Control of a Ring Laser Gyro Cavity According to a Preselected Model

The present invention relates to ring laser gyros and, more particularly, to a method of controlling such gyros according to a preselected cavity model to enhance gyro performance.

In a ring laser gyro, laser beams circulating in opposite directions around the same closed path are shifted in frequency when a cavity containing the path is rotated about a preselected input axis. With no angular motion about the input axis, the beams travel equal distances around the cavity and their optical frequencies are the same. Angular movement in either direction about the axis causes an apparent increase in cavity length for the beam traveling in the direction of movement and a corresponding decrease for the beam traveling in the opposite direction. Because the closed optical path is a resonant cavity providing sustained oscillation, the wavelengths of the beams increase and decrease, respectively. This causes a differential proportional to the angular rate of the input to occur between the beam frequencies. The frequencies heterodyne at a common photodetector, giving rise to a beat frequency directly proportional to the angular rotation rate.

At low angular rates, the frequency differential between the beams is small, causing the beams to resonate together or "lock-in" so that they oscillate at a single frequency. Thus, it is difficult to measure low angular rates because the frequency differential proportional to the angular rate does not exist. This problem is illustrated graphically in the upper portion of FIG. 4, wherein the gyro output signal (.psi.) is plotted against the angular rate of the gyro (.OMEGA..sub.in). In the graph, a diagonal line 10 bisecting the first and third quadrants represents the proportional output of a perfect gyro, while curves 11 represent the output of a real, undithered ring laser gyro having an output equal to zero at inputs between -.OMEGA..sub.1 and +.OMEGA..sub.1. The difference between the ideal and actual outputs is the bias error due to lock-in.

It is common practice to minimize bias error by mechanically oscillating or "dithering" the body of a gyro. Systems of this type are disclosed in U.S. Pat. Nos. 4,190,364, 4,314,174 and 4,344,706. They superimpose a relatively large dithering motion upon the gyro input, averaging the error so that low rates of input are detectable. At present, body dither is accomplished at frequencies on the order of 400 hertz and angular velocities of approximately 120 degrees per second. However, such movements are difficult to control and typically leave a significant level of bias error.

A variety of techniques have been proposed for further reducing the bias error of mechanically dithered gyros, the most common being to superimpose a secondary random dither which reduces error accumulation. However, such secondary dither significantly increases "random walk" and presents a practical lower limit on signals detectable by it.

In operating a ring laser gyro it is important to maintain cavity length constant, at a value corresponding to a preselected laser intensity within one of several "modes" of cavity operation. Selection of a mode is accomplished by applying a voltage to a transducer associated with a mirror of the cavity. Ring laser gyros have heretofore been constrained to operate within a single predetermined mode, chosen on the basis of lowest random walk at a typical operating temperature, and have relied upon high frequency modulation of the control mirror and a simple closed loop feedback system to track the laser intensity to the peak of the mode. The modulation frequency has typically been in the neighborhood of 6 kilohertz. In this context, prior gyros have operated under a rigid set of constraints which were believed necessary for satisfactory operation.

Therefore, it is desirable in many applications to provide an apparatus for controlling a ring laser gyro cavity in a manner which minimizes errors due to lock-in, random walk and other sources.

The present invention relates to a method and apparatus for controlling a ring laser gyro having a cavity with at least one control transducer associated with a mirror or other reflective surface thereof, and having at least one parameter characteristic of cavity operation, in which a preselected model of cavity operation is maintained; cavity data is sampled as a measure of said parameter; the sampled data is compared to the model; and the transducer is controlled so that the parameter conforms to the model. In a preferred embodiment, the model is maintained by storing digital information representative of it, and the sampled data is digitized and compared to the model using digital techniques. In another preferred embodiment, two mirrors are dithered and data as to the dither amplitude is sampled. The model then defines optimal dither amplitudes at which theoretical lock-in error is zero, and the transducers are controlled accordingly. In an alternative embodiment, the sampled data corresponds to the intensity of the laser beam within the cavity and the model represents a cavity operated at a preselected variable intensity displaced from the peak intensity within the mode. The model may also define a plurality of operating modes of the cavity and contain information as to the relative performance of the gyro in each mode as a function of at least one environmental condition, such as temperature. The mode giving rise to optimal performance at the sensed condition value is then selected and acquired through the control transducer.

The cavity control system of the present invention significantly reduces bias error and random walk by precisely controlling a laser cavity according to a preselected model of cavity operation. In a first significant embodiment, cavity length control mirrors are dithered at an optimal magnitude corresponding to a zero point of the error portion of the gyro output signal near zero rate.

The gyro output signal (.psi.) can be expressed as: ##EQU1## the first two terms being a "true signal" consisting of angular input from vessel motion (2.pi..OMEGA..sub.in T) and the dither signal (M.multidot.SIN.omega..sub.D T); where M, the modulation index of dither motion, equals 2.pi..beta..sub.M /.omega..sub.D). The remaining terms of the expression represent the bias error of the gyro, expanded as a Bessel series which periodically goes to zero. In the method of the present invention, dither amplitude is carefully controlled so that the system operates at one of the zero points of the first Bessel term, essentially eliminating the error terms near zero rate. Such control is difficult in a mechanically dithered gyro but is attainable in the context of the present invention by accurately dithering the cavity mirrors at the desired amplitude. Random walk is also kept to a minimum because secondary dither is not required.

The gyro can be subjected to mirror dither alone, yielding the greatest reduction in bias error, or to a combination of mirror dither and body dither. In the latter case, the body dither component is lower in amplitude than that required without mirror dither and therefore is more easily controllable.

The present system of controlling a gyro cavity according to a sophisticated mathematical model permits lock-in error to be reduced even further by dynamically selecting a mode of cavity operation for which random walk is lowest under the environmental conditions encountered, and by operating the gyro off the peak of a mode at a point giving rise to reduced random walk. Each of these methods, taken independently, is capable of increasing gyro performance by at least 10 to 20 percent. Furthermore, the increases in performance are additive between methods, making it possible to combine them to produce gyros vastly superior to those of the prior art.

The above and other features of the present invention may be more fully understood from the following detailed description, together with the accompanying drawings, wherein similar reference characters refer to similar elements throughout and in which:

FIG. 1 is a functional block diagram of a cavity control system constructed according to a preferred embodiment of the present invention;

FIG. 2 is a generalized hardware block diagram of the system of FIG. 1;

FIG. 3 is a flow diagram of a mirror dither control system constructed in accordance with another preferred embodiment of the present invention;

FIG. 4 is a graphical representation of the output characteristics of a simple, unbiased ring laser gyro, with a mirror dither input typical of the present invention shown below it for purposes of comparison;

FIG. 5 is a graphical representation of the zero order term of the lock-in error equation for a ring laser gyro, expanded as a Bessel series, with the resultant error shown in broken lines;

FIG. 6 is a flow diagram of a cavity length control system constructed according to a further embodiment of the present invention;

FIG. 7A is a graphical representation of experimental intensity data within a ring laser gyro cavity;

FIG. 7B is an enlargement of a portion of the graph of FIG. 7A near the peak of a mode of the gyro; and

FIG. 8 is a graphical representation of random walk data obtained by the methods of the present invention over one of the modes of a ring laser gyro cavity.

FIG. 1 illustrates a system 20 for controlling a cavity 22 of a ring laser gyro having a closed optical path 24 defined by mirrors M1, M2, MD1 and MD2. Laser beams are reflected in opposite directions around the path 12 to sense rotation about an input axis perpendicular to the path. An interference pattern corresponding to the beat frequency of the combined laser beams is detected by a photodiode 26 disposed behind the mirror M2, and the maximum intensities of the counter-propagating laser beams are detected by similar photodiodes 28 and 30 positioned behind the mirror M1. The output of the photodiode 26 follows a path 31 for use in connection with a cavity sensing means (32) and a primary guidance/navigation system (not shown) of which the system 20 is a part. The outputs of the photodiodes 28 and 30 are used exclusively for cavity sensing and, along with the output of the photodiode 26, are evaluated for comparison with a preselected cavity model 33.

The cavity model may be a sophisticated model of cavity operation, such as a model in which a pair of mirrors are dithered at a carefully controlled amplitude to minimize lock-in error and random walk. Alternatively, it may be a scheme of cavity operation which is dynamically dependent on one or more environmental conditions, such as the temperature to which the gyro is subjected. In either case, the comparison function, indicated schematically as a summing point 34, produces a cavity error signal for use by a cavity drive control means 37 to drive the mirrors MD1 and MD2. Contingent modes of operation can also be incorporated into the cavity model 33 or the cavity drive control means 37 to keep the system operating after a failure of one or more of its components.

The laser cavity 22 may take any of a variety of forms having three or more mirrors for defining the optical path 24. In the embodiment illustrated, the mirrors M1 and M2 are partially transmissive mirrors which permit light to reach the photodiodes 26,28 and 30, while the mirrors MD1 and MD2 are conventional cavity control mirrors having reflective surface portions 38 and piezolectric transducers 40 for driving the reflective surface portions.

The system 20 may take any of a variety of forms, including a special purpose analog or digital control circuit, but is most easily implemented by a microprocessor, a sequencer or a similar controller in which the cavity model is stored in memory. The microprocessor implementation is illustrated generally in FIG. 2, wherein the control apparatus is outlined by broken lines 42. The outputs of the photodiodes 28 and 30 are applied to individual amplifiers 44 and are compared by an AC comparator 46 and a DC comparator 48 to derive the maximum intensity of the laser beams. The resultant intensity signals and an ambient temperature signal 50 are passed through a multiplexer 51 and an analog-to-digital converter 52 to a microprocessor 54 which evaluates the intensity data and compares it to the cavity model. Sampling of intensity and temperature information is controlled by the microprocessor 54 which transmits a sampling signal to the multiplexer 51 along a line 56. The digital outputs of the processor are converted to analog mirror drive signals by digital-to-analog converters 53 for application through amplifiers 55 to the mirrors MD1 and MD2.

The output of the photodiode 26 is a heterodyned ("het") signal corresponding to passing lines of an interference fringe produced by the counter-propagating laser beams. It is an analog signal representing the angle through which the gyro has been rotated, and is applied to a counter 58 which digitizes and counts it. The output of the counter 58, which is the output signal of the gyro, passes to guidance/navigation systems (not shown) along a line 60 and to the microprocessor 54 along a line 62. Thus, the microprocessor 54 receives "up" and "down" counts of the het signal as well as laser intensity and ambient temperature information, all for use in feedback control of the cavity according to the preselected model.

Operation of the system 20 to control the cavity according to a preselected model is best illustrated by reference to certain preferred functions of the system. FIG. 3 is a functional block diagram of a preferred embodiment in which equal and opposite dither signals are applied to the mirrors MD1 and MD2 at a magnitude corresponding to a zero point of the first order Bessel term of the bias error expression. A high frequency (AC) component of the het signal is extracted by taking the sum and difference of the het "up" counts and the het "down" counts, which correspond to opposite rotations about the input axis of the gyro, and subtracting the difference of the counts from the sum of the counts. The sum of the up and down counts is taken at a point 64, the difference between the up and down counts is taken at a point 66, and the difference is subtracted from the sum at a point 68. The "sum" and "difference" signals are summed over a 4,096 bit cycle, as indicated by summation blocks 70 and 72, respectively, reducing the iteration rate from a sample rate of 2,048 hertz to a comparison rate of one-half hertz.

The output of the subtraction at the point 68 is proportional to the total reciprocal motion applied to the system by dithering the mirrors. The component of the het signal caused by movement of the gyro about its input axis is essentially a DC signal which is removed by subtracting the difference of the up and down counts from their sum. The resulting signal is compared at 74 with a reference signal computed from theory to satisfy the "Bessel zero condition" at which the bias error of the gyro is a minimum. The output of the point 74 is integrated over time at the block 76, producing an output signal 78 which represents the amount by which the dither drive signal must be corrected. Thus, the signal 78 is added to the mirror dither signal to achieve Bessel zero operation.

The concept of dither control according to the method of the present invention is best understood in conjunction with FIGS. 4 and 5, wherein FIG. 4 is a plot of the gyro output equation set out above. As described briefly above, the first two terms of the output equation represent (i) movement of the airplane or other vessel about the input axis of the gyro and (ii) dither input to the gyro, respectively. The remaining terms represent the bias error due to lock-in, expanded as a Bessel series. A simple, unbiased gyro would ideally have an output given by the first term of the output equation, in which the output (.psi.) would be proportional to rotation about the input axis (.OMEGA..sub.IN). Such an output is represented by the straight line 80 of FIG. 4. However, the phenomenon of lock-in distorts the output for rotations in the neighborhood of .OMEGA..sub.L and eliminates output signals for inputs less than that value, introducing the bias error defined by the Bessel terms of the output equation. Thus, the output of a real, undithered gyro is more in the nature of the curves 11 of FIG. 4.

In prior ring laser gyros, bias error has been reduced by moving the gyro body rapidly through large angles so that the time during which the absolute value of the combined input is less than .OMEGA..sub.L is small. A typical angular velocity of such body dither is approximately 100 degrees per second, which is difficult to control and can lead to substantial errors of its own. For this reason, gyros relying on body dither often incorporate a "secondary" random component of body dither to minimize error accumulation. However, such random motion introduces noise known as "random walk", requiring that the gyro be made more precise in other ways to achieve a desired level of performance.

The effect of dither amplitude on bias error is shown graphically in FIG. 5, which is a plot of the zero order term of the Bessel expansion of bias error due to lock-in. The zero order term, which is a good approximation of the entire series near zero rate, is a function 81 which generally decreases with increasing dither amplitude and periodically goes to zero at modulation points or "indices" M1, M2, M3, etc. This results in a total bias error which is always positive but goes to zero at the modulation points, as represented by the broken line curve 83 of FIG. 5.

In the embodiment of FIG. 3, the control system of the present invention drastically reduces bias error by applying a dither signal to the cavity control mirrors (MD1 and MD2) at a magnitude which is carefully controlled so that the gyro operates at one of the "Bessel zero" indices (M1, M2, etc.). The amplitude of mirror dither can be much less than that of conventional body dither because the components of the output signal resulting from bias error cancel each other at the Bessel zero points. This is shown graphically in FIG. 4, wherein a mirror dither signal 12 is shown parallel to and offset beneath the true input signal (.OMEGA..sub.IN) of the gyro. The effective angular rate of the dither motion exceeds the minimum input below which lock-in occurs (.OMEGA..sub.L), but need not reach a point at which the output signal (.psi.) approaches the diagonal line of an ideal gyro. Thus, the problems associated with large dither amplitudes are largely absent in the case of mirror dither according to the present invention. The cancellation of errors also reduces bias error far below that achieved with body dither, obviating the need for a random secondary dither component. Consequently, random walk is greatly reduced.

In accordance with the present invention, a plurality of mirrors are dithered out-of-phase with one another so that cavity length is unaffected by the dithering motion. For example, two mirrors can be dithered at equal amplitudes 180 degrees out-of-phase. Mirror dither movement at a frequency of 2,000 hertz and a magnitude corresponding to a Bessel zero point between approximately 1/10th degree and 10 degrees per second is then sufficient to overcome bias error due to lock-in in a typical ring laser gyro. Alternatively, it is sometimes desirable to apply body dither at a greatly reduced amplitude while simultaneously dithering mirrors in a carefully controlled fashion. This is preferred when the mirrors MD1 and MD2 cannot be moved through the distances required to control the cavity by mirror dither alone.

In each of the circumstances described above, a specific model of cavity operation is generated and embodied either as a hardware circuit implementing the function of FIG. 1 or as digital information stored within the microprocessor 54 (FIG. 2).

The mirror dither described above is to be distinguished from "modulation" signals applied to ring laser cavity mirrors for the purpose of tracking laser intensity to the peak of a mode within which the cavity operates. Such modulation takes the form of a voltage of approximately 0.5 volts applied to the mirrors at a frequency of approximately 6 kilohertz to increase and decrease cavity length. If more than one mirror is used, the control signals are typically in phase so that cavity length is modulated. By contrast, the mirror dither disclosed herein requires voltages out-of-phase with each other and an order of magnitude greater than that used for mirror modulation.

Another model for mirror dither according to the method of the present invention is a dynamic model in which mirror dither is varied over a range of amplitudes as bias error is measured. The resulting data is substituted into the error expression of the lock-in error equation to calculate .OMEGA..sub.L for each Bessel zero index. .OMEGA..sub.L is a convenient measure of mirror quality, and thus the quality of the gyro itself. Data as to .OMEGA..sub.L Bessel zero point enables the indices to be ranked according to bias error.

Other cavity models useful to control a gyro cavity in the context of the present invention include models in which cavity length is controlled to operate at a point displaced from the peak of an operating mode or to select a preferred operating mode on a dynamic basis according to temperature or other environmental conditions to which the cavity is subjected. With regard to the first such model, applicants have determined that a cavity operated to one side of the peak of laser intensity within a mode gives rise to lower random walk than the same cavity operated at the peak. This is true for ring laser gyros, generally. That is, there is a measurable point displaced from the peak of each mode for which the gyro exhibits a lower random walk than it does at the peak (FIG. 8). Although not bound by any theory, the point of lowest random walk is believed to be a function of the gas mixture within the gyro. It may be approximately 3 percent of the applied voltage when the gas is a blend of helium and neon.

The off-peak operating point of the present invention is illustrated in FIGS. 7A and 7B, wherein the curve 82 represents the intensity profile of a mode in the region of its peak 84. The operating point used in the practice of the invention is a location 86 displaced from the peak 84.

FIG. 6 is a functional block diagram of an algorithm used to control cavity length according to the foregoing models. The algorithm is essentially as follows:

The input to the algorithm is the laser intensity signal (Li) which has been sampled and digitized by the amplifiers 44, the comparators 46 and 48, the multiplexer 51 and the analog-to-digital converter 52, all of FIG. 2. The resulting digital signal is the feedback by which the system 20 controls cavity length to generate a pair of output voltages (V.sub.cout1, V.sub.cout2) to the transducer-controlled mirrors, MD1 and MD2, respectively. The first step of the method, accomplished at block 88 of FIG. 6 (line 1 of the above listing), is to differentiate the laser intensity signal by subtracting a previously sampled laser intensity from the current laser intensity. The result of this step (.DELTA.Li) is an error signal corresponding to movement away from the previous intensity value. The value of the current laser intensity is then stored (line 2) at the memory address of the previous intensity to prepare the system for the next differentiation step.

The incremental error signals (.DELTA.Li) are demodulated at block 90 (line 4) and integrated at block 92 (line 5) to yield a signal representative of the voltage (V.sub.ci) to be applied to the mirrors to reach a desired mean operating point within the mode. The block 90 is essentially a digital demodulator which keeps track of the sign of the error signal (.DELTA.Li) according to the sign of an applied modulation voltage (V.sub.cm). For present purposes, the modulation voltage is assumed to be a 2,000 hertz square wave signal modulating cavity length in the manner known to the art. The error signals are numerically integrated at the block 92 to yield the total error of the system over the time period involved. The time constant of the integration, determined by the value "K" of the block 92, can be as short as a few milliseconds or as long as a few seconds in the present context. The modulation signal (V.sub.cm) is added to the cavity correction signal (V.sub.ci) at 94 to yield a mirror drive signal along a pair of lines 96 and 98.

The cavity models discussed herein are implemented in the method of FIG. 6 by adding appropriate signals to either the error signal (.DELTA.Li) or the control voltage (V.sub.ci). The operating point is displaced from the peak of the mode by adding a "mode offset" signal at 97 to the error signal (.DELTA.Li), and the mode in which the system operates is selected by applying a displacement control voltage (V.sub.cd) to the correction voltage (V.sub.ci) at the point 94. These inputs control the mean operating point of the laser cavity.

The voltage output from the summing point 94 is a digital signal capable of maintaining cavity length according to a preselected static or dynamic model. Because it is digital in character, other signals can be added to it without disrupting cavity length control. Thus, a "mirror dither" control voltage generated by the method of FIG. 3 is applied in opposite polarities to the output lines 96 and 98 to superimpose the mirror dither function onto the mirrors. In addition, a "backscatter offset" signal can be applied to one of the lines to offset the laser beam relative to the mirrors so that the beam is not scattered by known imperfections in the mirrors.

The outputs along the lines 96 and 98, after any mirror dither and backscatter offset signals are applied, constitute the output control voltages (V.sub.cout1 and V.sub.cout2) to the mirrors. These voltages have large DC components corresponding to the displacement control voltage (V.sub.cd) and the "mode offset" voltage, and AC components corresponding to the modulation signal (V.sub.cm) and the "mirror dither" signal. When the mirrors MD1 and MD2 are conventional piezoelectric-controlled ring laser gyro mirrors, the displacement control voltage (V.sub.cd) is typically between -65 volts and +65 volts, and the "mode offset" voltage is approximately 3 percent of the applied voltage. For example, when the displacement control voltage is 30 volts, the mode offset may be approximately 1 volt. The mirror modulation voltage (V.sub.cm) and the "mirror dither" voltages are widely variable in frequency but may be approximately 2,000 hertz. In that case, the modulation voltage may be as high as approximately 1 volt and the mirror dither voltage may be as high as approximately 30 to 40 volts. More typical values for the modulation and dither voltage amplitudes are approximately 0.5 volts for modulation and approximately 10 to 20 volts for mirror dither.

The operation of the cavity length control system of FIG. 6 can be understood most easily in the context of FIGS. 7A and 7B, which represent a series of intensity peaks or modes 100 within a ring laser gyro cavity, such as the cavity 22 of the present invention. FIG. 7A shows the peaks 100 obtainable by sweeping the cavity through a wide range of cavity lengths. Random walk of the gyro can then be measured for each mode and the modes can be ranked according to random walk characteristics. Measurements are preferably made over ranges of temperature or other environmental conditions, enabling the system to select an operating mode of least random walk and/or greatest operating range in response to conditions encountered in operation. Thus, the cavity model 33 (FIG. 1) may contain information as to the optimal mode for each of a number of different temperatures, along with the displacement control voltages (V.sub.cd) required to drive the cavity to each mode.

A mode is initially chosen during the "mode acquisition" phase of system operation, when the intensity feedback loop of blocks 88-92 (FIG. 6) and the modulation voltage (V.sub.cm) are turned off. The choice is made on the basis of the mode having the lowest random walk and/or the highest dynamic tracking range at a sensed temperature. After acquisition, the feedback loop operates to maintain the intensity at a value offset from the peak of the mode, according to the "mode offset" input of the cavity model. When the temperature or other physical condition changes, that information is monitored by the processor 54 and is used to select a new displacement control voltage and an offset voltage, as required. This assures that the system always operates within the mode of optimal performance under the sensed environmental conditions.

The use of a microprocessor in the system of the present invention permits the model by which the cavity is controlled to be made even more sophisticated, if desired. Thus, the system may continuously test itself and act to overcome abnormalities in cavity operation as soon as they are detected. The abnormalities monitored and the manner in which they are overcome are then part of the model. For example, continued operation of the drive mirrors MD1 and MD2 can be monitored by the processor. If one mirror fails, the cavity length control signal to the other mirror can be doubled to keep the system in operation. This enables the system to continue functioning, although in a somewhat narrower performance range, so that the aircraft or other vessel with which it is associated can remain in operation.

Although the foregoing description is believed adequate to enable a worker skilled in the art to practice the invention, a program listing incorporating the methods of the invention is attached hereto as an Appendix. The program, implemented in the context of the system described herein, has been used to demonstrate the utility of the present methods, as described in detail below.

The performance of a ring laser gyro controlled by the mirror dither method of the present invention was investigated at room temperature using a stationary 52 centimeter ring laser gyro manufactured by Litton Systems, Inc. and identified as model S77. The cavity was controlled by a Zilog Z8000 processor using the cavity length control program of the Appendix, with "mode offset" set to zero. The gyro was initially subjected to sinusoidal body dither of approximately 20 degrees per second at a frequency of approximately 75 hertz. The resulting gyro output, including both the earth's rate of rotation and the bias error, was 8.4600 degrees per hour. The random walk of the gyro under these conditions was measured to be 0.0003 degrees per (hour).sup.1/2, representing the best random walk achievable with the gyro by conventional methods. Next, a random secondary component of body dither was applied at an average amplitude of approximately 180 arcseconds and a frequency of 32 hertz in accordance with conventional body dither techniques. In doing so, the gyro output was reduced to 8.4150 degrees per hour, which is substantially equal to earth rate, but random walk increased to 0.0005 degrees per (hour).sup.1/2. Finally, mirror dither was substituted for both primary and secondary body dither, using the mirror dither program of the Appendix. A 2000 hertz mirror dither signal was superimposed on the modulation and displacement signals to a pair of cavity control mirrors to dither the mirrors 180 degrees out-of-phase at an amplitude chosen to operate the gyro at one of the Bessel zero indices discussed above. The overall rate of dither motion was approximately 5.5 degrees per second, resulting in an output of 8.4153 degrees per hour and a random walk of 0.0003 degrees per (hour).sup.1/2. Thus, the mirror dither method of the invention has been shown to virtually eliminate bias error due to lock-in while reducing random walk by 40 percent from the value encountered with body dither having a random secondary component.

The effect of operating a ring laser gyro cavity at a point displaced from the peak of an operating mode has also been investigated. In this case, tests were performed at 97 degrees Fahrenheit using a stationary 28 centimeter ring laser gyro manufactured by Litton Systems, Inc., and identified as Serial No. 1088. The cavity was controlled by the same processor using the cavity length control program of the Appendix. In the program, the digital feedback signal is compared first to a model having a stationary operating point displaced from the peak of a mode and then to a model which "sweeps" the gyro through a number of modes. Measurements of random walk during operation off the peak of the mode showed improvement of better than ten (10) percent in random walk. Typical results are illustrated in FIG. 8, wherein a point 110 of lowest random walk is displaced from the mode center 112 by a distance corresponding to one (1) additional volt applied to the cavity length control mirrors. Specifically, random walk, at the point 110 was measured to be 0.00028 degrees per (hour).sup.1/2, as opposed to 0.00031 degrees per (hour).sup.1/2 at mode center.

From the above, it can be seen that there has been provided a method and apparatus for accurately controlling a ring laser gyro cavity according to a preselected static or dynamic model to significantly reduce output errors, including bias error, random walk and other forms of signal noise. Depending upon the form of the cavity model, the system can implement one or more of the novel methods of mirror dither, off-mode control and mode selection, for which the reductions in random walk are cumulative.

The appended claims are not limited to the embodiments described herein, but rather are intended to cover all variations and adaptations falling within the true scope and spirit of the present invention. As an example, the laser cavity 22 may take the form of any known laser cavity useful for gyroscopic purposes, and the cavity sensing, cavity model and cavity drive control functions can be implemented by any of a variety of alternative techniques, including analog or digital hardware circuits. ##SPC1##