@@ -36,24 +36,24 @@
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36 | 36 | |
37 | 37 | # contributed by Sawyer B. Fuller <minster@uw.edu> |
38 | 38 | def lqe(*args, **kwargs): |
39 | | -"""lqe(A, G, C, QN, RN, [, NN]) |
| 39 | +r"""lqe(A, G, C, QN, RN, [, NN]) |
40 | 40 | |
41 | 41 | Linear quadratic estimator design (Kalman filter) for continuous-time |
42 | 42 | systems. Given the system |
43 | 43 | |
44 | 44 | .. math:: |
45 | 45 | |
46 | | - x &= Ax + Bu + Gw \\\\ |
| 46 | + dx/dt &= Ax + Bu + Gw \\ |
47 | 47 | y &= Cx + Du + v |
48 | 48 | |
49 | 49 | with unbiased process noise w and measurement noise v with covariances |
50 | 50 | |
51 | | - .. math:: E{ww'} = QN, E{vv'} = RN, E{wv'} = NN |
| 51 | + .. math:: E\{w w^T\} = QN, E\{v v^T\} = RN, E\{w v^T\} = NN |
52 | 52 | |
53 | 53 | The lqe() function computes the observer gain matrix L such that the |
54 | 54 | stationary (non-time-varying) Kalman filter |
55 | 55 | |
56 | | - .. math:: x_e = A x_e + B u + L(y - C x_e - D u) |
| 56 | + .. math:: dx_e/dt = A x_e + B u + L(y - C x_e - D u) |
57 | 57 | |
58 | 58 | produces a state estimate x_e that minimizes the expected squared error |
59 | 59 | using the sensor measurements y. The noise cross-correlation `NN` is |
@@ -195,7 +195,7 @@ def dlqe(*args, **kwargs):
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195 | 195 | |
196 | 196 | with unbiased process noise w and measurement noise v with covariances |
197 | 197 | |
198 | | - .. math:: E{ww'} = QN, E{vv'} = RN, E{wv'} = NN |
| 198 | + .. math:: E\{w w^T\} = QN, E\{v v^T\} = RN, E\{w v^T\} = NN |
199 | 199 | |
200 | 200 | The dlqe() function computes the observer gain matrix L such that the |
201 | 201 | stationary (non-time-varying) Kalman filter |
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