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nterest-rate derivatives are said to be the largest and most liquid market in the world Options on these products are traded on multiple exchanges and of varying contract speci cations Interest-rate products often operate in opposition to the equity market as a safe haven for capital in rough market seas Our focus for interest-rate markets is not to get into a detailed strategy discussion on commercial credit, swaps, and commercial hedging, but to discuss how options function on the market and to highlight some of the options used for defending a portfolio against changes in interest rates Interest-rate products in the United States are mostly traded on two major exchanges: the Chicago Board of Options Exchange (CBOE) and the Chicago Board of Trade (CBOT) which is now part of the CME Group These two exchanges trade interestrate products based on the same underlying assets, but in very different ways:

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Prior to starting a heterogeneous data replication project, verify GoldenGate s support for the non-Oracle source system and the specific version you are interested in migrating If GoldenGate is selected as the tool of choice, refer to the best practices for configuring GoldenGate for the Database Machine as discussed in 6

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The error state and F matrix are de ned as in Section 94 With these assumptions, the observability matrix is 1 0 0 0 0 0 1 0 0 0 0 0 sin( ) uL cos( ) uR cos( ) u H 2RL 2RR O = HF = 0 0 uL uR u cos( ) sin( ) sin( ) 2RL 2RR HF2 0 0 O55 0 O54 0 0 0 O64 O65 where O54 O55 O64 O65 = = = = uL RL uR RR uL RL uR RR R u sin( ) cos( ) L 2 R u sin( ) cos( ) L 2 R u cos( ) sin( ) L 2 u R cos( ) sin( ) L 2

Several speci c cases can be considered For u = = 0: In this case uL = uR = 0 Therefore, the third through fth columns of O are zero In this case, the unobservable subspace is three dimensional and includes the yaw angle and wheel radii errors For u = 0: In this case the third column of O is zero which shows that at least the yaw angle is not observable If = 0, then uL = 0, uR = 0, and is changing with time Under these conditions, the last two columns of O are linearly independent of each other and of the rst two columns, which shows that the rank of O is four Therefore, the wheel radii and position are observable For uL = 0: In this case the fourth column of O is zero which shows that at least the RL is not observable

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For uR = 0: In this case the fth column of O is zero which shows that at least the RR is not observable Over time intervals where uL and uR are time varying, the state vector may not be observable at a given time instant; nonetheless, the state vector can be observable over the time interval This is easily demonstrated via covariance analysis

The main purpose of this section is to present an covariance analysis demonstrating that the state can be observable over an interval of time even though the observability matrix is not full rank at any time instant during that interval The covariance analysis results are presented in Figure 94 During this simulation, GPS aiding measurements are assumed to occur at a one Hertz rate with tk = kT and T = 1s The vehicle forward speed is u(t) = 1 m for all t The angular rate is periodic with a period of 10s s For t [0, 10], the angular rate is de ned as (t) = 0

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