US4764871A — Method for converting a rotational speed transduc…

Claim 1

Independent Claim 228 words

A method using a Kalman filter for converting a sinusoidal output signal of a rotational speed transducer, which in its frequency and amplitude is subject to distortion and is dependent on a varying rotational speed that is to be ascertained, into a low-distortion signal which signal is directed to an anti-skid-anti-lock system to prevent wheel slippage, which includes the steps of (a) forming at predetermined time intervals, a difference between an output signal (z(k+1)) of the speed transducer and a simulation value (z(k+1)) ascertained in the Kalman filter based on a previous measurement; (b) converting this difference (z(k+1)) by multiplication with a Kalman amplification factor K, which represents a vector, into a difference vector x(k+1/k); (c) forming a sum x(k+1/k+1) of this difference vector x(k+1/k) and a simulation vector x(k+2)/k+1) and directing the sum x(k+1/k+1) to the anti-skid system to prevent wheel slippage; (d) storing this summed vector x(k+2/k+1), which contains the desired low-distortion signal, in a memory, after multiplication by a transition matrix Φ, as a simualtion vector x(k+2/k+1) for the following sum formation; (e) and storing the simulation vector x(k+2/k+1), after multiplication by a measurement vector H, in memory as a simulation value z(k+2) for the following cycle, wherein the terms in parentheses (k+m) or (k+m/k+n) indicate that the corresponding variable is used in the evaluation cycle (k+m) and was obtained in the evaluation cycle (k+n).

Claim 2

Independent Claim 228 words

A method using a Kalman filter for converting a sinusoidal output signal of a rotational speed transducer, which in its frequency and amplitude is subject to distortion and is dependent on a varying rotational speed that is to be ascertained, into a low-distortion signal which signal is directed to an anti-skid-anti-lock system to prevent wheel slippage, which includes the steps of (a) forming at predetermined time intervals, a difference between an output signal (z(k+1)) of the speed transducer and a simulation value (z(k+1)) ascertained in the Kalman filter based on a previous measurement; (b) converting this difference (z(k+1)) by multiplication with a Kalman amplification factor K, which represents a vector, into a difference vector x(k+1/k); (c) forming a sum x(k+1/k+1) of this difference vector x(k+1/k) and a simulation vector x(k+2)/k+1) and directing the sum x(k+1/k+1) to the anti-skid system to prevent wheel slippage; (d) storing this summed vector x(k+2/k+1), which contains the desired low-distortion signal, in a memory, after multiplication by a transition matrix Φ, as a simualtion vector x(k+2/k+1) for the following sum formation; (e) and storing the simulation vector x(k+2/k+1), after multiplication by a measurement vector H, in memory as a simulation value z(k+2) for the following cycle, wherein the terms in parentheses (k+m) or (k+m/k+n) indicate that the corresponding variable is used in the evaluation cycle (k+m) and was obtained in the evaluation cycle (k+n).

Claim 3

Dependent Claim 19 words

A method as defined by claim 1, wherein said Kalman amplification factor is a previously calculated and constant vector.

Claim 4

Dependent Claim 298 words

A method as defined by claim 1, in which said Kalman amplification factor K(k+m) in each instance is ascertained in accordance with the following method: (a) multiplying a transposed transition matrix Φ T by a covariance matrix P(k/k) obtained in the previous cycle, and multiplying this product by the transition matrix Φ; (b) adding this product to a constant matrix ΓQΓ T , in order to obtain a prediction valve for a new covariance matrix P(k+1/k); (c) multiplying this prediction valve by the transposed variable measurement vector H T (k), storing the resultant vector P(k+1/k)·H T (k) in memory and multiplying this vector by the measurement vector H(k); (d) adding the resultant scalar to a further variable scalar R(k) and forming the reciprocal of the resultant sum S u ; (e) multiplying the stored vector P(k+1/k)·H T (k) by this reciprocal value, resulting in the Kalman amplification vector K(k+1); (f) multiplying this factor with the difference z(k+1), on the one hand, and on the other by the variable measurement vector H(k); (g) subtracting the resultant product K(k+1)·H(k) from a constant matrix I; (h) multiplying this difference I-K(k+1)·H(k) by the prediction, obtained in accordance with step (b), for the covariance matrix P(k+1/k), and the product is made available, as the newly ascertained covariance matrix P(k+1/k+1), for the following cycle; (i) obtaining the variable scalar R(k+1) for the following cycle by multiplication of the simulation vector x(k+1/k) by a constant vector S and addition of a scalar R o to the scalar x(k+1/k+1)·S obtained by the multiplication; and (k) obtaining the variable measurement vectors H(k+1) for the following cycle by multiplication of the ascertained simulation value z(k+1) with a vector M(k+1), wherein the vector M(k+1) results from an estimated status x(k+1/k+1) and constant scalars ω o , A and NZ.

Claim 5

Dependent Claim 26 words

A method as defined by claim 1, which includes ascertaining the wheel acceleration b(k) from the relationship b(k)=x 3 (k/k)/J wherein x 3 results from x(k/k).

Claim 6

Dependent Claim 25 words

A method as defined by claim 2 which includes ascertaining the wheel acceleration b(k) from the relationship b(k)=x.sub.3 (k/k)/J wherein x 3 results from x(k/k).

Claim 7

Dependent Claim 25 words

A method as defined by claim 3 which includes ascertaining the wheel acceleration b(k) from the relationship b(k)=x.sub.3 (k/k)/J wherein x 3 results from x(k/k).

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1991-08-16	1992-02-15	1992-08-16	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1995-08-16	1996-02-15	1996-08-16	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	1999-08-16	2000-02-15	2000-08-16	$7700.00	Window Closed / Lapsed

Method for converting a rotational speed transducer output signal into a low-distortion signal

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