are sometimes proposed and may, in some applications, be appropriate However, the classical approach built on the theory in Part I of this text, outlined in 7, and discussed for several speci cs applications in Part II is a complete and rigorous approach to the design and analysis of navigation systems It is highly recommended that the researcher understand this classical approach, its strengths, and its weaknesses before moving on to more advanced concepts

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