Jack Crenshaw

Research & Development Engineering Management

Jack Crenshaw is a systems engineer and the author of Math Toolkit for Real-Time Programming. He holds a PhD in physics from Auburn University. E-mail him at jcrens@earthlink.net.


's contributions
    • Crenshaw is back with gambling tips in Part 4 in his series on parameter estimation, which is supposed to end us somewhere near the Kalman filter.

    • Understanding the intimate relationship between vectors and reality means means understanding vectors, their properties, and how to manipulate them.

    • In the February, 1992 issue of Embedded Systems Programming, a new column, Programmer's Toolbox, was introduced. The name was not chosen at random: The intent of the column is to provide useful tools and techniques that readers can apply to their own problems in embedded systems development. The idea is to have a library of reusable modules. written in several languages, that others can use to avoid re-invention of the wheel and improve their productivity and software quality. In this paper, I'll describe the thoughts behind the column. the software tools that have already been presented, the ones yet to come, and the ultimate goal of the effort. A successful effort will require support from the user community. Part of the message of this paper is a plea for help and feedback.

    • If you've studied calculus at all, you learned early on a sad but true fact of life: There are many more calculus problems that can't be solved than there are problems that can be. Getting a neat, closed-form solution to a tough problem is always satisfying, and makes a mathematician or physicist feel like a real hero. But in that real world, no closed-form solution ever seems to exist for the problem that's facing us at the moment. So when an integral or derivative can't be found ... when that elusive closed-form solution doesn't exist ... what do we do?

    • Understand how to cut down on the noise in your system, using the math behind the Kalman filter.

    • You need math to estimate a curve. Here's part two in Jack's series on state estimation.

    • On the road to the Kalman filter: The job of the least squares fit is to give an estimate of the unknown coefficients of the mental model.

    • Jack Crenshaw tells you how to calculate trajectories to get your space craft to the Moon and back.

    • I'm very sorry to keep all my readers waiting. It's not my usual way of doing business. I'm well aware that, because I tend to write multiple related columns, I owe it to you guys to keep 'em coming. In my defense, I can only say: Two really vicious computer malware attacks, one heart surgery, seven weeks of in-home therapy, and two sessions in civil court. Please be patient, folks. I'm pedaling as fast as I can.

    • About reliability: Around 1999-2000 I went through an orgy of buying old Heathkits on eBay. The thing that amazed me was how many of these 40-year-old kits still worked, and worked nicely. My pals all told me that I'd have to replace all the electrolytic caps, that I'd have to replace the tubes, and that I'd better bring the units up on a Variac to make sure I didn't smoke'em. I did none of that. Oh, sure, some of the units were non-functional or way out of spec. But the majority of them simply came up, and worked as well as when they were new. For a time, I used to check all the electrolytics, as my pals suggested. But every time I tested one, I found it not only good, but with the correct capacitance. After awhile, it just got too boring. I went through the test equipment first. In fact, one of the earliest purchases was a tube tester. Then I tried a few to see which units were still working at shop quality. After that, I used my best units like the VTVM to test everything else.